1536-1276 (c) 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TWC.2017.2670540, IEEE Transactions on Wireless Communications IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 1 Parametrization and Applications of Precoding Reuse and Downlink Interference Alignment Eduardo Casta˜ neda, Member, IEEE, Daniel Castanheira, Member, IEEE, Ad˜ ao Silva, Member, IEEE, and At´ ılio Gameiro Abstract—In this paper, we consider the downlink communication of an arbitrary number of transmitters over broadcast interference channels. In order to suppress interference we investigate a network-level linear precod- ing scheme dubbed precoding reuse. Such a technique is leveraged on the interference alignment (IA) princi- ple, where the undesired signals overlap in a reduced- dimension subspace at the receivers. Precoding reuse relies on two cascaded precoders to suppress intra- and inter-cell interference and requires feedback only within a cell. We designed precoding reuse schemes for which interference suppression can be attained in a coordinated or uncoordi- nated fashion over a fixed number of quasi-static channel uses. We provide expressions for the parametrization of the precoders and investigate the advantages, limitations, suit- able scenarios and applications of the proposed IA scheme. Finally, we pointed out open problems where the proposed IA scheme and parametrization can be implemented with little effort, demanding minimum changes to an existing cellular system supporting multi-user MIMO. Index Terms—Interference alignment, Kronecker prod- uct, precoding reuse, spatial multiplexing. I. I NTRODUCTION I NTERFERENCE management is a major challenge in wireless networks and complementary approaches are necessary to increase the robustness of conventional methods that allocate resources at the network-level, e.g., frequency reuse, sectoring, spread spectrum, co- operative transmission, or time/frequency multiplexing [1]. Contemporary interference management techniques for wireless communications make use of multiple-input multiple-output (MIMO), a key technology for enabling significant throughput and link range gains by making use of spatial signal spaces without an additional in- crease in bandwidth or transmit power [2]. However, in cellular networks the MIMO processing gains are This work was supported by the Portuguese Fundac ¸˜ ao para a Ciˆ encia e Tecnologia (FCT) PURE-5GNET (UID/EEA/50008/2013) project. The authors are with the Department of Electronics, Telecommu- nications and Informatics at the Aveiro University, and the Insti- tuto de Telecomunicac ¸˜ oes (IT), Aveiro, 3810-193, Portugal (e-mail: {ecastaneda, dcastanheira, asilva}@av.it.pt; amg@ua.pt). limited by inter-cell interference (ICI) as the operational signal to noise ratio (SNR) increases [1]. In scenarios with multiple transmitters, different approaches for ICI coordination rely on cooperative transmission, which can be performed according to the network configuration, e.g., adaptive transmission based on knowledge of the channel state information (CSI) or predefined settings of the network parameters (designed off-line), cf. [3]. Recent multi-cell coordinated beamforming schemes at- tempt to suppress inter-user interference (IUI) and ICI simultaneously with minimum coordination or control signaling between transmitters. This kind of hierarchical precoders rely on instantaneous or statistical CSI, whose objective is to maximize the system capacity [2], [3], [4]. The interference is canceled through the sequential construction of outer and inner precoders that suppress ICI and IUI, respectively. The ICI cancellation is attained by overlapping interference subspaces at the receivers, whilst the IUI is canceled at the transmitters using linear precoding and local CSI, e.g., [5], [6]. Although these works efficiently enhance system performance, they re- quire the exchange of control parameters through the backhaul network in order to fully mitigate interference. Other hierarchical precoding schemes, constructed upon the interference alignment (IA) principles [7], can operate without message exchange between transmitters, e.g., [8], [9]. In IA the signaling dimensions provided by MIMO (or any other orthogonalizable resource) can be used by the transmitters in such a way that the interference collapses into a reduced subspace at the receivers. Several IA schemes have been developed using channel extensions, where additional dimensions can be attained by signaling over different frequency bands [10], [11], [12]. Conventional IA schemes (cf. [7]) require global CSI knowledge, in addition to other requirements in practical scenarios, e.g., synchronization and limited backhaul/feedback rates. Nonetheless, distributed IA schemes have been de- veloped to address the issues described above for the downlink of cellular networks under different CSI condi- tions at the transmitters. The authors in [8] extended the concept of IA to non-cooperative multi-cell scenarios,