Arab J Sci Eng DOI 10.1007/s13369-017-2883-6 RESEARCH ARTICLE - ELECTRICAL ENGINEERING Design of an Intelligent q -LMS Algorithm for Tracking a Non-stationary Channel M. Arif 1 · I. Naseem 1,2 · M. Moinuddin 3,4 · U. M. Al-Saggaf 3,4 Received: 20 February 2017 / Accepted: 10 October 2017 © King Fahd University of Petroleum & Minerals 2017 Abstract Tracking of a time-varying channel is a challeng- ing task, especially when channel is non-stationary. In this work, we propose a time-varying q -LMS algorithm to effi- ciently track a random-walk channel. To do so, we first perform tracking analysis of the q -LMS algorithm in a non- stationary environment and then derive the expressions for the transient and steady-state tracking excess mean-square- error (EMSE). Thus, we evaluate an optimum value of q parameter which minimizes the tracking EMSE. Next, by utilizing the derived optimum q , we design a time-varying mechanism to vary the parameter q according to the esti- mation of instantaneous error energy which provides faster convergence in the initial phase while attain a lower EMSE near final stages of adaptation. Keywords Adaptive filtering · q -LMS · Steady-state analysis · Mean-square error · Tracking analysis B M. Moinuddin mmsansari@kau.edu.sa M. Arif marif@pafkiet.edu.pk I. Naseem imrannaseem@pafkiet.edu.pk ; imran.naseem@uwa.edu.au U. M. Al-Saggaf usaggaf@kau.edu.sa 1 Electrical Engineering Department, Karachi Institute of Economics and Technology, Karachi, Pakistan 2 School of Electrical, Electronic and Computer Engineering, University of Western Australia, Perth, Australia 3 Electrical and Computer Engineering Department, King Abdul Aziz University, Jeddah 21859, Saudi Arabia 4 Center of Excellence in Intelligent Engineering Systems (CEIES), King Abdul Aziz University, Jeddah 21859, Saudi Arabia 1 Introduction Tracking of channel in a non-stationary environment is a challenging task as the parameters of the channel are con- tinuously changing with time. Whenever channel is random and the statistical properties of the channel are changing with respect to time, tracking of such continuously changing environments is a challenge as they can have a great impact on signal-tracking performance. Adaptive filtering is an effi- cient tool for the estimation of parameters in the continuously changing environments. Since adaptive filters rely on instan- taneous data, they are able to effectively track the statistical variations in the input signal and therefore provide good esti- mates for both stationary and non-stationary environments [1–3] and hence adaptive filters provides good estimates for both stationary and non-stationary environments. Adaptive filters have been successfully used in a number of applications [4–9]. In the context of tracking for instance, a unified approach based on energy is proposed in [10]. The idea of energy conservation is proposed in [11], and the extended form was utilized in [10, 12, 13], and [14]. In a recent work, the q -LMS adaptive algorithm is pro- posed in [15], in which the cost function is minimized by using q -gradient instead of conventional gradient as in LMS. The steady-state performance is provided for station- ary environments. However, in real practice, most of the environments are non-stationary and time-variant in nature. This motivates us to analyze the q -LMS for a non-stationary environment and proposed steady-state EMSE by using the idea of q -gradient. Moreover, there is a need to design time-varying q parameter which can provide better track- ing performance. The main aims of our work are highlighted in the next subsection. 123