Spatially Sparse Precoding in Millimeter Wave MIMO Systems
21 Jan 2014-IEEE Transactions on Wireless Communications (Institute of Electrical and Electronics Engineers Inc.)-Vol. 13, Iss: 3, pp 1499-1513
TL;DR: This paper considers transmit precoding and receiver combining in mmWave systems with large antenna arrays and develops algorithms that accurately approximate optimal unconstrained precoders and combiners such that they can be implemented in low-cost RF hardware.
Abstract: 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.
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TL;DR: 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.
Abstract: 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.
7,139 citations
TL;DR: Simulation results demonstrate that an IRS-aided single-cell wireless system can achieve the same rate performance as a benchmark massive MIMO system without using IRS, but with significantly reduced active antennas/RF chains.
Abstract: Intelligent reflecting surface (IRS) is a revolutionary and transformative technology for achieving spectrum and energy efficient wireless communication cost-effectively in the future. Specifically, an IRS consists of a large number of low-cost passive elements each being able to reflect the incident signal independently with an adjustable phase shift so as to collaboratively achieve three-dimensional (3D) passive beamforming without the need of any transmit radio-frequency (RF) chains. In this paper, we study an IRS-aided single-cell wireless system where one IRS is deployed to assist in the communications between a multi-antenna access point (AP) and multiple single-antenna users. We formulate and solve new problems to minimize the total transmit power at the AP by jointly optimizing the transmit beamforming by active antenna array at the AP and reflect beamforming by passive phase shifters at the IRS, subject to users’ individual signal-to-interference-plus-noise ratio (SINR) constraints. Moreover, we analyze the asymptotic performance of IRS’s passive beamforming with infinitely large number of reflecting elements and compare it to that of the traditional active beamforming/relaying. Simulation results demonstrate that an IRS-aided MIMO system can achieve the same rate performance as a benchmark massive MIMO system without using IRS, but with significantly reduced active antennas/RF chains. We also draw useful insights into optimally deploying IRS in future wireless systems.
3,045 citations
Cites background from "Spatially Sparse Precoding in Milli..."
...Although beamforming optimization under unit-modulus constraints has been studied in the research on constant-envelope precoding [11], [12] as well as hybrid digital/analog processing [13], [14], such designs are mainly restricted to either the transmitter or the receiver side, which are not applicable to our considered joint active and passive beamforming optimization at both the AP and IRS....
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TL;DR: An adaptive algorithm to estimate the mmWave channel parameters that exploits the poor scattering nature of the channel is developed and a new hybrid analog/digital precoding algorithm is proposed that overcomes the hardware constraints on the analog-only beamforming, and approaches the performance of digital solutions.
Abstract: 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.
2,424 citations
Cites background or methods from "Spatially Sparse Precoding in Milli..."
...The path amplitudes are assumed to be Rayleigh distributed, i.e., with the average power gain....
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...This difference leads to a novel formulation of the arbitrary beamwidth beamforming design problem in addition to a completely new way for realizing these vectors using analog/digital architecture as will be explained shortly....
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...If is the combined BS precoding matrix, the discrete-time transmitted signal is then (1) where is the 1 vector of transmitted symbols, such that , and is the average total transmit power....
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...Despite the reduced complexity of [3], [7]–[11], they generally share the disadvantage of converging towards only one communication beam....
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...This formulation captures the sparse nature of the channel, and enables leveraging tools developed in the adaptive compressed sensing (CS) field to design efficient estimation algorithms for mmWave channels....
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TL;DR: 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.
Abstract: 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.
2,380 citations
TL;DR: An overview of 5G research, standardization trials, and deployment challenges is provided, with research test beds delivering promising performance but pre-commercial trials lagging behind the desired 5G targets.
Abstract: There is considerable pressure to define the key requirements of 5G, develop 5G standards, and perform technology trials as quickly as possible. Normally, these activities are best done in series but there is a desire to complete these tasks in parallel so that commercial deployments of 5G can begin by 2020. 5G will not be an incremental improvement over its predecessors; it aims to be a revolutionary leap forward in terms of data rates, latency, massive connectivity, network reliability, and energy efficiency. These capabilities are targeted at realizing high-speed connectivity, the Internet of Things, augmented virtual reality, the tactile internet, and so on. The requirements of 5G are expected to be met by new spectrum in the microwave bands (3.3-4.2 GHz), and utilizing large bandwidths available in mm-wave bands, increasing spatial degrees of freedom via large antenna arrays and 3-D MIMO, network densification, and new waveforms that provide scalability and flexibility to meet the varying demands of 5G services. Unlike the one size fits all 4G core networks, the 5G core network must be flexible and adaptable and is expected to simultaneously provide optimized support for the diverse 5G use case categories. In this paper, we provide an overview of 5G research, standardization trials, and deployment challenges. Due to the enormous scope of 5G systems, it is necessary to provide some direction in a tutorial article, and in this overview, the focus is largely user centric, rather than device centric. In addition to surveying the state of play in the area, we identify leading technologies, evaluating their strengths and weaknesses, and outline the key challenges ahead, with research test beds delivering promising performance but pre-commercial trials lagging behind the desired 5G targets.
1,659 citations
Cites background from "Spatially Sparse Precoding in Milli..."
...Design strategies for HBF can maximize some performance metric over the feasible space of (FRF, FBB) which is limited by transmit power and phase shifting constraints (elements of FRF must have unit magnitude [19], [120])....
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...Another common approach is to select a target precoder and minimize ||Ftarget− FRFFBB|| over the feasible space [19], [123], [124]....
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...directions as well as global channel information in precoder design [19], [120]....
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...A typical “fully connected” structure [17], [19], [20], [120] breaks the precoder down into F = FRFFBB, where the Nt × NRF analog precoder, FRF, links the Nt antennas to the NRF chains and performs analog phase shifting, while the NRF × Ns precoder, FBB operates digitally (see Fig....
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...base station [19], [20], [87], [88], [120], [121]....
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Abstract: SUMMARY We propose a new method for estimation in linear models. The 'lasso' minimizes the residual sum of squares subject to the sum of the absolute value of the coefficients being less than a constant. Because of the nature of this constraint it tends to produce some coefficients that are exactly 0 and hence gives interpretable models. Our simulation studies suggest that the lasso enjoys some of the favourable properties of both subset selection and ridge regression. It produces interpretable models like subset selection and exhibits the stability of ridge regression. There is also an interesting relationship with recent work in adaptive function estimation by Donoho and Johnstone. The lasso idea is quite general and can be applied in a variety of statistical models: extensions to generalized regression models and tree-based models are briefly described.
40,785 citations
"Spatially Sparse Precoding in Milli..." refers background in this paper
...Alternatively, (18) can be solved using tools from [39]–[42], [49]....
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TL;DR: In this article, the focus is on recognizing convex optimization problems and then finding the most appropriate technique for solving them, and a comprehensive introduction to the subject is given. But the focus of this book is not on the optimization problem itself, but on the problem of finding the appropriate technique to solve it.
Abstract: Convex optimization problems arise frequently in many different fields. A comprehensive introduction to the subject, this book shows in detail how such problems can be solved numerically with great efficiency. The focus is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. The text contains many worked examples and homework exercises and will appeal to students, researchers and practitioners in fields such as engineering, computer science, mathematics, statistics, finance, and economics.
33,341 citations
TL;DR: It is demonstrated theoretically and empirically that a greedy algorithm called orthogonal matching pursuit (OMP) can reliably recover a signal with m nonzero entries in dimension d given O(m ln d) random linear measurements of that signal.
Abstract: This paper demonstrates theoretically and empirically that a greedy algorithm called orthogonal matching pursuit (OMP) can reliably recover a signal with m nonzero entries in dimension d given O(m ln d) random linear measurements of that signal. This is a massive improvement over previous results, which require O(m2) measurements. The new results for OMP are comparable with recent results for another approach called basis pursuit (BP). In some settings, the OMP algorithm is faster and easier to implement, so it is an attractive alternative to BP for signal recovery problems.
8,604 citations
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...Alternatively, (18) can be solved using tools from [39]–[42], [49]....
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...So, for the general case of Ns ≥ 1, we present an algorithmic solution based on the well-known concept of orthogonal matching pursuit [39], [41], [49]....
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01 Aug 2007
TL;DR: In this paper, a greedy algorithm called Orthogonal Matching Pursuit (OMP) was proposed to recover a signal with m nonzero entries in dimension 1 given O(m n d) random linear measurements of that signal.
Abstract: This report demonstrates theoretically and empirically that a greedy algorithm called
Orthogonal Matching Pursuit (OMP) can reliably recover a signal with m nonzero entries in dimension
d given O(mln d) random linear measurements of that signal. This is a massive improvement
over previous results, which require O(m2) measurements. The new results for OMP are comparable
with recent results for another approach called Basis Pursuit (BP). In some settings, the
OMP algorithm is faster and easier to implement, so it is an attractive alternative to BP for signal
recovery problems.
7,124 citations
TL;DR: This article presents new results on using a greedy algorithm, orthogonal matching pursuit (OMP), to solve the sparse approximation problem over redundant dictionaries and develops a sufficient condition under which OMP can identify atoms from an optimal approximation of a nonsparse signal.
Abstract: This article presents new results on using a greedy algorithm, orthogonal matching pursuit (OMP), to solve the sparse approximation problem over redundant dictionaries. It provides a sufficient condition under which both OMP and Donoho's basis pursuit (BP) paradigm can recover the optimal representation of an exactly sparse signal. It leverages this theory to show that both OMP and BP succeed for every sparse input signal from a wide class of dictionaries. These quasi-incoherent dictionaries offer a natural generalization of incoherent dictionaries, and the cumulative coherence function is introduced to quantify the level of incoherence. This analysis unifies all the recent results on BP and extends them to OMP. Furthermore, the paper develops a sufficient condition under which OMP can identify atoms from an optimal approximation of a nonsparse signal. From there, it argues that OMP is an approximation algorithm for the sparse problem over a quasi-incoherent dictionary. That is, for every input signal, OMP calculates a sparse approximant whose error is only a small factor worse than the minimal error that can be attained with the same number of terms.
3,865 citations