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IOSR Journal of Electronics and Communication Engineering (IOSR-JECE)
e-ISSN: 2278-2834,p- ISSN: 2278-8735.Volume 10, Issue 5, Ver. I (Sep - Oct .2015), PP 21-26
www.iosrjournals.org
DOI: 10.9790/2834-10512126 www.iosrjournals.org 21 | Page
Reconfigurable architecture for the déteteur ML system
MIMO
Ogbi Menouar1, M.Bouziani2, Bouamama Réda Sadouki3,
1
(Electronics Department, University of Sidi Bel Abbès Telecom Laboratory LTTNS
2
(Electronics Department, University of Sidi Bel Abbès Telecom Laboratory LTTNS
2
(Electronics Department, University of Sidi Bel Abbès Telecom Laboratory LTTNS
Abstract: MIMO systems based on the use of multiple antennas for transmission and reception is one of the
most promising approaches to increase the rates in communication systems). The implementation of these
techniques therefore necessary to develop specific hardware architectures guaranteeing high flows. The work of
this paper focuses on finding flexible hardware architecture dedicated to the implementation of the functions
used in MIMO decoders, and concludes with the integration of architecture used on a target FPGA.
Mots Clés : Systèmes de communication, algorithmes, implémentation, architecture reconfigurable, FPGA,
décodeur MIMO, radio-logicielle, débit.
I. Introduction
With The Integration Of The Internet And New Multimedia Applications In Wireless Communication
Systems , The Demand In Terms Of Throughput Is Increasing . Mimo Technique Is Most Promising [1] . For
Example, Standard Wireless Broadband , Such As Ieee 802.11n And Hiperlan2 Lans, The Mimo System Must
Support Different Types Of Modulations And Propagation. These Are The Reasons Why A Reconfigurable
Architecture Finds Its Interest In Mimo Systems. Mimo Algorithms Are Typically Implemented On Dsp , It Is
Difficult To Achieve High -Speed Performance . The Traditional Asic Solution Is Used Programmable Fpga
Circuits To Meet Our Reconfiguration Problem. The Rest Of The Paper Is Organized As Follows: Section 2
Briefly Presents The Mimo System. Section 3 Describes The Different Receiver Algorithms And Illustrates Our
Choice Of Algorithm "Ml" In Terms Performance . The Following Section Details The Algorithm "Ml" , Which
We Accepted. Section 5 Discusses The Functional Architecture Of The Algorithm. Section 6 Presents The
Reconfigurable Architecture , We Analyze The Implementation Through Concrete Examples And Present The
Results Of The Synthesis Of Different Architectures On Fpga. Finally , We Emphasize The Dynamic Aspect
(Real Time) Reconfiguration .
II. Présentation Du Système Mimo :
Communications on the mobile radio channel have developed strongly in recent years, both in terms of
number of users per user flow . This causes saturation radiofrequency resources in areas of high population.
Therefore, there is a strong demand to increase the spectral efficiency of the communications. On the other hand
, transmissions over the wireless radio channel are heavily penalized by the signal fading due to both multipath
and intersymbol interference . a solution has been studied for some years . This is a transmission architecture
based on the use of multiple antennas for transmission and reception. These architectures, called MIMO, were
developed by Bell Laboratories in 1997. [2]
At the reception, each antenna receives the sum of symbols If issued simultaneously by each Ni transmitting
antennas. The signal received by the , antennas wrote:
∑ ( ) (1)
The received value y can be written in the following matrix form:
(2)
With [ ] the vector of transmitted symbols. H is the channel matrix of dimension Nr ×
Nt, is given by:
[ ]
Reconfigurable architecture for the déteteur ML system MIMO
DOI: 10.9790/2834-10512126 www.iosrjournals.org 22 | Page
And [ ] the vector of additive Gaussian noise on reception.
Fig (1) Principle of a MIMO system
there are two main types of techniques for transmission over MIMO systems the first is based on the space-
time codes, the other on the spatial multiplexing [3].
2.1 Space-timecoding:
Improving The Quality Of Transmission Wing, Alamouti [4] And Tarokh [5] Have Designed Systems Based
Primarily On The Diversity And Offering No Coding Un Spouses Of Label. This Space Coding-Temp (Sct)
Also Allows Communications And Accurate, It Is Added To Redundancy Bit Data Issued To Increase Diversity
And Space Avoid Specific Fading Mimo Channel. Pay More Details On Codes Spatiotemporal Refer [4] [5].
2.2 Multiplixage Space:
Spatial multiplexing, or V-BLAST (Vertical Bell Labs Layered Space-Time) [6], can be seen as a special class
of space-time codes, its principle is to divide the data stream at the entrance in several sub-streams, the latter are
transmitted on different antennas. This architecture is primarily intended to increase the system capacity.
Fig (2) Principle of spatial multiplexing
III. Detection Algorithms With MIMO Systems:
There are many possible algorithms for recovering the reception symbols in a multi-antenna transmission.
3.1 Receiver of Forcing A Zero (ZF):
The simplest linear receiver is the receiver based on the criterion of zero-forcing (ZF zeroforcing) that simply
reverses the channel matrix [7]. Assuming that H is invertible, the vector of estimated symbols size nT * 1 is
then given by the relation
̂
3.2 receivers which minimizes the mean squared error (MMSE)
The consideration for the complete separation of the signals is increased noise. The receiver which
minimizes the mean squared error (MMSE) is an excellent alternative. [8] That other linear receiver minimizes
the overall error due to noise and mutual interference of signals passing through the same channel. The mean
square error is given by:
{ ̂ ̂ }
In this case, s is estimated from the relationship:
̂
Reconfigurable architecture for the déteteur ML system MIMO
DOI: 10.9790/2834-10512126 www.iosrjournals.org 23 | Page
3.3 Detector successive interference cancellation (ASI):
The detection algorithm uses the nonlinearity and thus exploits the inherent synchronization model.
The principle, based on "the cancellation of symbols" is quite simple: the contribution of elements s already
found is subtracted from the received vector r, which gives a received vector containing less interference. Using
such a method, the order in which the elements of are detected becomes important to improve the system
performance.
3.4 Receiver Maximum Likelihood (ML):
This receiver provides better performance in terms of error rate [9]. Assuming a Gaussian noise and channel
state well known receiver side, the receiver gives the estimated MV s using the formula symbols
̂ ‖ ‖ (7)
3.5 receiver decision feedback V-BLAST:
This receiver is the simplest and also the least efficient. It seeks to cancel the contributions of other issuers in
each symbol. This is equivalent to the reverse transfer matrix of the channel [10]:
3.6 Comparison of performance between the different receptors:
Figure (3) shows an evaluation of the BER for different receivers. These results are obtained in a 2x2 MIMO
system provided with an antenna with BPSK modulation.
Fig (3) performance across 2x2 MIMO receivers
It is important to note that the algorithm of maximum likelihood (ML) has a better performance in terms of
BER.
IV. The ML decoding algorithm:
The ML criterion is to minimize the distance between the received point and the point decoded. The Schnorr-
Euchner algorithm used this criterion [11]. The equation which gives the network point representation of a
MIMO system is:
The SE algorithm is performed to find this point, the steps to find this point are:
Case A: Whenever the algorithm finds a Uk component, it passes the layer k-1.
Case B: If the distance between the received and decoded item exceeds the current minimum distance, we move
to the upper layer.
Case C: the algorithm afranchi every layer and you do get a point. This network point will be stored, and the
distance will be updated.
V. The ML decoding algorithm using Simulink.
The decoding algorithm used in this paper applies the method of Schnorr-Euchner [12], Figure (4) shows
schematically the algorithm using simulink.
0 5 10 15 20 25
10
-5
10
-4
10
-3
10
-2
10
-1
Eb/No (dB)
Tauxd'ErreurBinaire
TEB en modulation BPSK utilisant les antennes MIMO(2x2)
sim (nTx=2, nRx=2, MMSE)
sim1 (nTx=2, nRx=2, ML)
sim2 (nTx=2, nRx=2, ZF)
Reconfigurable architecture for the déteteur ML system MIMO
DOI: 10.9790/2834-10512126 www.iosrjournals.org 24 | Page
Fig (4) decoding algorithm using Simulink
This model is obtained in a 4x4 MIMO antenna system provided with a BPSK modulation.
Figure (5) shows the complete model of MIMO decoder based on the ML criterion was developed and adapted
to MATLAB Simulink model contains seven modules: [13]
Fig (5) MIMO decoder block
VI. Result of the implementation:
Figure (6) shows the following bit error rate based on this model SNR
Fig (6) performance of the algorithm for MIMO decoding (SE)
The MIMO system has been presented in the previous model is modeled using VHDL and simulated in modele
Sim. Each block is tested separately for its functionality.
Fig (7) the timing associated with MIMO decoder
EnS
Rx
G
X
H
Hkk
Preprocessing
EnS
X
H
Hkk
Decode_Done
Rx_decoded
MIMODecoder
Tx
Rx_decoded
Error
ErrorRate
Calculation
DoneSEnS
Ens_gen
CM
EnS
Tx
Rx
Encoder_enabled
0.006643
11
1656
CM
Channel Matrix
AWGN
Reconfigurable architecture for the déteteur ML system MIMO
DOI: 10.9790/2834-10512126 www.iosrjournals.org 25 | Page
Fig (8) MIMO decoder architecture associated
the implementation of MIMO decoder was simulated a heterogeneous platform, the different functional modules
of the decoder are described on FPGA [14].
VII. Implementation of a MIMO algorithm on FPGA :
A general view of MIMO decoder after placement / routing on Xilinx Virtex 4
Fig (9) MIMO decoder after placement / routing on Xilinx Virtex 4
VIII. Conclusion:
The work presented in this paper focuses on the reconfigurable architecture for MIMO systems for the
execution of signal processing applications, including software defined radio.
At first, we briefly compared the best known MIMO algorithms and we chose the algorithm ML Shnorr
- Euchner (SE) as the best compromise in terms of performance.
Reconfigurable architectures offer new alternatives between the flexibility of DSP programmable
processors and high-performance specific ASICs. After briefly analyzed and compared reconfigurable
architectures, we rely on the FPGA technology to meet our need for reconfiguration.
To explore the use of reconfigurable architecture for MIMO decoding algorithm, we analyzed the
MIMO detection algorithm with simulations in Matlab. We used a combination of MATLAB / Simulink and
Xilinx System Generator for a simple hardware design and introduce a graphical interface for simulation tools.
Bibliography:
[1]. Z. Guo and P. Nilsson: A VLSI implementation of MIMO detection for future wireless communications , in Proc . PIMRC'03 IEEE
, vol. 3 , 2003, p. From 2852 to 2856.
[2]. GJ Foschini , " Layered Space- Time Architecture for Wireless Communication in Fading Environments When using Multiple
Antennas , " Bell Labs Technical Journal , Vol. 1. , No. 2, Autumn 1997 , p. 41-59
[3]. Rajn Ratti S / O Satya Nand , "Simulation and Performance of Multiple Input Multiple Output Orthogonal Frequency Division
Multiplixing 802.11a Wireless Local Area Network " University Teknologi Malaysia , september 2006.
[4]. V. Tarokh , N. Seshadri and AR Calderbank , " Space- time codes for high data rate wireless communications : Performance
Criteria and code construction". IEEE Transactions on Information Theory , vol. 44, pages 744-765 , March 1998 .
[5]. M. Alamouti , "A Simple transmitted technical diversity for wireless communications, " IEEE Journal on Selected Areas in
Communications , vol. 16, no. 8 , pp . 1451-1458 , October 1998 .
[6]. B. Hassibi , "An efficient square -root algorithm for BLAST , " Proc. IEEE Int . Conf . Acoustics , Speech , Signal Processing (
ICASSP'00 ), June 2000 , p. 737-740 .
[7]. Ludovic Collin1 , Rostaing2 Philippe Olivier Berder2 and Gilles Burel , "Application of the estimator of Julier and Uhlmann rapid
assessment Bit Error Rate in a MIMO transmission system / OFDM " in September 2001 .
Reconfigurable architecture for the déteteur ML system MIMO
DOI: 10.9790/2834-10512126 www.iosrjournals.org 26 | Page
[8]. Christian Mehlf ¨ uhrer and Markus Rupp, "A Robust MMSE Equalizer for MIMO Enhanced HSDPA " IEEE.Oct 2006.pacific
Grove , CA , USA.
[9]. Nicholas D. Sidiropoulos and Zhi- Quan Luo , "A Semidefinite Relaxation Approach to MIMO Detection for High -Order QAM
Constellations" IEEE SIGNAL PROCESSING LETTERS, VOL . 13 , NO. 9, SEPTEMBER 2006.
[10]. GD Golden, GJ Foschini , RA Valenzuela , PW Wolniansky , " Detection algorithm and initial laboratory results using V -BLAST
space-time communication architecture, " Electronics Letters , vol. 35, no . 1 , pp . 14-15 January 1999.
[11]. Erik Agrell, Thomas Eriksson, Alexander Vardy , "Closest Point Search in Lattices " IEEE Transactions on Information Theory ,
vol. 48, NO. 8 august 2002.
[12]. Georg Brandmayr Gerhard Humer, Markus Rupp, "AUTOMATIC CO- VERIFICATION OF FPGA DESIGNS IN SIMULINK "
[13]. Frank Liu, Arun Mulpur " code generation and verification for FPGAs " 2006 The Mathworks.Inc .
[14]. Joseph R. Cavallaro , Predrag Radosavljevic , " ASIP Architecture for Future Wireless Systems : Flexibility and Customization "
Department of Electrical and Computer Engineering"

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D010512126

  • 1. IOSR Journal of Electronics and Communication Engineering (IOSR-JECE) e-ISSN: 2278-2834,p- ISSN: 2278-8735.Volume 10, Issue 5, Ver. I (Sep - Oct .2015), PP 21-26 www.iosrjournals.org DOI: 10.9790/2834-10512126 www.iosrjournals.org 21 | Page Reconfigurable architecture for the déteteur ML system MIMO Ogbi Menouar1, M.Bouziani2, Bouamama Réda Sadouki3, 1 (Electronics Department, University of Sidi Bel Abbès Telecom Laboratory LTTNS 2 (Electronics Department, University of Sidi Bel Abbès Telecom Laboratory LTTNS 2 (Electronics Department, University of Sidi Bel Abbès Telecom Laboratory LTTNS Abstract: MIMO systems based on the use of multiple antennas for transmission and reception is one of the most promising approaches to increase the rates in communication systems). The implementation of these techniques therefore necessary to develop specific hardware architectures guaranteeing high flows. The work of this paper focuses on finding flexible hardware architecture dedicated to the implementation of the functions used in MIMO decoders, and concludes with the integration of architecture used on a target FPGA. Mots Clés : Systèmes de communication, algorithmes, implémentation, architecture reconfigurable, FPGA, décodeur MIMO, radio-logicielle, débit. I. Introduction With The Integration Of The Internet And New Multimedia Applications In Wireless Communication Systems , The Demand In Terms Of Throughput Is Increasing . Mimo Technique Is Most Promising [1] . For Example, Standard Wireless Broadband , Such As Ieee 802.11n And Hiperlan2 Lans, The Mimo System Must Support Different Types Of Modulations And Propagation. These Are The Reasons Why A Reconfigurable Architecture Finds Its Interest In Mimo Systems. Mimo Algorithms Are Typically Implemented On Dsp , It Is Difficult To Achieve High -Speed Performance . The Traditional Asic Solution Is Used Programmable Fpga Circuits To Meet Our Reconfiguration Problem. The Rest Of The Paper Is Organized As Follows: Section 2 Briefly Presents The Mimo System. Section 3 Describes The Different Receiver Algorithms And Illustrates Our Choice Of Algorithm "Ml" In Terms Performance . The Following Section Details The Algorithm "Ml" , Which We Accepted. Section 5 Discusses The Functional Architecture Of The Algorithm. Section 6 Presents The Reconfigurable Architecture , We Analyze The Implementation Through Concrete Examples And Present The Results Of The Synthesis Of Different Architectures On Fpga. Finally , We Emphasize The Dynamic Aspect (Real Time) Reconfiguration . II. Présentation Du Système Mimo : Communications on the mobile radio channel have developed strongly in recent years, both in terms of number of users per user flow . This causes saturation radiofrequency resources in areas of high population. Therefore, there is a strong demand to increase the spectral efficiency of the communications. On the other hand , transmissions over the wireless radio channel are heavily penalized by the signal fading due to both multipath and intersymbol interference . a solution has been studied for some years . This is a transmission architecture based on the use of multiple antennas for transmission and reception. These architectures, called MIMO, were developed by Bell Laboratories in 1997. [2] At the reception, each antenna receives the sum of symbols If issued simultaneously by each Ni transmitting antennas. The signal received by the , antennas wrote: ∑ ( ) (1) The received value y can be written in the following matrix form: (2) With [ ] the vector of transmitted symbols. H is the channel matrix of dimension Nr × Nt, is given by: [ ]
  • 2. Reconfigurable architecture for the déteteur ML system MIMO DOI: 10.9790/2834-10512126 www.iosrjournals.org 22 | Page And [ ] the vector of additive Gaussian noise on reception. Fig (1) Principle of a MIMO system there are two main types of techniques for transmission over MIMO systems the first is based on the space- time codes, the other on the spatial multiplexing [3]. 2.1 Space-timecoding: Improving The Quality Of Transmission Wing, Alamouti [4] And Tarokh [5] Have Designed Systems Based Primarily On The Diversity And Offering No Coding Un Spouses Of Label. This Space Coding-Temp (Sct) Also Allows Communications And Accurate, It Is Added To Redundancy Bit Data Issued To Increase Diversity And Space Avoid Specific Fading Mimo Channel. Pay More Details On Codes Spatiotemporal Refer [4] [5]. 2.2 Multiplixage Space: Spatial multiplexing, or V-BLAST (Vertical Bell Labs Layered Space-Time) [6], can be seen as a special class of space-time codes, its principle is to divide the data stream at the entrance in several sub-streams, the latter are transmitted on different antennas. This architecture is primarily intended to increase the system capacity. Fig (2) Principle of spatial multiplexing III. Detection Algorithms With MIMO Systems: There are many possible algorithms for recovering the reception symbols in a multi-antenna transmission. 3.1 Receiver of Forcing A Zero (ZF): The simplest linear receiver is the receiver based on the criterion of zero-forcing (ZF zeroforcing) that simply reverses the channel matrix [7]. Assuming that H is invertible, the vector of estimated symbols size nT * 1 is then given by the relation ̂ 3.2 receivers which minimizes the mean squared error (MMSE) The consideration for the complete separation of the signals is increased noise. The receiver which minimizes the mean squared error (MMSE) is an excellent alternative. [8] That other linear receiver minimizes the overall error due to noise and mutual interference of signals passing through the same channel. The mean square error is given by: { ̂ ̂ } In this case, s is estimated from the relationship: ̂
  • 3. Reconfigurable architecture for the déteteur ML system MIMO DOI: 10.9790/2834-10512126 www.iosrjournals.org 23 | Page 3.3 Detector successive interference cancellation (ASI): The detection algorithm uses the nonlinearity and thus exploits the inherent synchronization model. The principle, based on "the cancellation of symbols" is quite simple: the contribution of elements s already found is subtracted from the received vector r, which gives a received vector containing less interference. Using such a method, the order in which the elements of are detected becomes important to improve the system performance. 3.4 Receiver Maximum Likelihood (ML): This receiver provides better performance in terms of error rate [9]. Assuming a Gaussian noise and channel state well known receiver side, the receiver gives the estimated MV s using the formula symbols ̂ ‖ ‖ (7) 3.5 receiver decision feedback V-BLAST: This receiver is the simplest and also the least efficient. It seeks to cancel the contributions of other issuers in each symbol. This is equivalent to the reverse transfer matrix of the channel [10]: 3.6 Comparison of performance between the different receptors: Figure (3) shows an evaluation of the BER for different receivers. These results are obtained in a 2x2 MIMO system provided with an antenna with BPSK modulation. Fig (3) performance across 2x2 MIMO receivers It is important to note that the algorithm of maximum likelihood (ML) has a better performance in terms of BER. IV. The ML decoding algorithm: The ML criterion is to minimize the distance between the received point and the point decoded. The Schnorr- Euchner algorithm used this criterion [11]. The equation which gives the network point representation of a MIMO system is: The SE algorithm is performed to find this point, the steps to find this point are: Case A: Whenever the algorithm finds a Uk component, it passes the layer k-1. Case B: If the distance between the received and decoded item exceeds the current minimum distance, we move to the upper layer. Case C: the algorithm afranchi every layer and you do get a point. This network point will be stored, and the distance will be updated. V. The ML decoding algorithm using Simulink. The decoding algorithm used in this paper applies the method of Schnorr-Euchner [12], Figure (4) shows schematically the algorithm using simulink. 0 5 10 15 20 25 10 -5 10 -4 10 -3 10 -2 10 -1 Eb/No (dB) Tauxd'ErreurBinaire TEB en modulation BPSK utilisant les antennes MIMO(2x2) sim (nTx=2, nRx=2, MMSE) sim1 (nTx=2, nRx=2, ML) sim2 (nTx=2, nRx=2, ZF)
  • 4. Reconfigurable architecture for the déteteur ML system MIMO DOI: 10.9790/2834-10512126 www.iosrjournals.org 24 | Page Fig (4) decoding algorithm using Simulink This model is obtained in a 4x4 MIMO antenna system provided with a BPSK modulation. Figure (5) shows the complete model of MIMO decoder based on the ML criterion was developed and adapted to MATLAB Simulink model contains seven modules: [13] Fig (5) MIMO decoder block VI. Result of the implementation: Figure (6) shows the following bit error rate based on this model SNR Fig (6) performance of the algorithm for MIMO decoding (SE) The MIMO system has been presented in the previous model is modeled using VHDL and simulated in modele Sim. Each block is tested separately for its functionality. Fig (7) the timing associated with MIMO decoder EnS Rx G X H Hkk Preprocessing EnS X H Hkk Decode_Done Rx_decoded MIMODecoder Tx Rx_decoded Error ErrorRate Calculation DoneSEnS Ens_gen CM EnS Tx Rx Encoder_enabled 0.006643 11 1656 CM Channel Matrix AWGN
  • 5. Reconfigurable architecture for the déteteur ML system MIMO DOI: 10.9790/2834-10512126 www.iosrjournals.org 25 | Page Fig (8) MIMO decoder architecture associated the implementation of MIMO decoder was simulated a heterogeneous platform, the different functional modules of the decoder are described on FPGA [14]. VII. Implementation of a MIMO algorithm on FPGA : A general view of MIMO decoder after placement / routing on Xilinx Virtex 4 Fig (9) MIMO decoder after placement / routing on Xilinx Virtex 4 VIII. Conclusion: The work presented in this paper focuses on the reconfigurable architecture for MIMO systems for the execution of signal processing applications, including software defined radio. At first, we briefly compared the best known MIMO algorithms and we chose the algorithm ML Shnorr - Euchner (SE) as the best compromise in terms of performance. Reconfigurable architectures offer new alternatives between the flexibility of DSP programmable processors and high-performance specific ASICs. After briefly analyzed and compared reconfigurable architectures, we rely on the FPGA technology to meet our need for reconfiguration. To explore the use of reconfigurable architecture for MIMO decoding algorithm, we analyzed the MIMO detection algorithm with simulations in Matlab. We used a combination of MATLAB / Simulink and Xilinx System Generator for a simple hardware design and introduce a graphical interface for simulation tools. Bibliography: [1]. Z. Guo and P. Nilsson: A VLSI implementation of MIMO detection for future wireless communications , in Proc . PIMRC'03 IEEE , vol. 3 , 2003, p. From 2852 to 2856. [2]. GJ Foschini , " Layered Space- Time Architecture for Wireless Communication in Fading Environments When using Multiple Antennas , " Bell Labs Technical Journal , Vol. 1. , No. 2, Autumn 1997 , p. 41-59 [3]. Rajn Ratti S / O Satya Nand , "Simulation and Performance of Multiple Input Multiple Output Orthogonal Frequency Division Multiplixing 802.11a Wireless Local Area Network " University Teknologi Malaysia , september 2006. [4]. V. Tarokh , N. Seshadri and AR Calderbank , " Space- time codes for high data rate wireless communications : Performance Criteria and code construction". IEEE Transactions on Information Theory , vol. 44, pages 744-765 , March 1998 . [5]. M. Alamouti , "A Simple transmitted technical diversity for wireless communications, " IEEE Journal on Selected Areas in Communications , vol. 16, no. 8 , pp . 1451-1458 , October 1998 . [6]. B. Hassibi , "An efficient square -root algorithm for BLAST , " Proc. IEEE Int . Conf . Acoustics , Speech , Signal Processing ( ICASSP'00 ), June 2000 , p. 737-740 . [7]. Ludovic Collin1 , Rostaing2 Philippe Olivier Berder2 and Gilles Burel , "Application of the estimator of Julier and Uhlmann rapid assessment Bit Error Rate in a MIMO transmission system / OFDM " in September 2001 .
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