Optimizing the MIMO Cellular Downlink: Multiplexing, Diversity, or Interference Nulling?

Abstract

A base-station (BS) equipped with multiple antennas can use its spatial dimensions in three different ways: (1) to serve multiple users, thereby achieving a multiplexing gain, (2) to provide spatial diversity in order to improve user rates and (3) to null interference in neighboring cells. This paper answers the following question: What is the optimal balance between these three competing benefits? We answer this question in the context of the downlink of a cellular network, where multi-antenna BSs serve multiple single-antenna users using zero-forcing beamforming with equal power assignment, while nulling interference at a subset of out-of-cell users. Any remaining spatial dimensions provide transmit diversity for the scheduled users. Utilizing tools from stochastic geometry, we show that, surprisingly, to maximize the per-BS ergodic sum rate, with an optimal allocation of spatial resources, interference nulling does not provide a tangible benefit. The strategy of avoiding inter-cell interference nulling, reserving some fraction of spatial resources for multiplexing and using the rest to provide diversity, is already close-to-optimal in terms of the sum-rate. However, interference nulling does bring significant benefit to cell-edge users, particularly when adopting a rangeadaptive nulling strategy where the size of the cooperating BS cluster is increased for cell-edge users.

Robust adaptive beamforming using convex optimization

“…We initialize the beamforming weights with an equal-power matched-filtering solution; in other words, the power for each user is set to Pmax K BS similar to the schemes proposed in [4], [6]. Figure 1 illustrates the convergence of the network SLqP rate for a random set of channel realizations.…”

“…The block-concavity of the auxiliary objective now enables us to derive an efficient algorithm to iteratively optimize the original objective. Observe that when V is fixed, an optimal choice of auxiliary variable X is given by (6). Crucially, as with the power control problem, since the SLqP utility function is not strictly concave, there may be infinitely many optimal choices of X that optimize the auxiliary objective; however, the choice in (6) maintains equivalence with the original objective as explained in Lemma 1.…”

“…Using tools from probability theory and stochastic geometry, closed-form expressions for user rates are derived, and the parameters which improve throughput at a desired percentile are determined empirically. Numerous prior works have adopted this approach to improve 10 th -percentile rate [6], [15] and 5 th -percentile rate [10]. A more general framework for stochastically optimizing cell-edge rates was also presented in [16].…”

SLINR-Based Downlink Optimization in MU-MIMO Networks

“…We now introduce the SLINR-based pseudorates as Rkb = W B log 1 + γLI kb . We optimize these as a proxy for the rate maximization problem, with the understanding that system performance must ultimately be evaluated via the real (SINR-based) rates using (2). Accordingly, the weighted sum-pseudorate maximization problem can be written like the original decentralized formulation (12), except that the rates in the objective are replaced by pseudorates, i.e., for BS b:…”

“…Since each active link causes interference to other links, it is essential for base stations (BSs) to consider the impacts their transmissions have on the performance of the network as a whole. In this regard, a key technique proposed for multi-cell multiuser multiple input multiple output (MU-MIMO) wireless networks is beamforming in the downlink [1], [2], [3], [4], which coordinates transmissions between BSs to maximize a chosen function of the SINR at scheduled users, e.g., our choice of maximizing the weighted sum-rate (WSR).…”