Chapter 2 OFDM and MIMO Fundamentals
2.3 Signal Detection Algorithms for MIMO Systems
2.3.3 Detection Methods based on V-BLAST
2.3.3.4 V-BLAST Technique with Parallel Symbol Cancellation
2.3.3.4.1 Two-Stage V-BLAST Detection Algorithm
In order to avoid long time delay, parallel symbol cancellation (PSC) was proposed [26]. However the performance will be degraded. To reduce the problem, this two-stage algorithm combines SSC with PSC techniques so as to improve the BER performance. The proposed scheme is combined with ZF technique. The algorithm is divided into two distinct stages.
Stage1: use V-BLAST method to obtain a good initial decision.
Stage2: use parallel symbol cancellation to attain the estimated value of the transmitted vector.
The proposed algorithm based on ZF criterion is described below:
Stage 1:initialization
Stage 2:initialization
for (k=1; k <=Nt; k++)
Equation (2.24) can obtain a diversity order equals the receiver antennas. We will compare this method with the proposed algorithm in Chapter 3.
2.3.4 Complexity Comparisons of Data Detection Algorithms
The 0th-order simplified detection denotes the approach of copied vectors in Section 2.3.3.1. The 1st-order simplified Detection (approximation) denotes is mentioned in section 2.3.3.1. Shen’s and Li’s iterative methods [19] are discussed in Section 2.3.3.2.1. Akhtar’s method [22] denotes the new K approach in Section 2.3.3.2.2, Baro’s method [23] denotes joint ML and DFE scheme in Section 2.3.3.2.3, Duong’s method [25]
denotes the approach with modified channel matrix in Section 2.3.3.3.1, while Xiaofeng’s method [26] denotes the PSC method in Section 2.3.3.4.1.
Although complexity of the 0th-order simplified detection method is smaller than the others, it only saves 20% simulation time. For Shen’s and Li’s iterative methods, their performances are similar. However the Li’s iterative method can get more diversity order. Baro’s method is complicated, because it must do V-BLAST detection and ML detection. Moreover, it must computep , which is hard to solve. That is not feasible.
Xiaofeng’s PSC method must detect signal at the same time, so it need many parallel ZF and PSC units [28].
Table 2.4 Complexity comparisons of data detection algorithms (0th-order appr.)
6 )
(Nt2 +NtNr × 192
Simplified Detection (1st-order appr.)
6 ) (
2Nt2Nr + Nt2 +NtNr × 320
Shen’s iterative method [19]
Li’s iterative method [21]
Baro’s joint ML and DFE
modified H method [24]
Xiaofeng’s PSC method [25]
Chapter 3
The Proposed Data Detection Algorithms
Since the performance gap between V-BLAST detection and ML detection is significant, we still have a lot of room to improve the V-BLAST techniques. Through technique survey we got some idea from the algorithms in Chapter 2. We will propose a hybrid ML detection and V-BLAST detection method in this chapter. The method will reduce a great deal of the comparison operations in ML detection. It will get better performance than V-BLAST method, without increasing too many comparison operations.
Besides, it will decrease complex multiplication in calculating pseudo-inverses.
3.1 The New Detection Methods
As we know joint ML and V-BLAST can get better performance, it provides an idea for further improvement. Specifically, after the initial values x1 to
Nt
x are detected, we can use further other detection method like ML detection to do the detection again.
First, let us suppose N transmitter antennas and t Nr receiver antennas. If we use QPSK modulation, and want to detect the transmitted signals, then a total of (Nt)4
comparisons will have to be made. Generally, in detecting M-QAM by using ML method, a total of (N )t M comparisons need to be made.
We suppose that some of signals are already known. As such, in this way we don’t need to do all the comparisons and it will decrease a large number of comparison operations in ML detection, while still maintain good performances.
3.1.1 New Hybrid ML and V-BLAST Detection Method
As mentioned before, one can reduce the complexity of equation (2.8), if we already know some detected signals. For example if in M-PSK modulation there is only one unknown symbol, then we just only need to compare M values in ML detection.
Based on the idea, first V-BLAST method is used to detect all the initial values, and then we update it by ML detection. Suppose L is the level we want to do the detection, ranging from 1 to N . In other word, we will update L value by ML detection. t
The algorithm is summarized below and shown in Figure 3.1:
Step 1:
Figure 3.1 The proposed hybrid ML and V-BLAST detection For illustration, we show the detection flow for L=1 and L=Nt in Figure 3.2 and Figure 3.3, respectively.
Figure 3.2 The proposed hybrid ML and V-BLAST detection (simplest case forL=1)
Figure 3.3 Flow diagram of the proposed hybrid ML and V-BLAST detection (the most complex case, L=Nt)
In this approach we can confine error propagation, meantime reduce computation complexity. For ML detection, the number of minimum norm we calculate ranging from
M
N )t
( to L×Nt (Θ is M-QAM). We will discuss complexity of the proposed design in Section 3.4 and verify its in Chapter 4.
3.1.2 Extension of the new method
When a system has a large number of transmitter antennas, we can use this approach to detect two or more values at the same time. But here we only discuss the case of detecting two values at the same time. Figure 3.4 depicts the algorithm flow as shown below. The algorithm is summarized below:
Step1:
adopt V-BLAST to get the initial 1'... '
NT
x x
∩
∩
values Step2:
with the detected x1'...xNt'
Figure 3.4 Extension of the proposed algorithm
Although the proposed extended method can get better performance than the proposed method in section 3.1.1, will increase complexity. The complexity will be discussed in section 3.4.
3.2 The Compared Detection Techniques
Li’s and Shen’s methods [19,21]
In 2.3.3.2.1 we introduce these two iterative detection methods, which have similar performances and complexities. In Chapter 4 we will compare Li’s and Shen’s methods in simulation.
Our Improved Li’s method
Shen’s method focuses on optimizing diversity order. It increases diversity order in second loop to get better performance than V-BLAST method. Here, we can modify the Li’s method and increase its diversity order. Precisely equation (3.2) will be used to increase diversity order in the second loop. Therefore, in second loop all the signals will have N diversity orders. The algorithm steps are shown below. (t −1−
~
Hi means the resulting
~
H matrix after nulling the i-1th column of
~
H ) Step 1:
Perform the optimal ordering and SIC according to V-BLAST method and get the detected symbols Nt
old
1 (the optimal order is assumed to be 1,2,….Nt.
3.3 Reducing Computational Complexities in Pseudo-Inverse
If H is a m× matrix, then n (HHH)H =(HH)HHH =HHH , and HHH is Hermitian [27]. We can simply compute the elements above diagonal and those below
diagonal are their complex conjugate. In this way we can save some multiplication and addition complexities.
Suppose the thansmitter has N antennas and receiver has t Nr antennas, then H
HH is Nt byN . Normally, the required number of multiplication operation t HHH is (Nt)3 . However, considering the mentioned symmetry one can save
2
N multiplication operations. The
complexity reduction ratio is
t
5 . The simplification skill is used in the simulations of Chapter 4.
Figure 3.5 Hermitian symmetry of matrix HHH
3.4 Complexity Analysis and Comparison
In this section, we will compare the multiplication complexities of the proposed technique with those of V-BLAST detection, ML detection, and the two methods in section 3.2. Table 3.1 shows the approximate multiplication complexities which roughly fit the simulation time complexities as will be shown in Chapter 4. Multiplication complexities of various detection algorithms for V-BLAST’s channel inversion are
r
From Table 3.1 we know that the ML detection is roughly six-times complicated than that of V-BLAST method. The complexity of the proposed method (L=1) is similar to V-BLAST. But its performance is better than V-BLAST method. Chapter 4 will verify the performances. Table 3.2 considers the matrix symmetry.
Table 3.1 Multiplication complexities of various detection algorithms without considering matrix symmetry
No of Multiplications Nt=4,Nr=4
(or 5,6) QPSK(A=4) V-BLAST Nt4 +2Nt3Nr +Nt2Nr +(Nt2 +NtNr)×6 1024
ML ANtNr(Nt +1) 5120
Shen’s method
2
Our Improved Li’s method
+ method (two values at a
Table 3.2 Multiplication complexities of various detection algorithms, considering matrix symmetry
No. of Multiplications Nt=4,Nr=4 (or Li’s method
+ (two values at a time)
Chapter 4
Simulation Results
In this chapter, we conduct computer simulations and test the performances of the discussed algorithms in Chapters 2 and 3 by using Matlab programs. Those simulations are performed according to EWC 802.11n specifications. Table 4.1 lists the parameter settings of EWC used in the simulations including frame structure, multi-antenna preambles format, signal bandwidth, subcarrier number, et cetera. Modulation scheme is fixed to QPSK and channel coding is neglected. It is also assumed that channel state information (CSI) is perfectly known during the periods of preambles.
First of all, based on the previously mentioned complexity analysis, simulation time is examined. Then bit error rates (BER) are simulated.
Table 4.1 Simulated EWC 802.11n system parameters Signal bandwidth 20MHz
Sample duration 50ns
FFT length 64
Used subcarriers 52 Data subcarriers 48
Symbol period 3.2µs (64 samples) Cyclic prefix 0.8µs (16 samples) Subcarrier spacing 312.5 kHz
Modulation QPSK Channel Coding No
Transmit antenna 2, 3, or 4 Receive antenna 4, 5, or 6 Data symbol 6 symbols
Doppler frequency 150 Hz( 9m/s at 5GHz )
4.1 Performance – Execution Time
In the following figures, computation time is measured in seconds using Matlab elapse time functions. Only signal detection is measured and other parts are not, because we are only interested in complexities of detections. 4 transmit and 4, 5, and 6 receive antennas are assumed.
In Figure 4.1, the fractional numbers represent the ratio normalized to the methods of V-BLAST, Li’s method, Shen‘s method, our improved Li’s method, ML1 (the proposed method L=1), ML2 (the proposed method L=2), ML3 (the proposed method L=3), ML4 (the proposed method L=4), ML two values (the new extended method) and ML detection. For simplicity, the proposed methods assuming (L=1~Nt) will be discussed separately. Therefore, from figures we can judge which one has better performance and less cost.
From Figures 4.1 to 4.3, the ratios of simulation time are roughly equal to Table 3.2 and Table 4.2. The proposed method’s (L=1) simulation time is 1.1 times the length of the V-BLAST method. As shown, ML method is very time consuming.
Figure 4.1 Computation time comparison of existing detection methods and the proposed methods (Nt=4 Nr=4)
Figure 4.2 Computation time comparison of the existing detection methods and the proposed methods (Nt=4 Nr=5)
Figure 4.3 Computation time comparison of the existing detection methods and the proposed methods (Nt=4 Nr=6)
Table 4.2 Multiplication complexities of the proposed detection algorithms vs. L value, considering matrix symmetry
L No. of Multiplications Nt=4,Nr=4
4.2 Performance – Bit Error Rate
In our discussion, correlations between transmit antennas and receive antennas are assumed independent, and each transmit and receive antenna pair has the same channel model. In the BER simulations, indoor channel model [28] is adopted, because both EWC 802.11n and 802.11a assume similar indoor wireless applications, and the simulated channel is generated by a hand-written program using Jake’s model. Besides, the correlation between any of the two taps of the models is small. As shown before, a simulated packet consists of the preamble part and 6 data symbols. In our simulation, perfect channel state information (CSI) is assumed.
The first simulated channel, as listed in Table 4.3, is measured in a typical old office environment where partitions are often made of bricks. The longest tap has a delay of 127ns, which is about 2.5 samples for 802.11a system. The delay is so small that a very large coherent bandwidth is expected.
Table 4.3 Indoor channel model [28] with short delays, office environment Tap
No.
Delay (ns)
Power (dB)
Amplitude Distribution
Doppler Spectrum
1 0 0 Rayleigh Classical/Flat
2 36 -5 Rayleigh Classical/Flat
3 84 -13 Rayleigh Classical/Flat
4 127 -19 Rayleigh Classical/Flat
Figure 4.4 shows performances of various techniques, where 2x2 means that there are 2 transmit and 2 receive antennas. ML denotes ML detection, BLAST denotes V-BLAST detection, Shen’s denote Shen’s method, Li’s denotes Li’s method [22] in section 3.2, improved Li’s denotes our improved Li’s method in section 3.2, ML1 denotes L=1 in section 3.1.1, ML2 denotes L=2 in section 3.1.1, ML3 denote L=3 in section 3.1.1, ML4 denote L=4 in section, ML_ext denote the new extended method (detect two values) at a time in section 3.1.2. In Figure 4.5, 2x3 means that there are 2 transmit and 3 receive antennas, similarly for Figure 4.6. ML1 to ML4 are compared separately in Figure 4.13.
It is obvious that the proposed method (L=1) Nt =Nr, has better performance than V-BLAST, with little increase in complexity. And in the figures there is no performance difference between V-BLAST algorithms and comparison algorithms. The condition is also observed in Figure 4.5 and Figure 4.6. Figure 4.7, 4.8, and 4.9 are for the case of 3 transmitter antennas 3, 4, and 5 receiver antennas, respectively.
In each figure the performance of the V-BLAST, Shen’s method, Li’s method, and our improved Li’s method are the same. The reasons are that algorithm of the Li’s method in section 2.3.3.2.1 [21] channel response H are the same in Step 1 and Step 2.
The difference is just the part of data detection is recomputed, but H are the same. And in [21] the approach is fit to use in ideal detection and cancellation. When the error propagation exists the performance of every detected layer are very close. Hence Li’s method has no effect in enhancing performance here. The performances of Shen and Li’s and our improved Li’s method are the same. And its reason and Li’s method are the same.
Figure 4.4 BER performance versus SNR of various detection techniques (2x2), office environment
Figure 4.5 BER performance versus SNR of various detection techniques (2x3), office environment
Figure 4.6 BER performance versus SNR of various detection techniques (2x4), office environment
Figure 4.7 BER performance versus SNR of various detection techniques (3x3), office environment
Figure 4.8 BER performance versus SNR of various detection techniques (3x4), office environment
Figure 4.9 BER performance versus SNR of various detection techniques (3x5), office environment
Figure 4.10 BER performance versus SNR of various detection techniques (4x4), office environment
Figure 4.11 BER performance versus SNR of various detection techniques (4x5), office environment
Figure 4.12 BER performance versus SNR of various detection techniques (4x6), office environment
Figure 4.13 BER performance versus SNR of our various detection techniques and V-BLAST (4x4), office environment
Figure 4.14 BER performance versus SNR of our various detection techniques and V-BLAST (4x5), office environment
Figure 4.15 BER performance versus SNR of the proposed detection techniques and V-BLAST (4x6), office environment
The second simulated channel is measured in an airport representing a typical large hall area. The channel has a few very long delay paths which indicate bad channel conditions and is harmful to communication. After simulation, the results in large hall are similar to results in office environment.
Table 4.4 Indoor channel model [28], large hall environment Tap
No.
Delay (ns)
Power (dB)
Amplitude Distribution
Doppler Spectrum
1 0 0 Rayleigh Classical
2 174 -8 Rayleigh Classical
3 274 -15 Rayleigh Classical
4 560 -18 Rayleigh Classical
Figure 4.16 BER performance versus SNR of various detection techniques (2x2), large hall environment
Figure 4.17 BER performance versus SNR of various detection techniques (2x3), large hall environment
Figure 4.18 BER performance versus SNR of various detection techniques (2x4), large hall environment
Figure 4.19 BER performance versus SNR of various detection techniques (3x3), large hall environment
Figure 4.20 BER performance versus SNR of various detection techniques (3x4), large hall environment
Figure 4.21 BER performance versus SNR of various detection techniques (3x5), large hall environment
Figure 4.22 BER performance versus SNR of various detection techniques (4x4), large hall environment
Figure 4.23 BER performance versus SNR of various detection techniques (4x5), large hall environment
Figure 4.24 BER performance versus SNR of various detection techniques (4x6), large hall environment
Figure 4.25 BER performance versus SNR of the proposed detection techniques and V-BLAST (4x4), large hall environment
Figure 4.26 BER performance versus SNR of the proposed detection techniques and V-BLAST (4x5), large hall environment
Figure 4.27 BER performance versus SNR of the proposed detection techniques and V-BLAST (4x6), large hall environment
Chapter 5 Conclusion
In this thesis, many algorithms based on V-BLAST are introduced and simulated, and new algorithms for MIMO OFDM detection are proposed, followed by their investigations and verifications in terms of complexity and BER performance by testing EWC 802.11n systems. Although ML algorithm results in the best performance, it demands the highest computation cost. Therefore, we combine ML and V-BLAST methods, and reduce the complexity of ML detection by utilizing known detected values.
Since designs of detection methods are trade-off problems between cost and performance, complexity and performance analysis helps a lot to decide a suitable design.
In complexity analysis, the proposed methods (L=1) is roughly equal to V-BLAST method but its performance is better than V-BLAST method. Usually a detected layer will produce error and propagate to the following layers. The proposed methods have the better performance and less error propagation problem than other algorithm compare in the simulation. Testing 802.16e is considered as future work. It is also future work to reduce the complexity of pseudoinverse.
Bibliography
[1] T.Ojanpera and R. Prasad, “An overview of wireless broadband communications,”
IEEE Commun. Mag. Vol.35, No. 1, pp. 28-34, Jan 1997.
[2] C. L.Ng, K. B. Letaief, and R.D. Murch, “Antenna diversity combing and finite-tap decision feedback equalization for high-speed data transmission,” IEEE Journal on Selected Areas in Communication, Vol. 16, No.8, pp. 1367-1375, Qct. 1998.
[3] B. Yang, K .B. Latief, R. S. Cheng, and Z. Cao, “Channel estimation for OFDM transmission in multipath fading channels based on parameter channel modeling,”
IEEE Transactions on Communications, Vol. 49, No. 3, March 2001.
[4] W. K. Wang, R. S. Cheng, K. B. Latief, and R. D. Murch, “Adaptive antennas at the mobile and base station in an OFDM/TDMA systems,” IEEE Transactions on Communications, Vol. 49, No.1, Jan. 2001.
[5] C. Y. Yue, R. S. Cheng, K. B. Letaief, and R. D. Murch, “Multiuser OFDM with subcarrier, bit, and power allocation,” IEEE Journal on Selected Areas in Communications, Vol. 17, No. 10, pp. 1747-1758, October 1999.
[6] G. J. Foschini and M. J. Cans, “On limits of wireless communications in a fading environment when using multiple antennas,” Wireless Personal Communications, Vol.
6, NO. 3, pp. 311-335, 1998.
[7] G. G. Raleigh and J. M. Cioffi, “Spatio-temporal coding for wireless communi-cation,” IEEE Trans. Communications, Vol. 46, No. 3, pp. 357-366, March 1998.
[8] G. J. Foschini, “Layered space-time architecture for wireless communication in a fading environment when using multiple antennas,” Bell laboratories Technical Journul, Vol. 1, No. 2, pp. 41-59, 1996.
[9] P. W. Wolniansky, G. J. Foschini, G. D. Golden, R. A. Valenzuela, “V-BLAST an architecture for realizing very high data rates over the rich-scattering wireless channel,” Invited paper; Proc. ISSSE-98, Pisa, Italy, 1998.
[10] N. Boubaker, K. B. Letaief, and R. D. Murch, “A layered space-time coded wideband OFDM architecture for dispersive wireless links,” Computers and Communications, 2001, Proceedings, Page(s): 518 – 523, July 2001
[11] http://www.enhancedwirelessconsortium.org/home
[12] IEEE Std 802.11a-1999, Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) Specifications, 1999 edition.
[13] N. Boubaker, K. B. Letaief, R. D. Murch, “A low complexity multicarrier BLAST architecture for realizing high data rates over dispersive fading channels,” VTC 2001 Spring, IEEE VTS 53rd Volume 2, Page(s): 800 - 804 vol.2, 6-9 May 2001.
[14] Y. Li, J.C. Chuang and N.R. Sollenberger, “Transmitter diversity for OFDM systems and its impact high rate data wireless networks,” IEEE Journal on Selected Areas in Communications, Vol. 17, NO. 7, pp. 1233-1243, July 1999.
[15] S.B. Bulumulla, S.A. Kassam and S.S. Venkatesh, “An adaptive diversity receiver for OFDM in fading channels,” IEEE Conference on Communications 88, Proc. 1998, Vol. 3, pp. 1325-1329.
[16] G. Yi and K. B. Letaief, “Performance evaluation and analysis of space-time coding in unequalized multipath fading links,” IEEE Transactions on Communications, Vol.
48, pp. 1778-1782, Nov. 2000.
[17] J.J. Wang and Ta-Sung Lee, “Applications of dynamic subcarrier allocation and adaptive modulation in multiuser MIMO-OFDM systems” Master thesis, Institute of Communication Engineering, Hsinchu, Taiwan, National Chiao Tung University, 2004.
[18] G.Y. Lin and S.G. Chen, “On signal Detection of MIMO OFDM Systems” Master thesis, Institute of Electronics College of Electrical Engineering, Hsinchu, Taiwan, National Chiao Tung University, 2004.
[19] C. Shen, H. Zhuang, L. Dai, S. Zhou, and Y. Yao, “Performance Improvement of V-BLAST through an Iterative Approach,” Personal, Indoor and Mobile Radio Communications, 2003. PIMRC 2003. 14th IEEE Proceedings , Vol. 3, pp. 2553 - 2557,Sept. 2003.
[20] Q. Liu, and L. Yang, “A simplified method for V-BLAST detection in MIMO OFDM communication,” Communications, 2004 and the 5th International Symposium on Multi-Dimensional Mobile Communications Proceedings. The 2004 Joint Conference of the 10th Asia-Pacific Conference on Volume 1, 29 Aug.-1 Sept.
2004 Page(s): 30 - 33 vol.1.
[21]D. Li, L. Cai, and H. Yang, “New iterative detection algorithm for V-BLAST,”IEEE Conference on Vehicular Technology Conference, Vol. 4, pp. 2444 - 2448,Sept. 2004.
[22] J. Akhtar “Enhanced detection for zero-forced V-BLAST,” IEEE Conference on Vehicular Technology Conference, Vol. 2, pp. 848 - 852,May 2004.
[23] S. Baro, G. Bauch, A Pavlic, and A. Semmler, “Improving BLAST performance using space-time block codes and turbo decoding,” IEEE Conference on Global Telecommunications,Vol. 2, pp. 1067 - 1071, Nov. 2000.
[24] G.D. Golden, C.J Foschini, R.A. Valenzuela, and P.W. Wolniansky, “Detection algorithm and inital laboratory results using V-BLAST space-time communication architecture,” Electronics Letters, Vol. 35, pp. 14-16, Jan. 1999
[25] T.Q. Duong, E.K. Hong, and S.Y. Lee, “Effect of the Modified Channel Matrix on the MMSE V-BLAST System Performance” IEEE Conference on Wireless And Mobile Computing, Networking And Communications, Vol. 1, pp. 133-136, Jan.
2005
[26] T. Xiaofeng, C.Elena, Y. Zhuizhuan, Q. Haiyan and Z. Ping “New detection algorithm of V-BLAST space-time code,” IEEE Conference on Vehicular Technology Conference, Vol. 4, pp. 2421 - 2423, Oct. 2001.
[26] T. Xiaofeng, C.Elena, Y. Zhuizhuan, Q. Haiyan and Z. Ping “New detection algorithm of V-BLAST space-time code,” IEEE Conference on Vehicular Technology Conference, Vol. 4, pp. 2421 - 2423, Oct. 2001.