In this paper, we investigate the problem of optimal base station (BS) ON-OFF switching and user association in a heterogeneous network (HetNet) with massive MIMO, with the objective to maximize the system energy efficiency (EE). The joint BS ON-OFF switching and user association problem is formulated as an integer programming problem. We first develop a centralized scheme, in which we relax the integer constraints and employ a series of Lagrangian dual methods that transform the original problem into a standard linear programming (LP) problem. Due to the special structure of the LP, we prove that the optimal solution to the relaxed LP is also feasible and optimal to the original problem. We then propose a distributed scheme by formulating a repeated bidding game for users and BS's, and prove that the game converges to a Nash Equilibrium (NE). Simulation studies demonstrate that the proposed schemes can achieve considerable gains in EE over several benchmark schemes in all the scenarios considered.
@cite_14: Massive MIMO is envisioned as a promising technology for 5G wireless networks due to its high potential to improve both spectral and energy efficiency. Although the massive MIMO system is based on innovations in the physical layer, the upper layer techniques also play important roles in harvesting the performance gains of massive MIMO. In this article, we begin with an analysis of the benefits and challenges of massive MIMO systems. We then investigate the multi-layer techniques for incorporating massive MIMO in several important network deployment scenarios. We conclude this article with a discussion of open and potential problems for future research.
@cite_27: In this paper we study the performance of cellular networks when their base stations have an unlimited number of antennas. In previous work, the asymptotic behavior of the signal to interference plus nose ratio (SINR) was obtained. We revisit these results by deriving the rigorous expression for the SINR of both downlink and uplink in the scenario of infinite number of antennas. We show that the contamination of the channel estimates happens whenever a pilot sequence is received at a base station simultaneously with non-orthogonal signals coming from other users. We propose a method to avoid such simultaneous transmissions from adjacent cells, thus significantly decreasing interference. We also investigate the effects of power allocation in this interference-limited scenario, and show that it results in gains of over 15dB in the signal to interference ratio for the scenario simulated here. The combination of these two techniques results in rate gains of about 18 times in our simulations.
@cite_31: A cellular base station serves a multiplicity of single-antenna terminals over the same time-frequency interval. Time-division duplex operation combined with reverse-link pilots enables the base station to estimate the reciprocal forward- and reverse-link channels. The conjugate-transpose of the channel estimates are used as a linear precoder and combiner respectively on the forward and reverse links. Propagation, unknown to both terminals and base station, comprises fast fading, log-normal shadow fading, and geometric attenuation. In the limit of an infinite number of antennas a complete multi-cellular analysis, which accounts for inter-cellular interference and the overhead and errors associated with channel-state information, yields a number of mathematically exact conclusions and points to a desirable direction towards which cellular wireless could evolve. In particular the effects of uncorrelated noise and fast fading vanish, throughput and the number of terminals are independent of the size of the cells, spectral efficiency is independent of bandwidth, and the required transmitted energy per bit vanishes. The only remaining impairment is inter-cellular interference caused by re-use of the pilot sequences in other cells (pilot contamination) which does not vanish with unlimited number of antennas.
@cite_16: Massive multiple-input–multiple-output (MIMO) and small cell are both recognized as key technologies for the future fifth-generation 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 BSs 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 develop a repeated game model, which leads to distributed user association algorithms with proven convergence to the Nash equilibrium. We demonstrate the efficacy of these optimal schemes by comparing with several greedy algorithms through simulations.
@cite_20: Multiple-input multiple-output (MIMO) technology is maturing and is being incorporated into emerging wireless broadband standards like long-term evolution (LTE) [1]. For example, the LTE standard allows for up to eight antenna ports at the base station. Basically, the more antennas the transmitter receiver is equipped with, and the more degrees of freedom that the propagation channel can provide, the better the performance in terms of data rate or link reliability. More precisely, on a quasi static channel where a code word spans across only one time and frequency coherence interval, the reliability of a point-to-point MIMO link scales according to Prob(link outage) SNR-ntnr where nt and nr are the numbers of transmit and receive antennas, respectively, and signal-to-noise ratio is denoted by SNR. On a channel that varies rapidly as a function of time and frequency, and where circumstances permit coding across many channel coherence intervals, the achievable rate scales as min(nt, nr) log(1 + SNR). The gains in multiuser systems are even more impressive, because such systems offer the possibility to transmit simultaneously to several users and the flexibility to select what users to schedule for reception at any given point in time [2].
As key technologies for 5G network, massive MIMO and small cells have been extensively studied in prior works. The fundamental PHY layer techniques of massive MIMO were introduced in @cite_31 @cite_20 . Beyond the PHY, upper layer technologies in a wireless network with massive MIMO are also considered, such as @cite_14 @cite_16 @cite_27 . @cite_16 , user association and resource allocation in a massive MIMO HetNet were investigated with the objectives of rate maximization and rate maximization with proportional fairness. @cite_27 , a time-shift frame structure was proposed to mitigate inter-cell interference caused by pilot contamination in a multi-cell massive MIMO system. Since neighboring cells transmit pilots at different time instants, the inter-cell interference can be well mitigated.