Optimal Correlators and Waveforms for Mismatched Detection

We consider the classical Neymann–Pearson hypothesis testing problem of signal detection, where under null ( ${\mathcal{ H}}_{0}$ ), received is white Gaussian noise, and alternative H}}_{1}$ includes also an additional non–Gaussian random signal, which in turn can be viewed as a deterministic waveform plus zero–mean, non-Gaussian noise. However, instead likelihood ratio test detector, might difficult to implement, general, we impose (mismatched) correlation relatively easy characterize optimal correlator weights sense best trade-off between false-alarm error exponent missed-detection exponent. Those depend (non-linearly, general) on underlying . then assume that may free optimized (subject power constraint), jointly with correlator, show both take values small finite set typically no more than two four levels, depending distribution noise component. Finally, outline extension scope wider class detectors are based linear combinations energy signal.