VSS-LMS algorithms for multichannel system identification using volterra filtrering

Abstract

Adaptive filtering comprises one of the primary technologies in signal processing and investigates numerous applications in arenas of industry and science. These techniques are employed in a vast range of applications, for example adaptive echo and noise cancellation system, adaptive equalization, and adaptive beamforming. The recent custom in the telecommunication system design is the process of identification and minimization of undesired nonlinearities, as they have an element effect on its rendition. The employ of nonlinear models can tackle all these nonlinearities. Adaptive approaches and algorithms are extensively utilized for the estimation of Volterra kernels, under the constraint of unknown nonlinear system. The correctness of the kernels will investigate the precision of the system model and inverse system, which is incorporated for compensation. This thesis propounds the adaptive polynomial filtering deploying the multifarious variable step-size least mean square (VSS-LMS) algorithms for the nonlinear Volterra multichannel system identification, and all are compared with a fixed step-size Volterra least mean square (VLMS) algorithm, under the various noise constraints comprising an individual signal-to-noise ratio (SNR). The VSS-LMS algorithm corroborates steady behaviour during convergence, and the step-size of the adaptive filter is altered in compliance with a gradient descent algorithm delineated to abate the squared estimation error in the course of each iteration, and it also revamps tracking rendition in the smoothly time-varying environments to the choice of the parameters and the boundaries of adaptive filter. In multitudinous practical implementations, the autocorrelation matrix of the input signal has the immense eigenvalue spread in the manifestation of nonlinear Volterra filter than in respect of the linear impulse response filter. In such circumstances, an adaptive step-size is a pertinent option to mitigate the unpropitious effects of eigenvalue spread on the convergence of VLMS adaptive algorithm. The simulation results are exhibited to reinforce the analysis, which compare the VSS-LMS algorithms with fixed step-size of the second-order Volterra filter, and also substantiate that the VSS-LMS algorithms are more robust than the fixed step-size algorithm when the input noise is logistic chaotic type.