Direct projection decoding algorithm for sigma-delta modulated signals

Usually, sigma-delta modulators (ΣΔM) are modeled by replacing the quantizer with an additive white noise source. Based on this linear model, linear decoder structures can be designed. However, the ΣΔM is a nonlinear system, and corresponding nonlinear decoder structures may be able to achieve a better signal-to-quantization-noise ratio (SQNR) performance. In this paper, a new nonlinear decoding algorithm is presented. It is based on the projection onto complex sets (POCS) algorithm developed by Hein and Zakhor. Our algorithm reduces the decoding problem to the solution of a single quadratic programming problem based on the state equations of the modulator and the condition that the modulator input signal is bandlimited. The bandlimitation constraint is directly applied to the state equations. Thus, the resulting quadratic programming problem needs to be solved only once.