The performance of the MIMO generalized MLP/BP-based DFE is evaluated through the simulations for the distorted NRZ signal recovery in the band-limited channels with co-channel interference. The data rate is ten times of the channel bandwidth.
It is a wireline application so we can select a longer training set to achieve better performance.
In the training procedure, the length of the training set is equal to 104 symbols and the total training epochs are 102. The two-phase learning is used with the learning rate of 0.5 (2-1) when the mean square error of the training set is larger than 10-3, and the learning rate of 0.125 (2-3), otherwise. When the training epochs exceed eighty percent of the total epochs, the best parameters will be recorded to achieve the lowest mean square error of the training set in the last twenty percent of the training epochs. Hence the steady-state
training results can be recognized. In fact, the simulations indicate no unstable problems as all training processes are converged.
Because different initial conditions lead to different effects, the non-training evaluation set that has 105 symbols is used to examine the training quality of numerous independent simulation outcomes. After numerous independent training and evaluation runs, those yielding better outcomes will be chosen to perform a long trial with the test set, and then the best one will be the final test result. The length of the test set is 107 symbols, and the evaluation set is its subset. In this work, we execute fifty independent runs and select the best one as the final result.
Similarly, we compare the performance of our proposed approach with that of a set of LMS DFEs. We use a LMS DFE without cross inputs for a channel among these parallel channels. The simulation conditions are listed in Tab. 4-4.
The band-limited channel described by the transfer function, H0(z) =0.4665 + 0.2489z-1 + 0.1328z + 0.0708z + 0.0378z , with the co-channel interference described -2 -3 -4 by the transfer function, Cr(z) = 0.408 + 0.816z-1 + 0.408z , is used to estimate the -2 system performance of the LMS DFEs, the MIMO MLP/BP-based DFE, and the MIMO generalized MLP/BP-based DFE. This ISI channel response indicates that the data rate is ten times of the channel bandwidth. The training noise and the evaluation noise are assumed to be SNR=20dB, and SNR of the test signal is between 10dB and 25dB. The signal to co-channel interference ratio (SIR) is equal to 10, 12.5, 15, 17.5, and 20, respectively.
Fig. 4-12 shows the comparisons of the BER performance vs. SNR for the LMS DFEs, the MIMO MLP/BP-based DFE, and the MIMO GMLP/BP-based DFE in the band-limited channels with different SIR. In this figure, we find that the MIMO GMLP/BP-based DFE outperform the MIMO MLP/BP-based DFE under small
background noise with large co-channel interference. Considering different SIR in the band-limited channels at SNR=15dB and 20dB, Fig. 4-13 also shows the comparisons of the BER performance vs. SIR for the LMS DFEs, the MIMO MLP/BP-based DFE, and the MIMO GMLP/BP-based DFE. As compared with LMS DFEs and the MIMO MLP/BP-based DFE, the MIMO GMLP/BP-based DFE can improve the SIR performance about 2.5dB and 0.3dB at BER=10-3. Moreover, we can find that the suitable summation function order is equal to two when small interference presented, or three when large distortion appeared.
Fig. 4-12: BER vs. SNR for different types of equalizers in the wireline band-limited channels with co-channel interference at SIR=10, 15 and 20dB.
Table 4-4: Simulation conditions for MIMO GMLP/BP-based DFE.
MIMO GMLP/BP-based Simulation Conditions LMS DFEs DFE
Input Channel Number 1 8 channels
Forward Length 11 symbols
Feedback Length 5 symbols
Input Number per Channel 16 symbols
Input Numbers 16 128 (16x8)
Hidden Neuron Number --- 16
Output Number 1 8
Summation Function Order --- 1, 2, and 3
Training Set 10 symbols 4
Evaluation Set 10 symbols 5
Test Set 106 symbols
Training Epochs 100 cycles
Re-training Times 1 50
Learning Rate
Searching Range 20 ~ 2-10 20 ~ 2 / 2-4 0 ~ 2-4 Most Suitable Learning Rate 2-8
2-1 / 2-3 (Two phase learning,
MSE Bound=10 ) -3
Training SNR 20 dB
Test SNR 10 to 25 dB (Step = 1 dB)
SIR 10, 12.5, 15, 17.5, and 20 dB
Equalizer Number
for 8 channels 8 1
Fig. 4-13: BER vs. SIR for different types of equalizers in the wireline band-limited channels with co-channel interference at SNR= 15 and 20dB.
4-2-4 Summary
According to the simulation results, the MIMO GMLP/BP-based DFE can recover severe distorted NRZ signals and suppress CCI to achieve better BER performance than LMS DFEs and the MIMO MLP/BP-based DFE in wireline band-limited channels in which the data rate is ten times as much as the channel bandwidth. Also the proposed scheme is a multi-input multi-output architecture, we can extend the input and output number for more complex system. Overall, the MIMO GMLP/BP-based DFE can yield a substantial improvement over the MIMO MLP/BP-based DFE that performs better than the LMS DFEs.
CHAPTER 5 MLP/BP-based Soft DFEs with TCM
for Wireless Communications
For more efficient data transmissions, a new MLP/BP-based channel equalizer is proposed to compensate for multi-path fading in wireless applications. In this chapter, for better system performance, we apply the soft output and the soft feedback structure as well as the soft decision channel decoding. Moreover, to improve packet error rate (PER) and bit error rate (BER), we search for the optimal scaling factor of the transfer function in the output layer of the MLP/BP neural networks and add small random disturbances to the training data. As compared with the conventional MLP/BP-based DFEs and the soft output MLP/BP-based DFEs, the proposed MLP/BP-based soft DFEs under multi-path fading channels can improve over 3dB ~ 0.6dB at PER=10-1 and over 3.3dB ~ 0.8dB at BER=10-3.
The system diagram of wireless digital communication systems is shown in Fig. 5-1.
This chapter is organized as follows. The wireless channel environment is presented in section 1. Section 2 makes a discussion for the error control coding while section 3 shows
the architecture of the MLP/BP-based soft DFEs with bit-interleaved TCM. Afterward, the simulation results show in section 4. Finally, we make a summary in section 5.
Transmitted
Fig. 5-1: System Diagram.