# On the Capacity of the AWGN Channel with Additive Radar Interference

## TL;DR

This paper analyzes the capacity of an AWGN channel affected by radar interference, revealing the optimal input distribution and quantifying the capacity loss due to interference.

## Contribution

It characterizes the capacity-achieving input distribution and capacity limits of an AWGN channel with radar interference, a scenario not previously fully understood.

## Key findings

- Optimal input has independent modulo and phase, with phase uniform in [0, 2π].
- Gaussian inputs perform well under weak interference.
- Capacity reduces to half the degrees of freedom in strong interference.

## Abstract

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 $[0,2\pi]$. The modulo is discrete with countably infinitly 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, capacity is equal to $1/2\log (1 + S)$ 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 to an AWGN channel without radar interference.