An upper bound on the error probability of quadratic-detection in noisy phase channels

A rigorous method to find the upper bound of the error probability of noncoherent quadratically detected signals in the presence of both additive white Gaussian noise and Brownian carrier phase noise is presented. An analytical upper bound on the bit error probability is derived, relying on a bivariate moment-generating function of two bounded exponential functionals of the Brownian phase path. These functionals, whose exact statistics are unknown, yield the two basic impairments arising due to phase noise: in-band signal suppression and intersymbol crosstalk . The classical theory of Chebyshev systems is applied to obtain the limiting values of the involved generating function, utilizing a multidimensional moment characterization of the involved functionals. The impact of the incomplete-statistical characterization used on the resultant upper-bound tightness is addressed. Assessing the design and performance of lightwave heterodyned systems using this method is discussed. The method enables the analysis of interchannel crosstalk effects in frequency-division multiplexing systems