A "Rayleigh-ness" test for DS/SS code acquisition

Testing for statistical distribution has received increasing attention in signal processing for communications. Noncoherent receivers, based on correlation magnitude, are employed when the actual carrier phase of the received samples is unknown. This paper presents a new test, based on high-order statistics, to decide whether a real positive white series is a realization of a Rayleigh-distributed random process. Such a "Rayleigh-ness" test is based on a testing variable that measures the "Ricianity" of the series under investigation. That is, it estimates the possible presence of the mean of the complex Gaussian model generating both Rayleigh and Rice distributions. The asymptotic testing statistics have been derived as explicit functions of the higher order moments of the noise-plus-interference distribution. The performance of the Rayleigh-ness test has been analyzed in comparison with a conventional power detector. The devised test has application to noncoherent initial synchronization of the chip offset (code acquisition) in a symbol-length spreading sequence of direct-sequence code-division multiple-access systems. In such a case, the noise-plus-interference variance under the out-of-sync condition is much larger than the effective variance in the in-sync case. The obtained results evidence the robustness of the Rayleighness test, avoiding the severe performance degradation in the presence of large Gaussian and non-Gaussian noise, as well as multiuser interference in a downlink scenario.