Robust detection in digital communications

This paper deals with the problem of communicating through unspecified noise. Detectors, robust against variations in the probability density function of the noise, are developed and discussed. The paper covers three issues. First, the relation between a distance measuring receiver and a correlating receiver in a general case is shown. Second, a theoretical method for the computation of an upper limit for the probability of symbol error is presented. This computation fits into the ordinary framework for computation of the error probability by changing the inverted noise density 2/N₀ to efficacy, ε. Efficacy is defined in the paper. Third, detectors based on M-, i.e., maximum likelihood type, and R-, i.e., rank, statistics are tested and compared for GMSK and π/4-shifted DQPSK. From numerical comparisons of the upper bounds and their simulated estimates for robust detectors, it is concluded that the loss in Gaussian noise is very small compared to the optimum quadratic detector. The gain, compared to a nonrobust receiver optimized to Gaussian noise, is around 0.5 to 2 dB for large SNR and around 2 to 4 dB for low SNR in impulsive noise. This offers new methods of significantly improving communication when the noise is unknown