Hybrid Beamforming for Massive MIMO - A Survey

Molisch, Andreas F.; Ratnam, V. V.; Han, Shengqian; Li, Zheda; Nguyen, Sinh Le Hong; Li, Linsheng; Haneda, Katsuyuki

doi:10.48550/arxiv.1609.05078

Cited by 10 publications

(19 citation statements)

References 72 publications

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“…2, we investigate the lower bound on the per-cell achievable rate in (32) of different MMSE precoding schemes in downlink, where r = 8. While the 'full-dimensional MMSE' represents the conventional M -dimensional MMSE channel estimation and precoding scheme based on s s s k in (17) without spatial (de)spreading, the 'low-dimensional MMSE' is given by ( 19) and (23), where d indicates the number of Fourier coefficients used out of r ones under the Fourier correlation model for spatial (de)spreading. The 8-dimensional (d = 8) channel estimation and precoding are shown to cause only graceful performance degradation, compared to the 100-dimensional vector operation.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…Furthermore, spatial despreading/spreading is in fact long-term or wideband (i.e., frequency non-selective) processing, while low-dimensional combining/precoding is short-term or narrowband (frequency selective) processing. Therefore, they are amenable to the hybrid beamforming architecture (see [23] and references therein) that is beneficial to realize massive MIMO in practice by saving hardware cost and channel training/feedback overhead.…”

Section: C(snr)mentioning

confidence: 99%

“…The random partial Fourier model in (7) was used for channel covariance matrices. For low-dimensional MMSE precoding, we used(23).…”

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confidence: 99%

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Capacity Scaling of Massive MIMO in Strong Spatial Correlation Regimes

Nam

Caire

Debbah

et al. 2020

IEEE Trans. Inform. Theory

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This paper investigates the capacity scaling of multicell massive MIMO systems in the presence of spatially correlated fading. In particular, we focus on the strong spatial correlation regimes where the covariance matrix of each user channel vector has a rank that scales sublinearly with the number of base station antennas, as the latter grows to infinity. We also consider the case where the covariance eigenvectors corresponding to the non-zero eigenvalues span randomly selected subspaces. For this channel model, referred to as the "random sparse angular support" model, we characterize the asymptotic capacity scaling law in the limit of large number of antennas. To achieve the asymptotic capacity results, statistical spatial despreading based on the second-order channel statistics plays a pivotal role in terms of pilot decontamination and interference suppression. A remarkable result is that even when the number of users scales linearly with base station antennas, a linear growth of the capacity with respect to the number of antennas is achievable under the sparse angular support model. We note that the achievable rate lower bound based on massive MIMO "channel hardening", widely used in the massive MIMO literature, yields rather loose results in the strong spatial correlation regimes and may significantly underestimate the achievable rate of massive MIMO. This work therefore considers an alternative bounding technique which is better suited to the strong correlation regimes. In fading channels with sparse angular support, it is further shown that spatial despreading (spreading) in uplink (downlink) has a more prominent impact on the performance of massive MIMO than channel hardening. Index TermsLarge-scale MIMO, asymptotic capacity scaling, multiplexing gain, correlated fading channels. arXiv:1812.08898v1 [cs.IT] 21 Dec 2018 K M = 0, i.e., K is finite or at most grows slower than M . For instance, if KL > M , the linear independence of the subspaces of covariance matrices in [12], [13] is never attainable. Likewise, if lim inf M →∞ K M > 0, then the asymptotic linear independence of covariance matrices in [16] does not hold any longer. Therefore, the results based on the linear independence of the signal subspaces or of the covariance matrices cannot capture the capacity scaling with respect to the ratio K M > 0, as both M and K grow large. This poses a fundamental methodological question since in reality we are in the presence of a finite system with given M and K. Which of the following large system analyses will produce the more meaningful prediction of its behavior: considering finite K and letting M → ∞ [1], [2], [16] or considering both K and M → ∞ with fixed ratio equal to the actual ratio K M of the practical finite system [4]? We claim that the latter methodology yields a more relevant asymptotics.

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Section: Numerical Resultsmentioning

confidence: 99%

Section: C(snr)mentioning

confidence: 99%

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Capacity Scaling of Massive MIMO in Strong Spatial Correlation Regimes

Nam

Caire

Debbah

et al. 2020

IEEE Trans. Inform. Theory

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“…2) Partially-connected RF Precoding Structure: In this case, each RF chain is connected to a sub-array of antennas via phase shifters and each antenna is only connected to a single RF chain [9], as illustrated in Fig. 3-(b).…”

Section: B Various Implementation Methods For Rf Precodermentioning

confidence: 99%

“…The optimal THP design depends on the RF precoding structure and the specific application scenario. There are two major RF precoding structures: the fully-connected structure where each antenna is connected to all the RF chains, and the partially-connected structure where each antenna is only connected to a single RF chain [9]. For each structure, there are two methods to implement the dynamic RF precoder.…”

Section: Introductionmentioning

confidence: 99%

Stochastic Successive Convex Optimization for Two-Timescale Hybrid Precoding in Massive MIMO

Liu

Lau

Zhao

2018

IEEE J. Sel. Top. Signal Process.

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Hybrid precoding, which consists of an RF precoder and a baseband precoder, is a popular precoding architecture for massive MIMO due to its low hardware cost and power consumption. In conventional hybrid precoding, both RF and baseband precoders are adaptive to the real-time channel state information (CSI). As a result, an individual RF precoder is required for each subcarrier in wideband systems, leading to high implementation cost. To overcome this issue, two-timescale hybrid precoding (THP), which adapts the RF precoder to the channel statistics, has been proposed. Since the channel statistics are approximately the same over different subcarriers, only a single RF precoder is required in THP. Despite the advantages of THP, there lacks a unified and efficient algorithm for its optimization due to the non-convex and stochastic nature of the problem. Based on stochastic successive convex approximation (SSCA), we propose an online algorithmic framework called SSCA-THP for general THP optimization problems, in which the hybrid precoder is updated by solving a quadratic surrogate optimization problem whenever a new channel sample is obtained. Then we prove the convergence of SSCA-THP to stationary points. Finally, we apply SSCA-THP to solve three important THP optimization problems and verify its advantages over existing solutions.

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Multiplexing Gain of Millimeter-Wave Massive MIMO Systems with Distributed Antenna Arrays

Yue

Nguyen

2019

IOP Conf. Ser.: Earth Environ. Sci.

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This paper is concerned with spatial multiplexing analysis for millimeter-wave (mmWave) massive MIMO systems. For a single-user mmWave system employing distributed antenna subarray architecture in which the transmitter and receiver consist of Kt and Kr subarrays, respectively, an asymptotic multiplexing gain formula is firstly derived when the numbers of antennas at subarrays go to infinity. Specifically, assuming that all subchannels have the same average number of propagation pathsL, the formula implies that by employing such a distributed antenna-subarray architecture, an exact average maximum multiplexing gain of KrKtL can be achieved. This result means that compared to the co-located antenna architecture, using the distributed antenna-subarray architecture can statistically scale up the maximum multiplexing gain proportionally to KrKt. In order to further reveal the relation between diversity gain and multiplexing gain, a simple characterization of the diversity-multiplexing tradeoff is also given. The multiplexing gain analysis is then extended to the multiuser scenario as well as the conventional partially-connected RF structure in the literature. Moreover, simulation results obtained with the hybrid analog/digital processing corroborate the analysis results.

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Hybrid Beamforming for Massive MIMO - A Survey

Cited by 10 publications

References 72 publications

Capacity Scaling of Massive MIMO in Strong Spatial Correlation Regimes

Capacity Scaling of Massive MIMO in Strong Spatial Correlation Regimes

Stochastic Successive Convex Optimization for Two-Timescale Hybrid Precoding in Massive MIMO

Multiplexing Gain of Millimeter-Wave Massive MIMO Systems with Distributed Antenna Arrays

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