Balancing Egoism and Altruism on Interference Channel: The MIMO Case

Abstract

This paper considers the so-called Multiple-Input-Multiple-Output interference channel (MIMO-IC) which has relevance in applications such as multi-cell coordination in cellular networks as well as spectrum sharing in cognitive radio networks among others. We address the design of precoding (i.e. beamforming) vectors at each sender with the aim of striking a compromise between beamforming gain at the intended receiver (Egoism) and the mitigation of interference created towards other receivers (Altruism). Combining egoistic and altruistic beamforming has been shown previously to be instrumental to optimizing the rates in a Multiple-Input-Single-Output (MISO) interference channel (i.e. where receivers have no interference canceling capability) [1], [2]. Here we explore these game-theoretic concepts in the more general context of MIMO channels and use the framework of Bayesian games [3] which allows us to derive (semi-)distributed precoding techniques. We draw parallels with important existing work on the MIMO-IC, including rate-optimizing and interference-alignment precoding techniques, and show how such techniques may be re-interpreted through a common prism based on balancing egoistic and altruistic beamforming. Our analysis and simulations attest the improvements in terms of complexity and performance.

Multi-Cell MIMO Cooperative Networks: A New Look at Interference

“…In this realm, [106] used an approach based on the first-order condition of the optimization problem, and [107] used a rate profile approach to reach the boundary points of the rate region. In addition, much work has also been done to identify solutions from a competitive (e.g., [108]) or egotistic vs. altruistic points of view [109], [93], [110].…”

Precoder design in user-centric virtual cell networks

“…Proposition 1: Problem (11) is equivalent to (6). Proof: It is obvious that P mmse k in formula (9) is the optimal solution of problem (11). Let f (F k , P k , W k ) be the objective function in problem (11).…”

“…From the implementation point of view, some reasonable assumptions were made to implement the distributed WMMSE algorithm [11]. We assume that local channel information can be available for each user, in other word, each RRH m knows the local channel matrix H m,k to UE k. We also assume that each UE can feedback information (e.g., the updated decoding matrix P k ) to the RRHs.…”

Network Formation Games in Cooperative MIMO Interference Systems

“…A practical suboptimal algorithm for finding the Nash Bargaining (NB) solution in MIMO interference system was designed in [15]. The authors of [16] designed the precoding vectors by combining egostic and altruistic beamforming vectors, and this idea has been shown to achieve Pareto boundary in two-player MISO interference systems [23]. The Pareto boundary for multi-player MIMO interference channels was characterized in [24].…”

“…However, IA-based approach requires global channel state information (CSI), which is hard to acquire in practice. Another avenue to deal with the problem is the gametheoretic approach [10][11][12][13][14][15][16][17]. Scutari et al [10][11] formulated the problem as a noncooperative game, designed an iterative waterfilling (IWF) algorithm that was suitable for arbitrary channel matrix to maximize the mutual information, and analyzed the existence and uniqueness of the Nash Equilibrium (NE).…”