Performance bounds for noncoherent detection under Brownian phase noise

The performance of noncoherent detection of orthogonal phase-noise impaired signals in the presence of additive white Gaussian noise is considered. The authors present a novel class of upper and lower bounds on the error probability of a binary hypothesis test, comprising quadratic forms of the additive noise and of the filtered noisy-phase signal plus noise. Filtering the noisy-phase signal gives rise to bounded nonlinear functionals of the Brownian motion sample-path, the exact statistics of which are unknown. The classical theory of Chebyshev systems is utilized to solve the limiting values of the required stochastic expectations, based on the availability of the corresponding generalized moments. The resulting multidimensional moment bounds constitute the tightest possible error bounds for the given set of generalized moments, and require only modest computational efforts. The theory is applicable to assess the design and performance of optical heterodyne systems and is most suitable for coded systems employing hard-decisions, for which the obtained bounds are remarkably tight.<>