A q-Noise Constrained Least Mean Square Algorithm

The Least Mean Square (LMS) algorithm has an inherent trade-off issue between convergence speed and steady-state error performance. One of the algorithms proposed to tackle this issue is called the Noise Constrained LMS algorithm, which uses the noise variance to iteratively vary the step-size. This work uses the q-derivative to propose an improved Noise Constrained LMS algorithm. Simulation results show that the proposed algorithm shows better performance than the conventional algorithm at the cost of only a minimal increase in complexity. Steady-state analysis for the proposed algorithm has also been carried out.