A linear piecewise suboptimum detector for signals in class-A noise

In this paper, we consider the detection problem of binary signals corrupted by Class-A interference for two observations per symbol. The Class-A density contains infinitely many terms of scaled Gaussian-mixture densities, which yields an optimum detector that requires a high computational complexity. The linear (Gaussian) detector can be used, but it suffers from a significant performance degradation in strong impulse environments. The main objective of this paper is to design a simple detector with optimum performance. We start from the optimum decision boundaries, where we propose a piecewise linear approximation for nonlinear regions. As a result, we introduce a novel piecewise detector, which has much less complexity compared with the optimum one. Simulation results show a near-optimal performance for the proposed detectors in different impulse channel environments. Moreover, we show that one and two piecewise linear approximation per each nonlinear region is sufficient to approach the optimum performance.