Optimal Memoryless Pre-Processing and Signal Detection for Impulsive Noise

Abstract

In many communication scenarios, the signal is corrupted by impulsive noise, which is modeled as symmetric $\alpha-$ stable $(\mathrm{S}\alpha \mathrm{S})$ distribution. In this paper, we investigate the signal pre-processing and detection techniques in $\mathrm{S}\alpha \mathrm{S}$ noise. Due to its near-optimal performance, the myriad filter is a commonly used pre-processing method in $\mathrm{S}\alpha \mathrm{S}$ nolse. However, due to its memory, the myriad filter has high computation complexity. Hence, we propose an optimal memoryless pre-processing in this paper. We provide the criteria of optimizing the memoryless pre-processing function and propose a feasible optimization procedure. Based on the obtained pre-processing method, the signal detection method for $\mathrm{S}\alpha \mathrm{S}$ noise is further investigated. In order to evaluate the performance of the pre-processing based signal detection, the optimal signal detection in $\mathrm{S}\alpha \mathrm{S}$ noise is also studied. In our work, it is assumed that the pulse shape of the transmitted signal occupies multiple symbol periods. In this case, each transmitted symbol will have influence on detecting its following symbols. Thus, a multiple symbols aided maximum likelihood detection (MLD) is proposed, and its theoretical symbol error rate (SER) is also analyzed. Simulation results verify that the proposed memoryless pre-processing method can achieve nearly the same waveform recovery performance as myriad filter. Moreover, the SER performance of the proposed memoryless pre-processing based signal detection can approach that of optimal MLD.