High SNR Analysis for MIMO Broadcast Channels: Dirty Paper Coding vs. Linear Precoding

TL;DR

This paper analytically compares the throughput of dirty paper coding and linear precoding in MIMO broadcast channels at high SNR, revealing the throughput gap and optimal power allocation strategies.

Contribution

It provides an analytical expression for the sum rate difference at high SNR and demonstrates optimal power allocation for maximizing weighted sum rate.

Findings

Sum rate difference is accurately characterized at high SNR.

Power allocation proportional to user weights maximizes weighted sum rate.

Asymptotic analysis remains valid at moderate SNR levels.

Abstract

We study the MIMO broadcast channel and compare the achievable throughput for the optimal strategy of dirty paper coding to that achieved with sub-optimal and lower complexity linear precoding (e.g., zero-forcing and block diagonalization) transmission. Both strategies utilize all available spatial dimensions and therefore have the same multiplexing gain, but an absolute difference in terms of throughput does exist. The sum rate difference between the two strategies is analytically computed at asymptotically high SNR, and it is seen that this asymptotic statistic provides an accurate characterization at even moderate SNR levels. Furthermore, the difference is not affected by asymmetric channel behavior when each user a has different average SNR. Weighted sum rate maximization is also considered, and a similar quantification of the throughput difference between the two strategies is performed. In the process, it is shown that allocating user powers in direct proportion to user weights asymptotically maximizes weighted sum rate. For multiple antenna users, uniform power allocation across the receive antennas is applied after distributing power proportional to the user weight.