We study the achievable capacity regions of full-duplex links in the single- and multi-channel cases (in the latter case, the channels are assumed to be orthogonal -- e.g., OFDM). We present analytical results that characterize the uplink and downlink capacity region and efficient algorithms for computing rate pairs at the region's boundary. We also provide near-optimal and heuristic algorithms that "convexify" the capacity region when it is not convex. The convexified region corresponds to a combination of a few full-duplex rates (i.e., to time sharing between different operation modes). The algorithms can be used for theoretical characterization of the capacity region as well as for resource (time, power, and channel) allocation with the objective of maximizing the sum of the rates when one of them (uplink or downlink) must be guaranteed (e.g., due to QoS considerations). We numerically illustrate the capacity regions and the rate gains (compared to time division duplex) for various channel and cancellation scenarios. The analytical results provide insights into the properties of the full-duplex capacity region and are essential for future development of scheduling, channel allocation, and power control algorithms.
The capacity region for an FD MIMO two-way relay channel was studied in @cite_18 as a joint problem of beamforming and power allocation. For a fixed beamforming, the problem reduces to determining a single channel FD capacity region. Yet, the joint problem is significantly different from the problems considered here. The FD capacity region for multiple channels was considered in @cite_20 . While @cite_20 considers both fixed and general power allocation for determining an FD capacity region, the analytical results are obtained only for the fixed power case and the non-convex problem of general power allocation was addressed heuristically. Specifically, for the fixed power case, our proof of Lemma is more accurate than the proof of Theorem 3 in @cite_20 (see the proof of Lemma @cite_6 ).
@cite_18 @cite_6 @cite_20
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We provide an overview of the extensive results on the Shannon capacity of single-user and multiuser multiple-input multiple-output (MIMO) channels. Although enormous capacity gains have been predicted for such channels, these predictions are based on somewhat unrealistic assumptions about the underlying time-varying channel model and how well it can be tracked at the receiver, as well as at the transmitter. More realistic assumptions can dramatically impact the potential capacity gains of MIMO techniques. For time-varying MIMO channels there are multiple Shannon theoretic capacity definitions and, for each definition, different correlation models and channel information assumptions that we consider. We first provide a comprehensive summary of ergodic and capacity versus outage results for single-user MIMO channels. These results indicate that the capacity gain obtained from multiple antennas heavily depends on the available channel information at either the receiver or transmitter, the channel signal-to-noise ratio, and the correlation between the channel gains on each antenna element. We then focus attention on the capacity region of the multiple-access channels (MACs) and the largest known achievable rate region for the broadcast channel. In contrast to single-user MIMO channels, capacity results for these multiuser MIMO channels are quite difficult to obtain, even for constant channels. We summarize results for the MIMO broadcast and MAC for channels that are either constant or fading with perfect instantaneous knowledge of the antenna gains at both transmitter(s) and receiver(s). We show that the capacity region of the MIMO multiple access and the largest known achievable rate region (called the dirty-paper region) for the MIMO broadcast channel are intimately related via a duality transformation. This transformation facilitates finding the transmission strategies that achieve a point on the boundary of the MIMO MAC capacity region in terms of the transmission strategies of the MIMO broadcast dirty-paper region and vice-versa. Finally, we discuss capacity results for multicell MIMO channels with base station cooperation. The base stations then act as a spatially diverse antenna array and transmission strategies that exploit this structure exhibit significant capacity gains. This section also provides a brief discussion of system level issues associated with MIMO cellular. Open problems in this field abound and are discussed throughout the paper. We study the capacity of multiple-input multiple- output (MIMO) relay channels. We first consider the Gaussian MIMO relay channel with fixed channel conditions, and derive upper bounds and lower bounds that can be obtained numerically by convex programming. We present algorithms to compute the bounds. Next, we generalize the study to the Rayleigh fading case. We find an upper bound and a lower bound on the ergodic capacity. It is somewhat surprising that the upper bound can meet the lower bound under certain regularity conditions (not necessarily degradedness), and therefore the capacity can be characterized exactly; previously this has been proven only for the degraded Gaussian relay channel. We investigate sufficient conditions for achieving the ergodic capacity; and in particular, for the case where all nodes have the same number of antennas, the capacity can be achieved under certain signal-to-noise ratio (SNR) conditions. Numerical results are also provided to illustrate the bounds on the ergodic capacity of the MIMO relay channel over Rayleigh fading. Finally, we present a potential application of the MIMO relay channel for cooperative communications in ad hoc networks. Recently, the capacity region of a multiple-input multiple-output (MIMO) Gaussian broadcast channel, with Gaussian codebooks and known-interference cancellation through dirty paper coding, was shown to equal the union of the capacity regions of a collection of MIMO multiple-access channels. We use this duality result to evaluate the system capacity achievable in a cellular wireless network with multiple antennas at the base station and multiple antennas at each terminal. Some fundamental properties of the rate region are exhibited and algorithms for determining the optimal weighted rate sum and the optimal covariance matrices for achieving a given rate vector on the boundary of the rate region are presented. These algorithms are then used in a simulation study to determine potential capacity enhancements to a cellular system through known-interference cancellation. We study both the circuit data scenario in which each user requires a constant data rate in every frame and the packet data scenario in which users can be assigned a variable rate in each frame so as to maximize the long-term average throughput. In the case of circuit data, the outage probability as a function of the number of active users served at a given rate is determined through simulations. For the packet data case, long-term average throughputs that can be achieved using the proportionally fair scheduling algorithm are determined. We generalize the zero-forcing beamforming technique to the multiple receive antennas case and use this as the baseline for the packet data throughput evaluation. Large multiple-input multiple-output (MIMO) networks promise high energy efficiency, i.e., much less power is required to achieve the same capacity compared to the conventional MIMO networks if perfect channel state information (CSI) is available at the transmitter. However, in such networks, huge overhead is required to obtain full CSI especially for Frequency-Division Duplex (FDD) systems. To reduce overhead, we propose a downlink antenna selection scheme, which selects S antennas from M > S transmit antennas based on the large scale fading to serve K ≤ S users in large distributed MIMO networks employing regularized zero-forcing (RZF) precoding. In particular, we study the joint optimization of antenna selection, regularization factor, and power allocation to maximize the average weighted sum-rate. This is a mixed combinatorial and non-convex problem whose objective and constraints have no closed-form expressions. We apply random matrix theory to derive asymptotically accurate expressions for the objective and constraints. As such, the joint optimization problem is decomposed into subproblems, each of which is solved by an efficient algorithm. In addition, we derive structural solutions for some special cases and show that the capacity of very large distributed MIMO networks scales as O(KlogM) when M→∞ with K, S fixed. Simulations show that the proposed scheme achieves significant performance gain over various baselines.