What will 5G be? What it will not be is an incremental advance on 4G. The previous four generations of cellular technology have each been a major paradigm shift that has broken backward compatibility. Indeed, 5G will need to be a paradigm shift that includes very high carrier frequencies with massive bandwidths, extreme base station and device densities, and unprecedented numbers of antennas. However, unlike the previous four generations, it will also be highly integrative: tying any new 5G air interface and spectrum together with LTE and WiFi to provide universal high-rate coverage and a seamless user experience. To support this, the core network will also have to reach unprecedented levels of flexibility and intelligence, spectrum regulation will need to be rethought and improved, and energy and cost efficiencies will become even more critical considerations. This paper discusses all of these topics, identifying key challenges for future research and preliminary 5G standardization activities, while providing a comprehensive overview of the current literature, and in particular of the papers appearing in this special issue.

What Will 5G Be

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.

Noncooperative Cellular Wireless with Unlimited Numbers of Base Station Antennas

Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

Convergence of Probability Measures

The use of space-division multiple access (SDMA) in the downlink of a multiuser multiple-input, multiple-output (MIMO) wireless communications network can provide a substantial gain in system throughput. The challenge in such multiuser systems is designing transmit vectors while considering the co-channel interference of other users. Typical optimization problems of interest include the capacity problem - maximizing the sum information rate subject to a power constraint-or the power control problem-minimizing transmitted power such that a certain quality-of-service metric for each user is met. Neither of these problems possess closed-form solutions for the general multiuser MIMO channel, but the imposition of certain constraints can lead to closed-form solutions. This paper presents two such constrained solutions. The first, referred to as "block-diagonalization," is a generalization of channel inversion when there are multiple antennas at each receiver. It is easily adapted to optimize for either maximum transmission rate or minimum power and approaches the optimal solution at high SNR. The second, known as "successive optimization," is an alternative method for solving the power minimization problem one user at a time, and it yields superior results in some (e.g., low SNR) situations. Both of these algorithms are limited to cases where the transmitter has more antennas than all receive antennas combined. In order to accommodate more general scenarios, we also propose a framework for coordinated transmitter-receiver processing that generalizes the two algorithms to cases involving more receive than transmit antennas. While the proposed algorithms are suboptimal, they lead to simpler transmitter and receiver structures and allow for a reasonable tradeoff between performance and complexity.

/pdf/zero-forcing-methods-for-downlink-spatial-multiplexing-in-12aoeacvaq.pdf

Zero-forcing methods for downlink spatial multiplexing in multiuser MIMO channels

It is shown that, particularly for terrestrial cellular telephony, the interference-suppression feature of CDMA (code division multiple access) can result in a many-fold increase in capacity over analog and even over competing digital techniques. A single-cell system, such as a hubbed satellite network, is addressed, and the basic expression for capacity is developed. The corresponding expressions for a multiple-cell system are derived. and the distribution on the number of users supportable per cell is determined. It is concluded that properly augmented and power-controlled multiple-cell CDMA promises a quantum increase in current cellular capacity. >

On the capacity of a cellular CDMA system

We investigate optimum zero-forcing beamforming in multiple antenna broadcast channels with per-antenna power constraints. We show that standard zero-forcing techniques, such as the Moore-Penrose pseudo-inverse, considered mainly in the context of sum-power constrained systems are suboptimal when there are per-antenna power constraints. We formulate convex optimization problems to find the optimum zero-forcing beamforming vectors. Our results indicate that optimizing the antenna outputs based on the per-antenna constraints may improve the rate considerably when the number of transmit antennas is larger the number of receive antennas. Having more transmit antennas gives rise to additional signal space dimensions that may be exploited effectively to reduce transmit power at particular antennas with limited power budget.

Optimum Zero-forcing Beamforming with Per-antenna Power Constraints

The capacity of a microcellular system using dynamic channel allocation was studied. It was found that these systems can self-organize, with little loss in capacity, by using channel-allocation algorithms that are simple, practical, and local. The performances of both deterministic and probabilistic algorithms were calculated. Two classes of isotropic algorithms look particularly promising: the timid class, which is the simplest, and the aggressive class, which could provide improvements in system capacity and blocking probability. In particular, at the expense of additional rearrangements per call, these local algorithms can approach the capacity achieved by a global channel-allocation strategy. >

https://ieeexplore.ieee.org/iel2/657/6293/00245314.pdf

Distributed algorithms for dynamic channel allocation in microcellular systems

Multi-element system capacities are usually thought of as being limited only by correlations between elements. We show that degenerate channel phenomena, called "keyholes" may arise under realistic assumptions which have zero correlation between the entries of the channel matrix H and yet only a single degree of freedom. Canonical physical examples of keyholes are presented. For indoor environments, it is shown that the number of communication modes in a hallway may not exceed the number of waveguide modes.

Keyholes, correlations and capacities of multi-element transmit and receive antennas

We demonstrate the capacity growth of multiple-element antenna arrays (MEAs) in a realistic propagation environment using WiSE, an experimental ray tracing tool. WiSE is used to construct the channel response for MEAs operating at 1.9 GHz for two situations: (a) (16-16)-MEAs located inside an office building and (b) (4, 4)-MEAs located in an outdoor fixed wireless loop. We define effective degrees of freedom (EDOFs) as parallel spatial modes of transmission for an MEA. We quantify the increase in both the number of EDOFs and capacity with transmit power, received SNR, and antenna spacing. More EDOFs are present when receiving MEAs are physically closer to the transmitting MEA, regardless of the scattering effect.

/pdf/capacity-growth-of-multi-element-arrays-in-indoor-and-41h7rti0wh.pdf

Capacity growth of multi-element arrays in indoor and outdoor wireless channels

We consider the problem of optimal dynamic allocation of a limited number of processors to service the demands from different types of users. The types are differentiated by the rates at which they enter requests for service and the mean length of time they occupy a single processor. The decision to accept or reject a request for service may be based on the number of processors occupied by each type. Throughput, or utilization of processors, weighted differently for each type may be used as a performance measure. While the optimum allocation question is formulated for any finite number of customer types, our solution is limited to the case of two competing customer classes. For two types of users we show that among a large class of policies, the optimum is the easily implemented policy of restricting the maximum number of processors that one of the two types can occupy at any time. The requests from the other type are always honored as long as a processor is available for service. It is intuitively reasonable that, despite the complex interactivity permitted in some policies and the multidimensional characterization of a customer type, one of the customer types should have a relative advantage and be permitted open access while a hard limitation is enforced on the competition. The crux of the proof involves a policy space perturbation argument relying on the structure of the equilibrium density.

G.J. Foschini

Papers

Optimum Zero-forcing Beamforming with Per-antenna Power Constraints

Distributed algorithms for dynamic channel allocation in microcellular systems

Keyholes, correlations and capacities of multi-element transmit and receive antennas

Capacity growth of multi-element arrays in indoor and outdoor wireless channels

Optimum Allocation of Servers to Two Types of Competing Customers