The overall performance of the MLP/BP-based soft DFEs with bit-interleaved TCM is evaluated through the simulations for the distorted QPSK signal recovery in multi-path fading channels under different AWGN power. In these simulations, we apply the proposed architecture to different packet size and prove the proposed scheme with better performance.
The length of the training symbols within a packet is equal to 128 symbols and the total training epochs are 40. When the training epochs exceed fifty percent of total epochs,
the best parameters will be recorded to achieve the lowest mean square error of the training set. The length of transmitted data within a packet is 103, 2×103, 4×103, and 8×103 bits, respectively. There are 103 packets tested in different configurations.
In this work, different learning rates, equal to 1, 0.5, 0.25, and 0.125, have been evaluated for all of the equalization schemes. For the conventional MLP/BP-based DFE, the soft output MLP/BP-based DFE, the MLP/BP-based soft DFE, and the MLP/BP-based soft DFE with transfer function scaling factor adjustment, the most suitable learning rate is equal to 0.5, 0.25, 0.25, and 0.5, respectively.
For the MLP/BP-based soft DFEs, different scaling factor of the transfer function in the output layer of the MLP/BP neural networks, equal to 1, 0.5, 0.25, and 0.125, have been evaluated. For this application, the most suitable scaling factor is 0.5. Moreover, different magnitudes of extra small random disturbances have been added to the training data to improve the training quality. From experiments, the most suitable magnitude is about 10% of the training signal. Thus, the proposed MLP/BP-based soft DFEs has included the suitable scaling factor to the transfer function of the output neurons and added the suitable magnitude of extra random disturbances to the training data.
In this work, the system configurations and simulation conditions are listed in Tab.
5-1. When the packet data length is equal to 103 bits, the PER performance for different types of equalizers is shown in Fig. 5-6. As compared with the conventional MLP/BP-based DFE and the soft output MLP/BP-based DFE, the proposed MLP/BP-based soft DFE under multi-path fading channels with AWGN can improve over 3.0dB and 0.6dB at PER=10-1. When the packet data length is set to 8×103 bits, the PER performance for different types of equalizers is shown in Fig. 5-7. The proposed approach improves 0.4dB over the soft output MLP/BP-based DFE and 3.4dB over the conventional MLP/BP-based DFE at PER=10-1. Fig. 5-8 shows the PER performance for
different types of equalizers with different packet data length at Eb/N0 = 7.5dB and 10.0dB. We can observe the large packet size results in poor performance. Since the multi-path fading channels are time varying, we select a smaller packet size for faster channel variant rate. Also, a smaller packet size is selected for large background noise.
For data communications, we focus on the PER performance, whereas the BER performance is the major concern for audio or multi-media communications. When the packet data length is equal to 103 bits, the BER performance for different types of equalizers is shown in Fig. 5-9. As compared with the conventional MLP/BP-based DFE and the soft output MLP/BP-based DFE, the proposed MLP/BP-based soft DFE under multi-path fading channels with AWGN can improve over 3.6dB and 0.9dB at BER=10-3. When the packet data length is 8×103 bits, the BER performance for different equalizer types is shown in Fig. 5-10. As compared with the conventional MLP/BP-based DFE and the soft output MLP/BP-based DFE, the proposed MLP/BP-based soft DFE under multi-path fading channels with AWGN can improve over 3.3dB and 0.8dB at BER=10-3. The BER performance for different types of equalizers with different packet data length at Eb/N0 = 7.5dB and 10.0dB is shown in Fig. 5-11. The PER performance improvement at PER=10-1 and the BER performance improvement at BER=10-3 are listed in Tab. 5-2.
Table 5-1: System configurations and simulation conditions.
MLP/BP-based DFE MLP/BP-based Soft DFE Type
Hard Output Soft Output
Without Scaling factor
adjustment
With Scaling Factor
adjustment
Forward Length 17 symbols
Feedback Length 8 symbols
Input Tap Number 25 symbols
Input Neuron Numbers 50 (25×2)
Hidden Neuron Number 25
Output Neuron Number 2 (1×2)
Training Symbol Number 128 symbols
Training Epochs 40 cycles
Packet Data Length 1K, 2K, 4K, and 8K
Test Packet Number 1000 packets
Learning Rate
Searching Range 20 ~ 2-3
Most Suitable
Learning Rate 2-1 2-2 2-2 2-1
Scaling Factor
Searching Range --- --- --- 20 ~ 2-3
Most Suitable
Scaling Factor --- --- --- 2-1
Test Eb/N0 5dB – 13 dB (Step=0.5dB)
Fig. 5-6: PER Performance for different types of equalizers when packet data length is equal to 103.
Fig. 5-7: PER Performance for different types of equalizers when packet data length is equal to 8×103.
Fig. 5-8: PER Performance for different types of equalizers with different packet data length at Eb/N = 7.5dB and 10.0dB. 0
Fig. 5-9: BER Performance for different types of equalizers when packet data length is equal to 103.
Fig. 5-10: BER Performance for different types of equalizers when packet data length is equal to 8×103.
Fig. 5-11: BER Performance for different types of equalizers with different packet data lengths at Eb/N = 7.5dB and 10dB. 0
Table 5-2: The PER and BER performance improvement.
MLP/BP-based DFE MLP/BP-based Soft DFE With Scaling Factor
Adjustment and Extra
Random Disturbances Type
Original Setting Hard Output Soft Output
5-5 Summary
With the soft output and the soft decision, the MLP/BP-based channel equalizers can offer more information for the soft decision channel decoding. Moreover, the system performance is further improved by searching the most suitable scaling factor for the transfer function in the output neurons and adding the suitable magnitude of extra small random disturbances to the training data. The proposed approach is applied to compensate
Packet Data Length Eb/N Improvement at PER=100 -1
1K --- > 2.3 dB > 2.6 dB > 3.0 dB 2K --- > 2.5 dB > 2.7 dB > 3.0 dB 4K --- >2.3 dB >2.6 dB > 2.8 dB 8K --- > 3.0 dB > 3.2 dB > 3.4 dB Packet Data Length Eb/N Improvement at BER=100 -3
1K --- > 2.7 dB > 3.2 dB > 3.6 dB 2K --- > 2.7 dB >3.1 dB > 3.4 dB 4K --- > 2.6 dB > 3.1 dB > 3.4 dB 8K --- > 2.5 dB > 3.0 dB > 3.3 dB
for the distorted QPSK signals in multi-path fading channels with AWGN and results in a significant performance improvement. In conclusion, the proposed MLP/BP-based soft DFE with bit-interleaved TCM provides a potential solution for wireless communications.
CHAPTER 6 Conclusion and Future Works
6-1 Conclusion
In this study, we propose a new neural network model that applies a multivariate power series as the summation function of the MLP/BP neural networks. Compared to the conventional approach using a first order multivariate polynomial, the boundaries separating the pattern space change from piecewise linear into piecewise nonlinear. In addition, when deduced by the gradient steepest descent method, the corresponding training algorithm is a gradient method; consequently, the convergence solutions exist.
Therefore, this new model is a generalized MLP/BP neural network (GMLP/BP) that is more flexible than other piecewise linear approaches because of the nonlinear separating pattern space. The traditional MLP/BP neural network is a special case of the proposed generalized MLP/BP neural network.
As the channel equalization schemes can be thought of a mapping from the received waveform to the transmitted data. The pattern recognition techniques have been used to identify the severely distorting date. Having the capability of classifying the sampling
pattern and fault tolerance, artificial neural networks are very suitable for the channel equalizers. As a result, we apply the traditional and the generalized MLP/BP neural networks to channel equalization designs. From the simulation results, the proposed neural-based channel equalization schemes can outperform the conventional LEs and LMS DFEs.
For wireline communications, we apply the MLP/BP-based channel equalization schemes to different applications. In the wireline band-limited channels that the data rate is about ten times as much as the channel bandwidth, the MLP/BP-based DFEs provide better performance, tolerate sampling clock skew, and permit channel response variance.
However, the traditional MLP/BP-based DFEs are not good enough for the severe ISI channels with nonlinear distortions. In such channels, the GMLP/BP-based DFEs can outperform the traditional MLP/BP-based DFEs that do better than the LMS DFEs. In wireline band-limited parallel channels, the MIMO MLP/BP-based DFEs and the MIMO GMLP/BP-based DFEs can suppress ISI, CCI and AWGN, simultaneously. By the computer simulations, the MIMO GMLP/BP-based DFEs can yield a substantial improvement over the MIMO MLP/BP-based DFEs that perform better than a set of the LMS DFEs.
For wireless communications, a modified approach, which is also based on the MLP/BP neural network, is presented. We apply the soft output and the soft decision feedback structure to the MLP/BP-based channel equalization scheme that concatenates with the soft decision channel decoder to improve whole performance on multi-path fading channels. Moreover, the performance of the MLP/BP-based soft DFE is also increased with the optimal scaling factor searching of the transfer function in the output layer of the MLP/BP neural networks and extra small random disturbances added to the training data. By the simulations, the MLP/BP-based soft DFEs with bit-interleaved TCM
outperform the MLP/BP-based DFEs with bit-interleaved TCM and the soft output MLP/BP-based DFEs with bit-interleaved TCM in multi-path fading channels.