# On Cooperation and Interference in the Weak Interference Regime (Full Version with Detailed Proofs)

## TL;DR

This paper investigates how cooperation via relaying can improve the sum-rate capacity and degrees-of-freedom in weak interference wireless channels with phase fading, demonstrating gains under certain conditions.

## Contribution

It characterizes the sum-rate capacity and GDoF for the ergodic phase fading Z-ICR in the weak interference regime, revealing conditions where relaying enhances performance.

## Key findings

- Relaying can strictly increase sum-rate capacity.
- Relaying can strictly increase maximal GDoF.
- Treating interference as noise is optimal under certain conditions.

## Abstract

Handling interference is one of the main challenges in the design of wireless networks. In this paper we study the application of cooperation for interference management in the weak interference (WI) regime, focusing on the Z-interference channel with a causal relay (Z-ICR), when the channel coefficients are subject to ergodic phase fading, all transmission powers are finite, and the relay is full-duplex. In order to provide a comprehensive understanding of the benefits of cooperation in the WI regime, we characterize, for the first time, two major performance measures for the ergodic phase fading Z-ICR in the WI regime: The sum-rate capacity and the maximal generalized degrees-of-freedom (GDoF). In the capacity analysis, we obtain conditions on the channel coefficients, subject to which the sum-rate capacity of the ergodic phase fading Z-ICR is achieved by treating interference as noise at each receiver, and explicitly state the corresponding sum-rate capacity. In the GDoF analysis, we derive conditions on the exponents of the magnitudes of the channel coefficients, under which treating interference as noise achieves the maximal GDoF, which is explicitly characterized as well. It is shown that under certain conditions on the channel coefficients, {\em relaying strictly increases} both the sum-rate capacity and the maximal GDoF of the ergodic phase fading Z-interference channel in the WI regime. Our results demonstrate {\em for the first time} the gains from relaying in the presence of interference, {\em when interference is weak and the relay power is finite}, both in increasing the sum-rate capacity and in increasing the maximal GDoF, compared to the channel without a relay.