Modified PSO-Based Equalizers for Channel Equalization
This work proposes a modified particle swarm optimization (PSO) as an adaptive algorithm to search for optimum equalizer weights of transversal and decision feedback equalizers. Inertia weight is one of the PSO’s critical parameters which manage the searc
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Modified PSO-Based Equalizers for Channel Equalization D.C. Diana and S.P. Joy Vasantha Rani
12.1
Introduction
Adaptive equalization [1] plays an important role in the high-speed digital transmission to remove and recover the problem of inter-symbol interference (ISI). The adaptive algorithms [2] such as steepest descent, least mean square (LMS), recursive least square (RLS), affine projection algorithm (APA), and their variants [3] reported in literature have the chance of getting trapped in local minima [4–6] while optimizing the equalizer weights. The performance of these algorithms further degraded in nonlinear channel conditions [6]. To overcome these problems, different derivative-free optimization algorithms are proposed, whereas PSO is one among them. For solving optimization algorithms, PSO is proven as an efficient method and was applied successfully in the area of adaptive equalization [6]. PSO stays as one of the best algorithms for channel equalization in the recent years [5–7]. And also it provides minimum mean square error (MSE) compared to genetic algorithms used in the channel equalization [6]. From the first introduction of PSO [8], several variants [9–16] are proposed. The inertia weight parameter ‘w’ is the first modification found in literature which plays a major role in convergence and improves the simulation time. Initially, Shi and Eberhart introduced inertia weight [10]. In their work, a range of constant w values are used and found that PSO shows a weak exploration for large w values, i.e., w > 1.2, and it tends to trap in local optima with w < 0.8. When w is in the range [0.8, 1.2], PSO shows the global optimum in least average
D.C. Diana (&) S.P. Joy Vasantha Rani Department of Electronics Engineering, Madras Institute of Technology, Anna University, Chennai, India e-mail: [email protected] S.P. Joy Vasantha Rani e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2017 V. Nath (ed.), Proceedings of the International Conference on Nano-electronics, Circuits & Communication Systems, Lecture Notes in Electrical Engineering 403, DOI 10.1007/978-981-10-2999-8_12
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number of iterations. A random value is selected to track the optima in [11], as given in Eq. (1.1). w ¼ 0:5 þ
randðÞ 2
ð12:1Þ
where rand() is a random value between [0, 1]. Time-varying inertia weight is a common approach used in PSO, which determines the inertia weight based on the current and total iteration. Time-decreasing inertia weight methods are used in literature to improve the convergence rate. A linearly decreasing inertia weight has been used for adaptive equalization in [6], based on the update law: wn ¼ wi wf ðm nÞ=ðm 1Þ þ wf ð12:2Þ where wi is the initial weight, wf the is maximum weight, ‘m’ is the maximum iteration value, and ‘n’ is the current iteration index. A nonlinear decreasing inertia weight is proposed by Chatterjee and Siarry [12] based on the equation: wn ¼ wi wf ðm nÞnp =ðm 1Þnp þ wf ð12:3Þ where np is the no
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