Showing papers by "Mats Bengtsson published in 2013"
TL;DR: It is proved analytically that such physical MIMO channels have a finite upper capacity limit, for any channel distribution and SNR, and it is proved that the relative capacity gain of employing MIMo is at least as large as with ideal transceivers.
Abstract: The capacity of ideal MIMO channels has a high-SNR slope that equals the minimum of the number of transmit and receive antennas. This letter analyzes if this result holds when there are distortions from physical transceiver impairments. We prove analytically that such physical MIMO channels have a finite upper capacity limit, for any channel distribution and SNR. The high-SNR slope thus collapses to zero. This appears discouraging, but we prove the encouraging result that the relative capacity gain of employing MIMO is at least as large as with ideal transceivers.
191 citations
01 Jun 2013
TL;DR: This paper considers a robust MIMO precoding design with deterministic imperfect CSIT, formulated as a maximin problem, to maximize the worst-case received signal-to-noise ratio or minimize the best-case error probability, and shows that, for general convex uncertainty sets, the robust precoder can be efficiently computed by solving a single convex optimization problem.
Abstract: The full potential of multi-input multi-output (MIMO) communication systems relies on exploiting channel state information at the transmitter (CSIT), which is, however, often subject to some uncertainty In this paper, following the worst-case robust philosophy, we consider a robust MIMO precoding design with deterministic imperfect CSIT, formulated as a maximin problem, to maximize the worst-case received signal-to-noise ratio or minimize the worst-case error probability Given different types of imperfect CSIT in practice, a unified framework is lacking in the literature to tackle various channel uncertainty In this paper, we address this open problem by considering several classes of uncertainty sets that include most deterministic imperfect CSIT as special cases We show that, for general convex uncertainty sets, the robust precoder, as the solution to the maximin problem, can be efficiently computed by solving a single convex optimization problem Furthermore, when it comes to unitarily-invariant convex uncertainty sets, we prove the optimality of a channel-diagonalizing structure and simplify the complex-matrix problem to a real-vector power allocation problem, which is then analytically solved in a waterfilling manner Finally, for uncertainty sets defined by a generic matrix norm, called the Schatten norm, we provide a fully closed-form solution to the robust precoding design, based on which the robustness of beamforming and uniform-power transmission is investigated
78 citations
TL;DR: This paper tries to answer the question if the N data streams should be divided among few users or many users (few streams per user, enabling receive combining), and shows that selecting many users and allocating one stream per user is the best candidate under realistic conditions.
Abstract: In downlink multi-antenna systems with many users, the multiplexing gain is strictly limited by the number of transmit antennas N and the use of these antennas. Assuming that the total number of receive antennas at the multi-antenna users is much larger than N, the maximal multiplexing gain can be achieved with many different transmission/reception strategies. For example, the excess number of receive antennas can be utilized to schedule users with effective channels that are near-orthogonal, for multi-stream multiplexing to users with well-conditioned channels, and/or to enable interference-aware receive combining. In this paper, we try to answer the question if the N data streams should be divided among few users (many streams per user) or many users (few streams per user, enabling receive combining). Analytic results are derived to show how user selection, spatial correlation, heterogeneous user conditions, and imperfect channel acquisition (quantization or estimation errors) affect the performance when sending the maximal number of streams or one stream per scheduled user-the two extremes in data stream allocation. While contradicting observations on this topic have been reported in prior works, we show that selecting many users and allocating one stream per user (i.e., exploiting receive combining) is the best candidate under realistic conditions. This is explained by the provably stronger resilience towards spatial correlation and the larger benefit from multi-user diversity. This fundamental result has positive implications for the design of downlink systems as it reduces the hardware requirements at the user devices and simplifies the throughput optimization.
61 citations
TL;DR: This paper analytically establishes that the QRD-based design is indeed optimal for any performance measure under a SPC, and proposes an optimal beamformer design method for ZF-DPC with per-antenna power constraints (PAPCs), using a convex optimization framework.
Abstract: We consider the beamformer design for multiple-input multiple-output (MISO) broadcast channels (MISO BCs) using zero-forcing dirty paper coding (ZF-DPC). Assuming a sum power constraint (SPC), most previously proposed beamformer designs are based on the QR decomposition (QRD), which is a natural choice to satisfy the ZF constraints. However, the optimality of the QRD-based design for ZF-DPC has remained unknown. In this paper, first, we analytically establish that the QRD-based design is indeed optimal for any performance measure under a SPC. Then, we propose an optimal beamformer design method for ZF-DPC with per-antenna power constraints (PAPCs), using a convex optimization framework. The beamformer design is first formulated as a rank-1-constrained optimization problem. Exploiting the special structure of the ZF-DPC scheme, we prove that the rank constraint can be relaxed and still provide the same solution. In addition, we propose a fast converging algorithm to the beamformer design problem, under the duality framework between the BCs and multiple access channels (MACs). More specifically, we show that a BC with ZF-DPC has the dual MAC with ZF-based successive interference cancellation (ZF-SIC). In this way, the beamformer design for ZF-DPC is transformed into a power allocation problem for ZF-SIC, which can be solved more efficiently.
53 citations
TL;DR: The optimal precoder design for PAPCs is computed by solving the relaxed problem, for which the proposed numerical method is applicable for finding the optimal precoders for block diagonalization scheme.
Abstract: We consider precoder design for maximizing the weighted sum rate (WSR) of successive zero-forcing dirty paper coding (SZF-DPC). For this problem, the existing precoder designs often assume a sum power constraint (SPC) and rely on the singular value decomposition (SVD). The SVD-based designs are known to be optimal but require high complexity. We first propose a low-complexity optimal precoder design for SZF-DPC under SPC, using the QR decomposition. Then, we propose an efficient numerical algorithm to find the optimal precoders subject to per-antenna power constraints (PAPCs). To this end, the precoder design for PAPCs is formulated as an optimization problem with a rank constraint on the covariance matrices. A well-known approach to solve this problem is to relax the rank constraints and solve the relaxed problem. Interestingly, for SZF-DPC, we are able to prove that the rank relaxation is tight. Consequently, the optimal precoder design for PAPCs is computed by solving the relaxed problem, for which we propose a customized interior-point method that exhibits a superlinear convergence rate. Two suboptimal precoder designs are also presented and compared to the optimal ones. We also show that the proposed numerical method is applicable for finding the optimal precoders for block diagonalization scheme.
52 citations
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TL;DR: In this paper, a set of low-complexity Bayesian channel estimators, coined Polynomial ExpAnsion CHannel (PEACH) estimators are introduced.
Abstract: This paper considers pilot-based channel estimation in large-scale multiple-input multiple-output (MIMO) communication systems, also known as "massive MIMO". Unlike previous works on this topic, which mainly considered the impact of inter-cell disturbance due to pilot reuse (so-called pilot contamination), we are concerned with the computational complexity. The conventional minimum mean square error (MMSE) and minimum variance unbiased (MVU) channel estimators rely on inverting covariance matrices, which has cubic complexity in the multiplication of number of antennas at each side. Since this is extremely expensive when there are hundreds of antennas, we propose to approximate the inversion by an L-order matrix polynomial. A set of low-complexity Bayesian channel estimators, coined Polynomial ExpAnsion CHannel (PEACH) estimators, are introduced. The coefficients of the polynomials are optimized to yield small mean square error (MSE). We show numerically that near-optimal performance is achieved with low polynomial orders. In practice, the order L can be selected to balance between complexity and MSE. Interestingly, pilot contamination is beneficial to the PEACH estimators in the sense that smaller L can be used to achieve near-optimal MSEs.
31 citations
11 Dec 2013
TL;DR: Numerical results show that the proposed relay selection scheme with zero-forcing beamforming (ZFB)-based IRI cancellation approaches the average end-to-end capacity of IRI-free upper bound as the numbers of relays and antennas increase.
Abstract: In this paper, we study virtual full-duplex (FD) buffer-aided relaying to recover the multiplexing loss of half-duplex (HD) relaying in a network with multiple buffer-aided relays, each of which has multiple antennas, through opportunistic relay selection and beamforming. The main idea of virtual FD buffer-aided relaying is that a source and a relay simultaneously transmit their own information to another relay and a destination, respectively. In this network, inter-relay interference (IRI) is a crucial problem which has to be resolved like self-interference in the FD relaying. In contrast to previous work that neglected the IRI, we propose two buffer-aided relay selection and beam-forming schemes taking the IRI into consideration. Numerical results show that our proposed relay selection scheme with zero-forcing beamforming (ZFB)-based IRI cancellation approaches the average end-to-end capacity of IRI-free upper bound as the numbers of relays and antennas increase.
26 citations
11 Dec 2013
TL;DR: This paper considers pilot-based channel estimation in large-scale multiple-input multiple-output (MIMO) communication systems, and shows numerically that near-optimal performance is achieved with low polynomial orders.
Abstract: This paper considers pilot-based channel estimation in large-scale multiple-input multiple-output (MIMO) communication systems, also known as “massive MIMO”. Unlike previous works on this topic, which mainly considered the impact of inter-cell disturbance due to pilot reuse (so-called pilot contamination), we are concerned with the computational complexity. The conventional minimum mean square error (MMSE) and minimum variance unbiased (MVU) channel estimators rely on inverting covariance matrices, which has cubic complexity in the multiplication of number of antennas at each side. Since this is extremely expensive when there are hundreds of antennas, we propose to approximate the inversion by an L-order matrix polynomial. A set of low-complexity Bayesian channel estimators, coined Polynomial ExpAnsion CHannel (PEACH) estimators, are introduced. The coefficients of the polynomials are optimized to yield small mean square error (MSE). We show numerically that near-optimal performance is achieved with low polynomial orders. In practice, the order L can be selected to balance between complexity and MSE. Interestingly, pilot contamination is beneficial to the PEACH estimators in the sense that smaller L can be used to achieve near-optimal MSEs.
25 citations
TL;DR: It is shown that frequency-domain smoothing techniques can minimize the variance of the LS channel estimator, while they can further reduce its MSE by trading bias for variance.
17 citations
09 Jun 2013
TL;DR: For frequency extended multiple antenna systems where precoding is performed over a combination of space and frequency dimensions, a necessary condition on IA feasibility is derived using the properness framework and the sum rate performance is investigated using simulations.
Abstract: Time or frequency extensions are integral in most information theoretic studies of interference alignment (IA), but a large majority of the more practically oriented studies have focused on narrowband space-only schemes. As wideband systems are now common, it is natural to investigate IA for frequency extended multiple antenna systems where precoding is performed over a combination of space and frequency dimensions. For this setting, we derive a necessary condition on IA feasibility using the properness framework and investigate the sum rate performance using simulations. Applying frequency extensions to multiple antenna systems allows for some additional users to be served interference-free, but our numerical results with synthetic channels indicate a practically more important improvement in terms of a power gain. Emulating a particular scenario using channel measurements, with real-world path losses and channel correlations, we see similar performance gains.
17 citations
TL;DR: In this paper, the problem of training optimization for estimating a MIMO flat fading channel in the presence of spatially and temporally correlated Gaussian noise is studied in an application-oriented setup.
Abstract: In this paper, the problem of training optimization for estimating a multiple-input multiple-output (MIMO) flat fading channel in the presence of spatially and temporally correlated Gaussian noise is studied in an application-oriented setup. So far, the problem of MIMO channel estimation has mostly been treated within the context of minimizing the mean square error (MSE) of the channel estimate subject to various constraints, such as an upper bound on the available training energy. We introduce a more general framework for the task of training sequence design in MIMO systems, which can treat not only the minimization of channel estimator’s MSE but also the optimization of a final performance metric of interest related to the use of the channel estimate in the communication system. First, we show that the proposed framework can be used to minimize the training energy budget subject to a quality constraint on the MSE of the channel estimator. A deterministic version of the 'dual’ problem is also provided. We then focus on four specific applications, where the training sequence can be optimized with respect to the classical channel estimation MSE, a weighted channel estimation MSE and the MSE of the equalization error due to the use of an equalizer at the receiver or an appropriate linear precoder at the transmitter. In this way, the intended use of the channel estimate is explicitly accounted for. The superiority of the proposed designs over existing methods is demonstrated via numerical simulations.
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TL;DR: A more general framework for the task of training sequence design in MIMO systems is introduced, which can treat not only the minimization of channel estimator’s MSE but also the optimization of a final performance metric of interest related to the use of the channel estimate in the communication system.
Abstract: In this paper, the problem of training optimization for estimating a multiple-input multiple-output (MIMO) flat fading channel in the presence of spatially and temporally correlated Gaussian noise is studied in an application-oriented setup. So far, the problem of MIMO channel estimation has mostly been treated within the context of minimizing the mean square error (MSE) of the channel estimate subject to various constraints, such as an upper bound on the available training energy. We introduce a more general framework for the task of training sequence design in MIMO systems, which can treat not only the minimization of channel estimator's MSE, but also the optimization of a final performance metric of interest related to the use of the channel estimate in the communication system. First, we show that the proposed framework can be used to minimize the training energy budget subject to a quality constraint on the MSE of the channel estimator. A deterministic version of the "dual" problem is also provided. We then focus on four specific applications, where the training sequence can be optimized with respect to the classical channel estimation MSE, a weighted channel estimation MSE and the MSE of the equalization error due to the use of an equalizer at the receiver or an appropriate linear precoder at the transmitter. In this way, the intended use of the channel estimate is explicitly accounted for. The superiority of the proposed designs over existing methods is demonstrated via numerical simulations.
TL;DR: A metric to judge orthogonality among users only using their average channel gains is derived, based on which a semi-orthogonal scheduler is proposed that can be applied in a two-stage transmission strategy.
Abstract: We study low-signalling overhead scheduling for downlink coordinated multi-point (CoMP) transmission with multi-antenna base stations (BSs) and single-antenna users. By exploiting the asymmetric channel feature, i.e., the path-loss differences towards different BSs, we derive a metric to judge orthogonality among users only using their average channel gains, based on which we propose a semi-orthogonal scheduler that can be applied in a two-stage transmission strategy. Simulation results demonstrate that the proposed scheduler performs close to the semi-orthogonal scheduler with full channel information, especially when each BS is with more antennas and the cell-edge region is large. Compared with other overhead reduction strategies, the proposed scheduler requires much less training overhead to achieve the same cell-average data rate.
TL;DR: An estimator is developed that efficiently utilizes a set of noise-only samples and can incorporate prior knowledge of the DOAs with varying degrees of certainty, exhibiting improved performance for smaller sample sets and in poor signal conditions.
Abstract: For array processing, we consider the problem of estimating signals of interest, and their directions of arrival (DOA), in unknown colored noise fields. We develop an estimator that efficiently utilizes a set of noise-only samples and, further, can incorporate prior knowledge of the DOAs with varying degrees of certainty. The estimator is compared with state of the art estimators that utilize noise-only samples, and the Cramer-Rao bound, exhibiting improved performance for smaller sample sets and in poor signal conditions.
01 Jan 2013
TL;DR: This document describes the research activity in multi-node/multi-antenna technologies within METIS and positions it with respect to the state-of-the-art in the academic literature and in the standardization bodies.
Abstract: This document describes the research activity in multi-node/multi-antenna technologies within METIS and positions it with respect to the state-of-the-art in the academic literature and in the standardization bodies. Based on the state-of-the-art and as well as on the METIS objectives,
we set the research objectives and we group the different activities (or technology components) into research clusters with similar research objectives. The technology
components and the research objectives have been set to achieve an ambidextrous purpose. On one side we aim at providing the METIS system with those technological components that are a natural but non-trivial evolution of 4G. On the other side, we aim at seeking for disruptive
technologies that could radically change 5G with respect to 4G. Moreover, we mapped the different technology components to METIS’ other activities and to the overall goals of the
project.
26 May 2013
TL;DR: It is shown that for a unitarily-invariant uncertainty set, the optimally robust training sequence shares its eigenvectors with the channel covariance matrix, and analytical closed-form solutions for robust training sequences are given if the spectral norm or nuclear norm are considered as constraints to bound the existing uncertainty.
Abstract: In this paper, the problem of robust training sequence design for multiple-input single-output (MISO) channel estimation is investigated. The mean-squared error (MSE) of the channel estimates is considered as a performance criterion to design an optimized training sequence which is a function of channel covariance matrix. In practice, the channel covariance matrix is not perfectly known at the transmitter side. Our goal is to take such imperfection into account and propose a robust design following the worst-case philosophy which results in finding the optimal training sequences for the least favorable channel covariance matrix within a deterministic uncertainty set. In this work, we address the formulated minimax design problem under different assumptions of the uncertainty set, and we show that for a unitarily-invariant uncertainty set, the optimally robust training sequence shares its eigenvectors with the channel covariance matrix. Furthermore, we give analytical closed-form solutions for robust training sequences if the spectral norm or nuclear norm are considered as constraints to bound the existing uncertainty.
01 Dec 2013
TL;DR: Although the proposed scheme falls under the broad category of stochastic optimization, it has a quasi-deterministic convergence that it is exploited to improve on the worst case performance of its predecessor, resulting in significantly better sum-rate capacity and average cost function value.
Abstract: In this work, we study the so-called leakage minimization problem, within the context of interference alignment (IA). For that purpose, we propose a novel approach based on controlled perturbations of the leakage function, and show how the latter can be used as a mechanism to control the algorithm's convergence (and thus tradeoff convergence speed for reliability). Although the proposed scheme falls under the broad category of stochastic optimization, we show through simulations that it has a quasi-deterministic convergence that we exploit to improve on the worst case performance of its predecessor, resulting in significantly better sum-rate capacity and average cost function value.
Proceedings Article•
01 Sep 2013TL;DR: The Correlation Matrix Distance (CMD) method previously proposed for the evaluation of MIMO channel non-stationarity is considered and a couple of problems with the CMD measure are highlighted and two new metrics that are more appropriate for non- stationarity evaluation are proposed.
Abstract: Several MIMO processing algorithms have been proposed that exploit long-term channel statistics, relaying on the critical assumption that this long-term information is valid long enough. In this paper, we consider the Correlation Matrix Distance (CMD) method previously proposed for the evaluation of MIMO channel non-stationarity. We highlight a couple of problems with the CMD measure and propose two new metrics that are more appropriate for non-stationarity evaluation. The performance of the CMD method and new correlation matrix distance metrics is investigated using measured 4×4 MIMO channels. Both Line-of-Sight (LOS) and Non-LOS (NLOS) environments are considered.
TL;DR: In this article, an estimator that efficiently utilizes a set of noise-only samples and incorporates prior knowledge of the directions of arrival (DOA) with varying degrees of certainty is presented.
Abstract: For array processing, we consider the problem of estimating signals of interest, and their directions of arrival (DOA), in unknown colored noise fields. We develop an estimator that efficiently utilizes a set of noise-only samples and, further, can incorporate prior knowledge of the DOAs with varying degrees of certainty. The estimator is compared with state of the art estimators that utilize noise-only samples, and the Cram\'{e}r-Rao bound, exhibiting improved performance for smaller sample sets and in poor signal conditions.
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TL;DR: This paper focuses on examining the optimality of usual estimators such as the minimum variance unbiased (MVU) and the minimum mean square error (MMSE) estimators for these metrics and on proposing better estimators whenever it is necessary.
Abstract: The fundamental task of a digital receiver is to decide the transmitted symbols in the best possible way, i.e., with respect to an appropriately defined performance metric. Examples of usual performance metrics are the probability of error and the Mean Square Error (MSE) of a symbol estimator. In a coherent receiver, the symbol decisions are made based on the use of a channel estimate. This paper focuses on examining the optimality of usual estimators such as the minimum variance unbiased (MVU) and the minimum mean square error (MMSE) estimators for these metrics and on proposing better estimators whenever it is necessary. For illustration purposes, this study is performed on a toy channel model, namely a single input single output (SISO) flat fading channel with additive white Gaussian noise (AWGN). In this way, this paper highlights the design dependencies of channel estimators on target performance metrics.