A novel impulsive noise cancelation method using sigma-delta quantization of geometrically uniform finite frames

In this paper, we propose a new method that efficiently cancels the impulsive noise that is present in communication systems, when a Sigma-Delta (SD) quantizer is used for the reconstruction of the transmitted signal. We start from the SD quantization of Cyclic Geometrically Uniform (CGU) finite frames and we consider the widely used L-th order noise shaping filter G(z)= (1 - z^-1)^L in the signal reconstruction. We show that when the signal is sent over a channel with Gaussian plus impulsive noise, the impulsive noise can be efficiently removed by a procedure similar to channel decoding, using the information that is carried by the “syndrome” sequence contained in the transmitted signal. Furthermore, we prove that considering the SD as a quantization scheme leads to a reduced background noise caused by the SD quantizer, which increases the reliability of the proposed impulsive noise cancelation algorithm. The efficiency of this impulsive noise cancelation technique is corroborated with simulation results.