Chapter 4 Maximum Likelihood Sequence Estimation for Alamouti Decoding
4.2 MLSE Equalizer based on Viterbi Algorithm
MLSE is one of the most effective techniques for equalization [18]. A MLSE equalizer determines a sequence s as the most likely transmitted sequence when the condition probabilityP
( )
y s is maximized. Therefore, the maximization of the conditional probability | is equivalent to minimization operation of the Euclidean distance [19] and here it can be written as follows=arg min || − ||2
X＾ X r HX (4.3), MLSE can be implemented effectively by utilizing the Viterbi algorithm which is based on a state trellis structure is shown in Fig. 4.1, and the constellation point is given by the mapping
⎯⎯→
⎯⎯→
⎯⎯→
⎯⎯→
M M M
M M M M M M M M
M M M M M M M M
M M M M
Fig. 4.1 MLSE based detection utilizing Viterbi algorithm with QPSK
4.3 Simulation Results
As in literature [20]. We choose K= 0, 1. The signal to interference plus noise ratio (SINR) gain within different K is showed in TABLE 4.1.
of pre-whitenig gain
of post-whitenig SINR SINR
= SINR
TABLE 4.1 SINR gain in different K value in SD case
K SINR gain
0 11 1 12
Fig. 4.2 to Fig. 4.9 show that the channel magnitude of pre-whitening and post-whitening in different K condition. In order to easily explain the channel, we choose the cross section of the 50th row of both channel matrices. Through analysis and simulation, we can say that the SINR gain increase after whitening, but we need to increase the range to do MLSE in our case.
It would cause the complexity to high so that the implementation is a question.
0 20 40 60 80 100 120 140 0
0.2 0.4 0.6 0.8 1 1.2 1.4
Fig. 4.2 The magnitude of 50th row of H1 when K = 0
0 20 40 60 80 100 120 140
0 0.5 1 1.5 2 2.5 3
Fig. 4.3 The magnitude of 50th row of H1,w when K = 0
0 20 40 60 80 100 120 140
0 20 40 60 80 100 120 140 0
0.1 0.2 0.3 0.4 0.5 0.6 0.7
Fig. 4.6 The magnitude of 50th row of H1 when K =1
0 20 40 60 80 100 120 140
0 0.2 0.4 0.6 0.8 1 1.2 1.4
Fig. 4.7 The magnitude of 50th row of H1,w when K = 1
0 20 40 60 80 100 120 140 0
0.05 0.1 0.15 0.2 0.25
Fig. 4.8 The magnitude of 50th row of H2 when K = 1
0 20 40 60 80 100 120 140
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
Fig. 4.9 The magnitude of 50th row of H2,w when K = 1
Chapter 5
MLSE for Spatial Multiplexing
5.1 Spatial Multiplexing in Cooperative Communication
In this chapter, we try to apply the approach in [20] to the case of spatial multiplexing (SM). The cooperative communication system model with one source node, two relay nodes, and one destination node with two antennas is shown in Fig.5.1.
Y1
Y2
Fig.5.1 A cooperative communication system model in SM case.
The mathematical derivation is
5.2 Simulation Results
First of all, Fig. 5.2 to Fig. 5.4 shows that the channel matrix of SM in different MCFOs condition. When the MCFOs become large, the channel magnitude would not concentrate around the diagonal anymore. Unfortunately, this phenomenon caused by MCFOs is quite different from what have been observed in the case of Doppler affect.
If we still want to use this method of [20], we have to choose the MCFOs value which is not too large. Because the MCFOs value is not too large, the channel magnitude will concentrate around the diagonal. We choose MCFOs value that are within 0.4 and K= 0, 1.
Finally, we calculate the signal to interference plus noise ratio (SINR) gain with different K is showed in TABLE 5.1. When K = 0, the SINR gain is only 1.04. This means that whitening or
not will not greatly affect the performance. Therefore, we choose the condition of K = 1 to further the investigation. Moreover, the normalized correlation at K = 1 shows in Fig. 5.5. The figure shows that the covariance matrix will not remain approximately constant as it does in the case studied in [20].
Fig. 5.6 and Fig. 5.7 show that the channel magnitude of pre-whitening and post-whitening. In order to easily explain the channel, we choose the cross section of the 50th row of both channel matrices. Fig. 5.7 shows that we have to include at least four off diagonal terms to get the performance improvement. Therefore, the calculative complexity is a problem.
of pre-whitenig gain
of post-whitenig SINR SINR
= SINR
TABLE 5.1 SINR gain in different K value in SM case
K SINR gain
0 1.04 1 1.5
20 40 60 80 100 120 20
40
60
80
100
120
Fig.5.2 The channel matrix of SM when |εR1−εR2 | 0= .
20 40 60 80 100 120
20
40
60
80
100
120
Fig.5.3 The channel matrix of SM when |εR1−εR2 | 0.8= .
20 40 60 80 100 120
Fig.5.5 Normalized correlation at K =1, FFT size =128.
0 20 40 60 80 100 120 140
Chapter 6 Summary
6.1 Conclusions
Various compensation schemes of synchronization errors in the cooperative MIMO system are investigated in this thesis. We used a modified SFBC decoding and detection rule to improve the performance. Iterative interference cancellation is used to further mitigate the ICI and reduce the error floor. Through simulation results it has been show that the BER performance and tolerance range of MCFOs is superior. The Alamouti diversity can be maintained up to when relative CFO is 0.8.
We also investigate other ways to improve the performance, especially the approach of using MLSE with whitening proposed in [20]. We apply this method to both the cases of spatial diversity and spatial multiplexing. However, simulation and analysis show that this approach may not be suitable for combating MCFOs.
6.2 Future Work
Channel estimation should be taken account instead of perfect CSI known in practical system.
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About the Author
姓 名：李俊育 Jyun-Yu Lee 出 生 地：台灣省彰化縣
出生日期：1984. 09. 13
學 歷：1991. 09 ~ 1997. 06 彰化縣溪湖國民小學 學 歷：1997. 09 ~ 2000. 06 彰化縣溪湖國民中學 學 歷：2000. 09 ~ 2003. 06 彰化縣彰化高級中學
學 歷：2003. 09 ~ 2008. 06 中原大學 電機工程學系 學士 學 歷：2008. 09 ~ 2011. 02 國立交通大學 電子研究所系統組
碩士