Performance and Joint Design of Co-existing Radar and Communications Systems

Spectrum sharing between radar and communications systems, as a means to address spectrum crunch, is an active research area. This paper considers Complex-valued Additive White Gaussian Noise (C-AWGN) communication systems co-existing with pulsed radar systems, and characterizes performance from two angles: 1) the effect of radar interference on a communications system is examined in terms of average error rate and constellation design, and 2) the effect of communications interference on a radar system is examined in terms of the Receiver Operating Characteristic (ROC). For the first part, we started with a simpler single-carrier communications system interfered by a radar signal, where we investigated the error rate performance and optimized a constellation based on the strength of the radar interference power with respect to the communications power. We then extended the work to a more complicated multi-carrier communications system, in which the error rate expressions and various detectors were derived based on the correlation of the received signal due to the unknown arrival time of the radar signal at the communications receiver. For the last part, we studied the dual problem, where the ROC performance of a radar receiver with an interfering communications signal is analyzed. Two hypothesis testings were derived: 1) the optimal Average Likelihood Ratio Test (ALRT) based on the Bayesian approach that requires prior distributions of unknown parameters, and 2) the suboptimal Generalized Likelihood Ratio Test (GLRT) that estimates the unknown parameters by maximum likelihood.