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

Millimeter wave (mmWave) signals experience orders-of-magnitude more pathloss than the microwave signals currently used in most wireless applications and all cellular systems. MmWave systems must therefore leverage large antenna arrays, made possible by the decrease in wavelength, to combat pathloss with beamforming gain. Beamforming with multiple data streams, known as precoding, can be used to further improve mmWave spectral efficiency. Both beamforming and precoding are done digitally at baseband in traditional multi-antenna systems. The high cost and power consumption of mixed-signal devices in mmWave systems, however, make analog processing in the RF domain more attractive. This hardware limitation restricts the feasible set of precoders and combiners that can be applied by practical mmWave transceivers. In this paper, we consider transmit precoding and receiver combining in mmWave systems with large antenna arrays. We exploit the spatial structure of mmWave channels to formulate the precoding/combining problem as a sparse reconstruction problem. Using the principle of basis pursuit, we develop algorithms that accurately approximate optimal unconstrained precoders and combiners such that they can be implemented in low-cost RF hardware. We present numerical results on the performance of the proposed algorithms and show that they allow mmWave systems to approach their unconstrained performance limits, even when transceiver hardware constraints are considered.

Spatially Sparse Precoding in Millimeter Wave MIMO Systems

Millimeter wave (mmWave) cellular systems will enable gigabit-per-second data rates thanks to the large bandwidth available at mmWave frequencies. To realize sufficient link margin, mmWave systems will employ directional beamforming with large antenna arrays at both the transmitter and receiver. Due to the high cost and power consumption of gigasample mixed-signal devices, mmWave precoding will likely be divided among the analog and digital domains. The large number of antennas and the presence of analog beamforming requires the development of mmWave-specific channel estimation and precoding algorithms. This paper develops an adaptive algorithm to estimate the mmWave channel parameters that exploits the poor scattering nature of the channel. To enable the efficient operation of this algorithm, a novel hierarchical multi-resolution codebook is designed to construct training beamforming vectors with different beamwidths. For single-path channels, an upper bound on the estimation error probability using the proposed algorithm is derived, and some insights into the efficient allocation of the training power among the adaptive stages of the algorithm are obtained. The adaptive channel estimation algorithm is then extended to the multi-path case relying on the sparse nature of the channel. Using the estimated channel, this paper proposes a new hybrid analog/digital precoding algorithm that overcomes the hardware constraints on the analog-only beamforming, and approaches the performance of digital solutions. Simulation results show that the proposed low-complexity channel estimation algorithm achieves comparable precoding gains compared to exhaustive channel training algorithms. The results illustrate that the proposed channel estimation and precoding algorithms can approach the coverage probability achieved by perfect channel knowledge even in the presence of interference.

Channel Estimation and Hybrid Precoding for Millimeter Wave Cellular Systems

Communication at millimeter wave (mmWave) frequencies is defining a new era of wireless communication. The mmWave band offers higher bandwidth communication channels versus those presently used in commercial wireless systems. The applications of mmWave are immense: wireless local and personal area networks in the unlicensed band, 5G cellular systems, not to mention vehicular area networks, ad hoc networks, and wearables. Signal processing is critical for enabling the next generation of mmWave communication. Due to the use of large antenna arrays at the transmitter and receiver, combined with radio frequency and mixed signal power constraints, new multiple-input multiple-output (MIMO) communication signal processing techniques are needed. Because of the wide bandwidths, low complexity transceiver algorithms become important. There are opportunities to exploit techniques like compressed sensing for channel estimation and beamforming. This article provides an overview of signal processing challenges in mmWave wireless systems, with an emphasis on those faced by using MIMO communication at higher carrier frequencies.

An Overview of Signal Processing Techniques for Millimeter Wave MIMO Systems

We provide a comprehensive overview of mathematical models and analytical techniques for millimeter wave (mmWave) cellular systems. The two fundamental physical differences from conventional sub-6-GHz cellular systems are: 1) vulnerability to blocking and 2) the need for significant directionality at the transmitter and/or receiver, which is achieved through the use of large antenna arrays of small individual elements. We overview and compare models for both of these factors, and present a baseline analytical approach based on stochastic geometry that allows the computation of the statistical distributions of the downlink signal-to-interference-plus-noise ratio (SINR) and also the per link data rate, which depends on the SINR as well as the average load. There are many implications of the models and analysis: 1) mmWave systems are significantly more noise-limited than at sub-6 GHz for most parameter configurations; 2) initial access is much more difficult in mmWave; 3) self-backhauling is more viable than in sub-6-GHz systems, which makes ultra-dense deployments more viable, but this leads to increasingly interference-limited behavior; and 4) in sharp contrast to sub-6-GHz systems cellular operators can mutually benefit by sharing their spectrum licenses despite the uncontrolled interference that results from doing so. We conclude by outlining several important extensions of the baseline model, many of which are promising avenues for future research.

Modeling and Analyzing Millimeter Wave Cellular Systems

We propose and investigate a compressive architecture for estimation and tracking of sparse spatial channels in millimeter (mm) wave picocellular networks. The base stations are equipped with antenna arrays with a large number of elements (which can fit within compact form factors because of the small carrier wavelength) and employ radio frequency (RF) beamforming, so that standard least squares adaptation techniques (which require access to individual antenna elements) are not applicable. We focus on the downlink, and show that “compressive beacons,” transmitted using pseudorandom phase settings at the base station array, and compressively processed using pseudorandom phase settings at the mobile array, provide information sufficient for accurate estimation of the two-dimensional (2D) spatial frequencies associated with the directions of departure of the dominant rays from the base station, and the associated complex gains. This compressive approach is compatible with coarse phase-only control, and is based on a near-optimal sequential algorithm for frequency estimation which approaches the Cramer Rao Lower Bound. The algorithm exploits the geometric continuity of the channel across successive beaconing intervals to reduce the overhead to less than 1% even for very large ( $32 \times 32$ ) arrays. Compressive beaconing is essentially omnidirectional, and hence does not enjoy the SNR and spatial reuse benefits of beamforming obtained during data transmission. We therefore discuss system level design considerations for ensuring that the beacon SNR is sufficient for accurate channel estimation, and that inter-cell beacon interference is controlled by an appropriate reuse scheme.

/pdf/compressive-channel-estimation-and-tracking-for-large-arrays-2en5dx7s2w.pdf

Compressive Channel Estimation and Tracking for Large Arrays in mm-Wave Picocells

We propose a fast sequential algorithm for the fundamental problem of estimating frequencies and amplitudes of a noisy mixture of sinusoids. The algorithm is a natural generalization of Orthogonal Matching Pursuit (OMP) to the continuum using Newton refinements, and hence is termed Newtonized OMP (NOMP). Each iteration consists of two phases: detection of a new sinusoid, and sequential Newton refinements of the parameters of already detected sinusoids. The refinements play a critical role in two ways: 1) sidestepping the potential basis mismatch from discretizing a continuous parameter space and 2) providing feedback for locally refining parameters estimated in previous iterations. We characterize convergence and provide a constant false alarm rate (CFAR) based termination criterion. By benchmarking against the Cramer–Rao Bound, we show that NOMP achieves near-optimal performance under a variety of conditions. We compare the performance of NOMP with classical algorithms such as MUSIC and more recent Atomic norm Soft Thresholding (AST) and Lasso algorithms, both in terms of frequency estimation accuracy and run time.

/pdf/newtonized-orthogonal-matching-pursuit-frequency-estimation-2o0x3rcvnb.pdf

Newtonized Orthogonal Matching Pursuit: Frequency Estimation Over the Continuum

We consider the problem of adapting very large antenna arrays (e.g., with 1000 elements or more) for tasks such as beamforming and nulling, motivated by emerging applications at very high carrier frequencies in the millimeter (mm) wave band and beyond, where the small wavelengths make it possible to pack a very large number of antenna elements (e.g., realized as a printed circuit array) into nodes with compact form factors. Conventional least squares techniques, which rely on access to baseband signals for individual array elements, do not apply. Hence the preferred approach is to perform radio frequency (RF) beamsteering, with a single complex baseband signal emerging from a receive array, or going into a transmit array. Further, we are interested in what can be achieved with coarse-grained control of individual elements (e.g., four-phase, or even binary phase, control). In this paper, we propose an adaptation architecture matched to these hardware constraints. Our approach comprises the following two steps. The first step is compressive estimation of a sparse spatial channel using a small number of measurements, each using a different set of randomized weights. However, unlike the standard compressive sensing formulation, we are interested in estimating continuous-valued parameters such as the angles of arrivals of various paths. The second step is quantized beamsteering, where weights for beamforming and nulling, subject to the constraint of severe quantization, are computed using the channel estimates from the first step. We provide promising preliminary results illustrating the efficacy of this approach.

Compressive adaptation of large steerable arrays

We propose and demonstrate the feasibility of multi-Gbps cellular downlinks using the mm-wave band. The small wavelengths allows deployment of compact base station antenna arrays with a very large number (32×32) of elements, while a compressive approach to channel acquisition and tracking reduces overhead while simplifying hardware design (RF beamforming with four phases per antenna element). The base station array transmits multiple compressive (« 32 × 32) training beacons by choosing different sets of phases from 0°, 90°, 180°, 270° at random at each of the elements. Each mobile, equipped with a single antenna, reports the observations corresponding to the different beacons (e.g., on an existing LTE link at a lower frequency), allowing the array to estimate the angles of departure. We observe that tracking overhead can be reduced by exploiting the sparsity of the spatial channel to a given mobile (which allows parametric estimation of departure angles for the different paths), and the continuity in the user's mobility at microsecond timescales (for tracking the evolution of departure angles). We first illustrate the basic feasibility of such a system for realistic values of system parameters, including range of operation, user mobility and hardware constraints. We then propose a compressive channel tracking algorithm that exploits prior channel estimates to drastically reduce the number of beacons and demonstrate the efficacy of the system using simulations.

Compressive tracking with 1000-element arrays: A framework for multi-Gbps mm wave cellular downlinks

Compressed sensing is by now well-established as an effective tool for extracting sparsely distributed information, where sparsity is a discrete concept, referring to the number of dominant nonzero signal components in some basis for the signal space. In this paper, we establish a framework for estimation of continuous-valued parameters based on compressive measurements on a signal corrupted by additive white Gaussian noise (AWGN). While standard compressed sensing based on naive discretization has been shown to suffer from performance loss due to basis mismatch, we demonstrate that this is not an inherent property of compressive measurements. Our contributions are summarized as follows: (a) We identify the isometries required to preserve fundamental estimation-theoretic quantities such as the Ziv-Zakai bound (ZZB) and the Cramer-Rao bound (CRB). Under such isometries, compressive projections can be interpreted simply as a reduction in “effective SNR.” (b) We show that the threshold behavior of the ZZB provides a criterion for determining the minimum number of measurements for “accurate” parameter estimation. (c) We provide detailed computations of the number of measurements needed for the isometries in (a) to hold for the problem of frequency estimation in a mixture of sinusoids. We show via simulations that the design criterion in (b) is accurate for estimating the frequency of a single sinusoid.

Dinesh Ramasamy

Papers

Compressive Channel Estimation and Tracking for Large Arrays in mm-Wave Picocells

Newtonized Orthogonal Matching Pursuit: Frequency Estimation Over the Continuum

Compressive adaptation of large steerable arrays

Compressive tracking with 1000-element arrays: A framework for multi-Gbps mm wave cellular downlinks

Compressive Parameter Estimation in AWGN