The distribution of the amplitude and phase of the mean of a sample of complex random variables

Edgeworth-type expansions are given for the distribution of (normalized versions of) the amplitude and phase of the mean of a sample of complex random variables. These expansions are transformed to polar forms with applications to modeling signals from a cell-phone. Limiting distributions of (normalized versions of) the amplitude and phase of the mean are given for the cases: (1) population mean is zero, and (2) population mean is non-zero. The results apply for distributions with finite cumulants.