Quadriphase sequences for spread-spectrum multiple-access communication

Detection of weak signals in a special v-mixing noise class isthe signals are weak, asymptotic performance is of interest.considered. The detector structure is restricted to sums of memorylessnonl inear transformations of the observat ions, correlated with the dataA common measure of asymptotic performance is the sequenceand compared to a f ixed threshold. Using the efficacy to measure efficacy. It is well-known that for independent identicallyperformance, the nonlinearity that has min-max performance is derived. distributed (i.i.d.) observations the efficacy is maximizedwhen the nonl inear transformation is given by the locally I. INTR~DLJCTI~Nopt imum nonlinearity def ined by the marginal density.When this density is not known exactly, optimality is oftenF OR the detection of signals in additive noise, a very def ined in a m in-max way. Following the ideas of Hubercommonly used detector structure consists of a sum on robust estimation and hypothesis testing [l], [2] theof memoryless nonl inear transformations of the observam in-max nonlinearities for detection are derived in [3]-[5]tions, correlated with the signals and compared to a fixed for the i.i.d. case and for densities belonging to an e-con-threshold. When the number of observations is large and tamination class. In [3], [4] the noise densities are assumedto be symmetric. In [5] noise symmetry is assumedinsideManuscript received January 24, 1983; revised June 27, 1983. This work an interval around the origin.was supported in part by the US. Army under Grant DAAG29-82-K0095and in part by the National Science Foundat ion under Grant ECS-79-All of these approaches assume independent observa18915.tions. For the dependent case, in order to calculate theG. V. Monstakides was with the Department of Electrical Engineering efficacy we must know the bivariate densities of all pairs ofand Computer Science, Princeton University, Princeton, NJ 08544; he isnow with the Institut de Rechercheen Informatique et SystemesAleatoires,observations. F inding the nonlinearity that maximizes the Rennes, France.efficacy is not easy as in the i.i.d. case. This problem forJ. B. Thomas is with the Department of Electrical Engineering and stationary sequencesis consideredin [6] for the m-depen-Computer Science, Princeton University, Princeton, NJ 08544.dent caseand in [7] for the q-mixing case.It is shown that, OO lB-9448/84/0500-0529$01.0