Chapter 6 Computer Simulation
6.2 Simulation Results
The following three cases are used in the simulation for comparison.
(A) CSI and data known: The curves with ideal CSI initialization and perfect initial data can be regarded as a performance lower bound.
(B) CSI known: This kind of curves is generated by using ideal CSI initialization and initial data given from the one tap equalizer.
(C) CSI est: The curves labeled as “CSI est” are made by setting initial CSI estimated and initial data given from the one tap equalizer.
The ways to produce initial data make difference between (A) and (B), and the modes of CSI initialization make (B) perform better than (C) if other conditions remain the same.
Most of the figures come from the simulation in the two-path channel, while Fig.6.9 and Fig.6.10 are given by the simulation in both the two-path channel and the ITU Veh-A channels.
The group size of the ML-EM receiver must be decided first of all, and the BER
performance curves are compared with each other in the case of “CSI and data known”. As depicted in Fig.6.1 and Fig.6.2 for the normalized MDF=0.05 and 0.1 respectively, joint detection of more subcarriers improves the performance, so the receiver with group sizes of 1 and 2 are worse than with group sizes of 4 and 8 which have nearly identical performance, and we choose the group size of 4 for the reason that a smaller group size takes less
computational time. Next, the BER performance makes progress by applying the residual ICI power described in chapter 5 to the Gibbs sampling. Based on the case of “CSI known”, it can be shown in both Fig.6.3 and Fig.6.4 for comparison between the performance of the ML-EM receiver with ICI power update and without ICI power update, and then the former is proved to be better. We subsequently develop the receiver combined with ICI power update.
Fig.6.5 and Fig.6.6 demonstrate the BER performance of the ML-EM receiver with ICI power update in the cases of “CSI known” and “CSI est”. It is observed that the curves with perfect CSI initialization perform better than the curves with CSI initialization estimated by zero forcing criteria and the performance improves as the outer loop iterates more times.
Moreover, Fig.6.7 and Fig.6.8 show that the ML-EM receiver with CE refinement has better performance than without CE refinement in the case of “CSI est”. And the “CSI est” curve with CE refinement is quite close to the “CSI known” curve, which means the receiver with CE refinement decrease the gap between the two modes of CSI initialization. CE refinement can obviously make the performance better for a channel with more paths, i.e. the ITU Veh-A
channel, and the BER performance is illustrated in Fig.6.9 and Fig.6.10.
Fig.6.11 and Fig.6.12 demonstrate the BER performance of the ML-EM receiver with the group size of 4 and CE refinement. Compared with the “CSI and data known” curve for the normalized MDF=0.05, the “CSI and data known” curve for the normalized MDF=0.1 has lower BER at the same Eb N , because time-variant channels introduce more diversity gains 0 for higher speed when the initial CSI and data are both perfect. And it is seen from Fig.6.11 that the three curves in different cases are rather close; however, there is a gap between the performance lower bound and the two curves else due to the error propagation effect observed from Fig.6.12. Finally, the number of samples required for Gibbs sampling affects the BER performance shown in Fig.6.13 and Fig.6.14, and thus we find that the receiver with more samples attain better performance, and the improvement is gradually saturated as the number of samples increases.
12 14 16 18 20 22 24 26 28 30 10-6
10-5 10-4 10-3 10-2 10-1
Eb/No(dB)
BER
FdT=0.05
One Tap EQ (CSI known) EM (G=1)
EM (G=2) EM (G=4) EM (G=8)
Fig. 6.1 BER performance of the ML-EM receiver with different group sizes for the normalized MDF=0.05.
12 14 16 18 20 22 24 26 28 30 10-6
10-5 10-4 10-3 10-2 10-1
Eb/No(dB)
BER
FdT=0.1
One Tap EQ (CSI known) EM (G=1)
EM (G=2) EM (G=4) EM (G=8)
Fig. 6.2 BER performance of the ML-EM receiver with different group sizes for the normalized MDF=0.1.
12 14 16 18 20 22 24 26 28 30 10-5
10-4 10-3 10-2 10-1
Eb/No(dB)
BER
FdT=0.05
One Tap EQ (CSI known) EM (w.o. ICI Power updated) EM (with ICI Power updated)
Fig.6.3 BER performance of the ML-EM receiver with/w.o. ICI power update for the normalized MDF=0.05.
12 14 16 18 20 22 24 26 28 30 10-5
10-4 10-3 10-2 10-1
Eb/No(dB)
BER
FdT=0.1
One Tap EQ (CSI known) EM (w.o. ICI Power updated) EM (with ICI Power updated)
Fig.6.4 BER performance of the ML-EM receiver with/w.o. ICI power update for the normalized MDF=0.1.
12 14 16 18 20 22 24 26 28 30 10-6
10-5 10-4 10-3 10-2 10-1
Eb/No(dB)
BER
FdT=0.05
One Tap EQ (CSI known) One Tap EQ (CSI est)
ICI cancel (iter.=1) (CSI known) ICI cancel (iter.=1) (CSI est) ICI cancel (iter.=2) (CSI known) ICI cancel (iter.=2) (CSI est) ICI cancel (iter.=3) (CSI known) ICI cancel (iter.=3) (CSI est) ICI cancel (iter.=4) (CSI known) ICI cancel (iter.=4) (CSI est)
Fig.6.5 BER performance of the ML-EM receiver for the normalized MDF=0.05.
12 14 16 18 20 22 24 26 28 30 10-6
10-5 10-4 10-3 10-2 10-1
Eb/No(dB)
BER
FdT=0.1
One Tap EQ (CSI known) One Tap EQ (CSI est)
ICI cancel (iter.=1) (CSI known) ICI cancel (iter.=1) (CSI est) ICI cancel (iter.=2) (CSI known) ICI cancel (iter.=2) (CSI est) ICI cancel (iter.=3) (CSI known) ICI cancel (iter.=3) (CSI est) ICI cancel (iter.=4) (CSI known) ICI cancel (iter.=4) (CSI est)
Fig.6.6 BER performance of the ML-EM receiver for the normalized MDF=0.1.
12 14 16 18 20 22 24 26 28 30 10-5
10-4 10-3 10-2 10-1
Eb/No(dB)
BER
FdT=0.05
CSI known (iter.=4)
CSI est (iter.=4) (w.o CE refined) CSI est (iter.=4) (with CE refined)
Fig.6.7 BER performance of the ML-EM receiver with/w.o. CE refinement for the normalized MDF=0.05.
12 14 16 18 20 22 24 26 28 30 10-4
10-3 10-2 10-1
Eb/No(dB)
BER
FdT=0.1
CSI known (iter.=4)
CSI est (iter.=4) (w.o CE refined) CSI est (iter.=4) (with CE refined)
Fig.6.8 BER performance of the ML-EM receiver with/w.o. CE refinement for the normalized MDF=0.1.
12 14 16 18 20 22 24 26 28 30 10-5
10-4 10-3 10-2 10-1
Eb/No(dB)
BER
FdT=0.05
CSI known (iter.=4)
CSI est (iter.=4) (w.o CE refined) CSI est (iter.=4) (with CE refined)
Fig.6.9 BER performance of the ML-EM receiver with different cases in the ITU Veh-A channel for the normalized MDF=0.05.
12 14 16 18 20 22 24 26 28 30 10-4
10-3 10-2 10-1
Eb/No(dB)
BER
FdT=0.1
CSI known (iter.=4)
CSI est (iter.=4) (w.o CE refined) CSI est (iter.=4) (with CE refined)
Fig.6.10 BER performance of the ML-EM receiver with different cases in the ITU Veh-A channel for the normalized MDF=0.1.
12 14 16 18 20 22 24 26 28 30 10-6
10-5 10-4 10-3 10-2 10-1
Eb/No(dB)
BER
FdT=0.05
EM(CSI and data known) EM (CSI known)
EM (CSI est with CE refined)
Fig.6.11 BER performance of the ML-EM receiver in different cases for the normalized MDF=0.05.
12 14 16 18 20 22 24 26 28 30 10-6
10-5 10-4 10-3 10-2 10-1
Eb/No(dB)
BER
FdT=0.1
EM(CSI and data known) EM (CSI known)
EM (CSI est with CE refined)
Fig.6.12 BER performance of the ML-EM receiver in different cases for the normalized MDF=0.1.
12 14 16 18 20 22 24 26 28 30 10-5
10-4 10-3 10-2 10-1
Eb/No(dB)
BER
FdT=0.05
sample no.=10 sample no.=20 sample no.=30 sample no.=40 sample no.=50
Fig.6.13 BER performance of the ML-EM receiver with various numbers of samples for the normalized MDF=0.05.
12 14 16 18 20 22 24 26 28 30 10-4
10-3 10-2 10-1
Eb/No(dB)
BER
FdT=0.1
sample no.=10 sample no.=20 sample no.=30 sample no.=40 sample no.=50
Fig.6.14 BER performance of the ML-EM receiver with various numbers of samples for the normalized MDF=0.1.