Optimum and Suboptimum Detector Performance for Signals in Cyclostationary Noise

The detection of known and partially known signals in additive white Gaussian uonstationary noise is considered, with primary attention to the ease where the time-varying noise intensity parameter N_{o}(t) is a periodic function. Optimum receiver structures are derived for three detection cases, namely completely known signals, sinusoids with random phase, and sinusoids with both random amplitude and phase. It is demonstrated that optimum receiver performance can be achieved only if proper synchronization to the noise intensity N_{o}(t) is accomplished. Large performance penalties can be demonstrated when an improperly synchronized receiver is used. Consequently, suboptimum receivers that ignore the noise intensity time variations and therefore require no synchronization, have been considered, and their performance compared to their optimum counterparts. Depending on the type of time-varying noise intensity being considered, results show that performance differences between optimum and suboptimum receivers can be negligible in some cases, and yet can be substantial in other cases. Several examples have been worked out using two different forms for N_{o}(t) and corresponding performance evaluations have been carried out and presented graphically in terms of receiver error probability as a function of signal-to-noise ratio.