Massive MIMO and small cell are both recognized as the key technologies for the future 5G wireless systems. In this paper, we investigate the problem of user association in a heterogeneous network (HetNet) with massive MIMO and small cells, where the macro base station (BS) is equipped with a massive MIMO and the picocell BS's are equipped with regular MIMOs. We first develop centralized user association algorithms with proven optimality, considering various objectives such as rate maximization, proportional fairness, and joint user association and resource allocation. We then model the massive MIMO HetNet as a repeated game, which leads to distributed user association algorithms with proven convergence to the Nash Equilibrium (NE). We demonstrate the efficacy of these optimal schemes by comparison with several greedy algorithms through simulations. Massive MIMO; small cells; heterogeneous networks (HetNet); user association; unimodularity; game theory. Over the past two decades, Multiple Input Multiple Output (MIMO) has evolved from a pure theory to a practical technology, and has greatly enhanced the wireless system capacity by offering many degrees of freedom (DoF) for wireless transmissions. However, due to the so-called "smartphone" revolution, mobile users are demanding increasingly higher data rates for rich multimedia applications. Existing and future wireless networks are facing the grand challenge of a 1000-time increase in mobile data in the near future [1] . There have been tremendous efforts made aiming to cater for this demand. For example, based on MIMO and OFDM, LTE-Advanced targets at a peak rate of 1 Gbps, but the average rate is still less than 100 Mbps. In the foreseeable future, such rates can hardly be satisfactory for data-hungry wireless users. To boost wireless capacity, two technologies have gained most attention from both industry and academia. The first one is massive MIMO (a.k.a., large-scale MIMO, full-dimension MIMO, or hyper MIMO) [2] , [3] . The idea is to equip a base station (BS) with hundreds, thousands, or even tens of thousands of antennas, hereby providing an unprecedented level of DoF for mobile users. The massive MIMO concept has been successfully demonstrated in recent works [4], [5] . The second technology is small cell. A great benefit of deploying small cells is that the distance of the user-BS link can be effectively reduced, leading to reduced transmit power, higher data rate, enhanced coverage, and better spatial reuse of spectrum. Both massive MIMO and small cells are recognized as key technologies of the future 5G wireless systems [6] . In this paper, we consider a heterogeneous network (HetNet) with massive MIMO and small cells, where the macrocell BS (MBS) is equipped with a massive MIMO and the picocell BS's (PBS) are equipped with regular MIMOs. To fully harvest the benefits promised by these two technologies in an integrated HetNet system, it is critical to investigate the user association problem, i.e., how to assign active users to the BS's such that the system-wide capacity can be maximized and users' experience can be enhanced. There are already several recent works pushing forward in this direction. In [7]-[10], the authors consider the problem of user association in massive MIMO systems operated in the frequency-division duplexing (FDD) mode.
In REF , user association and resource allocation in a massive MIMO HetNet were investigated with the objectives of rate maximization and rate maximization with proportional fairness.
User Association in Massive MIMO HetNets
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Computer Science Mathematics