masters degree project proposal
Content
UNIVERSITY OF KWAZULU-NATAL
School of Electrical Electronic and Computer Engineering
Implementation of a Test bed in MIMO OFDM Communication Systems Research Project Proposal
W.M Duma Supervisor: 205523495 Prof. Mneney
5/24/2010
ii
1 Abstract
The report discusses the motivation for the Implementation of a test bed of a MIMO OFDM communications system. The channel estimation methods developed by Mr Oyerinde for his PhD will be verified with the test bed. A literature review is presented which discusses all the concepts involved in the project. The feasibility of the project is discussed and the steps to be taken to achieve the project requirements are presented.
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2 Table of contents
Table of Contents
1 2 3 Abstract ........................................................................................................................................... ii Table of contents ............................................................................................................................ iii Introduction .................................................................................................................................... 1 3.1 3.2 4 Motivation for the Project ........................................................................................................ 1 Project Requirements............................................................................................................... 2
Literature Review ............................................................................................................................ 3 4.1 4.2 Orthogonal Frequency Division Multiplexing (OFDM) ............................................................... 3 Multiple Input and Multiple Output (MIMO) Channels ............................................................. 7 SIMO Channel (Receive Diversity) ..................................................................................... 7 MISO Channel (Transmit Diversity) ................................................................................... 8 MIMO Channel ................................................................................................................. 9 Spatial Multiplexing ........................................................................................................ 10
4.2.1 4.2.2 4.2.3 4.2.4 4.3 4.4
MIMO OFDM.......................................................................................................................... 11 Indoor Channel ...................................................................................................................... 12 Model1........................................................................................................................... 13 Model 2 .......................................................................................................................... 13 Model 3 .......................................................................................................................... 13
4.4.1 4.4.2 4.4.3 4.5
Channel Estimation ................................................................................................................ 14 Least Squares Channel Estimation .................................................................................. 16 MMSE Estimator............................................................................................................. 17 Implementation Issues ................................................................................................... 18
4.5.1 4.5.2 4.5.3 5
Basic Communication Systems Simulations .................................................................................... 19 5.1 5.2 5.3 BPSK Communication System in a AWGN and a Rayleigh fading channel ................................ 19 MPSK Performance in a AWGN and a Rayleigh fading channel................................................ 24 OFDM Communication System Simulation ............................................................................. 27
6 7
Feasibility of the Project ................................................................................................................ 31 Conclusion ..................................................................................................................................... 34 iii
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References..................................................................................................................................... 35
iv
3 Introduction
A communication system using multiple input and multiple output (MIMO) antennas has an increased capacity which allows the system to send data at a higher rate [2]. This is due to spatial diversity contained in MIMO channels which allows spatial multiplexing to be performed. The MIMO system combined with OFDM is robust to multipath and has a high data rate and thus provides a good communication system with a high data rate and reliability [2]. In order to increase the fidelity of the information received through the channel and reduce the error rate adequate channel knowledge is needed. In [4] a MIMO OFDM communication system was implemented where the channel was measured and modeled in 3D with a Mascara ray based radio channel software simulator in order to obtain adequate channel knowledge which would then improve the information detection at the receiver. There they obtained a more accurate model of their indoor channel compared to theoretical BRAN- A indoor channel model. The test bed will be implemented in an indoor channel. In general it is not possible to obtain a general channel model, which would allow communication systems to be implemented anywhere, since the indoor channels are not all the same in terms of architecture and hence motivates further research into channel estimation techniques which allow communication systems to measure and track the channel they operate in. In this project a MIMO OFDM communication system will be implemented using channel estimation algorithms developed by Mr Olutayo Oyerinde. The performance of the algorithms will be quantified and compared to the theoretical results.
3.1 Motivation for the Project
Mr Olutayo Oyerinde has developed and simulated channel estimation algorithms for his PhD work and now the task is to verify their performance through measurements by implementing MIMO OFDM communication test bed utilizing his algorithms for channel estimation. The communication test bed should be flexible in order to change from the algorithm used to another one on demand. With the test-bed, the algorithms will be evaluated in terms of complexity and real time performance. If the algorithms are too complex then it would be impractical to use them with currently available hardware. It may also imply that more expensive and high performance hardware must be purchased in order to cope with the complexity of the algorithms. If the algorithms are implemented with success and the system performs sufficiently similar to the theoretical predictions then a good contribution to research in MIMO OFDM communication systems will be made in implementation and verification of the algorithms through measurements 1
3.2 Project Requirements
It is required that the results obtained by Mr Oyerinde be reproduced and modified for an indoor channel so that they can be compared with the measured results from the test-bed. The reproduction of results will also give more understanding of the algorithms. SISO and MIMO OFDM communication systems should be studied for the indoor channel case. Algorithms for single antenna systems must be studied. This is to be a starting point in understanding channel estimation techniques and the knowledge of MIMO channel estimation algorithms will be developed from here. The starting point for the test bed implementation should be implementing a radio communication system for a single antenna system and acquire performance measurements from it. From there an OFDM system should be implemented which utilizes channel estimation for indoor channels and single antennas at the receiver and the transmitter. From the single antennas the development should progress to an implementation of a MIMO OFDM system under indoor channel conditions. Once the MIMO OFDM system is functional then development should progress to a radio communication test bed and then performance measurement should be done on this system. The results obtained should be analyzed and compared to the simulated results. The results should be exported to a software tool such as Matlab for the analysis.
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4 Literature Review
In this section concepts involved in the project will be discussed. This is to show how much research has been done in order to understand what the project involves. The concepts to be discussed are orthogonal frequency division multiplexing (OFDM); multiple input multiple output (MIMO) channels and their combination (MIMO OFDM).
4.1 Orthogonal Frequency Division Multiplexing (OFDM)
Frequency division multiplexing is a communication scheme for sending multiple signals containing different information at the same time. This is done by modulating the different signals to different centre frequencies and then using the signals at different center frequencies to modulate a carrier signal which is transmitted. In OFDM the sub carrier frequencies are orthogonal i.e.
, 4-1
where
and
are integers such that the signals do not interfere with each other and the receiver can
easily distinguish between them and there s no inter-carrier interference (ICI). In OFDM the data symbols within a frame are sent at different orthogonal frequencies at the same time hence the modulation levels of the symbols in each sub carrier can be reduced order to achieve the same data rate as for a single carrier system transmitting the same amount of symbols per unit time by having many modulation levels and decrease the symbol error probability. Figure 1 shows a block diagram of an OFDM block diagram.
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Figure 1: OFDM Block Diagram
The incoming serial data in the communication system is separated into frames of length N. The symbols in the frame are mapped in parallel into points on a constellation plane such that each symbol is given by
, 4-2
where carrier
is the amplitude and , where
.
is the phase. When the symbol
is multiplied with the
is the carrier frequency, the resulting signal is given by
4-3
Since the OFDM symbols are modulated at different frequencies that are integer multiples of each other and summed so that they can be transmitted at the same time the resulting signal is given by
. 4-4 . 4-4)
It can be seen from ( that is given by inverse DFT of since the frequencies are discrete and are multiples of
. The
DFT of a signal can be implemented more efficiently with a FFT when N is a power of 2. The mapped symbols given by can now be replaced by which is the FFT of . This means that OFDM can be implemented by taking the inverse FFT of the mapped symbols and thus at the receiver the received signal s FFT should be computed in order to obtain the symbols. The high data rate of OFDM allows the communication system to make use of a guard interval which is greater than the channel s delay spread. The guard interval helps to mitigate the inter-symbol 4
interference (ISI) caused by multipath. The RMS delay spread was measured to be 800ns in [4] and 150ns in [6] for indoor channels. From [9] it is stated that the maximum symbol rate should satisfy
, 4-5
where
is the RMS delay spread. During the guard interval a cyclic prefix is transmitted instead of not of
sending data since that would cause harmonics at the FFT output. For every frame of symbols length N given by
, 4-6
a sub block of symbols of length L given by
, 4-7
is inserted before the original symbols giving the overall frame to be transmitted given by
. 4-8
The modified block diagram is shown in Figure 2.
Figure 2: Modified OFDM block diagram
Since a whole frame of symbols is transmitted at the same time this makes the system able to combat short durations of noise bursts that are shorter than the symbol period [9]. Despite all the excellent advantages of OFDM there are also disadvantages which come from implementation. OFDM relies on the sub carriers being orthogonal and this makes it very sensitive to synchronization. Poor synchronization causes the carriers to be no longer orthogonal and this yields inter-carrier interference.
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Doppler frequency shift also causes poor synchronization and thus if the receiver and transmitter are in motion relative to each other ICI would also result in OFDM causing errors. Since the sub carriers used in OFDM are multiples of each other they occur at discrete frequencies in the utilized bandwidth. This causes a high peak to average power ratio (PAPR) and requires the power amplifiers at transmitter and receiver to have a high dynamic range. Power amplifiers operating in a wide dynamic range are non-linear in nature and designing linear amplifiers is complex and thus more expensive. OFDM is more sensitive to distortion caused by non-linear amplifiers since it will cause ICI so OFDM needs more expensive amplifiers to be implemented. In [7] a method of reducing the peak to average power ratio (PAPR) in OFDM by slightly disturbing the symbols in carriers used to transmit information and also sending dummy symbols in unused carriers is presented. The reduction of the PAPR will reduce the cost of the power amplifiers needed to be used in the OFDM system.
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4.2 Multiple Input and Multiple Output (MIMO) Channels
Similar to time diversity, frequency diversity and coding diversity MIMO offers spatial diversity in a communication system by using multiple antennas at the transmitter to transmit information and also at the receiver to receive the information. It allows independent data streams to be transmitted simultaneously in the same frequency band at the same time via spatial multiplexing which increases the capacity of the channel. It is better than frequency and time multiplexing because it doesn t need more bandwidth to achieve multiplexing [5]. By placing antennas at least /2 apart the signals transmitted with the different antennas are sent over different independent channels which will fade differently reducing the probability that all the paths are unreliable. Increased proximity of the antennas causes the channels to be correlated since the signals suffer the same scattering from the channels. The MIMO channel analysis will be broken up into SIMO and MISO channel analysis which yield receive and transmit diversity respectively. 4.2.1 SIMO Channel (Receive Diversity)
In this communication system there is only one transmitter antenna and NR receive antennas as depicted in Figure 3. The receiver receives NR signals and has to select the corresponding transmitted signal based on the received signal. The signals arrive through independent and uncorrelated paths.
Figure 3: SIMO channel with N transmit antennas and 1 receive antenna
There are 2 types of gains that are obtained as NR is increased. For BPSK the error probability is given by
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,
4-9
where
is the channel impulse response and
is the signal to noise ratio. The term
can be
written as
. The 1st term corresponds to a diversity gain; by averaging over multiple receive
paths the probability that all the paths have small channel gains is reduced since
if channel gains are normalized. The second term corresponds to a power gain from having many receive antennas and coherent combining at the receiver.
4.2.2
MISO Channel (Transmit Diversity)
In a MISO channel there are NT transmit antennas as depicted in Figure 4. There are many schemes used to achieve diversity such the repetition code and Alamouti. There s no diversity gain when transmitting the same signal over different antennas.
Figure 4: MISO channel with NT transmit antennas and 1 receive antenna
The received signal would be given by
4-10
8
Where
and
are the channel gains on the different paths and
is the channel noise and and have zero mean
are complex Gaussian distributed random variables. Suppose and unit variance such that
Since Let
and
are complex Gaussian distributed then Then we have that and
is also complex Gaussian distributed.
4-11
which shows that there was no diversity gained from transmitting the same signal from different antennas at the same time. The repetition code achieves transmit diversity by transmitting the same signal over different antennas in different intervals with 1 antenna transmitting in each interval. The repetition code is not efficient in using the available degrees of freedom from space diversity. It would cause delays in the transmission of information or require a higher transmission rate. In the Alamouti scheme 2 complex signals are transmitted over 2 symbol periods. In the 1st period is transmitted and in the 2nd period
is transmitted. If the channel is assumed to remain constant over the 2 symbol
times then
and
. Written in matrix form we obtain
The square matrix has orthogonal columns which makes the problem of detecting
and
decompose
to 2 separate orthogonal scalar problems. This makes the diversity gain 2 for the detection of each symbol since the signals and have been transmitted via 2 channels in 2 two symbol periods. This yields better bandwidth efficiency than the repetition code. The sacrifice is the power used to transmit each signal during the symbols period since 2 antennas are active during the symbol period each consuming half the total power. The diversity gain for the Alamouti scheme is 2 for the MISO channel. 4.2.3 MIMO Channel
The MIMO channel consists of the maximum diversity gain is
receiver antennas and
transmitter antennas as depicted in The hence for a MIMO channel
diversity gain for the SIMO channel was
and for the MISO channel was
. Thus using multiple antennas at the transmitter and receiver
increases the diversity of the system and hence the capacity. The other advantage of MIMO systems is discussed next which is spatial multiplexing.
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Figure 5: MIMO channel with NR receiver and NT transmitter antennas
4.2.4
Spatial Multiplexing
Multiplexing in communication systems is when multiple signals are sent simultaneously. In the space domain multiple signals are transmitted via different transmitter antennas and are received via different receiver antennas. This increases the data rate since instead of sending symbols via the same antenna serially one after the other, consecutive symbols equal to the number of transmitter antennas can be sent in parallel. Spatial multiplexing exploits the channels degrees of freedom which limited by the minimum between the number of transmitter or receiver antennas. An example of a spatial multiplexing is V-BLAST. Here NT signals are sent simultaneously through the channel with the different NT transmitter antennas. The kth signal is allocated a power Pk such that which is the total transmitted power. The kth data stream is encoded using a capacity achieving Gaussian code which achieves a rate Rk . The diversity of V-BLAST is at most NR because each data stream is received via the NR receiver antennas but is transmitted via only 1 transmitter antenna and not NT antennas. This shows that there is less diversity when there is more spatial multiplexing and hence there is a tradeoff between spatial multiplexing and diversity gain. From [8] it was shown that with channel state information (CSI) known at the receiver the capacity in a MIMO communication system with fast fading is given by
, 4-12
where
is the common signal to noise ratio at each receiver antenna. If and
are
the random and ordered singular values of transmitter antennas then
is the minimum of the number of receiver and
10
=
.
4-13
At high SNR the capacity reduces to
4-14
and at low SNR
4-15
with a normalized channel covariance. This indicates that the capacity of a MIMO channel is increased by a factor ,which is the number of degrees of freedom of the channel ,at high SNR and only by a factor at low SNR which only yields a power gain which makes the communication system have a channel. Thus the capacity increase due to spatial multiplexing is similar capacity to that of a 1 by only obtained at high SNR. In a slow fading channel, the capacity is related to the outage probability which is given by
4-16
for an i.i.d. Rayleigh fading channel. Unlike an AWGN channel the slow fading channel is dependent on H, which is random and quasi static, and thus the slow fading channel cannot be characterized by capacity but by outage probability which is the probability that the information transmission rate is smaller than the target rate R. For SISO channel the outage probability at high SNR is given by
4-17
which decays as 1/SNR. For MIMO channel using a repetition scheme the outage probability decays as and this is the upper bound of the decay of outage probability for a MIMO slow fading channel. The diversity from the use of multiple antennas improves the decaying compared to the SISO case hence there is a diversity gain. V-BLAST works well in a fast fading channel but is not optimal in slow fading channels. This is because the data streams are transmitted via different antennas hence different channels. If one of the channels is in a deep fade all the data transmitted through it will be lost. In a fast fading channel the channel variations occur more often and so the channel wouldn t be in a deep fade for a long time such that all the data through is lost. Spatial multiplexing achieves a higher data rate without having to use more bandwidth but this is achieved at the cost of diversity gain. One has to choose between the two benefits of MIMO channels.
4.3 MIMO OFDM
The use of OFDM increases the data rate since a serial data stream is transmitted in parallel via orthogonal sub carriers and if spatial multiplexing is used via multiple transmitter antennas at the 11
transmitter and multiple antennas at the receiver the capacity and reliability of communication increases even further due to the diversity gained from the multiple antennas and spatial multiplexing. With spatial multiplexing each OFDM block can be sent with different antennas which will increase the data rate by a factor equal to the degree of freedom gain of the channel. With spatial diversity each OFDM of block will be sent through all the antennas at different times to achieve both transmit and receive diversity which reduces the symbol error rate. In the design of the test bed schemes which provide the best compromise between spatial diversity and multiplexing will be researched and implemented if they are not too complex to meet real time requirements. The starting point should be implementing spatial diversity since it is less complex than spatial multiplexing. This is because with spatial multiplexing in systems such as V-BLAST, the transmitter has to transmit information at different rates and power at from each transmitter antenna and receiver has to extract the required data rate and power from a sum of NT received signals through NT channels. Synchronization to different data rates and cancelling other signals is very complex.
4.4 Indoor Channel
The channel transfer function in a multipath environment is given by [1]
4-18
where
is the complex amplitude,
is the temporal delay,
is the spatial Doppler shift in
rad.m-1 from the band phase shift shift is much
multipath scatterer,
is the base band angular frequency and z is the position , a carrier phase shift hence it is , a base from . The base band spatial Doppler phase signal neglected
along the direction of motion. The signal experiences attenuation and a carrier spatial Doppler phase shift smaller than that of the carrier
( 4-18). When the receiver moves along the z direction the received signal experiences a phase shift due to the time delay and the spatial Doppler phase shift. The inverse Fourier transform of is
, 4-19
which is the effective distribution of signals at the receiver antenna at a time delay and direction . In an indoor channel the scatterers are closer together due to a large density of objects. The result of this is that there is more fading due to multipath. Since OFDM has an advantage of being immune to multipath fading then this will not pose a problem to the test bed implementation in an indoor channel as long as the transmission rate satisfies (
,
4-5).
When there is no line of sight between the transmitter and receiver and the signal has to travel from one room to another the received signal will be weaker due to path loss. In [1] parametric models for an 12
indoor channel path loss are presented. The models are based on experiments and the path loss is in dB (Hata power law). 4.4.1 Model1
Here the path loss is given by:
4-20
where and
is the distance from the transmitter,
is the path loss at a distance 1m from the transmitter
is to be determined experimentally and determines how rapidly the path loss increases with
distance. In this model the path loss grows linearly with distance. 4.4.2 Model 2
In this model the path loss is given by:
4-21
where
is the free space path loss, ,
is a constant,
is the number of walls penetrated of type is obtained empirically. From the
with wall loss
is the loss between
adjacent floor and
above equation it is observable that the total floor loss is a non-linear function of the number of floors. 4.4.3 Model 3
In this model the path loss is given by:
4-22
where
is an attenuation constant. This path loss is exponential (in dB). The path losses were found to
be independent of frequency and the parameters of the models are to be determined experimentally. Once the parameters are obtained then the path loss can be obtained for any distance from the transmitter within the indoor channel. In [1] the parameters for the 3 models are presented which were obtained by 10 different institutions at an operating frequency of 1.8GHz. The parameters are presented in [1].
Table 1: Model parameters for the 3 models at 1.8 GHz
Condition Dense One floor Two floors
Model 1 (dB) 33.3 21.9 4 5.2
Model 2 (dB) 3.4 6.9
(dB)
(dB) 18.3 0.46
Model 3 (dBm-1) 0.62
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Three floors Open Large Corridor
44.9 42.7 37.5 29.2
5.4 1.9 2 1.4
3.4 3.4 3.4
6.9 6.9 6.9
18.3 18.3 18.3
0.46 0.46 0.46
2.8 0.22
The walls used in the experiment for Model 2 were light concrete, and
, which was a light wall such as plaster board or
which was a heavy and thick wall with thickness greater than 10cm made of
concrete or brick. From the table it can be seen that the thicker wall contributes a higher loss than the thinner wall of a lighter material as expected. In an indoor channel the receiver and transmitter are either static or moving at slow speeds such that the Doppler spread is very small and the channel can be considered as a slow fading channel. The small Doppler spread in indoor channels will allow OFDM to perform better since the carrier synchronization is less affected and thus the carriers will remain orthogonal. In addition to slow movements making the channel slow fading, the indoor channel does not experience heavy weather conditions such as rain which attenuates the transmitted signal power causing errors at the receiver. The conditions in an indoor channel remain static for multiple symbol times even if is there are changes which can occur such as doors being opened and closed, changes in the occupancy of personnel in the room, movement of furniture etc. The delay spread in the indoor channel is smaller than in the outdoor channel and this allows the communication to be at a higher data rate. This also allows wide band communication such as OFDM to be possible because the smaller delay spread corresponds to a wider coherence bandwidth which makes the channel flat fading as long as the transmission bandwidth is smaller than the coherence bandwidth.
4.5 Channel Estimation
In order to increase the reliability of communication it is desirable to know the channel in order to cancel the non-ideal effects that it introduces to the transmitted signal. The received signal at the receiver is given by
4-23
where
is the channel impulse response,
is the transmitted signal and
is the channel
AWGN. With knowledge of
the communication system can compensate for the effects that it
introduced and thus make better decisions about the transmitted information at the receiver. Channel state information refers to the knowledge of which is the channel impulse response or which is the channel transfer function. In order for the channel to be known measurements of it have to be made. Since the channel cannot be directly measured whilst communicating, it needs to be measured indirectly. At the receiver the channel 14
is obtained via the transmitter sending sufficiently many training or pilot symbols, which are known at the receiver, such that the receiver can accurately estimate the channel. At the transmitter channel knowledge can be obtained via the receiver sending back channel information. The transmitter and receiver operate in a transceiver structure. There are 2 methods available to obtain transmitter CSI. The 1st is using implicit feedback using reciprocity which is for the case when the receiver and transmitter use the same frequency band to transmit information such as time division duplex (TDD). In this case instantaneous channels are identical and thus estimates for CSI at the receiver can be employed at the transmitter. This system becomes very inaccurate when the channels changes rapidly in between the estimate being obtained and when the implicit feedback is being employed. The 2nd method is explicit feedback which is used when the transmitter and receiver use different frequency bands for transmitting information such as frequency division duplex (FDD) or when implicit feedback using reciprocity TDD method is unreliable due to the temporal variations of the channel. Here CSI can be sent back to the transmitter using explicit feedback. In order to obtain receiver CSI the pilot symbols need to be transmitted with the information symbols so the transmitter has to separate the pilot symbols from the information symbols so that the receiver can differentiate between the two. In OFDM there are two types of pilot arrangements used to obtain receiver CSI. The first type is called block pilot arrangement where the pilot symbols are transmitted periodically across all the sub carriers and the receiver can periodically use the received pilot symbols to estimate the channel. The second type of pilot arrangement is comb type pilot arrangement. Here the pilot symbols are transmitted simultaneously with the information symbols. The pilot symbols are interleaved with the information symbols. At the receiver the channel state at the sub carriers carrying information is interpolated from the information obtained from the sub carriers carrying pilots. The two types of pilot arrangements are shown in Figure 6. The block type pilot arrangement is used in slow fading channels since the channel does not vary a lot in between consecutive pilot symbol intervals. The benefit of this arrangement is that the channel is estimated at every sub carrier frequency thus producing accurate channel estimates for each sub carrier. The comb type of pilot arrangement is used in fast fading channels where channel estimation has to be done at every OFDM symbol time to provide more accurate estimates of the rapidly changing channel. The channel at the information baring sub carriers has to be interpolated and hence yielding less accurate estimates than the block type. The benefit of this arrangement is that the channel is estimated at every OFDM symbol period and thus caters more channel variations than the block type pilot arrangement.
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(a)
(b)
Figure 6: Pilot Arrangement in OFDM communication systems: (a) Comb Type, (b) Block Type
A number of OFDM channel estimation algorithms are discussed in [8] for block type and comb type pilot arrangement. The block type channel estimation algorithms discussed include the Least Squares (LS) estimator and the Minimum Mean Square Error (MMSE) estimator and for comb type pilot arrangement the algorithms discussed include the LS estimator with 1D Interpolation, Linear Interpolation, Second Order Interpolation and Spline Cubic Interpolation. Since in the project the test bed will be implemented for an indoor channel which was discussed to be of slow fading type the estimation methods discussed here are only of block type pilot arrangement which is for slow fading channels. 4.5.1 Least Squares Channel Estimation
Defining symbols as in [8],
and
,
and and
are the transmitted denote the and the DFT
symbols and N is the block length of the transmitted symbols. Let channel impulse response and AWGN respectively. Let the input matrix matrix be
,
4-24
where given by
. From here let
and
. The received signal
is
16
.
4-25
The LS estimator attempts to minimize the quantity conjugate transpose. The least square channel estimate is given by
.
where
denotes complex
4-26
The LS estimator has low complexity and thus can be easily implemented but it suffers from high mean square error since it aims to minimize the least square error. 4.5.2 MMSE Estimator
The MMSE estimator uses second order statistics which involve using the channel auto covariance in order to minimize the square error. Here the channel second order statistics are assumed to be known at the receiver. This means the auto covariance of the channel impulse response ( ) and transfer function ( ) are known. Defining
4-27 4-28 , 4-29
the MMSE estimator of
is given by
.
4-30
As can be seen the MMSE estimator is much more complex than the LS estimator. It involves more multiplications and matrix inversion. The modified MMSE reduces the complexity of the MMSE estimator by using methods such as singular value decomposition. In [5] it is mentioned that second order statistics of a channel vary much more slowly than the channel realization itself and this is the reason why the MMSE estimator performs much better than the LS estimator
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4.5.3
Implementation Issues
In [3] it is mentioned that the single antenna OFDM channel estimation techniques fail when they are exported to the MIMO case since the signals from the different transmit antennas interfere at the receiver. Modifying the SISO estimators is not straight forward since the channel is much more complex and there are more parameters to be estimated ( more). The MMSE estimator requires knowledge of the channel second order statistics. In [3] measurements of the channel impulse response were obtained from a television and a laboratory in order to find the channel second order statistics which were then used to determine the performances of different channel estimation methods. This implies that measurements of the channel in the environment where a communication system using the channel estimator is to be used in need to be taken. With CSI at the transmitter as well, the transmitter can track changes in the channel and compensate for them by increasing the power level or sending pilots that will achieve better estimation for the current channel state. The transceiver structure can reduce the systems real time performance in TDD due to the channel state having to be fed back after every channel estimation period at the receiver. It requires more bandwidth in FDD and OFDM would be already be consuming a lot of bandwidth due to the information being sent at different sub carriers.
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5 Basic Communication Systems Simulations
The basic digital communication systems have been simulated using Matlab in order to build knowledge of how a communication system works. The communication systems are implemented in a Matlab m file and the transmitted and received data are plotted so that the channel effects on the transmiited can be seen. The simulated communication systems include BPSK and 4 PSK for the cases where the channel is AWGN and when it is also Rayleigh fading. OFDM with BPSK modulated sub carriers is also simulated.
5.1 BPSK Communication System in a AWGN and a Rayleigh fading channel
In the BPSK communication system the carrier s phase is varied according to which bit is to be transmitted. The carrier s phase is made to be one of two phases, 0 and . The transmitted signal is given by
5-1
At the receiver the signal is correlated with
and
.The outputs of the correlator
blocks are summed and sampled at the end of the bit interval. The sampled output is compared with a threshold of 0. If the output is greater than 0 then 1 is assumed to bit the transmitted bit and if the output is less than 0 then 0 is assumed to be the transmitted bit. The threshold is set to be in the middle of the 2 possible outcomes in order to have a symmetrical decision region. The BPSK communication system for an AWGN channel was simulated and Figure 7 shows the graphs of the transmitted and received signals. The received signal to noise ratio is 3 dB and it can be seen the data is decoded without error for the given transmitted data.
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Serial Data 1 0.9 0.8 0.7 0.6 data 0.5 0.4 0.3 0.2 0.1 0
1
2
3
4
5 6 data index
7
8
9
10
(a)
Transmitted Signal vs time 2 1.5 1 Transmitted Signal 0.5 0 -0.5 -1 -1.5 -2
0
1
2
3
4
5 time (ms)
6
7
8
9
10
(b)
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Received Signal vs time 3
2
Received Signal
1
0
-1
-2
-3
0
1
2
3
4
5 time (ms)
6
7
8
9
10
(c)
Received Data 1 0.9 0.8 Received Data 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
1
2
3
4
5 6 data index
7
8
9
10
(d)
Figure 7: BPSK communication system in AWGN channel for a SNR= 3dB: (a) Serial data at transmitter. (b) Transmitted signal. (c) Received signal. (d) Decoded data at receiver.
In the Rayleigh fading channel the transmitted is attenuated by the channel attenuation which reduces the received power of the signal. The result of this is a smaller signal to noise ratio which yields more
21
errors in the communication system. This explains the waveform obtained in Figure 8 (b).
Serial Data 1 0.9 0.8 0.7 0.6 data 0.5 0.4 0.3 0.2 0.1 0
1
2
3
4
5 6 data index
7
8
9
10
(a)
Transmitted Signal vs time 2 1.5 1 0.5 0 -0.5 -1 -1.5 -2
Transmitted Signal
0
1
2
3
4
5 time (ms)
6
7
8
9
10
(b)
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Received Signal vs time 2 1.5 1 Received Signal 0.5 0 -0.5 -1 -1.5 -2
0
1
2
3
4
5 time (ms)
6
7
8
9
10
(c)
Received Data 1 0.9 0.8 Received Data 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
1
2
3
4
5 6 data index
7
8
9
10
(d)
Figure 8: BPSK communication system in Rayleigh fading channel for a SNR= 3dB: (a) Serial data at transmitter.
(b) Transmitted signal. (c) Received signal. (d) Decoded data at receiver.
23
5.2 MPSK Performance in a AWGN and a Rayleigh fading channel
MPSK consists of M possible symbols which can be sent during a symbol interval. The number of bits per symbol is which means that MPSK has a higher data rate than BPSK where only 1 bit is sent per symbol interval. The simulated MPSK communication system is 4PSK which consists of 4 levels. The transmitted signal is given by
5-2
As the number of modulation levels M is increased the distance in phase between adjacent levels decreases and the probability of decoding a symbol in error increases due to smaller decision region. A 4PSK communication system was simulated and the graphs obtained are given in Figure 9. It can be seen when comparing Figure 9 (a) and (d) that with the same SNR of 3dB used in the BPSK communication system there are more errors with the 4PSK communication system. As the modulation levels are increased the decision regions are reduced and thus more errors are made.
Serial Data 1 0.9 0.8 0.7 0.6 data 0.5 0.4 0.3 0.2 0.1 0
1
2
3
4
5 6 data index
7
8
9
10
(a)
24
Transmitted Signal vs time 2 1.5 1 0.5 0 -0.5 -1 -1.5 -2
Transmitted Signal
0
1
2
3
4
5 time (ms)
6
7
8
9
10
(b)
Received Signal vs time 2.5 2 1.5 Received Signal 1 0.5 0 -0.5 -1 -1.5 -2 -2.5
0
1
2
3
4
5 time (ms)
6
7
8
9
10
(c)
25
Received Data 1 0.9 0.8 Received Data 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
1
2
3
4
5 6 data index
7
8
9
10
(d)
Figure 9: BPSK communication system in Rayleigh fading channel for a SNR= 3dB: (a) Serial data at transmitter. (b) Transmitted signal. (c) Received signal. (d) Decoded data at receiver.
26
5.3 OFDM Communication System Simulation
An OFDM communication system was simulated for a channel model given in [3] which is the Advanced Television Technology Center (ATTC) Grande Aliance DTV laboratory s ensemble E model whose static impulse response is given by
.
5-3
Following the simulation parameters given in [3] where 128 subcarriers were used with a 1024 point FFT. The modulation used on the subcarriers was BPSK. The communication system was simulated and the graphs obtained are given in Figure 10.
Serial Data 1 0.9 0.8 0.7 0.6 data 0.5 0.4 0.3 0.2 0.1 0 0 20 40 60 80 data index 100 120 140
(a)
27
Transmitted Signal 2 1.5 Magnitude 1 0.5 0
0
20
40
60 data index
80
100
120
140
4 3 Phase (radians) 2 1 0
0
20
40
60 data index
80
100
120
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(b)
Received Signal 1024 FFT 100 80 Magnitude 60 40 20 0 0 20 40 60 data index 8 6 Phase (Radians) 4 2 0 80 100 120 140
0
20
40
60 data index
80
100
120
140
(c)
28
Received Data 1 0.9 0.8 0.7 0.6 Data 0.5 0.4 0.3 0.2 0.1 0
0
20
40
60 data index
80
100
120
140
(d)
Zero Padded Serial Data to 1024 Points 1 0.8 0.6 0.4 0.2 Magnitude 0 -0.2 -0.4 -0.6 -0.8 -1
0
200
400
600 data index
800
1000
1200
(e)
29
Real Part of FFT of Received Signal with 1024 Points 100 80 60 40 20 Magnitude 0 -20 -40 -60 -80 -100
0
200
400
600 data index
800
1000
1200
(f)
Figure 10: OFDM communication system simulation graphs (a) Serial data at transmitter. (b) Frequency domain
mapped transmitted data (c) Frequency domain mapped received data. (d) Decoded data at receiver. (e) 1024 point transmitted signal FFT. (f) 1024 point received signal FFT.
From Figure 10 (f) it can be seen that the channel introduces noise which also appears in the unused subcarriers of the FFT. The data can be decoded by remapping each subcarrier magnitude and phase onto the constalllation map and decide which symbol was transmitted based on the maximum likely hood.
30
6 Feasibility of the Project
Extensive research on the topic has been done and more attention was paid to MIMO channels, indoor channels and estimation in OFDM communication systems. At the moment not much has been achieved on implementation of a simple OFDM communication system on the DSP boards. A lot of knowledge of the TM320C6416T DSP board has been gained as well as that of the Code Composer studio which is used to write, simulate and download DSP programs. Due to the complexity of the project the scope was reduced to an implementation of a MISO OFDM communication system. Mr Oyerinde s algorithms will be modified for the indoor MISO channel. They will be simulated for this case and then implemented on the test bed to verify their performance. This is achievable because a MISO channel is a subset of a MIMO channel. The scope was reduced because a MIMO channel test bed implementation is a PhD level topic. The 1st step is to achieve implementing a simple OFDM communication system on the DSP boards. Once this is done channel estimation can be implemented and the real time performance of the implemented channel estimation algorithms will be analyzed. The real time performance of the algorithms in terms of CPU cycles and memory usage will be used as a benchmark of which platform has to be used for implementing the MISO OFDM test bed. The DSP board only has a digital PLL and is thus not enough to implement a full communication system. The other limitation is that the on board AIC23 codec which is used as an external interface for analogue signals has a maximum sampling frequency of 96kHz and is thus not ideal for RF wireless communication. Extra external hardware is needed to interface to an RF antenna, down mix the RF signal and achieve carrier phase synchronization. The available options are to either purchase such equipment or build it. Funds have been allocated to purchase other DSP kits which will have better real time performance than the TM320C6416. The use of a DSP board and programming using C language allows the software to be re usable on other DSPs without having to re write the whole software for the other platform. C language has the disadvantage of being slower than assembly but allows the programming to be flexible. Code Composer Studio has tools which allow the user to evaluate and tune the program performance and offers advice on how to improve the results. It also allows the program to contain linear assembly within the C source file which will speed up the performance. Choosing another platform such as an FPGA will slow down the development time of the project since it offers less flexibility. It was mentioned in Section 4.5.3 of this report that the channel estimation algorithms developed for SISO OFDM communication systems fail when exported to the MISO OFDM system due to added complexity. The limitation of the test bed implementation will be primary caused by the complexity of 31
the channel estimation algorithms which could cause poor real time performance. In the event that the real time performance of the channel estimation techniques developed by Mr Oyerinde is poor, DSP boards will be combined so to share the computation tasks and transfer information from one board to another and increase the amount of computation needed by only one DSP chip. This will imply that the implementation of the algorithms is expensive but the objective of the project will be achieved which is to implement a MISO OFDM test bed based in order to verify the performance of the channel estimation algorithms developed by Mr Oyerinde. The 1st 6 months of the project were dedicated to familiarization of the project topic and the modules involved in it. The next 6 months will be dedicated to further research on the project modules in order to obtain system design parameters such as standards for OFDM communications, channel statics for the proposed environment, power requirements for reliable communication in this environment which is affected by path loses. The next 6 months will also be dedicated to implementing a fully functional SISO OFDM test bed from which performance results can be viewed on a computer. The 3rd semester will dedicated to implementing a MISO communication system. This will require obtaining the necessary hardware, the simulation of the MISO channel in the proposed environment and the performance results for different MISO communication strategies such as Alamouti, V-BLAST and D-BLAST. The success of the OFDM communication system implemented in the 2nd semester and the MISO communication system will allow a MISO OFDM communication system to be implementable by integrating the two communication systems In the final system a MISO OFDM communication will implemented using what was achieved from the OFDM communication system implemented in the 2nd semester and the MISO communication system implemented in the 3rd semester. When the MISO OFDM test bed is functional then the channel estimation algorithms will be implemented and this will conclude the project. The tasks that need to be achieved in the project are given in Table 2.
Table 2: Table of tasks and their duration indicating how the project will be broken down and what is to be achieved at each period in order to achieve success of the project.
Task No. 1
Task Reproduction of Results
2
Description Duration The channel estimation simulation July December 2010 results are to be reproduced in order to gain understanding and to compare them to measured results Simple A simple communication should be July September 2010 Communication implemented to cover: System Ø Modulation Ø Encoding Ø Antenna Interfacing Ø Demodulation Ø Synchronization Ø Decoding Ø Performance analysis on 32
3
4.
5
6
Computer SISO OFDM A SISO OFDM implementation communication which covers the following: system Ø Subcarrier modulation Ø Cyclic prefix transmission during guard interval Ø SISO OFDM channel estimation Ø Demodulation of subcarriers Ø Recent achievements in OFDM such as PAPR reduction algorithm Ø Performance analysis on Computer MISO A MISO communication system communication should be implemented covering: system Ø Hardware to interface to antennas Ø Simulations of a MISO communication system Ø A communication which exploits spatial diversity Ø A communication system that exploits degrees of freedom to increase data rate Ø Analysis on computer MISO OFDM A flexible MISO OFDM communication communication system should be system implemented which will be a combination of the OFDM communication and the MISO communication system. Channel The proposed channel estimation estimation on algorithms should be implemented. the MISO OFDM test bed The system must be flexible to change to a required algorithm. The results are to be analyzed and compared to theoretical results.
September December 2010
January May 2011
May- June 2011
July October 2011
33
7 Conclusion
The motivation for the project requiring an implementation of a test bed in MIMO OFDM communication systems was that the communication system provides an increased data rate and diversity and channel estimation algorithms are needed to make it more reliable. The OFDM communication system was described along with MIMO channels and channel estimation algorithms in order to provide an understanding of the modules involved in the project. The MIMO channel provides spatial diversity and spatial degrees of freedom which can be used for spatial multiplexing in order to increase the data rate. It was shown that the two parameters to be gained from the MIMO channel cannot be achieved together and there s a tradeoff between the two. Diversity and the degrees of freedom increase with the number of antennas used but the optimum of both cannot be achieved at the same time. The communication environment that will be used in the project is an indoor channel. The indoor channel suffers from a lot of multipath due to the walls and furniture being at close distances from each other. The indoor channel is a slow fading channel since motion of terminals inside buildings is at slow speeds or static. Due to walls dividing rooms, the indoor channel suffers more from path loss and this decreases the power of the received signal hence the SNR. Channel estimation allows the receiver to compensate for variations in the communication channel in order to reduce the probability of error in the detected signal. The estimation is obtained by sending reference signals called pilots which are known at the receiver but the disadvantage of using them is that the data rate is reduced since less information is transmitted because pilots are known at the receiver and hence they are not information. Since the channel that will be used for the project is an indoor channel, which is a slow fading channel, block type pilot arrangement will be used for channel estimation. Due to the complexity of a MIMO OFDM communication system implementation the project scope was reduced to only a MISO OFDM communication system. The project would not be feasible if it was a MIMO OFDM communication system implementation because the topic is at a PhD level. The result of this would be a communication system that can only exploit the transmit diversity of the system and there s no spatial multiplexing available. The project requirements are achievable in the period of 2 years. More research will be conducted in the next 6 months to obtain more information about implementation of MISO OFDM communication. An OFDM communication will be implemented in the next 6 months. In the 3rd semester a MISO communication system will be implemented and in the 4th semester a full MISO OFDM communication system will be implemented which will then be used as a test bed for the verification of Mr Oyerinde s channel estimation techniques.
34
8 References
[1] Andersen, J.B. & Vaughan, R., Channels, Propagation and Antennas for Mobile Communications (IEE Electromagnetic Waves Series; no.50), 2003 [2] Angelosante, D., Biglieri,E. & Lops, M., Sequential Estimation of Multipath MIMO OFDM Channels , IEEE Transactions on Signal Processing, vol. 57,no. 8, Aug. 2009 [3] Bahai, A., Coleri, S., Ergen M. & Puri, A., Channel Estimation Techniques Based on Pilot Arrangement in OFDM Systems , IEEE Transactions on Broadcasting, vol. 48, no. 3, Sept 2002, pp 223- 229 [4] Bernadin, P., Caire, G., Corrat, J., Dias, A.R., Fábregas, A.G., Gosse, K., Guillaud, M.,Li, Z., Miet, X., Peden, A., Rouquette, S., Slock , D.T.M. & Toutain, Y., A MIMO OFDM Testbed for Wireless Local Area Networks , EURASIP Journal on Signal Processing, 21 June 2005 [5] Bölcskei, H., Gesbert, D., Papadias, C. B. & Van der Veen, A., Space Time Wireless Systems: From Array Processing to MIMO Communications, Cambridge University Press, 2006 [6] Eden, D., Hinostroza & V., Salous, S., High Resolution Indoor and Indoor to Indoor Measurements , European Cooperation In the Field of Scientific and Technical Research (Euro-Cost), 31 May 2002 [7] Cavalcante, R.L.G. & Yamada, I., A Flexible Peak-To-Average Power Ratio Reduction Scheme for OFDM Systems by Adaptive Projected Subgradient Method , IEEE transactions on Signal Processing, vol. 57,no. 4,April 2009
[8] Martinez, E. &Shen, Y., Channel Estimation in OFDM Systems , Freescale Semiconductor, Jan. 2006
[9] Peterson, R.L. & Ziemer, R.E., Introduction to Digital Communication, 2nd edn, Prentice-Hall, 2001 [10] Tse,D, & Viswanath,P., 2008, Fundamentals of Wireless Communications, Cambridge University Press, New York
35
School of Electrical Electronic and Computer Engineering
Implementation of a Test bed in MIMO OFDM Communication Systems Research Project Proposal
W.M Duma Supervisor: 205523495 Prof. Mneney
5/24/2010
ii
1 Abstract
The report discusses the motivation for the Implementation of a test bed of a MIMO OFDM communications system. The channel estimation methods developed by Mr Oyerinde for his PhD will be verified with the test bed. A literature review is presented which discusses all the concepts involved in the project. The feasibility of the project is discussed and the steps to be taken to achieve the project requirements are presented.
ii
2 Table of contents
Table of Contents
1 2 3 Abstract ........................................................................................................................................... ii Table of contents ............................................................................................................................ iii Introduction .................................................................................................................................... 1 3.1 3.2 4 Motivation for the Project ........................................................................................................ 1 Project Requirements............................................................................................................... 2
Literature Review ............................................................................................................................ 3 4.1 4.2 Orthogonal Frequency Division Multiplexing (OFDM) ............................................................... 3 Multiple Input and Multiple Output (MIMO) Channels ............................................................. 7 SIMO Channel (Receive Diversity) ..................................................................................... 7 MISO Channel (Transmit Diversity) ................................................................................... 8 MIMO Channel ................................................................................................................. 9 Spatial Multiplexing ........................................................................................................ 10
4.2.1 4.2.2 4.2.3 4.2.4 4.3 4.4
MIMO OFDM.......................................................................................................................... 11 Indoor Channel ...................................................................................................................... 12 Model1........................................................................................................................... 13 Model 2 .......................................................................................................................... 13 Model 3 .......................................................................................................................... 13
4.4.1 4.4.2 4.4.3 4.5
Channel Estimation ................................................................................................................ 14 Least Squares Channel Estimation .................................................................................. 16 MMSE Estimator............................................................................................................. 17 Implementation Issues ................................................................................................... 18
4.5.1 4.5.2 4.5.3 5
Basic Communication Systems Simulations .................................................................................... 19 5.1 5.2 5.3 BPSK Communication System in a AWGN and a Rayleigh fading channel ................................ 19 MPSK Performance in a AWGN and a Rayleigh fading channel................................................ 24 OFDM Communication System Simulation ............................................................................. 27
6 7
Feasibility of the Project ................................................................................................................ 31 Conclusion ..................................................................................................................................... 34 iii
8
References..................................................................................................................................... 35
iv
3 Introduction
A communication system using multiple input and multiple output (MIMO) antennas has an increased capacity which allows the system to send data at a higher rate [2]. This is due to spatial diversity contained in MIMO channels which allows spatial multiplexing to be performed. The MIMO system combined with OFDM is robust to multipath and has a high data rate and thus provides a good communication system with a high data rate and reliability [2]. In order to increase the fidelity of the information received through the channel and reduce the error rate adequate channel knowledge is needed. In [4] a MIMO OFDM communication system was implemented where the channel was measured and modeled in 3D with a Mascara ray based radio channel software simulator in order to obtain adequate channel knowledge which would then improve the information detection at the receiver. There they obtained a more accurate model of their indoor channel compared to theoretical BRAN- A indoor channel model. The test bed will be implemented in an indoor channel. In general it is not possible to obtain a general channel model, which would allow communication systems to be implemented anywhere, since the indoor channels are not all the same in terms of architecture and hence motivates further research into channel estimation techniques which allow communication systems to measure and track the channel they operate in. In this project a MIMO OFDM communication system will be implemented using channel estimation algorithms developed by Mr Olutayo Oyerinde. The performance of the algorithms will be quantified and compared to the theoretical results.
3.1 Motivation for the Project
Mr Olutayo Oyerinde has developed and simulated channel estimation algorithms for his PhD work and now the task is to verify their performance through measurements by implementing MIMO OFDM communication test bed utilizing his algorithms for channel estimation. The communication test bed should be flexible in order to change from the algorithm used to another one on demand. With the test-bed, the algorithms will be evaluated in terms of complexity and real time performance. If the algorithms are too complex then it would be impractical to use them with currently available hardware. It may also imply that more expensive and high performance hardware must be purchased in order to cope with the complexity of the algorithms. If the algorithms are implemented with success and the system performs sufficiently similar to the theoretical predictions then a good contribution to research in MIMO OFDM communication systems will be made in implementation and verification of the algorithms through measurements 1
3.2 Project Requirements
It is required that the results obtained by Mr Oyerinde be reproduced and modified for an indoor channel so that they can be compared with the measured results from the test-bed. The reproduction of results will also give more understanding of the algorithms. SISO and MIMO OFDM communication systems should be studied for the indoor channel case. Algorithms for single antenna systems must be studied. This is to be a starting point in understanding channel estimation techniques and the knowledge of MIMO channel estimation algorithms will be developed from here. The starting point for the test bed implementation should be implementing a radio communication system for a single antenna system and acquire performance measurements from it. From there an OFDM system should be implemented which utilizes channel estimation for indoor channels and single antennas at the receiver and the transmitter. From the single antennas the development should progress to an implementation of a MIMO OFDM system under indoor channel conditions. Once the MIMO OFDM system is functional then development should progress to a radio communication test bed and then performance measurement should be done on this system. The results obtained should be analyzed and compared to the simulated results. The results should be exported to a software tool such as Matlab for the analysis.
2
4 Literature Review
In this section concepts involved in the project will be discussed. This is to show how much research has been done in order to understand what the project involves. The concepts to be discussed are orthogonal frequency division multiplexing (OFDM); multiple input multiple output (MIMO) channels and their combination (MIMO OFDM).
4.1 Orthogonal Frequency Division Multiplexing (OFDM)
Frequency division multiplexing is a communication scheme for sending multiple signals containing different information at the same time. This is done by modulating the different signals to different centre frequencies and then using the signals at different center frequencies to modulate a carrier signal which is transmitted. In OFDM the sub carrier frequencies are orthogonal i.e.
, 4-1
where
and
are integers such that the signals do not interfere with each other and the receiver can
easily distinguish between them and there s no inter-carrier interference (ICI). In OFDM the data symbols within a frame are sent at different orthogonal frequencies at the same time hence the modulation levels of the symbols in each sub carrier can be reduced order to achieve the same data rate as for a single carrier system transmitting the same amount of symbols per unit time by having many modulation levels and decrease the symbol error probability. Figure 1 shows a block diagram of an OFDM block diagram.
3
Figure 1: OFDM Block Diagram
The incoming serial data in the communication system is separated into frames of length N. The symbols in the frame are mapped in parallel into points on a constellation plane such that each symbol is given by
, 4-2
where carrier
is the amplitude and , where
.
is the phase. When the symbol
is multiplied with the
is the carrier frequency, the resulting signal is given by
4-3
Since the OFDM symbols are modulated at different frequencies that are integer multiples of each other and summed so that they can be transmitted at the same time the resulting signal is given by
. 4-4 . 4-4)
It can be seen from ( that is given by inverse DFT of since the frequencies are discrete and are multiples of
. The
DFT of a signal can be implemented more efficiently with a FFT when N is a power of 2. The mapped symbols given by can now be replaced by which is the FFT of . This means that OFDM can be implemented by taking the inverse FFT of the mapped symbols and thus at the receiver the received signal s FFT should be computed in order to obtain the symbols. The high data rate of OFDM allows the communication system to make use of a guard interval which is greater than the channel s delay spread. The guard interval helps to mitigate the inter-symbol 4
interference (ISI) caused by multipath. The RMS delay spread was measured to be 800ns in [4] and 150ns in [6] for indoor channels. From [9] it is stated that the maximum symbol rate should satisfy
, 4-5
where
is the RMS delay spread. During the guard interval a cyclic prefix is transmitted instead of not of
sending data since that would cause harmonics at the FFT output. For every frame of symbols length N given by
, 4-6
a sub block of symbols of length L given by
, 4-7
is inserted before the original symbols giving the overall frame to be transmitted given by
. 4-8
The modified block diagram is shown in Figure 2.
Figure 2: Modified OFDM block diagram
Since a whole frame of symbols is transmitted at the same time this makes the system able to combat short durations of noise bursts that are shorter than the symbol period [9]. Despite all the excellent advantages of OFDM there are also disadvantages which come from implementation. OFDM relies on the sub carriers being orthogonal and this makes it very sensitive to synchronization. Poor synchronization causes the carriers to be no longer orthogonal and this yields inter-carrier interference.
5
Doppler frequency shift also causes poor synchronization and thus if the receiver and transmitter are in motion relative to each other ICI would also result in OFDM causing errors. Since the sub carriers used in OFDM are multiples of each other they occur at discrete frequencies in the utilized bandwidth. This causes a high peak to average power ratio (PAPR) and requires the power amplifiers at transmitter and receiver to have a high dynamic range. Power amplifiers operating in a wide dynamic range are non-linear in nature and designing linear amplifiers is complex and thus more expensive. OFDM is more sensitive to distortion caused by non-linear amplifiers since it will cause ICI so OFDM needs more expensive amplifiers to be implemented. In [7] a method of reducing the peak to average power ratio (PAPR) in OFDM by slightly disturbing the symbols in carriers used to transmit information and also sending dummy symbols in unused carriers is presented. The reduction of the PAPR will reduce the cost of the power amplifiers needed to be used in the OFDM system.
6
4.2 Multiple Input and Multiple Output (MIMO) Channels
Similar to time diversity, frequency diversity and coding diversity MIMO offers spatial diversity in a communication system by using multiple antennas at the transmitter to transmit information and also at the receiver to receive the information. It allows independent data streams to be transmitted simultaneously in the same frequency band at the same time via spatial multiplexing which increases the capacity of the channel. It is better than frequency and time multiplexing because it doesn t need more bandwidth to achieve multiplexing [5]. By placing antennas at least /2 apart the signals transmitted with the different antennas are sent over different independent channels which will fade differently reducing the probability that all the paths are unreliable. Increased proximity of the antennas causes the channels to be correlated since the signals suffer the same scattering from the channels. The MIMO channel analysis will be broken up into SIMO and MISO channel analysis which yield receive and transmit diversity respectively. 4.2.1 SIMO Channel (Receive Diversity)
In this communication system there is only one transmitter antenna and NR receive antennas as depicted in Figure 3. The receiver receives NR signals and has to select the corresponding transmitted signal based on the received signal. The signals arrive through independent and uncorrelated paths.
Figure 3: SIMO channel with N transmit antennas and 1 receive antenna
There are 2 types of gains that are obtained as NR is increased. For BPSK the error probability is given by
7
,
4-9
where
is the channel impulse response and
is the signal to noise ratio. The term
can be
written as
. The 1st term corresponds to a diversity gain; by averaging over multiple receive
paths the probability that all the paths have small channel gains is reduced since
if channel gains are normalized. The second term corresponds to a power gain from having many receive antennas and coherent combining at the receiver.
4.2.2
MISO Channel (Transmit Diversity)
In a MISO channel there are NT transmit antennas as depicted in Figure 4. There are many schemes used to achieve diversity such the repetition code and Alamouti. There s no diversity gain when transmitting the same signal over different antennas.
Figure 4: MISO channel with NT transmit antennas and 1 receive antenna
The received signal would be given by
4-10
8
Where
and
are the channel gains on the different paths and
is the channel noise and and have zero mean
are complex Gaussian distributed random variables. Suppose and unit variance such that
Since Let
and
are complex Gaussian distributed then Then we have that and
is also complex Gaussian distributed.
4-11
which shows that there was no diversity gained from transmitting the same signal from different antennas at the same time. The repetition code achieves transmit diversity by transmitting the same signal over different antennas in different intervals with 1 antenna transmitting in each interval. The repetition code is not efficient in using the available degrees of freedom from space diversity. It would cause delays in the transmission of information or require a higher transmission rate. In the Alamouti scheme 2 complex signals are transmitted over 2 symbol periods. In the 1st period is transmitted and in the 2nd period
is transmitted. If the channel is assumed to remain constant over the 2 symbol
times then
and
. Written in matrix form we obtain
The square matrix has orthogonal columns which makes the problem of detecting
and
decompose
to 2 separate orthogonal scalar problems. This makes the diversity gain 2 for the detection of each symbol since the signals and have been transmitted via 2 channels in 2 two symbol periods. This yields better bandwidth efficiency than the repetition code. The sacrifice is the power used to transmit each signal during the symbols period since 2 antennas are active during the symbol period each consuming half the total power. The diversity gain for the Alamouti scheme is 2 for the MISO channel. 4.2.3 MIMO Channel
The MIMO channel consists of the maximum diversity gain is
receiver antennas and
transmitter antennas as depicted in The hence for a MIMO channel
diversity gain for the SIMO channel was
and for the MISO channel was
. Thus using multiple antennas at the transmitter and receiver
increases the diversity of the system and hence the capacity. The other advantage of MIMO systems is discussed next which is spatial multiplexing.
9
Figure 5: MIMO channel with NR receiver and NT transmitter antennas
4.2.4
Spatial Multiplexing
Multiplexing in communication systems is when multiple signals are sent simultaneously. In the space domain multiple signals are transmitted via different transmitter antennas and are received via different receiver antennas. This increases the data rate since instead of sending symbols via the same antenna serially one after the other, consecutive symbols equal to the number of transmitter antennas can be sent in parallel. Spatial multiplexing exploits the channels degrees of freedom which limited by the minimum between the number of transmitter or receiver antennas. An example of a spatial multiplexing is V-BLAST. Here NT signals are sent simultaneously through the channel with the different NT transmitter antennas. The kth signal is allocated a power Pk such that which is the total transmitted power. The kth data stream is encoded using a capacity achieving Gaussian code which achieves a rate Rk . The diversity of V-BLAST is at most NR because each data stream is received via the NR receiver antennas but is transmitted via only 1 transmitter antenna and not NT antennas. This shows that there is less diversity when there is more spatial multiplexing and hence there is a tradeoff between spatial multiplexing and diversity gain. From [8] it was shown that with channel state information (CSI) known at the receiver the capacity in a MIMO communication system with fast fading is given by
, 4-12
where
is the common signal to noise ratio at each receiver antenna. If and
are
the random and ordered singular values of transmitter antennas then
is the minimum of the number of receiver and
10
=
.
4-13
At high SNR the capacity reduces to
4-14
and at low SNR
4-15
with a normalized channel covariance. This indicates that the capacity of a MIMO channel is increased by a factor ,which is the number of degrees of freedom of the channel ,at high SNR and only by a factor at low SNR which only yields a power gain which makes the communication system have a channel. Thus the capacity increase due to spatial multiplexing is similar capacity to that of a 1 by only obtained at high SNR. In a slow fading channel, the capacity is related to the outage probability which is given by
4-16
for an i.i.d. Rayleigh fading channel. Unlike an AWGN channel the slow fading channel is dependent on H, which is random and quasi static, and thus the slow fading channel cannot be characterized by capacity but by outage probability which is the probability that the information transmission rate is smaller than the target rate R. For SISO channel the outage probability at high SNR is given by
4-17
which decays as 1/SNR. For MIMO channel using a repetition scheme the outage probability decays as and this is the upper bound of the decay of outage probability for a MIMO slow fading channel. The diversity from the use of multiple antennas improves the decaying compared to the SISO case hence there is a diversity gain. V-BLAST works well in a fast fading channel but is not optimal in slow fading channels. This is because the data streams are transmitted via different antennas hence different channels. If one of the channels is in a deep fade all the data transmitted through it will be lost. In a fast fading channel the channel variations occur more often and so the channel wouldn t be in a deep fade for a long time such that all the data through is lost. Spatial multiplexing achieves a higher data rate without having to use more bandwidth but this is achieved at the cost of diversity gain. One has to choose between the two benefits of MIMO channels.
4.3 MIMO OFDM
The use of OFDM increases the data rate since a serial data stream is transmitted in parallel via orthogonal sub carriers and if spatial multiplexing is used via multiple transmitter antennas at the 11
transmitter and multiple antennas at the receiver the capacity and reliability of communication increases even further due to the diversity gained from the multiple antennas and spatial multiplexing. With spatial multiplexing each OFDM block can be sent with different antennas which will increase the data rate by a factor equal to the degree of freedom gain of the channel. With spatial diversity each OFDM of block will be sent through all the antennas at different times to achieve both transmit and receive diversity which reduces the symbol error rate. In the design of the test bed schemes which provide the best compromise between spatial diversity and multiplexing will be researched and implemented if they are not too complex to meet real time requirements. The starting point should be implementing spatial diversity since it is less complex than spatial multiplexing. This is because with spatial multiplexing in systems such as V-BLAST, the transmitter has to transmit information at different rates and power at from each transmitter antenna and receiver has to extract the required data rate and power from a sum of NT received signals through NT channels. Synchronization to different data rates and cancelling other signals is very complex.
4.4 Indoor Channel
The channel transfer function in a multipath environment is given by [1]
4-18
where
is the complex amplitude,
is the temporal delay,
is the spatial Doppler shift in
rad.m-1 from the band phase shift shift is much
multipath scatterer,
is the base band angular frequency and z is the position , a carrier phase shift hence it is , a base from . The base band spatial Doppler phase signal neglected
along the direction of motion. The signal experiences attenuation and a carrier spatial Doppler phase shift smaller than that of the carrier
( 4-18). When the receiver moves along the z direction the received signal experiences a phase shift due to the time delay and the spatial Doppler phase shift. The inverse Fourier transform of is
, 4-19
which is the effective distribution of signals at the receiver antenna at a time delay and direction . In an indoor channel the scatterers are closer together due to a large density of objects. The result of this is that there is more fading due to multipath. Since OFDM has an advantage of being immune to multipath fading then this will not pose a problem to the test bed implementation in an indoor channel as long as the transmission rate satisfies (
,
4-5).
When there is no line of sight between the transmitter and receiver and the signal has to travel from one room to another the received signal will be weaker due to path loss. In [1] parametric models for an 12
indoor channel path loss are presented. The models are based on experiments and the path loss is in dB (Hata power law). 4.4.1 Model1
Here the path loss is given by:
4-20
where and
is the distance from the transmitter,
is the path loss at a distance 1m from the transmitter
is to be determined experimentally and determines how rapidly the path loss increases with
distance. In this model the path loss grows linearly with distance. 4.4.2 Model 2
In this model the path loss is given by:
4-21
where
is the free space path loss, ,
is a constant,
is the number of walls penetrated of type is obtained empirically. From the
with wall loss
is the loss between
adjacent floor and
above equation it is observable that the total floor loss is a non-linear function of the number of floors. 4.4.3 Model 3
In this model the path loss is given by:
4-22
where
is an attenuation constant. This path loss is exponential (in dB). The path losses were found to
be independent of frequency and the parameters of the models are to be determined experimentally. Once the parameters are obtained then the path loss can be obtained for any distance from the transmitter within the indoor channel. In [1] the parameters for the 3 models are presented which were obtained by 10 different institutions at an operating frequency of 1.8GHz. The parameters are presented in [1].
Table 1: Model parameters for the 3 models at 1.8 GHz
Condition Dense One floor Two floors
Model 1 (dB) 33.3 21.9 4 5.2
Model 2 (dB) 3.4 6.9
(dB)
(dB) 18.3 0.46
Model 3 (dBm-1) 0.62
13
Three floors Open Large Corridor
44.9 42.7 37.5 29.2
5.4 1.9 2 1.4
3.4 3.4 3.4
6.9 6.9 6.9
18.3 18.3 18.3
0.46 0.46 0.46
2.8 0.22
The walls used in the experiment for Model 2 were light concrete, and
, which was a light wall such as plaster board or
which was a heavy and thick wall with thickness greater than 10cm made of
concrete or brick. From the table it can be seen that the thicker wall contributes a higher loss than the thinner wall of a lighter material as expected. In an indoor channel the receiver and transmitter are either static or moving at slow speeds such that the Doppler spread is very small and the channel can be considered as a slow fading channel. The small Doppler spread in indoor channels will allow OFDM to perform better since the carrier synchronization is less affected and thus the carriers will remain orthogonal. In addition to slow movements making the channel slow fading, the indoor channel does not experience heavy weather conditions such as rain which attenuates the transmitted signal power causing errors at the receiver. The conditions in an indoor channel remain static for multiple symbol times even if is there are changes which can occur such as doors being opened and closed, changes in the occupancy of personnel in the room, movement of furniture etc. The delay spread in the indoor channel is smaller than in the outdoor channel and this allows the communication to be at a higher data rate. This also allows wide band communication such as OFDM to be possible because the smaller delay spread corresponds to a wider coherence bandwidth which makes the channel flat fading as long as the transmission bandwidth is smaller than the coherence bandwidth.
4.5 Channel Estimation
In order to increase the reliability of communication it is desirable to know the channel in order to cancel the non-ideal effects that it introduces to the transmitted signal. The received signal at the receiver is given by
4-23
where
is the channel impulse response,
is the transmitted signal and
is the channel
AWGN. With knowledge of
the communication system can compensate for the effects that it
introduced and thus make better decisions about the transmitted information at the receiver. Channel state information refers to the knowledge of which is the channel impulse response or which is the channel transfer function. In order for the channel to be known measurements of it have to be made. Since the channel cannot be directly measured whilst communicating, it needs to be measured indirectly. At the receiver the channel 14
is obtained via the transmitter sending sufficiently many training or pilot symbols, which are known at the receiver, such that the receiver can accurately estimate the channel. At the transmitter channel knowledge can be obtained via the receiver sending back channel information. The transmitter and receiver operate in a transceiver structure. There are 2 methods available to obtain transmitter CSI. The 1st is using implicit feedback using reciprocity which is for the case when the receiver and transmitter use the same frequency band to transmit information such as time division duplex (TDD). In this case instantaneous channels are identical and thus estimates for CSI at the receiver can be employed at the transmitter. This system becomes very inaccurate when the channels changes rapidly in between the estimate being obtained and when the implicit feedback is being employed. The 2nd method is explicit feedback which is used when the transmitter and receiver use different frequency bands for transmitting information such as frequency division duplex (FDD) or when implicit feedback using reciprocity TDD method is unreliable due to the temporal variations of the channel. Here CSI can be sent back to the transmitter using explicit feedback. In order to obtain receiver CSI the pilot symbols need to be transmitted with the information symbols so the transmitter has to separate the pilot symbols from the information symbols so that the receiver can differentiate between the two. In OFDM there are two types of pilot arrangements used to obtain receiver CSI. The first type is called block pilot arrangement where the pilot symbols are transmitted periodically across all the sub carriers and the receiver can periodically use the received pilot symbols to estimate the channel. The second type of pilot arrangement is comb type pilot arrangement. Here the pilot symbols are transmitted simultaneously with the information symbols. The pilot symbols are interleaved with the information symbols. At the receiver the channel state at the sub carriers carrying information is interpolated from the information obtained from the sub carriers carrying pilots. The two types of pilot arrangements are shown in Figure 6. The block type pilot arrangement is used in slow fading channels since the channel does not vary a lot in between consecutive pilot symbol intervals. The benefit of this arrangement is that the channel is estimated at every sub carrier frequency thus producing accurate channel estimates for each sub carrier. The comb type of pilot arrangement is used in fast fading channels where channel estimation has to be done at every OFDM symbol time to provide more accurate estimates of the rapidly changing channel. The channel at the information baring sub carriers has to be interpolated and hence yielding less accurate estimates than the block type. The benefit of this arrangement is that the channel is estimated at every OFDM symbol period and thus caters more channel variations than the block type pilot arrangement.
15
(a)
(b)
Figure 6: Pilot Arrangement in OFDM communication systems: (a) Comb Type, (b) Block Type
A number of OFDM channel estimation algorithms are discussed in [8] for block type and comb type pilot arrangement. The block type channel estimation algorithms discussed include the Least Squares (LS) estimator and the Minimum Mean Square Error (MMSE) estimator and for comb type pilot arrangement the algorithms discussed include the LS estimator with 1D Interpolation, Linear Interpolation, Second Order Interpolation and Spline Cubic Interpolation. Since in the project the test bed will be implemented for an indoor channel which was discussed to be of slow fading type the estimation methods discussed here are only of block type pilot arrangement which is for slow fading channels. 4.5.1 Least Squares Channel Estimation
Defining symbols as in [8],
and
,
and and
are the transmitted denote the and the DFT
symbols and N is the block length of the transmitted symbols. Let channel impulse response and AWGN respectively. Let the input matrix matrix be
,
4-24
where given by
. From here let
and
. The received signal
is
16
.
4-25
The LS estimator attempts to minimize the quantity conjugate transpose. The least square channel estimate is given by
.
where
denotes complex
4-26
The LS estimator has low complexity and thus can be easily implemented but it suffers from high mean square error since it aims to minimize the least square error. 4.5.2 MMSE Estimator
The MMSE estimator uses second order statistics which involve using the channel auto covariance in order to minimize the square error. Here the channel second order statistics are assumed to be known at the receiver. This means the auto covariance of the channel impulse response ( ) and transfer function ( ) are known. Defining
4-27 4-28 , 4-29
the MMSE estimator of
is given by
.
4-30
As can be seen the MMSE estimator is much more complex than the LS estimator. It involves more multiplications and matrix inversion. The modified MMSE reduces the complexity of the MMSE estimator by using methods such as singular value decomposition. In [5] it is mentioned that second order statistics of a channel vary much more slowly than the channel realization itself and this is the reason why the MMSE estimator performs much better than the LS estimator
17
4.5.3
Implementation Issues
In [3] it is mentioned that the single antenna OFDM channel estimation techniques fail when they are exported to the MIMO case since the signals from the different transmit antennas interfere at the receiver. Modifying the SISO estimators is not straight forward since the channel is much more complex and there are more parameters to be estimated ( more). The MMSE estimator requires knowledge of the channel second order statistics. In [3] measurements of the channel impulse response were obtained from a television and a laboratory in order to find the channel second order statistics which were then used to determine the performances of different channel estimation methods. This implies that measurements of the channel in the environment where a communication system using the channel estimator is to be used in need to be taken. With CSI at the transmitter as well, the transmitter can track changes in the channel and compensate for them by increasing the power level or sending pilots that will achieve better estimation for the current channel state. The transceiver structure can reduce the systems real time performance in TDD due to the channel state having to be fed back after every channel estimation period at the receiver. It requires more bandwidth in FDD and OFDM would be already be consuming a lot of bandwidth due to the information being sent at different sub carriers.
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5 Basic Communication Systems Simulations
The basic digital communication systems have been simulated using Matlab in order to build knowledge of how a communication system works. The communication systems are implemented in a Matlab m file and the transmitted and received data are plotted so that the channel effects on the transmiited can be seen. The simulated communication systems include BPSK and 4 PSK for the cases where the channel is AWGN and when it is also Rayleigh fading. OFDM with BPSK modulated sub carriers is also simulated.
5.1 BPSK Communication System in a AWGN and a Rayleigh fading channel
In the BPSK communication system the carrier s phase is varied according to which bit is to be transmitted. The carrier s phase is made to be one of two phases, 0 and . The transmitted signal is given by
5-1
At the receiver the signal is correlated with
and
.The outputs of the correlator
blocks are summed and sampled at the end of the bit interval. The sampled output is compared with a threshold of 0. If the output is greater than 0 then 1 is assumed to bit the transmitted bit and if the output is less than 0 then 0 is assumed to be the transmitted bit. The threshold is set to be in the middle of the 2 possible outcomes in order to have a symmetrical decision region. The BPSK communication system for an AWGN channel was simulated and Figure 7 shows the graphs of the transmitted and received signals. The received signal to noise ratio is 3 dB and it can be seen the data is decoded without error for the given transmitted data.
19
Serial Data 1 0.9 0.8 0.7 0.6 data 0.5 0.4 0.3 0.2 0.1 0
1
2
3
4
5 6 data index
7
8
9
10
(a)
Transmitted Signal vs time 2 1.5 1 Transmitted Signal 0.5 0 -0.5 -1 -1.5 -2
0
1
2
3
4
5 time (ms)
6
7
8
9
10
(b)
20
Received Signal vs time 3
2
Received Signal
1
0
-1
-2
-3
0
1
2
3
4
5 time (ms)
6
7
8
9
10
(c)
Received Data 1 0.9 0.8 Received Data 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
1
2
3
4
5 6 data index
7
8
9
10
(d)
Figure 7: BPSK communication system in AWGN channel for a SNR= 3dB: (a) Serial data at transmitter. (b) Transmitted signal. (c) Received signal. (d) Decoded data at receiver.
In the Rayleigh fading channel the transmitted is attenuated by the channel attenuation which reduces the received power of the signal. The result of this is a smaller signal to noise ratio which yields more
21
errors in the communication system. This explains the waveform obtained in Figure 8 (b).
Serial Data 1 0.9 0.8 0.7 0.6 data 0.5 0.4 0.3 0.2 0.1 0
1
2
3
4
5 6 data index
7
8
9
10
(a)
Transmitted Signal vs time 2 1.5 1 0.5 0 -0.5 -1 -1.5 -2
Transmitted Signal
0
1
2
3
4
5 time (ms)
6
7
8
9
10
(b)
22
Received Signal vs time 2 1.5 1 Received Signal 0.5 0 -0.5 -1 -1.5 -2
0
1
2
3
4
5 time (ms)
6
7
8
9
10
(c)
Received Data 1 0.9 0.8 Received Data 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
1
2
3
4
5 6 data index
7
8
9
10
(d)
Figure 8: BPSK communication system in Rayleigh fading channel for a SNR= 3dB: (a) Serial data at transmitter.
(b) Transmitted signal. (c) Received signal. (d) Decoded data at receiver.
23
5.2 MPSK Performance in a AWGN and a Rayleigh fading channel
MPSK consists of M possible symbols which can be sent during a symbol interval. The number of bits per symbol is which means that MPSK has a higher data rate than BPSK where only 1 bit is sent per symbol interval. The simulated MPSK communication system is 4PSK which consists of 4 levels. The transmitted signal is given by
5-2
As the number of modulation levels M is increased the distance in phase between adjacent levels decreases and the probability of decoding a symbol in error increases due to smaller decision region. A 4PSK communication system was simulated and the graphs obtained are given in Figure 9. It can be seen when comparing Figure 9 (a) and (d) that with the same SNR of 3dB used in the BPSK communication system there are more errors with the 4PSK communication system. As the modulation levels are increased the decision regions are reduced and thus more errors are made.
Serial Data 1 0.9 0.8 0.7 0.6 data 0.5 0.4 0.3 0.2 0.1 0
1
2
3
4
5 6 data index
7
8
9
10
(a)
24
Transmitted Signal vs time 2 1.5 1 0.5 0 -0.5 -1 -1.5 -2
Transmitted Signal
0
1
2
3
4
5 time (ms)
6
7
8
9
10
(b)
Received Signal vs time 2.5 2 1.5 Received Signal 1 0.5 0 -0.5 -1 -1.5 -2 -2.5
0
1
2
3
4
5 time (ms)
6
7
8
9
10
(c)
25
Received Data 1 0.9 0.8 Received Data 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
1
2
3
4
5 6 data index
7
8
9
10
(d)
Figure 9: BPSK communication system in Rayleigh fading channel for a SNR= 3dB: (a) Serial data at transmitter. (b) Transmitted signal. (c) Received signal. (d) Decoded data at receiver.
26
5.3 OFDM Communication System Simulation
An OFDM communication system was simulated for a channel model given in [3] which is the Advanced Television Technology Center (ATTC) Grande Aliance DTV laboratory s ensemble E model whose static impulse response is given by
.
5-3
Following the simulation parameters given in [3] where 128 subcarriers were used with a 1024 point FFT. The modulation used on the subcarriers was BPSK. The communication system was simulated and the graphs obtained are given in Figure 10.
Serial Data 1 0.9 0.8 0.7 0.6 data 0.5 0.4 0.3 0.2 0.1 0 0 20 40 60 80 data index 100 120 140
(a)
27
Transmitted Signal 2 1.5 Magnitude 1 0.5 0
0
20
40
60 data index
80
100
120
140
4 3 Phase (radians) 2 1 0
0
20
40
60 data index
80
100
120
140
(b)
Received Signal 1024 FFT 100 80 Magnitude 60 40 20 0 0 20 40 60 data index 8 6 Phase (Radians) 4 2 0 80 100 120 140
0
20
40
60 data index
80
100
120
140
(c)
28
Received Data 1 0.9 0.8 0.7 0.6 Data 0.5 0.4 0.3 0.2 0.1 0
0
20
40
60 data index
80
100
120
140
(d)
Zero Padded Serial Data to 1024 Points 1 0.8 0.6 0.4 0.2 Magnitude 0 -0.2 -0.4 -0.6 -0.8 -1
0
200
400
600 data index
800
1000
1200
(e)
29
Real Part of FFT of Received Signal with 1024 Points 100 80 60 40 20 Magnitude 0 -20 -40 -60 -80 -100
0
200
400
600 data index
800
1000
1200
(f)
Figure 10: OFDM communication system simulation graphs (a) Serial data at transmitter. (b) Frequency domain
mapped transmitted data (c) Frequency domain mapped received data. (d) Decoded data at receiver. (e) 1024 point transmitted signal FFT. (f) 1024 point received signal FFT.
From Figure 10 (f) it can be seen that the channel introduces noise which also appears in the unused subcarriers of the FFT. The data can be decoded by remapping each subcarrier magnitude and phase onto the constalllation map and decide which symbol was transmitted based on the maximum likely hood.
30
6 Feasibility of the Project
Extensive research on the topic has been done and more attention was paid to MIMO channels, indoor channels and estimation in OFDM communication systems. At the moment not much has been achieved on implementation of a simple OFDM communication system on the DSP boards. A lot of knowledge of the TM320C6416T DSP board has been gained as well as that of the Code Composer studio which is used to write, simulate and download DSP programs. Due to the complexity of the project the scope was reduced to an implementation of a MISO OFDM communication system. Mr Oyerinde s algorithms will be modified for the indoor MISO channel. They will be simulated for this case and then implemented on the test bed to verify their performance. This is achievable because a MISO channel is a subset of a MIMO channel. The scope was reduced because a MIMO channel test bed implementation is a PhD level topic. The 1st step is to achieve implementing a simple OFDM communication system on the DSP boards. Once this is done channel estimation can be implemented and the real time performance of the implemented channel estimation algorithms will be analyzed. The real time performance of the algorithms in terms of CPU cycles and memory usage will be used as a benchmark of which platform has to be used for implementing the MISO OFDM test bed. The DSP board only has a digital PLL and is thus not enough to implement a full communication system. The other limitation is that the on board AIC23 codec which is used as an external interface for analogue signals has a maximum sampling frequency of 96kHz and is thus not ideal for RF wireless communication. Extra external hardware is needed to interface to an RF antenna, down mix the RF signal and achieve carrier phase synchronization. The available options are to either purchase such equipment or build it. Funds have been allocated to purchase other DSP kits which will have better real time performance than the TM320C6416. The use of a DSP board and programming using C language allows the software to be re usable on other DSPs without having to re write the whole software for the other platform. C language has the disadvantage of being slower than assembly but allows the programming to be flexible. Code Composer Studio has tools which allow the user to evaluate and tune the program performance and offers advice on how to improve the results. It also allows the program to contain linear assembly within the C source file which will speed up the performance. Choosing another platform such as an FPGA will slow down the development time of the project since it offers less flexibility. It was mentioned in Section 4.5.3 of this report that the channel estimation algorithms developed for SISO OFDM communication systems fail when exported to the MISO OFDM system due to added complexity. The limitation of the test bed implementation will be primary caused by the complexity of 31
the channel estimation algorithms which could cause poor real time performance. In the event that the real time performance of the channel estimation techniques developed by Mr Oyerinde is poor, DSP boards will be combined so to share the computation tasks and transfer information from one board to another and increase the amount of computation needed by only one DSP chip. This will imply that the implementation of the algorithms is expensive but the objective of the project will be achieved which is to implement a MISO OFDM test bed based in order to verify the performance of the channel estimation algorithms developed by Mr Oyerinde. The 1st 6 months of the project were dedicated to familiarization of the project topic and the modules involved in it. The next 6 months will be dedicated to further research on the project modules in order to obtain system design parameters such as standards for OFDM communications, channel statics for the proposed environment, power requirements for reliable communication in this environment which is affected by path loses. The next 6 months will also be dedicated to implementing a fully functional SISO OFDM test bed from which performance results can be viewed on a computer. The 3rd semester will dedicated to implementing a MISO communication system. This will require obtaining the necessary hardware, the simulation of the MISO channel in the proposed environment and the performance results for different MISO communication strategies such as Alamouti, V-BLAST and D-BLAST. The success of the OFDM communication system implemented in the 2nd semester and the MISO communication system will allow a MISO OFDM communication system to be implementable by integrating the two communication systems In the final system a MISO OFDM communication will implemented using what was achieved from the OFDM communication system implemented in the 2nd semester and the MISO communication system implemented in the 3rd semester. When the MISO OFDM test bed is functional then the channel estimation algorithms will be implemented and this will conclude the project. The tasks that need to be achieved in the project are given in Table 2.
Table 2: Table of tasks and their duration indicating how the project will be broken down and what is to be achieved at each period in order to achieve success of the project.
Task No. 1
Task Reproduction of Results
2
Description Duration The channel estimation simulation July December 2010 results are to be reproduced in order to gain understanding and to compare them to measured results Simple A simple communication should be July September 2010 Communication implemented to cover: System Ø Modulation Ø Encoding Ø Antenna Interfacing Ø Demodulation Ø Synchronization Ø Decoding Ø Performance analysis on 32
3
4.
5
6
Computer SISO OFDM A SISO OFDM implementation communication which covers the following: system Ø Subcarrier modulation Ø Cyclic prefix transmission during guard interval Ø SISO OFDM channel estimation Ø Demodulation of subcarriers Ø Recent achievements in OFDM such as PAPR reduction algorithm Ø Performance analysis on Computer MISO A MISO communication system communication should be implemented covering: system Ø Hardware to interface to antennas Ø Simulations of a MISO communication system Ø A communication which exploits spatial diversity Ø A communication system that exploits degrees of freedom to increase data rate Ø Analysis on computer MISO OFDM A flexible MISO OFDM communication communication system should be system implemented which will be a combination of the OFDM communication and the MISO communication system. Channel The proposed channel estimation estimation on algorithms should be implemented. the MISO OFDM test bed The system must be flexible to change to a required algorithm. The results are to be analyzed and compared to theoretical results.
September December 2010
January May 2011
May- June 2011
July October 2011
33
7 Conclusion
The motivation for the project requiring an implementation of a test bed in MIMO OFDM communication systems was that the communication system provides an increased data rate and diversity and channel estimation algorithms are needed to make it more reliable. The OFDM communication system was described along with MIMO channels and channel estimation algorithms in order to provide an understanding of the modules involved in the project. The MIMO channel provides spatial diversity and spatial degrees of freedom which can be used for spatial multiplexing in order to increase the data rate. It was shown that the two parameters to be gained from the MIMO channel cannot be achieved together and there s a tradeoff between the two. Diversity and the degrees of freedom increase with the number of antennas used but the optimum of both cannot be achieved at the same time. The communication environment that will be used in the project is an indoor channel. The indoor channel suffers from a lot of multipath due to the walls and furniture being at close distances from each other. The indoor channel is a slow fading channel since motion of terminals inside buildings is at slow speeds or static. Due to walls dividing rooms, the indoor channel suffers more from path loss and this decreases the power of the received signal hence the SNR. Channel estimation allows the receiver to compensate for variations in the communication channel in order to reduce the probability of error in the detected signal. The estimation is obtained by sending reference signals called pilots which are known at the receiver but the disadvantage of using them is that the data rate is reduced since less information is transmitted because pilots are known at the receiver and hence they are not information. Since the channel that will be used for the project is an indoor channel, which is a slow fading channel, block type pilot arrangement will be used for channel estimation. Due to the complexity of a MIMO OFDM communication system implementation the project scope was reduced to only a MISO OFDM communication system. The project would not be feasible if it was a MIMO OFDM communication system implementation because the topic is at a PhD level. The result of this would be a communication system that can only exploit the transmit diversity of the system and there s no spatial multiplexing available. The project requirements are achievable in the period of 2 years. More research will be conducted in the next 6 months to obtain more information about implementation of MISO OFDM communication. An OFDM communication will be implemented in the next 6 months. In the 3rd semester a MISO communication system will be implemented and in the 4th semester a full MISO OFDM communication system will be implemented which will then be used as a test bed for the verification of Mr Oyerinde s channel estimation techniques.
34
8 References
[1] Andersen, J.B. & Vaughan, R., Channels, Propagation and Antennas for Mobile Communications (IEE Electromagnetic Waves Series; no.50), 2003 [2] Angelosante, D., Biglieri,E. & Lops, M., Sequential Estimation of Multipath MIMO OFDM Channels , IEEE Transactions on Signal Processing, vol. 57,no. 8, Aug. 2009 [3] Bahai, A., Coleri, S., Ergen M. & Puri, A., Channel Estimation Techniques Based on Pilot Arrangement in OFDM Systems , IEEE Transactions on Broadcasting, vol. 48, no. 3, Sept 2002, pp 223- 229 [4] Bernadin, P., Caire, G., Corrat, J., Dias, A.R., Fábregas, A.G., Gosse, K., Guillaud, M.,Li, Z., Miet, X., Peden, A., Rouquette, S., Slock , D.T.M. & Toutain, Y., A MIMO OFDM Testbed for Wireless Local Area Networks , EURASIP Journal on Signal Processing, 21 June 2005 [5] Bölcskei, H., Gesbert, D., Papadias, C. B. & Van der Veen, A., Space Time Wireless Systems: From Array Processing to MIMO Communications, Cambridge University Press, 2006 [6] Eden, D., Hinostroza & V., Salous, S., High Resolution Indoor and Indoor to Indoor Measurements , European Cooperation In the Field of Scientific and Technical Research (Euro-Cost), 31 May 2002 [7] Cavalcante, R.L.G. & Yamada, I., A Flexible Peak-To-Average Power Ratio Reduction Scheme for OFDM Systems by Adaptive Projected Subgradient Method , IEEE transactions on Signal Processing, vol. 57,no. 4,April 2009
[8] Martinez, E. &Shen, Y., Channel Estimation in OFDM Systems , Freescale Semiconductor, Jan. 2006
[9] Peterson, R.L. & Ziemer, R.E., Introduction to Digital Communication, 2nd edn, Prentice-Hall, 2001 [10] Tse,D, & Viswanath,P., 2008, Fundamentals of Wireless Communications, Cambridge University Press, New York
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