Adaptive linear predictors in cascade for blind deconvolution of non-stationary and non-minimum-phase channels

Renan Brotto, Kenji Nose Filho, Romis Ribeiro Attux, João Romano

DOI: 10.14209/sbrt.2019.1570558960

Evento: XXXVII Simpósio Brasileiro de Telecomunicações e Processamento de Sinais (SBrT2019)

Keywords:

Abstract

Linear prediction plays a fundamental role in digital signal processing due to its interesting theoretical and practical aspects. An important application is the problem of predictive blind deconvolution. However, it is well known that the classical predictive technique, which assumes the use of the mean squared error (MSE) criterion together with a linear FIR (finite impulse response) fails when the distortion system is non-minimum-phase. In previous works, we have investigated alternative criteria for blind predictive deconvolution, replacing the MSE, which is related to the L2 norm, by the generalized Lp norm, with p different of 2. The results were effective for some non-minimum-phase systems, but not all of them, which clearly indicated a limitation of the linear FIR structure. In the present paper, we propose to employ a cascade of forward and backward linear predictors. The approach is applied to the blind equalization of communication channels. Due to the characteristics of the transmitted signals, the Lp criterion must be considered with p tending to infnity. We opt to use p=4, which corresponds to the MFE (Mean Fourth Error) criterion, as a smooth approximation of the LInf norm. Also, it allows applying the LMF (Least Mean Fourth) adaptive algorithm, in order to track non-stationary behaviors. Simulation results show that the proposed solution is able to deal effectively with the blind equalization of non-stationary and non-minimum-phase channels.

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