On the Capacity of the AWGN Channel With Additive Radar Interference

This paper investigates the capacity of a communications channel that, in addition to additive white Gaussian noise, also suffers from interference caused by a co-existing radar transmission. The radar interference (of short duty-cycle and of much wider bandwidth than the intended communication signal) is modeled as an additive term whose amplitude is known and constant, but whose phase is independent and identically uniformly distributed at each channel use. The capacity achieving input distribution, under the standard average power constraint, is shown to have independent modulo and phase. The phase is uniformly distributed in <inline-formula> <tex-math notation="LaTeX">$[0, 2\pi ]$ </tex-math></inline-formula>. The modulo is discrete with countably infinite many mass points, but only finitely many in any bounded interval. From numerical evaluations, a proper-complex Gaussian input is seen to perform quite well for weak radar interference. We also show that for very large radar interference, and for signal to noise ratio equal to <inline-formula> <tex-math notation="LaTeX">$ \mathsf {S}$ </tex-math></inline-formula>, the capacity is equal to <inline-formula> <tex-math notation="LaTeX">$({1}/{2})\log (1+ \mathsf {S})$ </tex-math></inline-formula> and a proper-complex Gaussian input achieves it. It is concluded that the presence of the radar interference results in a loss of half of the degrees of freedom compared with an AWGN channel without radar interference.

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