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Journal ArticleDOI

An Overview of Low-Rank Channel Estimation for Massive MIMO Systems

01 Nov 2016-IEEE Access (IEEE)-Vol. 4, pp 7313-7321
TL;DR: A general overview of the current low-rank channel estimation approaches is provided, including their basic assumptions, key results, as well as pros and cons on addressing the aforementioned tricky challenges.
Abstract: Massive multiple-input multiple-output is a promising physical layer technology for 5G wireless communications due to its capability of high spectrum and energy efficiency, high spatial resolution, and simple transceiver design. To embrace its potential gains, the acquisition of channel state information is crucial, which unfortunately faces a number of challenges, such as the uplink pilot contamination, the overhead of downlink training and feedback, and the computational complexity. In order to reduce the effective channel dimensions, researchers have been investigating the low-rank (sparse) properties of channel environments from different viewpoints. This paper then provides a general overview of the current low-rank channel estimation approaches, including their basic assumptions, key results, as well as pros and cons on addressing the aforementioned tricky challenges. Comparisons among all these methods are provided for better understanding and some future research prospects for these low-rank approaches are also forecasted.
Citations
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Journal ArticleDOI
TL;DR: Simulation results corroborate that the proposed deep learning based scheme can achieve better performance in terms of the DOA estimation and the channel estimation compared with conventional methods, and the proposed scheme is well investigated by extensive simulation in various cases for testing its robustness.
Abstract: The recent concept of massive multiple-input multiple-output (MIMO) can significantly improve the capacity of the communication network, and it has been regarded as a promising technology for the next-generation wireless communications. However, the fundamental challenge of existing massive MIMO systems is that high computational complexity and complicated spatial structures bring great difficulties to exploit the characteristics of the channel and sparsity of these multi-antennas systems. To address this problem, in this paper, we focus on channel estimation and direction-of-arrival (DOA) estimation, and a novel framework that integrates the massive MIMO into deep learning is proposed. To realize end-to-end performance, a deep neural network (DNN) is employed to conduct offline learning and online learning procedures, which is effective to learn the statistics of the wireless channel and the spatial structures in the angle domain. Concretely, the DNN is first trained by simulated data in different channel conditions with the aids of the offline learning, and then corresponding output data can be obtained based on current input data during online learning process. In order to realize super-resolution channel estimation and DOA estimation, two algorithms based on the deep learning are developed, in which the DOA can be estimated in the angle domain without additional complexity directly. Furthermore, simulation results corroborate that the proposed deep learning based scheme can achieve better performance in terms of the DOA estimation and the channel estimation compared with conventional methods, and the proposed scheme is well investigated by extensive simulation in various cases for testing its robustness.

577 citations


Cites background from "An Overview of Low-Rank Channel Est..."

  • ...However, massive MIMO encounters some practical challenges, including the sophisticated channel modeling, the high-dimensional channel state information (CSI), the scheduling of numerous accessing users and the limited radio frequency (RF) chains, etc [10]....

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Journal ArticleDOI
TL;DR: In this paper, the authors investigated the physical layer security of NOMA in large-scale networks with invoking stochastic geometry and derived new exact expressions of the security outage probability for both single-antenna and multipleantenna aided transmission scenarios.
Abstract: This paper investigates the physical layer security of non-orthogonal multiple access (NOMA) in large-scale networks with invoking stochastic geometry. Both single-antenna and multiple-antenna aided transmission scenarios are considered, where the base station (BS) communicates with randomly distributed NOMA users. In the single-antenna scenario, we adopt a protected zone around the BS to establish an eavesdropper-exclusion area with the aid of careful channel ordering of the NOMA users. In the multiple-antenna scenario, artificial noise is generated at the BS for further improving the security of a beamforming-aided system. In order to characterize the secrecy performance, we derive new exact expressions of the security outage probability for both single-antenna and multiple-antenna aided scenarios. For the single-antenna scenario, we perform secrecy diversity order analysis of the selected user pair. The analytical results derived demonstrate that the secrecy diversity order is determined by the specific user having the worse channel condition among the selected user pair. For the multiple-antenna scenario, we derive the asymptotic secrecy outage probability, when the number of transmit antennas tends to infinity. Monte Carlo simulations are provided for verifying the analytical results derived and to show that: 1) the security performance of the NOMA networks can be improved by invoking the protected zone and by generating artificial noise at the BS and 2) the asymptotic secrecy outage probability is close to the exact secrecy outage probability.

493 citations

Journal ArticleDOI
TL;DR: This paper investigates spatial- and frequency-wideband effects in massive MIMO systems from the array signal processing point of view, and develops the efficient uplink and downlink channel estimation strategies that require much less amount of training overhead and cause no pilot contamination.
Abstract: When there are a large number of antennas in massive MIMO systems, the transmitted wideband signal will be sensitive to the physical propagation delay of electromagnetic waves across the large array aperture, which is called the spatial-wideband effect. In this scenario, the transceiver design is different from most of the existing works, which presume that the bandwidth of the transmitted signals is not that wide, ignore the spatial-wideband effect, and only address the frequency selectivity. In this paper, we investigate spatial- and frequency-wideband effects, called dual-wideband effects in massive MIMO systems from the array signal processing point of view. Taking millimeter-wave-band communications as an example, we describe the transmission process to address the dual-wideband effects. By exploiting the channel sparsity in the angle domain and the delay domain, we develop the efficient uplink and downlink channel estimation strategies that require much less amount of training overhead and cause no pilot contamination. Thanks to the array signal processing techniques, the proposed channel estimation is suitable for both TDD and FDD massive MIMO systems. Numerical examples demonstrate that the proposed transmission design for massive MIMO systems can effectively deal with the dual-wideband effects.

250 citations


Cites background from "An Overview of Low-Rank Channel Est..."

  • ...However, when M and N are finite in practice, the region of the non-zero square will be expanded due to the power leakage effect [15], [31]....

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  • ...Note that the proposed soft grouping strategy is different from the conventional hard grouping one [11], [15], [31] in that the latter requires users with overlapped signature to transmit over completely non-overlapped time intervals while ours allows users to transmit in an “interlock” way by purposely postpone certain users such that (29) can be satisfied....

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  • ...The extension to low frequency-band communications can be straightforwardly made by counting the angular spread caused by local scattering [15], [31]....

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Journal ArticleDOI
TL;DR: The results demonstrate that: 1) the coverage probability of NOMA enhanced small cells is affected to a large extent by the targeted transmit rates and power sharing coefficients of two N OMA users; 2) massive MIMO enabled macro cells are capable of significantly enhancing the spectrum efficiency by increasing the number of antennas; 3) the energy efficiency of the whole network can be greatly improved by densely deploying NOMa enhanced small cell base stations.
Abstract: In this paper, the potential benefits of applying non-orthogonal multiple access (NOMA) technique in $K$ -tier hybrid heterogeneous networks (HetNets) is explored. A promising new transmission framework is proposed, in which NOMA is adopted in small cells and massive multiple-input multiple-output (MIMO) is employed in macro cells. For maximizing the biased average received power for mobile users, a NOMA and massive MIMO based user association scheme is developed. To evaluate the performance of the proposed framework, we first derive the analytical expressions for the coverage probability of NOMA enhanced small cells. We then examine the spectrum efficiency of the whole network by deriving exact analytical expressions for NOMA enhanced small cells and a tractable lower bound for massive MIMO enabled macro cells. Finally, we investigate the energy efficiency of the hybrid HetNets. Our results demonstrate that: 1) the coverage probability of NOMA enhanced small cells is affected to a large extent by the targeted transmit rates and power sharing coefficients of two NOMA users; 2) massive MIMO enabled macro cells are capable of significantly enhancing the spectrum efficiency by increasing the number of antennas; 3) the energy efficiency of the whole network can be greatly improved by densely deploying NOMA enhanced small cell base stations; and 4) the proposed NOMA enhanced HetNets transmission scheme has superior performance compared with the orthogonal multiple access-based HetNets.

197 citations


Cites background from "An Overview of Low-Rank Channel Est..."

  • ...The massive MIMO regime enables tens of hundreds/thousands antennas at a BS, and hence it is capable of offering an unprecedented level of freedom to serve multiple mobile users [14]....

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Journal ArticleDOI
TL;DR: In this article, a support detection (SD)-based channel estimation scheme was proposed to estimate the support of sparse beamspace channel with comparable or higher accuracy than conventional schemes, and the performance and complexity analyses were provided to prove that the proposed SD-based channel estimator can estimate the SBS with comparable performance and low pilot overhead.
Abstract: Millimeter-wave (mm-wave) massive MIMO with lens antenna array can considerably reduce the number of required radio-frequency (RF) chains by beam selection. However, beam selection requires the base station to acquire the accurate information of beamspace channel. This is a challenging task as the size of beamspace channel is large, while the number of RF chains is limited. In this paper, we investigate the beamspace channel estimation problem in mm-wave massive MIMO systems with lens antenna array. Specifically, we first design an adaptive selecting network for mm-wave massive MIMO systems with lens antenna array, and based on this network, we further formulate the beamspace channel estimation problem as a sparse signal recovery problem. Then, by fully utilizing the structural characteristics of the mm-wave beamspace channel, we propose a support detection (SD)-based channel estimation scheme with reliable performance and low pilot overhead. Finally, the performance and complexity analyses are provided to prove that the proposed SD-based channel estimation scheme can estimate the support of sparse beamspace channel with comparable or higher accuracy than conventional schemes. Simulation results verify that the proposed SD-based channel estimation scheme outperforms conventional schemes and enjoys satisfying accuracy even in the low SNR region as the structural characteristics of beamspace channel can be exploited.

183 citations

References
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Journal ArticleDOI
TL;DR: In this article, a description of the multiple signal classification (MUSIC) algorithm, which provides asymptotically unbiased estimates of 1) number of incident wavefronts present; 2) directions of arrival (DOA) (or emitter locations); 3) strengths and cross correlations among the incident waveforms; 4) noise/interference strength.
Abstract: Processing the signals received on an array of sensors for the location of the emitter is of great enough interest to have been treated under many special case assumptions. The general problem considers sensors with arbitrary locations and arbitrary directional characteristics (gain/phase/polarization) in a noise/interference environment of arbitrary covariance matrix. This report is concerned first with the multiple emitter aspect of this problem and second with the generality of solution. A description is given of the multiple signal classification (MUSIC) algorithm, which provides asymptotically unbiased estimates of 1) number of incident wavefronts present; 2) directions of arrival (DOA) (or emitter locations); 3) strengths and cross correlations among the incident waveforms; 4) noise/interference strength. Examples and comparisons with methods based on maximum likelihood (ML) and maximum entropy (ME), as well as conventional beamforming are included. An example of its use as a multiple frequency estimator operating on time series is included.

12,446 citations

Journal ArticleDOI
TL;DR: Although discussed in the context of direction-of-arrival estimation, ESPRIT can be applied to a wide variety of problems including accurate detection and estimation of sinusoids in noise.
Abstract: An approach to the general problem of signal parameter estimation is described. The algorithm differs from its predecessor in that a total least-squares rather than a standard least-squares criterion is used. Although discussed in the context of direction-of-arrival estimation, ESPRIT can be applied to a wide variety of problems including accurate detection and estimation of sinusoids in noise. It exploits an underlying rotational invariance among signal subspaces induced by an array of sensors with a translational invariance structure. The technique, when applicable, manifests significant performance and computational advantages over previous algorithms such as MEM, Capon's MLM, and MUSIC. >

6,273 citations


"An Overview of Low-Rank Channel Est..." refers background in this paper

  • ...However, there are three main reasons that the conventional MUSIC [12] and ESPRIT [13] are not applicable here: (i) They may suffer from very high computational complexity due to their SVD operation with massive antennas; (ii) They are designed for the scenario when the incoming signals do not have AS and would suffer from performance degradation with surrounding scattering; (ii) They are blind approaches originally designed for Radar application but do not utilize the training sequences embedded in communications systems....

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  • ...ANTENNA ARRAY THEORY BASED LOW-RANK CHANNEL ESTIMATION Now that the angular information is crucial for the low-rank channel estimation, a natural question arise: why don’t we directly achieve such angular information via certain canonical means, say, array signal processing? However, there are three main reasons that the conventional MUSIC [12] and ESPRIT [13] are not applicable here: (i) They may suffer from very high computational complexity due to their SVD operation with massive antennas; (ii) They are designed for the scenario when the incoming signals do not have AS and would suffer from performance degradation with surrounding scattering; (ii) They are blind approaches originally designed for Radar application but do not utilize the training sequences embedded in communications systems....

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Journal ArticleDOI
Thomas L. Marzetta1
TL;DR: A cellular base station serves a multiplicity of single-antenna terminals over the same time-frequency interval and a complete multi-cellular analysis yields a number of mathematically exact conclusions and points to a desirable direction towards which cellular wireless could evolve.
Abstract: 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.

6,248 citations


"An Overview of Low-Rank Channel Est..." refers background in this paper

  • ...If the same training sequences are reused or non-orthogonal training sequences are adopted, then the inter-user interference will arise during the channel estimation stage, which is known as pilot contamination [1]....

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  • ...Unfortunately, channel reciprocity is not applicable for frequency division duplexing (FDD) systems, which is still a dominant transmission mode in most communications systems [1]....

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  • ...INTRODUCTION Large-scale multiple-input multiple-output (MIMO) or ‘‘massive MIMO’’, a new technique that employs hundreds or even thousands of antennas at base station (BS) to simultaneously serve multiple users, has been widely investigated for its numerous merits, such as high spectrum and energy efficiency, high spatial resolution, and simple transceiver design [1]....

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Journal ArticleDOI
TL;DR: An overview of beamforming from a signal-processing perspective is provided, with an emphasis on recent research.
Abstract: An overview of beamforming from a signal-processing perspective is provided, with an emphasis on recent research. Data-independent, statistically optimum, adaptive, and partially adaptive beamforming are discussed. Basic notation, terminology, and concepts are included. Several beamformer implementations are briefly described. >

4,122 citations

Journal ArticleDOI
TL;DR: This work compute a lower bound on the capacity of a channel that is learned by training, and maximize the bound as a function of the received signal-to-noise ratio (SNR), fading coherence time, and number of transmitter antennas.
Abstract: Multiple-antenna wireless communication links promise very high data rates with low error probabilities, especially when the wireless channel response is known at the receiver. In practice, knowledge of the channel is often obtained by sending known training symbols to the receiver. We show how training affects the capacity of a fading channel-too little training and the channel is improperly learned, too much training and there is no time left for data transmission before the channel changes. We compute a lower bound on the capacity of a channel that is learned by training, and maximize the bound as a function of the received signal-to-noise ratio (SNR), fading coherence time, and number of transmitter antennas. When the training and data powers are allowed to vary, we show that the optimal number of training symbols is equal to the number of transmit antennas-this number is also the smallest training interval length that guarantees meaningful estimates of the channel matrix. When the training and data powers are instead required to be equal, the optimal number of symbols may be larger than the number of antennas. We show that training-based schemes can be optimal at high SNR, but suboptimal at low SNR.

2,466 citations


"An Overview of Low-Rank Channel Est..." refers background in this paper

  • ...From the conventional orthogonal training strategy [2], the required number of orthogonal training sequences as well as the length of the training sequences should be at least the number of transmit antennas....

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