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/N/sub 0/ to efficacy, /spl epsiv/. 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 /spl pi//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.>

The problem of extracting one out of a finite number of possible signals of known form given observations in an additive noise model is considered. Two approaches are studied: either the signal with shortest distance to the observed data or the signal having maximal correlation with some transformation of the observed data is chosen. With a weak signal approach, the limiting error probability is a monotone function of the Pitman efficacy and it is the same for both the distance-based and correlation-based detectors. Using the minimax theory of Huber, it is possible to derive robust choices of distance/correlation when the limiting error probability is used as performance criterion. This generalizes previous work in the area, from two signals to an arbitrary number of signals. Considered are M-type and R-type distances and also one-dimensional and two-dimensional signals. Some Monte Carlo simulations are performed to compare the finite sample size error probabilities with the asymptotic error probabilities.>