Abstract-In this correspondence, we compare the achievable throughput for the optimal strategy of dirty paper coding (DPC) to that achieved with suboptimal and lower complexity linear precoding techniques (zero-forcing and block diagonalization). 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. Furthermore, the difference is not affected by asymmetric channel behavior when each user has a different average SNR. Weighted sum rate maximization is also considered. In the process, it is shown that allocating user powers in direct proportion to user weights asymptotically maximizes weighted sum rate.Index Terms-Broadcast channels, channel capacity, multiple-inputmultiple-output (MIMO) systems.

A delay-constrained scheduling problem for point-to-point communication is considered: a packet of B bits must be transmitted by a hard deadline of T slots over a time-varying channel. The transmitter/scheduler must determine how many bits to transmit, or equivalently how much energy to transmit with, during each time slot based on the current channel quality and the number of unserved bits, with the objective of minimizing expected total energy. In order to focus on the fundamental scheduling problem, it is assumed that no other packets are scheduled during this time period and no outage is allowed. Assuming transmission at capacity of the underlying Gaussian noise channel, a closed-form expression for the optimal scheduling policy is obtained for the case T = 2 via dynamic programming; for T > 2, the optimal policy can only be numerically determined. Thus, the focus of the work is on derivation of simple, near-optimal policies based on intuition from the T = 2 solution and the structure of the general problem. The proposed bit-allocation policies consist of a linear combination of a delay-associated term and an opportunistic (channel-aware) term. In addition, a variation of the problem in which the entire packet must be transmitted in a single slot is studied, and a channel-threshold policy is shown to be optimal.

Abstract-This paper studies the symmetric capacity of the MIMO downlink channel, which is defined to be the maximum rate that can be allocated to every receiver in the system. The symmetric capacity represents absolute fairness and is an important metric for slowly fading channels in which users have symmetric rate demands. An efficient and provably convergent algorithm for computing the symmetric capacity is proposed, and it is shown that a simple modification of the algorithm can be used to compute the minimum power required to meet given downlink rate demands. In addition, the difference between the symmetric and sum capacity, termed the fairness penalty, is studied. Exact analytical results for the fairness penalty at high SNR are provided for the 2 user downlink channel, and numerical results are given for channels with more users.

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. Weighted sum rate maximization is also considered, and a similar quantification of the throughput difference between the two strategies is computed. In the process, it is shown that allocating user powers in direct proportion to user weights asymptotically maximizes weighted sum rate.

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