Maximum Likelihood Detection in the Presence of Non-Gaussian Jamming

We consider a scenario in which a transmitter sends complex symbols drawn from multi-dimensional constellations to a receiver in the presence of a jammer emitting proactively and continuously a zero-mean complex Gaussian signal over an unknown complex Gaussian channel. The complex Gaussian signal transmitted over the unknown complex Gaussian channel induces a non-Gaussian signal at the receiver. For this scenario, we develop the optimal maximum likelihood (ML) detector for cases corresponding to whether the receiver has full channel state information (CSI), full channel distribution information (CDI), or partial CDI about the transmitter channel. The jammer CDI is assumed to be either partially or fully available at the receiver. Using the derived likelihood expressions, we identify cases in which the non-Gaussian signals resulting from the jammer's transmission can be approximated by Gaussian signals without affecting the efficacy of the ML detector. In these cases, we show, analytically and numerically, that the exact and Gaussian approximation detectors are equivalent, but the ML detector based on the Gaussian approximation is computationally superior to its exact counterpart. Furthermore, we identify cases in which the Gaussian approximation ML detector is not equivalent to the exact ML detector. In these case, our numerical results suggest that the advantage of the exact ML detector over the Gaussian approximation one can be significant.