Chapter 3 The Proposed Data Detection Algorithms 35
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.
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