# Ergodic Fading MIMO Dirty Paper and Broadcast Channels: Capacity Bounds and Lattice Strategies

## TL;DR

This paper investigates capacity bounds and lattice strategies for ergodic fading MIMO dirty paper and broadcast channels, demonstrating near-capacity performance with novel coding schemes and insights into fading effects.

## Contribution

It introduces a constant-gap dirty paper coding variant and a lattice coding scheme with channel-independent decision regions, applicable to fading MIMO channels and broadcast scenarios.

## Key findings

- Lattice coding gap to capacity vanishes with more receive antennas at finite SNR.
- Proposed schemes achieve rates close to capacity under Rayleigh fading.
- Insights enable effective transmission strategies for MIMO broadcast channels.

## Abstract

A multiple-input multiple-output (MIMO) version of the dirty paper channel is studied, where the channel input and the dirt experience the same fading process and the fading channel state is known at the receiver (CSIR). This represents settings where signal and interference sources are co-located, such as in the broadcast channel. First, a variant of Costa's dirty paper coding (DPC) is presented, whose achievable rates are within a constant gap to capacity for all signal and dirt powers. Additionally, a lattice coding and decoding scheme is proposed, whose decision regions are independent of the channel realizations. Under Rayleigh fading, the gap to capacity of the lattice coding scheme vanishes with the number of receive antennas, even at finite Signal-to-Noise Ratio (SNR). Thus, although the capacity of the fading dirty paper channel remains unknown, this work shows it is not far from its dirt-free counterpart. The insights from the dirty paper channel directly lead to transmission strategies for the two-user MIMO broadcast channel (BC), where the transmitter emits a superposition of desired and undesired (dirt) signals with respect to each receiver. The performance of the lattice coding scheme is analyzed under different fading dynamics for the two users, showing that high-dimensional lattices achieve rates close to capacity.