# Joint Design of Overlaid Communication Systems and Pulsed Radars

## TL;DR

This paper explores the joint design of communication and pulsed radar systems sharing the same bandwidth, introducing a new optimization framework and analyzing the trade-offs and performance limits of their coexistence.

## Contribution

It proposes a novel co-design approach using a new figure of merit called the compound rate, with closed-form solutions for optimal transmit policies under different scattering models.

## Key findings

- Optimal transmit policies derived for different scattering models
- The compound rate effectively balances communication and radar performance
- Performance assessment highlights potential and limitations of coexistence

## Abstract

The focus of this paper is on co-existence between a communication system and a pulsed radar sharing the same bandwidth. Based on the fact that the interference generated by the radar onto the communication receiver is intermittent and depends on the density of scattering objects (such as, e.g., targets), we first show that the communication system is equivalent to a set of independent parallel channels, whereby pre-coding on each channel can be introduced as a new degree of freedom. We introduce a new figure of merit, named the {\em compound rate}, which is a convex combination of rates with and without interference, to be optimized under constraints concerning the signal-to-interference-plus-noise ratio (including {\em signal-dependent} interference due to clutter) experienced by the radar and obviously the powers emitted by the two systems: the degrees of freedom are the radar waveform and the afore-mentioned encoding matrix for the communication symbols. We provide closed-form solutions for the optimum transmit policies for both systems under two basic models for the scattering produced by the radar onto the communication receiver, and account for possible correlation of the signal-independent fraction of the interference impinging on the radar. We also discuss the region of the achievable communication rates with and without interference. A thorough performance assessment shows the potentials and the limitations of the proposed co-existing architecture.