Two-User Gaussian Interference Channel with Finite Constellation Input and FDMA

TL;DR

This paper investigates how finite constellation inputs and constellation rotation affect the capacity region of the two-user Gaussian interference channel, showing that FDMA cannot reach the capacity with finite constellations and that rotation can enlarge the capacity region.

Contribution

It introduces a metric for approximate optimal rotation angles to maximize capacity and compares FDMA and simultaneous decoding performance with finite constellations.

Findings

FDMA rate curve never touches the CC capacity region with finite constellations.

Rotation can enlarge the CC capacity region for finite constellations.

Simultaneous decoding outperforms FDMA in certain weak interference scenarios with finite constellations.

Abstract

In the two-user Gaussian Strong Interference Channel (GSIC) with finite constellation inputs, it is known that relative rotation between the constellations of the two users enlarges the Constellation Constrained (CC) capacity region. In this paper, a metric for finding the approximate angle of rotation (with negligibly small error) to maximally enlarge the CC capacity for the two-user GSIC is presented. In the case of Gaussian input alphabets with equal powers for both the users and the modulus of both the cross-channel gains being equal to unity, it is known that the FDMA rate curve touches the capacity curve of the GSIC. It is shown that, with unequal powers for both the users also, when the modulus of one of the cross-channel gains being equal to one and the modulus of the other cross-channel gain being greater than or equal to one, the FDMA rate curve touches the capacity curve of the GSIC. On the contrary, it is shown that, under finite constellation inputs, with both the users using the same constellation, the FDMA rate curve strictly lies within (never touches) the enlarged CC capacity region throughout the strong-interference regime. This means that using FDMA it is impossible to go close to the CC capacity. It is well known that for the Gaussian input alphabets, the FDMA inner-bound, at the optimum sum-rate point, is always better than the simultaneous-decoding inner-bound throughout the weak-interference regime. For a portion of the weak interference regime, it is shown that with identical finite constellation inputs for both the users, the simultaneous-decoding inner-bound, enlarged by relative rotation between the constellations, is strictly better than the FDMA inner-bound.