Scaling up MIMO: Opportunities and Challenges with Very Large Arrays

This paper surveys recent advances in the area of very large MIMO systems. With very large MIMO, we think of systems that use antenna arrays with an order of magnitude more elements than in systems being built today, say a hundred antennas or more. Very large MIMO entails an unprecedented number of antennas simultaneously serving a much smaller number of terminals. The disparity in number emerges as a desirable operating condition and a practical one as well. The number of terminals that can be simultaneously served is limited, not by the number of antennas, but rather by our inability to acquire channel-state information for an unlimited number of terminals. Larger numbers of terminals can always be accommodated by combining very large MIMO technology with conventional time- and frequency-division multiplexing via OFDM. Very large MIMO arrays is a new research field both in communication theory, propagation, and electronics and represents a paradigm shift in the way of thinking both with regards to theory, systems and implementation. The ultimate vision of very large MIMO systems is that the antenna array would consist of small active antenna units, plugged into an (optical) fieldbus.Comment: Accepted for publication in the IEEE Signal Processing Magazine, October 201

Secure Massive MIMO Communication with Low-resolution DACs

In this paper, we investigate secure transmission in a massive multiple-input multiple-output (MIMO) system adopting low-resolution digital-to-analog converters (DACs). Artificial noise (AN) is deliberately transmitted simultaneously with the confidential signals to degrade the eavesdropper's channel quality. By applying the Bussgang theorem, a DAC quantization model is developed which facilitates the analysis of the asymptotic achievable secrecy rate. Interestingly, for a fixed power allocation factor $\phi$, low-resolution DACs typically result in a secrecy rate loss, but in certain cases they provide superior performance, e.g., at low signal-to-noise ratio (SNR). Specifically, we derive a closed-form SNR threshold which determines whether low-resolution or high-resolution DACs are preferable for improving the secrecy rate. Furthermore, a closed-form expression for the optimal $\phi$ is derived. With AN generated in the null-space of the user channel and the optimal $\phi$, low-resolution DACs inevitably cause secrecy rate loss. On the other hand, for random AN with the optimal $\phi$, the secrecy rate is hardly affected by the DAC resolution because the negative impact of the quantization noise can be compensated for by reducing the AN power. All the derived analytical results are verified by numerical simulations.Comment: 14 pages, 10 figure

Distributed Multicell Beamforming Design Approaching Pareto Boundary with Max-Min Fairness

This paper addresses coordinated downlink beamforming optimization in multicell time-division duplex (TDD) systems where a small number of parameters are exchanged between cells but with no data sharing. With the goal to reach the point on the Pareto boundary with max-min rate fairness, we first develop a two-step centralized optimization algorithm to design the joint beamforming vectors. This algorithm can achieve a further sum-rate improvement over the max-min optimal performance, and is shown to guarantee max-min Pareto optimality for scenarios with two base stations (BSs) each serving a single user. To realize a distributed solution with limited intercell communication, we then propose an iterative algorithm by exploiting an approximate uplink-downlink duality, in which only a small number of positive scalars are shared between cells in each iteration. Simulation results show that the proposed distributed solution achieves a fairness rate performance close to the centralized algorithm while it has a better sum-rate performance, and demonstrates a better tradeoff between sum-rate and fairness than the Nash Bargaining solution especially at high signal-to-noise ratio.Comment: 8 figures. To Appear in IEEE Trans. Wireless Communications, 201

MIMO Networks: the Effects of Interference

Multiple-input/multiple-output (MIMO) systems promise enormous capacity increase and are being considered as one of the key technologies for future wireless networks. However, the decrease in capacity due to the presence of interferers in MIMO networks is not well understood. In this paper, we develop an analytical framework to characterize the capacity of MIMO communication systems in the presence of multiple MIMO co-channel interferers and noise. We consider the situation in which transmitters have no information about the channel and all links undergo Rayleigh fading. We first generalize the known determinant representation of hypergeometric functions with matrix arguments to the case when the argument matrices have eigenvalues of arbitrary multiplicity. This enables the derivation of the distribution of the eigenvalues of Gaussian quadratic forms and Wishart matrices with arbitrary correlation, with application to both single user and multiuser MIMO systems. In particular, we derive the ergodic mutual information for MIMO systems in the presence of multiple MIMO interferers. Our analysis is valid for any number of interferers, each with arbitrary number of antennas having possibly unequal power levels. This framework, therefore, accommodates the study of distributed MIMO systems and accounts for different positions of the MIMO interferers.Comment: Submitted to IEEE Trans. on Info. Theor

Robust Monotonic Optimization Framework for Multicell MISO Systems

The performance of multiuser systems is both difficult to measure fairly and to optimize. Most resource allocation problems are non-convex and NP-hard, even under simplifying assumptions such as perfect channel knowledge, homogeneous channel properties among users, and simple power constraints. We establish a general optimization framework that systematically solves these problems to global optimality. The proposed branch-reduce-and-bound (BRB) algorithm handles general multicell downlink systems with single-antenna users, multiantenna transmitters, arbitrary quadratic power constraints, and robustness to channel uncertainty. A robust fairness-profile optimization (RFO) problem is solved at each iteration, which is a quasi-convex problem and a novel generalization of max-min fairness. The BRB algorithm is computationally costly, but it shows better convergence than the previously proposed outer polyblock approximation algorithm. Our framework is suitable for computing benchmarks in general multicell systems with or without channel uncertainty. We illustrate this by deriving and evaluating a zero-forcing solution to the general problem.Comment: Published in IEEE Transactions on Signal Processing, 16 pages, 9 figures, 2 table

Robust Linear Precoder Design for Multi-cell Downlink Transmission

Coordinated information processing by the base stations of multi-cell wireless networks enhances the overall quality of communication in the network. Such coordinations for optimizing any desired network-wide quality of service (QoS) necessitate the base stations to acquire and share some channel state information (CSI). With perfect knowledge of channel states, the base stations can adjust their transmissions for achieving a network-wise QoS optimality. In practice, however, the CSI can be obtained only imperfectly. As a result, due to the uncertainties involved, the network is not guaranteed to benefit from a globally optimal QoS. Nevertheless, if the channel estimation perturbations are confined within bounded regions, the QoS measure will also lie within a bounded region. Therefore, by exploiting the notion of robustness in the worst-case sense some worst-case QoS guarantees for the network can be asserted. We adopt a popular model for noisy channel estimates that assumes that estimation noise terms lie within known hyper-spheres. We aim to design linear transceivers that optimize a worst-case QoS measure in downlink transmissions. In particular, we focus on maximizing the worst-case weighted sum-rate of the network and the minimum worst-case rate of the network. For obtaining such transceiver designs, we offer several centralized (fully cooperative) and distributed (limited cooperation) algorithms which entail different levels of complexity and information exchange among the base stations.Comment: 38 Pages, 7 Figures, To appear in the IEEE Transactions on Signal Processin

Fundamental Limits in MIMO Broadcast Channels

This paper studies the fundamental limits of MIMO broadcast channels from a high level, determining the sum-rate capacity of the system as a function of system paramaters, such as the number of transmit antennas, the number of users, the number of receive antennas, and the total transmit power. The crucial role of channel state information at the transmitter is emphasized, as well as the emergence of opportunistic transmission schemes. The effects of channel estimation errors, training, and spatial correlation are studied, as well as issues related to fairness, delay and differentiated rate scheduling

Performance Analysis of Massive MIMO Networks with Random Unitary Pilot Matrices

A common approach to obtain channel state information for massive MIMO networks is to use the same orthogonal training sequences in each cell. We call this the full-pilot reuse (FPR) scheme. In this paper, we study an alternative approach where each cell uses different sets of orthogonal pilot (DOP) sequences. Considering uplink communications with matched filter (MF) receivers, we first derive the SINR in the large system regime where the number of antennas at the base station, the number of users in each cell, and training duration grow large with fixed ratios. For tractability in the analysis, the orthogonal pilots are drawn from Haar distributed random unitary matrices. The resulting expression is simple and easy to compute. As shown by the numerical simulations, the asymptotic SINR approximates the finite-size systems accurately. Secondly, we derive the user capacity of the DOP scheme under a simple power control and show that it is generally better than that of the FPR scheme.Comment: Draf