Design, Analysis, and Optimization of the q-Normalized Least Mean Squares Algorithm and its application on real-time Signal Processing via DSP KIT

This project is proposed to explore a recently developed q-Normalized Least Mean Square (q-NLMS) algorithm. The applications of such algorithm are in various fields of signal processing such as in medical signal processing, control, wireless communications, seismic (oil and gas exploration), warfare and artificial intelligence. The q-NLMS algorithm, similar to the q-Least Mean-Squares (q-LMS) algorithm, is the result of q-calculus in the design of the Normalized Least Mean-Squares (NLMS) algorithm which is a very recent field of exploration in adaptive filtering. It has been shown in recent works that q-calculus can improve the performance significantly and provides a new dimension in the studies of adaptive filtering and/or adaptive signal processing. The q-LMS and its variants are designed by employing the concept of Jackson derivative or the q derivative in the evaluation of the derivative of the cost function. The q-NLMS has been proposed recently but it has certain limitations: 1) its q-parameter is fixed or constant; 2) the convergence analysis of the q-NLMS was performed for a specific scenario when the q-parameter is the same for all the elements of the input vector, and finally, 3) there is no procedure provided to optimize the q parameter dynamically for any given problem. In light of these facts, we propose the following tasks in this project: 1. Convergence analysis of the q-NLMS algorithm for generalized scenario where all the q-parameters can be same or different. 2. Design of a set-membership variant of the q-NLMS algorithm. 3. Optimization of the q parameters by minimizing the derived expression for the steady-state Mean-Square-Error (MSE) of the q-NLMS algorithm. The proposed algorithms will be benchmarked against the standard and well-established techniques in adaptive filtering applied in various areas like plant identification and signal processing for wireless communication channels. Moreover, the proposed method will be applied to real-time signal processing applications such as speech enhancement via DSP Board. A complete quantitative analysis of the algorithms will be done and tested through simulations. Analytical results will be validated via extensive simulations.