Dirty-Paper Coding Versus TDMA for MIMO Broadcast Channels

TLDR

The study compares the capacity of dirty‑paper coding to that of time‑division multiple access for a multiple‑antenna Gaussian broadcast channel. The authors compare DPC and TDMA capacities for a MIMO Gaussian broadcast channel and investigate the tightness of the resulting min(M,K) bound in a time‑varying Rayleigh‑fading channel with perfect CSIT/CSIR, showing that the dirty‑paper gain is upper‑bounded by the transmit‑to‑receive antenna ratio. Sum‑rate capacity achievable with dirty‑paper coding is bounded above by min(M,K) times the TDMA sum‑rate, a bound that holds for any channel matrix and SNR, and in time‑varying Rayleigh fading with perfect CSIT/CSIR the dirty‑paper gain is further limited by the transmit‑to‑receive antenna ratio, while the same min(M,K) bound limits the sum‑rate advantage of successive decoding over TDMA in the uplink.

Abstract

We compare the capacity of dirty-paper coding (DPC) to that of time-division multiple access (TDMA) for a multiple-antenna (multiple-input multiple-output (MIMO)) Gaussian broadcast channel (BC). We find that the sum-rate capacity (achievable using DPC) of the multiple-antenna BC is at most min(M,K) times the largest single-user capacity (i.e., the TDMA sum-rate) in the system, where M is the number of transmit antennas and K is the number of receivers. This result is independent of the number of receive antennas and the channel gain matrix, and is valid at all signal-to-noise ratios (SNRs). We investigate the tightness of this bound in a time-varying channel (assuming perfect channel knowledge at receivers and transmitters) where the channel experiences uncorrelated Rayleigh fading and in some situations we find that the dirty paper gain is upper-bounded by the ratio of transmit-to-receive antennas. We also show that min(M,K) upper-bounds the sum-rate gain of successive decoding over TDMA for the uplink channel, where M is the number of receive antennas at the base station and K is the number of transmitters.