Recent results have shown the benefits of widely linear precoding (WLP) in the MIMO interference channel (MIMO IC) assuming that all transmitters can follow the same strategy. Motivated by a transitional scenario where legacy linear transmitters coexist with widely linear ones, this work investigates the general K-user MIMO IC in a heterogeneous (linear and widely linear) transmitter deployment. In particular, we address the maximization of the weighted sum-rate (WSR) for (widely) linear transmit filters design through the use of the complexvalued formulation. Since the maximum WSR problem is nonconvex, and thus difficult to be solved, we formulate an equivalent minimum weighted mean square error problem that allows deriving closed-form expressions for (widely) linear transceivers. Then an iterative procedure is proposed, which is proven to reach a stationary point of the maximum WSR problem. Simulations show that the proposed procedure allows increasing the sumrate as compared to coordinated linear transceiver schemes. The gains are larger and significant in two different non-exclusive conditions: as the interference level increases or when the number of antennas is low. Index Terms-MIMO interference channel, heterogeneous transceivers, improper Gaussian signaling, widely linear precoding, widely linear estimation, weighted sum-rate maximization. I. INTRODUCTION T HE K-user multiple-input multiple-output interference channel (MIMO IC) is a generic model for cellular communication systems that consists of K transmitter-receiver pairs, each equipped with multiple antennas. All transmitters wish to send independent streams to its intended receiver simultaneously, such that interference is generated towards unintended receivers. Unfortunately, the optimal transmit/receive strategy with linear filters that maximizes the weighted sumrate (WSR) of the system is not known. From an optimization theory perspective, the problem is non-convex and NP-hard even in the single-antenna case [1]. Even so, there are two main approaches to find a stationary point to the maximum WSR problem. On the one hand, strategies in [2][3] (and references therein) focus on the coordination among transmitters based on the interference-cost concept, where each transmitter
Abstract-Recent results have elucidated the benefits of using improper Gaussian signaling (IGS) as compared to conventional proper Gaussian signaling (PGS) in terms of achievable rate for interference-limited conditions. This paper exploits majorization theory tools to formally quantify the gains of IGS along with widely linear transceivers for MIMO systems in interferencelimited scenarios. The MIMO point-to-point channel with interference (P2P-I) is analyzed, assuming that received interference can be either proper or improper, and we demonstrate that the use of the optimal IGS when received interference is improper strictly outperforms (in terms of achievable rate and mean square error) the use of the optimal PGS when interference is proper. Then, these results are extended to two practical situations. First, the MIMO Z-interference channel (Z-IC) is investigated, where a trade-off arises: with IGS we could increase the achievable rate of the interfered user while gracefully degrading the rate of the non-interfered user. Second, these concepts are applied to a two-tier heterogeneous cellular network (HCN) where macrocells and smallcells coexist and multiple MIMO Z-IC appear.Index Terms-Improper Gaussian signaling, widely linear processing, majorization theory, MIMO point-to-point channel with interference, MIMO Z-interference channel, heterogeneous cellular networks.
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