On noncoherent detection of noisy phase OOK signals

This paper considers the use of noncoherent detection using L-fold square-law combining for binary On Off Keying (OOK) modulation in a noisy phase channel. The channel presents both additive white Gaussian noise (AWGN) as well as Brownian phase noise. Approximating the unknown distribution law of the underlying phase functionals by a class of discrete distributions, we obtain an analytic expression for the BER of noisy phase OOK signals detected with square-law combining. The discrete distribution laws support any given number of power moments admitted by the phase functionals. These moments are exactly known and are given in closed form analytic expressions. The particular distribution laws chosen here are a pair called principal representations from the theory of Tchebycheff-Systems. The above numerical methods are used to investigate the dependence of the BER on the following parameters: decision threshold, IF bandwidth, the bit energy to noise spectral density ratio (E_b/N₀) and the Brownian phase 3 dB linewidth