Wireless Communications and Mobile Computing

Volume 2018, Article ID 5048419, 7 pages

https://doi.org/10.1155/2018/5048419

## Sampling Adaptive Learning Algorithm for Mobile Blind Source Separation

Correspondence should be addressed to Jianshan Sun; nc.ude.tufh@3149sjnus

Received 23 November 2017; Accepted 26 December 2017; Published 18 March 2018

Academic Editor: Yin Zhang

Copyright © 2018 Jingwen Huang and Jianshan Sun. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Learning rate plays an important role in separating a set of mixed signals through the training of an unmixing matrix, to recover an approximation of the source signals in blind source separation (BSS). To improve the algorithm in speed and exactness, a sampling adaptive learning algorithm is proposed to calculate the adaptive learning rate in a sampling way. The connection for the sampled optimal points is described through a smoothing equation. The simulation result shows that the performance of the proposed algorithm has similar Mean Square Error (MSE) to that of adaptive learning algorithm but is less time consuming.

#### 1. Introduction

With the fast development of the information and computation technologies, the big data analysis and cognitive computing have been widely used in many research areas such as medical treatment [1], transportation [2], and wireless communication [3, 4]. Blind Source Separation (BSS) is a popular research topic in the area of wireless communication. With the fast development of mobile computing, BSS has been widely used in the mobile signal analysis. BSS is an integration of artificial neural network, statistical signal processing, and information theory. The core of BSS is its ability to extract independent components from an observed mixture signal, without requiring a prior knowledge. Such flexibility has made BSS popular in many applications [5–7] especially in mobile intelligence [8, 9].

Artificial neural network based Independent Component Analysis (ICA) is the widely used method in BSS, because it provides powerful tools to capture the structure in data by learning. Based on this theory, Natural Gradient Algorithm (NGA) is employed to find the appropriate coefficient vector of artificial neural network [10]. Nonholonomic Natural Gradient Algorithm (NNGA) is addressed and applied in the BSS [11, 12]. In its application, learning rate for training coefficient vector plays an important role on the performance of the algorithm, which has relationship with not only the update times but also the speed of convergence. This attracts many researchers’ attention to the learning algorithms [13, 14].

Most well-known traditional learning algorithms assume that the learning rate is a small positive constant. Inappropriate constant will lead to relative slow convergence speed or big steady state error. There are lots of studies on the learning rate which aim at the better performance and higher convergence speed. von Hoff and Lindgren [15] developed adaptive step size control algorithm for gradient-based BSS. They used the coefficients of the estimating function to provide an appropriate “measure of error” and serve as the basis for a self-adjusting time-varying step-size. Hai proposed a conjugate gradient procedure for second-order gradient-based BSS [16]. The second-order gradient-based BSS was formulated as a constrained optimization problem. A conjugate gradient procedure with the step size derived optimally at each iteration was proposed to solve the optimization problem. In these algorithms, the step size is updated in iteration, whose value is adjusted according to the time-varying dynamics of the signals. These approaches lead to better performance. The real time search for the step size, however, requires more online calculations as well as recursion, resulting in an increase in computational complexity. On the other hand, in the recursion for optimal step size, there is still a constant left to be estimated, which leads to an endless loop.

The objective of this paper is to find appropriate learning algorithm, to provide better performance as well as less computation time. The proposed sampling learning rate is based on adaptive learning algorithm, which only calculates and samples a few appropriate points. These selected points are connected by the proposed normalized smooth equation.

In the following, we first review the principle of blind signal separation. Then, we discuss the adaptive learning algorithm and propose the sampling adaptive learning algorithm. Finally, we present two typical examples in mobile voice signal. Different constant learning rates are compared firstly to analyze the relationship between the convergence speed and steady state error. Then the comparison between the adaptive learning algorithm and the sampling adaptive learning algorithm is made, illustrating that the proposed algorithm has similar Mean Square Error (MSE) to that of the adaptive learning algorithm but consumes less computational time.

#### 2. Blind Signal Separation

The model considered in this paper is described by Figure 1. A set of individual source signals is mixed with matrix to produce a set of mixed signals .where is the an unknown mixing matrix independent of time, is the vector of source signals, and is the vector containing the observed signals.