Carrier Cooperation Can Reduce the Transmit Power in Parallel MIMO Broadcast Channels With Zero-Forcing

Even though parallel multiple-input multiple-output (MIMO) broadcast channels are known to be separable from an information theoretic point of view, performing separate encoding and decoding on each of the parallel channels has been shown to be potentially suboptimal in broadcast channels with linear transceivers. In this paper, we show that suboptimality of such a carrier-noncooperative transmission also occurs in broadcast channels with zero-forcing and quality of service constraints if time-sharing is not allowed. The proof is given by constructing a minimal example and identifying a rate tuple that is achievable using carrier-cooperative zero-forcing with a certain sum power but requires a higher sum power with carrier-noncooperative zero-forcing. This observation is of practical relevance since zero-forcing without time-sharing is a popular assumption in the design of low-complexity optimization algorithms.