JOINT PHASE AND ENVELOPE DENSITIES OF A HIGHER-ORDER

In dealing with narrowband noise processes the density p(R(1), R(2), D elta) in which R(1) and R(2) are envelope samples and Delta is the pha se difference can play an important role in determining system design features such as diversity performance, crossing rates, error probabil ities, optimum processing and frequency or phase distributions. Standa rd texts on signal detection or radar usually include a discussion of p(R) and, less often, of p(R(1), R(2)) but the number of instances in which p(R(1), R(2), Delta) can be specified is limited, and here known results are touched upon while a general form for this joint density is developed. The work extends an earlier treatment of p(R(1), R(2), D elta) and includes some important observations regarding the method us ed here and a SIRP (spherically invariant random process) approach whi ch has been widely proposed for the analysis of correlated radar retur ns. Two differing families of non-Gaussian processes are used to illus trate the working and a number of densities for the jointly correlated pair R(1) and R(2), and the phase difference Delta are given, so exte nding the pool of such results available to the analyst. The approach used is heuristic and although the positivity of p(Delta) is not prove n outright, experience and the cases illustrated point to this require ment being met.