Interference Pricing Mechanism for Downlink Multicell Coordinated Beamforming

Abstract

Abstract-We consider the downlink coordinated beamforming problem in a cellular network in which the base stations (BSs) are equipped with multiple antennas and each user is equipped with a single antenna. The BSs cooperate in sharing their local interference information, and they aim to maximize the sum-rate of the users in the network. A decentralized interference pricing beamforming (IPBF) algorithm is proposed to identify the coordinated beamformer, where a BS is penalized according to the interference it creates to its peers. We show that the decentralized pricing mechanism converges to an interference equilibrium, which is a KKT point of the sum-rate maximization problem. The proofs rely on the identification of rank-1 solutions of each BSs' interferencepenalized rate maximization problem. Numerical results show that the proposed iterative mechanism reduces significantly the exchanged information with respect to other state-of-the-art beamforming algorithms with very little sum-rate loss. The version of the algorithm that limits the coordination to a cluster of base stations (IPBF-L) is shown to have very small sum-rate loss with respect to the full coordinated algorithm with much less backhaul information exchange.Index Terms-Base station coordination, beamforming, interference equilibirum, multiple input-multiple output (MIMO), non-convex.

Decentralized Linear Transceiver Design in Multicell MIMO Broadcast Channels

“…The main idea is to manage the ICI received by a user by pricing the interfering BSs. Similar to [18], [31], we define the interference price as the marginal decrease in the user rate due to a marginal increase in the received interference. Mathematically, the MS nk interference price is given as…”

“…For multicell Multiple-Input Single-Output (MISO) BC, the problem was addressed in [16], [18], [19]. In [16], the authors derived the Karush-Kuhn-Tucker (KKT) conditions of the problem and then devised an iterative algorithm to solve them, without the need of resorting to convex optimization methods.…”

“…In [16], the authors derived the Karush-Kuhn-Tucker (KKT) conditions of the problem and then devised an iterative algorithm to solve them, without the need of resorting to convex optimization methods. In [18], an iterative pricing algorithm was proposed based on gametheory, which is guaranteed to converge to an interference equilibrium that corresponds to a KKT point for the original WSR maximization problem. Among all, the global optimum solution is guaranteed only in [19], where the problem was solved using a branch-reduce-and-bound algorithm.…”

“…The first algorithm uses an interference pricing approach, the same as in [18], where each BS maximizes its own utility that is formed by the local users' WSR minus the priced-ICI leakage. In [18], the authors assumed single-antenna users and formulated the problem as a relaxed Semidefinite Programming (SDP), whose solution requires each BS to first obtain the transmit covariance matrices, followed by an operation to guarantee and extract the rank-one transmit beamforming vectors. Different from [18], we consider multi-antenna users and the transmit beamforming matrices are obtained directly by investigating the KKT conditions of the problem.…”

“…In [18], the authors assumed single-antenna users and formulated the problem as a relaxed Semidefinite Programming (SDP), whose solution requires each BS to first obtain the transmit covariance matrices, followed by an operation to guarantee and extract the rank-one transmit beamforming vectors. Different from [18], we consider multi-antenna users and the transmit beamforming matrices are obtained directly by investigating the KKT conditions of the problem. The main ingredient is given by Lemma 1, which makes it possible to solve the transmit beamforming directly from the problem cost function, in contrast to the WSR-WMMSE from [20]- [25].…”