0090-6778 (c) 2018 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/TCOMM.2018.2821138, IEEE Transactions on Communications 1 Social-Aware User Cooperation in Full-Duplex and Half-Duplex Multi-Antenna Systems Mojtaba Vaezi, Hazer Inaltekin, Wonjae Shin, H. Vincent Poor, and Junshan Zhang Abstract—Social and communications networks interact with each other in multifaceted ways, yet these interactions are often considered to be secondary in throughput, privacy and security analysis for communications networks. In this paper, full-duplex (FD) and half-duplex (HD) multi-antenna cooperative communi- cation systems are studied by taking both physical links and social connections into account. An optimal beamformer for maximizing communication rate in the proposed socio-technological setting aims to balance between the direct link and the cooperating link as well as respecting the trust degree between the users. The resulting optimization problems are nontrivial to solve, even numerically, as they are not convex. The complexity of the problems is significantly reduced by showing that a linear combination of the direct and cooperating links’ channel vectors maximizes the achievable rate. Then, a computationally efficient numerical solution is used to maximize the rates both in the FD and HD modes. Numerical results demonstrate that significant gains in communication rates can be obtained with the proposed optimal beamforming design. Index Terms—Mobile/social networks, MIMO beamforming, cooperative communication, full-duplex, half-duplex. I. I NTRODUCTION A salient characteristic of mobile data networks is the dom- inant operating mode of one person behind each device, which differentiates them from other technological networks such as sensor networks. A direct consequence of this feature of mo- bile data networks is the existence of both physical coupling between mobile devices through shared communication re- sources such as wireless spectrum, and virtual coupling among the users behind these devices in the social domain. These virtual ties, in many ways, shape the data traffic flows and quality-of-service (QoS) requirements in the physical domain. Social interactions could be positive (representing friendship) or negative (representing antagonism), which yield non-trivial impact on users’ decision-making processes (e.g., in terms of cooperation) for data transmission and reception. We refer to this two-layered network structure as a mobile/social network. A growing number of recent works [2]–[9], have studied the integration of mobile data networks with social networks in a variety of settings. In [2], a game theoretic framework called social group utility maximization is developed to maximize a This research was supported by the U.S. Army Research Office under Grant W911NF-16-1-0448. This paper was presented in part at IEEE Globecom, in Singapore, 2017 [1]. Mojtaba Vaezi, Hazer Inaltekin, Wonjae Shin, and H. Vincent Poor are with the Department of Electrical Engineering, Princeton University, Princeton, NJ 08540, USA (e-mail: {mvaezi, hinaltek, wonjae.shin, poor}@princeton.edu). Wonjae Shin is also with the Department of Electronics Engineering, Pusan National University, Pusan 46241, South Korea. Junshan Zhang is with the School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, AZ 85287, USA (e-mail:junshan.zhang@asu.edu). weighted sum of the individual utilities rather than a totally selfish utility. In [3]–[6], social community-aware resource allocation is studied for device-to-device (D2D) networks. A social-aware peer discovery scheme for D2D systems is pro- posed in [7]. It exploits social network characteristics to assist ad hoc peer discovery and enhance data transmission perfor- mance. In [8], throughput of an ad hoc networks is maximized by adaptively utilizing different transmission schemes via a social-aware mechanism. Social-aware transmission strategies can be also employed to enhance transmission security [9]. Most of the above papers develop communication strategies based on single-antenna nodes. In a recent study, Ryu et al. [10] proposed the use of social connections for beamforming in a cooperative communication system with a single-antenna relay. This scheme uses trustworthiness between nodes to design beamforming for efficient data relaying. It is proved that a linear combination of channel vectors makes an optimal beamformer to maximize expected achievable rate. To find a closed-form solution for the optimal weights of the linear combination, a high signal-to-noise ratio (SNR) approximation is used which explicitly shows the effect of trust degrees on the beamforming design. We exploit the concept of trust degree for user cooperation in multi-antenna cooperative systems, both in the full-duplex (FD) and half-duplex (HD) settings, in this paper. We first improve the achievable rate of [10] and extend it to the case where the relay has multiple antennas. The rate improvement is based on two observations. First, we show that maximum trust degree does not always result in the best rate performance. Thus, we consider optimization over trust degree as well as the beamforming vectors at the source and relay nodes. Second, unlike [10], our design is for the exact achievable rate, not just in the high SNR regime. We propose a computationally practical numerical solution that achieves optimal beamformer performance. The resulting beamformer improves the rate performance when compared with the closed-form solution of the approximated rate given in [10]. Another important contribution of the current paper is the extension of the trust degree based beamforming design to the case in which the relay has an arbitrary number of antennas. In fact, the proposed beamforming is developed for multi-antenna relays which can be applied to single-antenna relays as well. Lastly, while existing social-aware strategies are commonly developed based on the FD relays, we introduce the use of relays in the more practical HD mode. We consider the HD relay both with equal and unequal receive/transmission periods. Optimizing the cooperative achievable rate via HD relays is in general