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In this paper we derive an upper bound on the sum-rate gain that dirty-paper coding provides over TDMA for MIMO broadcast channels. We find that the sum-rate capacity (achievable using dirty-paper coding) of the multiple-antenna broadcast channel 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. 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, where M is the number of receive antennas at the base station and K is the number of transmitters.
Jindal et al. (2004) studied this question.