To demonstrate the effectiveness of the MLSE equalizer approach for cooperative communication system with 105 Monte Carlo simulations, we compare the Bit Error Rate (BER) performance between the MLSE equalizer and MMSE equalizer.
We consider a BICM-OFDM system with N = 64, CP length = 8, and 4-QAM modulation. A two-path wide-sense stationary uncorrelated scattering (WSSUS) Rayleigh fading channel (generated using Jakes Model) between any relay nodes and each relay are equal power, the convotional code uses G(D)=(1+D2,1+D+D2) as the generator polynomial, and G(D)=1/(1+D2) is the generator polynomial for the precoder.
One frame consists of 10 OFDM symbols. Furthermore, perfect estimations of MCFOs and channel matrices are assumed. The diversity order of BICM-OFDM for cooperative communication is addressed in [17].
Fig. 5 shows the BER performance versus SNR for the comparison between conventional MMSE equalizer, traditional 1-tap equalizer and the MLSE equalizer in synchronous impairments.
For the simulation, normalized Doppler frequency fd=0.001 is employed at both relays, the normalized MCFOs are 0.2 and -0.2. With the large MCFOs, the 1-tap equalizer suffers an obvious error floor. In [17], the author use an MMSE equalizer to combat ICI, but an SNR loss occurred. On contrast, the MLSE equalizer not only successfully compensates for the ICI but also obtain an SNR gain about 3dB. The benefits of SNR gain, we can via SINR to explicit explanation and the derivation in appendix. The optimal solution is joint processing of demodulation and decoding is considered, which lead to approach low bound. The low bound is ideal cancel intercarrier-interference is obtained. Notice that with both equalizers the system achieves full diversity.
Fig 6 shows the results for the two relay nodes and three relay nodes. It can be seen from the figure that as the number of relay increases in the systems, the diversity order of distributed BICM-OFDM increases up to the maximum diversity of min{M rT L,dfree}, where r
T is rank of E[HHH]. is addressed in [17]. It can be observed that the tree relays case has a diversity order of 5 and the BER curve is steep.
In Fig. 7, all the realistic synchronous impairments are considered. The timing errors is [0 3], normalized Doppler frequency is 0.1 for both relays and MCFOs is [0.2 -0.2]. In our proposed the performance show efficiently collects the diversity form time diversity due to the Doppler effect, frequency diversity due to timing error and special
diversity converted to time diversity due to MCFOs. It observed that the diversity is more than four.
Fig. 5. BER comparison between MMSE equalizer, 1-tap equalizer and MLSE equalizer in the cooperative communication.
0 2 4 6 8 10 12 14 16 18
10-6 10-5 10-4 10-3 10-2 10-1 100
SNR
BER
Tradtional 1-tap equalizer Iteration=5 MMSE equalizer Iteration=5 MLSE equalizer D=1 Iteration=5 MLSE equalizer D=2 Iteration=5 Lower bound
Fig. 6. The BER curves compared with difference number of relay nodes
Fig. 7. The BER for cooperative communication under time error = [0 3], normalize Doppler frequency = 0.1, MCFOs = [0.2 -0.2].
0 5 10 15
CFOs=[0.2 -0.2] Fd=0.001 Timing error=[0 0]
CFOs=[0.2 -0.2] Fd=0.1, Timing error=[0 3]
Chapter 6 Conclusions
BICM has the potential to improve performance with relatively ease in many OFDM wireless communication systems. In this Thesis, it is shown that, with proper receiver design, the BICM-OFDM can be effective to combat synchronous errors as well as harvest potential diversity gain in cooperative communications. Typical BICM-OFDM systems suffer error floors due to ICI caused by MCFOs and Doppler effects. To deal with such a problem, we propose an MLSE-based frequency domain equalizer combined with a turbo decoder to break the error floor. The proposed
approach has BER approaching the performance bound, and it is flexible in a way that extension to more relays for improvement in diversity gain is straightforward. The complexity is a big problem in the receiver if D is greater than three, and future research in the complexity reduction will be considered.
Appendix
The received signal in frequency domain can be written
R GX Z (16) As the derivation in [22], it is derive the MMSE equalizer as
( 1/ ) 1
H H
wG GG SNR
(17) After the MMSE equalizer we can rewritten as
signal power noise power
' w w
R R X Z (18) The SNR of MMSE equalizer is obtained form (18) in high SNR
SNRMMSE ≈ The received signal can be decomposed signal part and interference & noise part for MLSE case
signal power interference and noise power
( )
R GX G - G X Z
(20) The SNR of MLSE equalizer is obtained form (20)
SINRMLSE≈
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