We consider the cell-free massive multiple-input multiple-output (MIMO) downlink, where a very large number of distributed multiple-antenna access points (APs) serve many single-antenna users in the same time-frequency resource. A simple (distributed) conjugate beamforming scheme is applied at each AP via the use of local channel state information (CSI). This CSI is acquired through time-division duplex operation and the reception of uplink training signals transmitted by the users. We derive a closed-form expression for the spectral efficiency taking into account the effects of channel estimation errors and power control. This closed-form result enables us to analyze the effects of backhaul power consumption, the number of APs, and the number of antennas per AP on the total energy efficiency, as well as, to design an optimal power allocation algorithm. The optimal power allocation algorithm aims at maximizing the total energy efficiency, subject to a per-user spectral efficiency constraint and a per-AP power constraint. Compared with the equal power control, our proposed power allocation scheme can double the total energy efficiency. Furthermore, we propose AP selections schemes, in which each user chooses a subset of APs, to reduce the power consumption caused by the backhaul links. With our proposed AP selection schemes, the total energy efficiency increases significantly, especially for large numbers of APs. Moreover, under a requirement of good quality-of-service for all users, cell-free massive MIMO outperforms the colocated counterpart in terms of energy efficiency.

Abstract-We investigate the spectral efficiency of full-duplex small cell wireless systems, in which a full-duplex capable base station (BS) is designed to send/receive data to/from multiple halfduplex users on the same system resources. The major hurdle for designing such systems is due to the self-interference at the BS and co-channel interference among users. Hence, we consider a joint beamformer design to maximize the spectral efficiency subject to certain power constraints. The design problem is first formulated as a rank-constrained optimization one, and the rank relaxation method is then applied. However the relaxed problem is still nonconvex, and thus optimal solutions are hard to find. Herein, we propose two provably convergent algorithms to obtain suboptimal solutions. Based on the concept of the Frank-Wolfe algorithm, we approximate the design problem by a determinant maximization program in each iteration of the first algorithm. The second method is built upon the sequential parametric convex approximation method, which allows us to transform the relaxed problem into a semidefinite program in each iteration. Extensive numerical experiments under small cell setups illustrate that the full-duplex system with the proposed algorithms can achieve a large gain over the half-duplex one.Index Terms-Full-duplex, self-interference, transmit beamforming, D.C. program, semidefinite programming.

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This paper studies beamforming techniques for energy efficiency maximization (EEmax) in multiuser multiple-input single-output (MISO) downlink system. For this challenging nonconvex problem, we first derive an optimal solution using branch-and-reduce-and-bound (BRB) approach. We also propose two low-complexity approximate designs. The first one uses the well-known zero-forcing beamforming (ZFBF) to eliminate inter-user interference so that the EEmax problem reduces to a concave-convex fractional program. Particularly, the problem is then efficiently solved by closed-form expressions in combination with the Dinkelbach's approach. In the second design, we aim at finding a stationary point using the sequential convex approximation (SCA) method. By proper transformations, we arrive at a fast converging iterative algorithm where a convex program is solved in each iteration. We further show that the problem in each iteration can also be approximated as a second-order cone program (SOCP), allowing for exploiting computationally efficient state-of-the-art SOCP solvers. Numerical experiments demonstrate that the second design converges quickly and achieves a near-optimal performance. To further increase the energy efficiency, we also consider the joint beamforming and antenna selection (JBAS) problem for which two designs are proposed. In the first approach we capitalize on the perspective reformulation in combination with continuous relaxation to solve the JBAS problem. In the second one, sparsity-inducing regularization is introduced to approximate the JBAS problem, which is then solved by the SCA method.Numerical results show that joint beamforming and antenna selection offers significant energy efficiency improvement for large numbers of transmit antennas. Index TermsMISO broadcast channel, energy efficiency, Dinkelbach method, mixed-integer programming, sequential convex approximation, second-order cone programming, fractional programming, antenna selection. 4 and mean squared error minimization [6]. Huang et al. [17] aimed at finding the Pareto boundary in MISO interference channel. Apart from the Dinkelbach's approach, [18] considered EEmax with userspecific signal-to-interference-plus-noise ratio (SINR) constraints by proposing ZFBF power allocation and zero-gradient based joint beamforming and power allocation strategy in multi-user MIMO downlink 1053-587X (c)

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