Chapter 3 Data detection in MIMO-OFDM with space frequency block code using
3.3 Error propagation mitigation method
In the previous section, we use Gram Schmidt decomposition to obtain two upper triangular matrixes. BER performance will be improved using particle filtering using such method in spatial multiplexing system. On the other hand, in MIMO-OFDM with space frequency block code system, this method can be implemented similar to spatial multiplexing system. In the previous section, we decompose channel matrix H into Q R and 1 1 Q R . 2 2 Now, after Cholesky decomposition, we obtain an upper triangular matrix U and the received vector is
H -1 H
Y = US + (U ) H Neq (3.30) The upper triangular matrix can be written as U=[U1 U2 .... .... UM],where U is K the kthcolumn vector in U. The upper triangular matrix U can be decomposed by
Gram-Schmidt QR decomposition and written as
Where the form of R is another form of upper triangular matrix as same as in the previous 2 section. Multiplying QH to R and obtain
=
H
Y = Q Y R S + n (3.32) 2
Since Q is an orthogonal matrix, the noise vector is still a white noise.
From the discussion above, we get two matrix forms
1 1
Now we define the upper triangular matrix
$ $ $
We observe from two equations shown above. In (3.33), we can use particle filtering, drawing particles from the bottom signal to the top one and using approach III to obtain the expectation value for each entry in signal vector. Interference will be severe inS . 1
On the other hand, in equation (3.34), draw particles from the top signal to the bottom
one and use approach III to obtain the expectation value, interference will be severe inS . M Finally, we average these two sets of soft information and make the decision of each symbol by searching the shortest distance for each entry in signal vector.
Block diagram for error mitigation method in
MIMO-OFDM with space frequency block code system
MIMO-Decoder
Whitening
Filter QR decomposition
Particle filtering using approach III
Particle filtering using approach III
Adder
Divided by 2
FFT FFT FFT
Remove CP Remove CP Remove CP
Figure 3.3 Block diagram for error propagation mitigation method in MIMO-OFDM with space frequency block code system
Chapter 4
Simulation results
4.1 Parameters for MIMO-OFDM spatial multiplexing system
Perfect channel information
Number of subcarriers 256 Length of CP 64
Channel Two paths model with (0,0)dB Particles 100 (if not mentioned in the figure) Approach I (if not mentioned in the figure)
Table 4.1 Parameters for MIMO-OFDM system
Figure 4.1 shows the BER performance for different approach for perfect CSI in 4X4 spatial multiplexing system for QPSK modulation. As can be observed from figure 4.1, Approach II and III have almost the same performance. For sorted QR decomposition using approach II, performance has 2 dB improvements as compared with unsorted QR using approach II. Approach I has the best performance as compared with approach II and approach III. However, the complexity for approach I is higher than the complexity for approach II and III.
Figure 4.2 shows the BER performance for QPSK modulation in 6X6 spatial
multiplexing system for sorted QR decomposition for approach I, QR decomposition with approach II and III with and without sorting. The result shows that the performance for sorted QR decomposition with approach I also has the best BER performance as compared with
approach II and III. Moreover, sorted QR decomposition using approach II has 2dB improvement better than without sorting QR decomposition in BER equal to 10^-2.
Figure 4.3 shows the performance of different detection scheme. Approach II is nearly to VBLAST ZF OSIC performance. Performance using sorted QR decomposition and approach II is nearly to the performance for VBLAST MMSE OSIC detection scheme. Moreover, the BER performance of iterative QR decomposition method has 3-4 dB improvement compare with VBLAST MMSE OSIC system and 1dB better than the BER performance of particle filtering using approach I.
Figure 4.4 shows the BER performance for 16QAM modulation with perfect CSI under MIMO-OFDM 4X4 system. As we can see from the figure shown, the performance for the iterative QR decomposition using approach II has 4dB improvement as compared with VBLAST MMSE OSIC. Sorted QR decomposition using approach I has better performance in this system than error propagation mitigation method using approach III.
Figure 4.5 shows the comparison between QR decomposition with and without sorting using approach I in 6X6 system, as shown in figure, the performance has 1 dB improvement under 50 particles as compared with unsorted QR decomposition method using approach I under 50 particles.
Figure 4.6 shows the performance for sorted QR decomposition using approach I in 6X6 system using 50 and 75 particles. There is a little improvement for 75 particles.
Figure 4.7 shows the comparison between the sorted QR decomposition method using approach I in 6X6 spatial multiplexing system with 16 QAM modulation, unsorted QR decomposition method using approach I in 6X6 MIMO-OFDM system and VBLAST MMSE OSIC. Sorted QR decomposition has 3-4 improvement compare with VBLAST MMSE OSIC and 1-2 dB improvement better than unsorted QR decomposition.
Figure 4.8 shows the performance for sorted QR decomposition using approach I in 6X6 system using 50 ,75 and 150 particles for 16 QAM modulation. There is a little
improvement for 150 particles and no different between 50 and 75 particles.
4.2 Parameters for MIMO-OFDM with Space frequency block code system
Perfect channel information Number of subcarriers 256 Length of CP 64
Channel Two paths model with (0,0)dB Particles 100 (if not mentioned in the figure) Approach I (if not mentioned in the figure) MIMO encoder 2 pairs of Alamouti code(DSTTD)
Table 4.2 Parameters for MIMO-OFDM with space frequency block code system
Figure 4.9 and figure 4.10 show the BER performance of 4X2 MIMO-OFDM for QPSK and 16 QAM modulation with space frequency block(2 pairs of Alamouti code) code system for five different detection schemes which are VBLAST MMSE OSIC, Cholesky
decomposition with decision feedback, particle filtering using approach I and error
propagation mitigation using approach III and ML. First of all, BER performance of particle filtering and error propagation mitigation method have 4dB better than the performance of VBLAST MMSE OSIC and 5dB better than performance of Cholesky decomposition with decision feedback. There are only 2dB worse than the performance of ML decision. For the same system using 16QAM modulation, as shown in figure 4.10, particle filtering has almost the same performance as error propagation mitigation method. Both of them have a 2dB improvement better than VBLAST performance.
In figure 4.11, for 4X4 MIMO-OFDM system with space frequency block code with QPSK modulation, the performance of particle filtering is better than the performance of VBLAST MMSE OSIC and almost the same as ML decision.
In figure 4.12, for 4X4 16QAM modulation system with space frequency block code, the performance of particle filtering is better than the performance of VBLAST MMSE OSIC and Cholesky decomposition with decision feedback.
Figure 4.1 Figure 4.1 MIMO-OFDM 4X4 QPSK modulation for different approaches
0 2 4 6 8 10 12 14 16 18
10-4 10-3 10-2 10-1 100
Es / No
BER
Sorted QR with Approach I joint probability particle =100 Approach I joint probability particle =100
Approach II marginal distribution Approach III expectation value sorted QR with Approach II
Figure 4.2 MIMO-OFDM 6X6 QPSK modulation for different approaches
0 2 4 6 8 10 12 14 16 18
10-4 10-3 10-2 10-1 100
Es / No
BER
Sorted QR decomposition with Approach II QR decomposition with Approach II Sorted QR decomposition with approach I
Figure 4.3 MIMO-OFDM 4X4 QPSK for different detection schemes
0 2 4 6 8 10 12 14 16 18
10-5 10-4 10-3 10-2 10-1 100
Es / No
BER
QR decision feedback VBLAST ZF-OSIC VBLAST MMSE-OSIC Sorted QR with particle filtering Error propagation mitigation method Sphere decoding with fixed radius ML
Figure 4.4 MIMO-OFDM 4X4 16 QAM for different detection schemes
0 5 10 15 20 25
10-4 10-3 10-2 10-1 100
Es / No
BER
QR decision feedback VBLAST MMSE-IC
Sorted QR with particle filtering Error propagation mitigation method
Figure 4.5 MIMO-OFDM 6X6 QPSK modulation with and without sorted QR decomposition
0 2 4 6 8 10 12 14 16 18
10-4 10-3 10-2 10-1 100
Es / No
BER
unsorted QR with particle filtering (particle = 50) sorted QR with particle filtering (particle = 50)
Figure 4.6 MIMO-OFDM 6X6 QPSK with particles equal to 50 and 75
0 2 4 6 8 10 12 14 16 18
10-4 10-3 10-2 10-1 100
Es / No
BER
sorted QR with particle filtering with particle = 50 sorted QR with particle filtering particle = 75
Figure 4.7 MIMO OFDM 6X6 16QAM modulation with and without sorted QR decomposition
0 5 10 15 20 25 30
10-3 10-2 10-1 100
Es / No
BER
VBLAST MMSE OSIC
sorted QR with particle filtering(particle = 50) using approach I QR with particle filtering(particle = 50) using approach I
Figure 4.8 MIMO-OFDM 6X6 16QAM modulation particles equal to 50,75 and 200
0 5 10 15 20 25 30
10-3 10-2 10-1 100
Es / No
BER
sorted QR with particle filtering( particle = 50) sorted QR with particle filtering( particle = 75) sorted QR with particle filtering( particle = 150)
Figure 4.9 MIMO-OFDM 4X2 QPSK with space frequency block code for different detection scheme
0 2 4 6 8 10 12 14 16 18 20
10-6 10-5 10-4 10-3 10-2 10-1 100
Es / No
BER
Cholesky decomposition with decision feedback VBLAST MMSE-OSIC
Particle filtering using approach I Error propagation mitigation method ML
Figure 4.10 MIMO-OFDM 4X2 16QAM with space frequency block code
0 5 10 15 20 25
10-3 10-2 10-1 100
Es / No
BER
Cholesky decomposition with decision feedback VBLAST MMSE-IC
Particle filtering using approach I Error propagation mitigation method
Figure 4.11 MIMO-OFDM 4X4 QPSK with space frequency block code
0 1 2 3 4 5 6 7 8 9 10
10-4 10-3 10-2 10-1 100
Es / No
BER
VBLAST MMSE-OSIC Particle filtering with approach I ML
Figure 4.12 MIMO-OFDM 4X4 16QAM with space frequency block code
0 2 4 6 8 10 12 14 16 18 20
10-6 10-5 10-4 10-3 10-2 10-1 100
Es / No
BER
Cholesky decomposition with decision feedback VBLAST MMSE-IC
Particle filtering using approach I
Chapter 5 Conclusion
Merits and drawbacks of particle filtering algorithm
Except for the complexity of QR decomposition and searching process mentioned in section 2.8, the complexity of particle filtering is directly proportional to three components, the scheme of modulation, the number of transmitting antennas and the number of particles.
The complexity for particle filtering is O(A*M*Np), where A is the modulation scheme, eg QPSK, 16QAM. M is number of transmitting antennas and Np is number of particles. The complexity of ML scheme exponentially increases either the number of transmitting antenna or the number of order of modulation increases. The complexity for ML decision is O(A ). M Particle filtering is a practical approach for data detection. As the simulation shown before, the performance of our proposed methods using particle filtering are close to ML decision either in spatial multiplexing system or with space frequency block code system. The complexity for QPSK modulation for 6X6 MIMO-OFDM BLAST system is only 4*4*50 = 800 trials, however, for ML decision method, number of trial is 46 =4096trials. The
complexity with particle filtering is 5 times lower than the complexity with ML decision, the BER performance of sorted QR decomposition with particle filtering using approach I is only 2 dB worse than ML decision. Moreover, for high order modulation, for example, 16 QAM for 4X4 MIMO-OFDM BLAST system, the complexity for ML will be 164 =65536 trials, however, particle filtering method only deal with 4*4*100 = 1600 trials. In conclusion, Particle filtering is a suitable approach for high modulation order and large amount of transmitting antenna system in MIMO-OFDM BLAST system.
One of the drawbacks of particle filtering is that the noise distribution is known at the receiver side. For example, if the noise distribution is white Gaussian noise, receiver need to
be estimate the variance of noise first, after that pass this variance information to particle filtering.
The second drawback is that particle filtering need the process of QR decomposition or Cholesky decomposition, the complexity will increase for when the number of transmitting antenna increases.
The third drawback is that the searching process mentioned in section 2.8 for approach I and approach II. Especially for approach I, the complexity will increase either the number of transmitting antennas or number of particles increase.
Bibliography
[1] G. L. Stuber, J. R. Barry, S. W. Mclaughlin, Y. Li, M. A. Ingram, and T. G. Pratt,
“Broadband MIMO-OFDM Wireless Communications,” in Proceedings of IEEE, vol. 92, no.2, pp. 271-294, Febuary 2004.
[2] G. J. Foschini, “Layered Space-Time Architecture for Wireless Communication in A Fading Environment When using Multiple Antennas,” Bell Labs Technical Journal, 1(2), pp41-59, Autumn 1996.
[3] P. W. Wolniansky, G. J. Foschini, G.D. Golden and R. A. Valenzuela, “V-BLAST : An Architecture for Realizing Very High Data Rates over Rich-scattering Wireless Channel,” in Proceedings of IEEE ISSSE-98, Pisa, Italy,29, September 1998.
[4] M. S. Arulampalam, S. Maskell, N. Gordon and T. Clapp, “A Tutorial on Particle Filters for Online Nonlinear/Non Gaussian Bayesian Tracking,” in Proceedings of IEEE Transactions on Signal Processing, vol.50, no.2, Febuary 2002.
[5] A. Doucet, J. F. G de Freitas, and N. J. Gordon, “An Introduction to Sequential Monte Carlo Methods,” in Proceedings of Sequential Monte Carlo Methods in Practice, Eds. New York; Springer-Verlag, 2001.
[6] A. Doucet, S. Gordon, and C. Andrieu, ”On Sequential Monte Carlo Sampling Methods for Bayesian Filtering,” Statist. Comput.vol.10, no.3, pp197-208.
[7] A. Doucet, “On Sequential Monte Carlo Methods for Bayesian Filtering,” Dept. Eng., Univ. Cambridge, UK, Tech. Rep., 1998.
[8] N. Bergman, ”Recursive Bayesian Estimation: Navigation and Tracking Applications,”
ph.D dissertation, LinkopingUniv., Linkoping, Sweden, 1999.
[9] J. S. Liu and R. Chen, “Sequential Monte Carlo Methods for Dynamical Systems,” J.
Amer, Statist. Assoc., vol.93, pp1032-1044, 1998.
[10] G. Kitagawa, “Monte Carlo Filter and Smoother for Non-gaussian Non-Linear State
Space Models,” J. Comput, Graph. Statist., vol.5, no.1, pp1-25, 1996.
[11] D. Wubber, R. Bohnke, J. Rinas, V. kuhn and K. D. Kammeyer, “Efficient Algorithm for Decoding Layered Space-time Codes,” In Proceedings of IEEE ISSSE-98, Pisa, Italy, 29, September 1998.
[12] K. Kwak, J. Kim, B. Park, and D. Hong, “Performance Analysis of DSTTD based on Diversity-multilexing Trade Off,” In Proceedings of VTC-2005, Spring, vol.2, pp1106-1109, 2005.