Optimal Detection in Barrage-Jammed Single-Input Double-Output Systems

We derive the likelihood functions and the maximum likelihood (ML) detectors for single-input double-output (SIDO) communication systems. The received signals are contaminated by a Gaussian noise and a non-Gaussian signal induced by the Gaussian transmissions of a proactive continuous single-antenna jammer over an unknown complex <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$2\times 1$</tex> Gaussian vector channel. We consider cases in which either full channel distribution information (CDI), or partial CDI about the transmitter channel and the jammer channel is available at the receiver. The vector channels considered herein interweave the components of the received signal vector, rendering the derivation of the likelihood function a daunting task for more than two receive antennas. The interweaving of the received signal components prevents the optimal ML detector for unit-norm constellations from reducing to the corresponding Gaussian approximation based detector. This contrasts with the scalar channel case, wherein the two detectors are equivalent for unit-norm constellations. Simulation results show that the difference between the two detectors can be significant, especially when the transmitter and jammer channels have substantial line-of-sight components.