AN UPPER BOUND ON THE ERROR-PROBABILITY OF QUADRATIC-DETECTION IN NOISY PHASE CHANNELS

A novel rigorous method to upper bound the error probability of noncoherent quadratically detected signals in the presence of both additive white Gaussian noise and Brownian carrier phase noise is presented. The received noisy phase signal is first filtered and then time-diversity is employed via square-law combining. 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, render the two basic impairments rising due to phase noise, that is in-band signal suppression and intersymbol crosstalk. The classical theory of Tchebycheff 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. This analytic approach renders a computationally feasible upper bound, whereas the exact derivation of the error probability appears intractable. The theory is applicable to assessing the design and performance of lightwave heterodyned systems employing noncoherent demodulation, such as frequency shift keying, on-off keying, pulse position modulation and transmitted-reference systems. It also enables the analysis of interchannel crosstalk effects in frequency division multiplexing systems. The general theory is exemplified, in providing explicit results referring to M-ary frequency shift keying scheme under a variety of operating conditions. The results obtained are remarkably tight with the use of just few power moments.