MLP/BP-based MIMO DFEs for Suppressing ISI and ACI in Non-minimum Phase Channels

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1 MLP/BP-based MIMO DFEs for Suppressing ISI and ACI in Non-minimum Phase Channels Terng-Ren Hsu ( 許騰仁 ) and Kuan-Chieh Chao Department of Microelectronics Engineering, Chung Hua University No.77, Sec. 2, Wufu Rd., Hsinchu, Taiwan, 312, R.O.C. Tel: , Fax: trhsu@chu.edu.tw Abstract In this wor, we base on multi-layered perceptron neural networs with bacpropagation algorithm (MLP/BP) to construct multi-input multi-output (MIMO) decision feedbac equalizers (DFEs). The proposal is used to recover severe distorted nonreturn-to-zero (NRZ) data in non-minimum phase channels. From the simulations, we note that the proposed scheme can recover severe distorted signals as well as suppress intersymbol interference (ISI), adjacent channel interference (ACI) and bacground noise. The better BER performance as compared to a set of LMS DFEs is achieved in non-minimum phase channels. Keywords: MLP/BP Neural Networ (Multi-Layered Perceptron Neural Networ with Bacpropagation Algorithm), DFE (Decision Feedbac Equalizer), NRZ (Nonreturn-to-zero), ISI (Intersymbol Interference), ACI (Adjacent Channel Interference) 1. Introduction In practical digital communication systems, the source data are transmitted over intersymbol interference channels, tainted by noise, and then received as distorted nonreturn-to-zero (NRZ) ones. Besides, adjacent channel interference (ACI) will lead to more distortions and worse performance. Besides, the additive white Gaussian noise (AWGN) is used to model the bacground noise. In this draft, we consider several parallel non-minimum phase channels. In such channels, intersymbol interference results in lac of zero crossing for the received signal. Also, adjacent signals result in color noises; the received signal will be tainted by such color noises. ISI and ACI mae the received signal with large distortion. As a result, it is necessary to apply data equalizers to recover the original waveform from the distorted one in practical digital communications [1]. Conventionally, the NRZ signal recovery is based on either linear equalizers (LEs) [1], or decision feedbac equalizers (DFEs) [1-2]. A linear equalizer can restore the original transmitted signal in a minimum phase channel, where the channel distortion is linear without spectral nulls in the channel response. Nevertheless, as the channel frequency response has spectral nulls, the received noise will be enhanced in the process of compensating these nulls, resulting in degraded performance. Such non-minimum phase channels lead to malfunctions of linear equalizers. The DFE employing previous decisions to remove the ISI on the current symbol has been extensively exploited to severe ISI rejection. The least mean squares (LMS) algorithm is used to estimate the coefficients of the equalizer [1-2] whose

2 accuracy determines the system performance. Recently, various equalization schemes based on artificial neural networs have been applied to the severely distorting signal recoveries. Having the capability of classifying the sampling pattern and fault tolerance, neural-based solutions provide better performance than conventional equalization methods. Based on the MLP/BP neural networs [3], the feedforward equalizers [4-5], and the decision feedbac equalizers [6] have been broadly used to NRZ data recovery in ISI channels. Besides, Perceptron neural networs have been used as data equalizers in ISI and ACI channels [7-8]. For high-speed data communications, it is common to use waveform equalization technique to improve the data rate or decrease the error rate [9-11]. The receiver must detect correct data under ISI, ACI, and AWGN conditions. In our previous wor [12], MLP/BP-based DFEs are used to tolerate sampling cloc sew and channel response variance in wireline band-limited channels. Moreover, we use an MLP/BP-based MIMO DFE [13] to suppress ISI, ACI, and AWGN in wireline parallel band-limited channels. This wor is based on above studies. We use an MLP/BP-based MIMO DFE to recover the distorted NRZ signal in non-minimum phase channels. From the simulations, better performances as compared to a set of LMS DFEs are achieved. This article is organized as follows. The equivalent channel model, and the proposed approach are presented in section 2 while section 3 shows the simulation results. Finally, the conclusions are presented in section Proposed Architecture In this section, an equivalent channel model is presented first followed by the proposed approach. The architecture and configuration of the generalized MLP/BP-based MIMO DFE are discussed in detail. A. Channel Models In non-minimum phase channels, the received signal pulse is unable to complete its transition within a symbol interval. Besides, neighbor channels would cause the adjacent channel interference and taint the received signals. The equivalent model for the ISI channels with ACI and AWGN is shown in Fig. 1 where finite impulse response (FIR) filters are used to model the ISI channel responses and ACI responses with the AWGN. TX 2-PAM Signal TX 2-PAM Signal TX 2-PAM Signal ISI Response Weight #11 ACI Response Weight #12 ISI Response Weight #1M Weight #21 ACI Response Weight #22 ISI Response ISI Weight #2M Weight #M1 ACI Response Weight #M2 Weight #MM ACI AWGN AWGN AWGN RX NRZ Signal RX NRZ Signal RX NRZ Signal Fig. 1. Equivalent model for the ISI channels with ACI and AWGN The ISI responses and ACI responses with AWGN can be written as follows: H 1 2 L (z) = f + f1 z + f 2 z f L z (1) A (z) = g y r = L i= 1 2 M r + g r1 z + g r 2 z g rm z (2) f x (3) i i

3 a = r M j= g x j r j (4) y ˆ = y + a + n (5) where H (z) is the transfer function of the ISI channel responses; L is the length of the ISI channel response; A r (z) is the transfer function of the ACI responses; M is the length of the ACI response; x o is the input sequence of ISI response; x r is the input sequence of r-th ACI response; y is the channel output which is warped by ISI only; a is the sum of adjacent channel interference; n is the AWGN; ŷ is the received signal which is distorted by ISI, ACI and AWGN. equal to 8. Table 1 Weighting of ACI among different channels. Ch Magnitude (db) Phase (degree) -5 Frequency Response ISI ACI Normalized Frequency Fig. 2. Frequency responses of ISI and ACI In this wor, the non-minimum phase channels with ACI are used to verify the proposed approaches. Such channel condition is practical in many digital communication systems, whose the transfer function of the ISI channels is H (z) = z z -2 and the transfer function of the ACI is A r (z) = z z -2. The frequency responses of them are illustrated in Fig. 2. We use uniform distribution random values between 1 and to simulate the effects between different channels and construct an N N matrix which is normalized to mae the sum of squares of all elements be N. The weighting of ACI between different channels is shown in Table 1 where N is B. MLP/BP-based MIMO DFEs An artificial neural networ consists of a set of highly interconnected neurons such that each neuron output is connected to other ones or/and to itself through weights with or without lag. Recently, there are many different artificial neural networs had been proposed, but the multi-layer perceptron neural networ with bacpropagation algorithm (MLP/BP) is the most important and popular one. [3] The MLP/BP neural networs are supervised learning, meaning that a training set includes an input vector and a desired output vector. The training patterns must characterize the system characteristic. Apposite training patterns can improve the training quality. Using the MLP/BP neural networs to solve problems includes two phases, one is training procedure and another is test procedure. In the training phase, we use the gradient steepest descent method to minimize the error function for updating the weights. After that we apply the training results to obtain the networ response in the test phase. The result is really a sub-optimal solution. Different networ configurations, different initial conditions or different learning rate, will lead

4 to different performance. Usually, we could perform quite a few independent runs and choose the most fitting outcome as the final solution. In this wor, we execute ten independent runs and select the best one as the final result. The bloc diagram of the MLP/BP-based MIMO DFEs is shown in Fig. 3. It is a single hidden layer MLP architecture. The inputs of this MLP/BP-based MIMO DFE consist of feed-forward signals, which come from the input symbols by tapped-delay-line registers, and feedbac signals, which come from previous decisions by another tapped-delay-line registers. Ch-n Feedbac Ch-n Z -1 Ch-1 Z -1 Z -1 Z -1 Z -1 Z -1 Z Input Input -1 X -n X -n X -2 X -1 X Y m Y 2 Y 1 Input Layer Hidden Layer Output Layer MIMO MLP/BP Neural Networ Threshold Threshold Ch-n Ch-1 Output Output Fig. 3. MLP/BP-based MIMO DFE 3. Simulation Results The performance of the MLP/BP-based MIMO DFE is evaluated through the simulations for the distorted NRZ signal recovery in the non-minimum phase ISI channels with the non-minimum phase ACI. On the other word, the frequency responses of both ISI and ACI are with deep spectrum null. All equalization schemes in this wor have eleven symbols per channel in the forward part and five symbols per channel in the feedbac part. We assume there are 8 channels in this system. The number of neurons in the input layer is equal to 128 (16 by 8). The MLP/BP-based MIMO DFE uses the single hidden layer MLP architecture. The number of neurons in the hidden layer is 32. Since all the proposed equalization schemes have a single output per channel, the number of neurons in the output layer is equal to 8 (1 by 8). In the training procedure, the length of the training set is equal to 1 4 symbols and the total training epochs are 1 3. The two-phase learning is used with the learning rate of.5 (2-1 ) when the mean square error of the training set is larger than 1-3, and the learning rate of.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 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 symbols, and the evaluation set is its subset. In this wor, we execute 1 independent runs and select the best one as the final result. Also, 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 adjacent channels. In this wor, the training noise and the evaluation noise are assumed to be SNR = 2dB, and SNR of the test signal is between 1dB and 25dB. The signal to adjacent channel interference ratio (SIR) is equal to 15, 2, and 25, respectively. Fig. 4 shows the comparisons of the BER vs. SNR performance for a set of LMS DFEs and the

5 proposed MLP/BP-based MIMO DFE in the non-minimum phase channels with different SIR. The proposed approach can improve SNR about 2dB at BER=1-3, where SIR=25dB. Considering different SIR in the non-minimum phase channels at SNR= 15, 2 and 25dB, respectively, Fig. 5 also shows the comparisons of the BER vs. SIR performance for a set of LMS DFEs and the MLP/BP-based MIMO DFE. The proposed approach can improve SIR over 5dB at BER=1-3, where SNR=25dB. From Fig. 4 and Fig. 5, the proposed approach reports better performance under larger intersymbol interference and larger adjacent channel interference. The proposed scheme can recover severe distorted NRZ signal as well as suppress ISI, ACI and AWGN. BER, (Test Symbol Per Channel = 1e6) BER, (Test Symbol Per Channel = 1e6) 1 BER Performance (Training Epoch = 1) LMS DFEs (SIR=15dB) BPN MIMO DFE (SIR=15dB) LMS DFEs (SIR=2dB) BPN MIMO DFE (SIR=2dB) LMS DFEs (SIR=25dB) BPN MIMO DFE (SIR=25dB) SNR (db), (Training SNR = 2dB) Fig. 4. BER vs. SNR performance at SIR = 15, 2, and 25 db 1 BER Performance (Training Epoch = 1) LMS DFE SNR=15 BPN DFE SNR=15 LMS DFE SNR=2 BPN DFE SNR=2 LMS DFE SNR=25 BPN DFE SNR= SIR (db), (Training SNR = 2dB) Fig. 5. BER vs. SIR performance at SNR= 15 and 2dB 4. Conclusion The present scheme can overcome ISI while suppress ACI. According to the simulation results, the MLP/BP-based MIMO DFE can recover severe distorted NRZ signals and suppress ACI to achieve better BER performance than LMS DFEs in the non-minimum phase channels. Because the proposed equalizer is a multi-input multi-output architecture, we can extend the input and output number for more complex system. Because the architecture of the proposed approach involves a large number of addition and multiplication, such requests cause high hardware complexity. For hardware implementations, the architecture of the MLP/BP-based MIMO DFEs is more complex than that of the conventional methods. However, we thin that the rapid progress of VLSI technology will afford more complex approaches for better performance. References [1] S. Hayin, Communication Systems 3e, Chapter 7, Wiley, [2] B. S. Song, and D. C. Soo, NRZ Timing Recovery Technique for Band-Limited Channels, IEEE J. Solid-State Circuits, vol. 32, no. 4, pp , [3] C. T. Lin, and C. S. G. Lee, Neural Fuzzy Systems, pp , pp , Prentice Hall, [4] G. J. Gibson, S. S., and C. F. N. Cowan, Multilayer Perceptron Structures Applied to Adaptive Equalisers for Data Communications, Proc. IEEE Int. Conf. on Acoustics, Speech and Signal, vol. 2, 1989, pp [5] T. R. Hsu, T. Y. Hsu, H. Y. Liu, S. D. Tzeng, J. N. Yang and C. Y. Lee, A MLP/BP-based Equalizer for NRZ Signal Recovery in

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