References of "Bjornson, Emil"
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See detailOptimal Multiuser Transmit Beamforming: A Difficult Problem with a Simple Solution Structure [Lecture Notes]
Björnson, Emil; Bengtsson; Ottersten, Björn UL

in IEEE Signal Processing Magazine (2014), 31(4), 142-148

Transmit beamforming is a versatile technique for signal transmission from an array of antennas to one or multiple users [1]. In wireless communications, the goal is to increase the signal power at the ... [more ▼]

Transmit beamforming is a versatile technique for signal transmission from an array of antennas to one or multiple users [1]. In wireless communications, the goal is to increase the signal power at the intended user and reduce interference to nonintended users. A high signal power is achieved by transmitting the same data signal from all antennas but with different amplitudes and phases, such that the signal components add coherently at the user. Low interference is accomplished by making the signal components add destructively at nonintended users. This corresponds mathematically to designing beamforming vectors (that describe the amplitudes and phases) to have large inner products with the vectors describing the intended channels and small inner products with nonintended user channels. [less ▲]

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See detailMultiobjective Signal Processing Optimization : The way to balance conflicting metrics in 5G systems
Bjornson, Emil; Jorswieck; Debbah et al

in IEEE Signal Processing Magazine (2014), 31(6), 14-23

The evolution of cellular networks is driven by the dream of ubiquitous wireless connectivity: any data service is instantly accessible everywhere. With each generation of cellular networks, we have moved ... [more ▼]

The evolution of cellular networks is driven by the dream of ubiquitous wireless connectivity: any data service is instantly accessible everywhere. With each generation of cellular networks, we have moved closer to this wireless dream; first by delivering wireless access to voice communications, then by providing wireless data services, and recently by delivering a Wi-Fi-like experience with wide-area coverage and user mobility management. The support for high data rates has been the main objective in recent years [1], as seen from the academic focus on sum-rate optimization and the efforts from standardization bodies to meet the peak rate requirements specified in IMT-Advanced. In contrast, a variety of metrics/objectives are put forward in the technological preparations for fifth-generation (5G) networks: higher peak rates, improved coverage with uniform user experience, higher reliability and lower latency, better energy efficiency (EE), lower-cost user devices and services, better scalability with number of devices, etc. These multiple objectives are coupled, often in a conflicting manner such that improvements in one objective lead to degradation in the other objectives. Hence, the design of future networks calls for new optimization tools that properly handle the existence of multiple objectives and tradeoffs between them. [less ▲]

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See detailReceive combining vs. multi-stream multiplexing in downlink systems with multi-antenna users
Bjornson, Emil; Bengtsson, M.; Ottersten, Björn UL

in IEEE Transactions on Signal Processing (2013), 13(61), 3431-3446

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 ... [more ▼]

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. [less ▲]

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See detailCapacity limits and multiplexing gains of MIMO channels with transceiver impairments
Bjornson, Emil; Zetterberg, P.; Bengtsson, M. et al

in IEEE Communications Letters (2013), 1(17), 91-94

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 ... [more ▼]

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. [less ▲]

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See detailPareto Characterization of the Multicell MIMO Performance Region With Simple Receivers
Björnson, Emil; Bengtsson, Mats; Ottersten, Björn UL

in IEEE Transactions on Signal Processing (2012), 60(8), 4464-4469

We study the performance region of a general multicell downlink scenario with multiantenna transmitters, hardware impairments, and low-complexity receivers that treat interference as noise. The Pareto ... [more ▼]

We study the performance region of a general multicell downlink scenario with multiantenna transmitters, hardware impairments, and low-complexity receivers that treat interference as noise. The Pareto boundary of this region describes all efficient resource allocations, but is generally hard to compute. We propose a novel explicit characterization that gives Pareto optimal transmit strategies using a set of positive parameters-fewer than in prior work. We also propose an implicit characterization that requires even fewer parameters and guarantees to find the Pareto boundary for every choice of parameters, but at the expense of solving quasi-convex optimization problems. The merits of the two characterizations are illustrated for interference channels and ideal network multiple-input multiple-output (MIMO). [less ▲]

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See detailRobust Monotonic Optimization Framework for Multicell MISO Systems
Björnson, Emil; Zheng, Gan UL; Bengtsson, Mats et al

in IEEE Transactions on Signal Processing (2012), 60(5), 2508-2523

The performance of multiuser systems is both difficult to measure fairly and to optimize. Most resource allocation problems are nonconvex and NP-hard, even under simplifying assumptions such as perfect ... [more ▼]

The performance of multiuser systems is both difficult to measure fairly and to optimize. Most resource allocation problems are nonconvex and NP-hard, even under simplifying assumptions such as perfect channel knowledge, homogeneous channel properties among users, and simple power constraints. We establish a general optimization framework that systematically solves these problems to global optimality. The proposed branch-reduce-and-bound (BRB) algorithm handles general multicell downlink systems with single-antenna users, multiantenna transmitters, arbitrary quadratic power constraints, and robust- ness to channel uncertainty. A robust fairness-profile optimization (RFO) problem is solved at each iteration, which is a quasiconvex problem and a novel generalization of max-min fairness. The BRB algorithm is computationally costly, but it shows better convergence than the previously proposed outer polyblock approximation algorithm. Our framework is suitable for computing benchmarks in general multicell systems with or without channel uncertainty. We illustrate this by deriving and evaluating a zero-forcing solution to the general problem. [less ▲]

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See detailOptimality Properties,Distributed Strategies, and Measurement-Based Evaluation of Coordinated Multicell OFDMA Transmission
Björnson, Emil; Jaldén, Niklas; Bengtsson, Mats et al

in IEEE Transactions on Signal Processing (2011), 59(12), 6086-6101

The throughput of multicell systems is inherently limited by interference and the available communication resources. Coordinated resource allocation is the key to efficient performance, but the demand on ... [more ▼]

The throughput of multicell systems is inherently limited by interference and the available communication resources. Coordinated resource allocation is the key to efficient performance, but the demand on backhaul signaling and computational resources grows rapidly with number of cells, terminals, and subcarriers. To handle this, we propose a novel multicell framework with dynamic cooperation clusters where each terminal is jointly served by a small set of base stations. Each base station coordinates interference to neighboring terminals only, thus limiting backhaul signalling and making the framework scalable. This framework can describe anything from interference channels to ideal joint multicell transmission. The resource allocation (i.e., precoding and scheduling) is formulated as an optimization problem (P1) with performance described by arbitrary monotonic functions of the signal-to-interference-and-noise ratios (SINRs) and arbitrary linear power constraints. Although (P1) is nonconvex and difficult to solve optimally, we are able to prove: 1) optimality of single-stream beamforming; 2) conditions for full power usage; and 3) a precoding parametrization based on a few parameters between zero and one. These optimality properties are used to propose low-complexity strategies: both a centralized scheme and a distributed version that only requires local channel knowledge and processing. We evaluate the performance on measured multicell channels and observe that the proposed strategies achieve close-to-optimal performance among centralized and distributed solutions, respectively. In addition, we show that multicell interference coordination can give substantial improvements in sum performance, but that joint transmission is very sensitive to synchronization errors and that some terminals can experience performance degradations. [less ▲]

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See detailChannel Quantization Design in Multiuser MIMO Systems: Asymptotic versus Practical Conclusions
Björnson, Emil; Ntontin, Konstantinos; Ottersten, Björn UL

in Channel Quantization Design in Multiuser MIMO Systems: Asymptotic versus Practical Conclusions (2011, May)

Feedback of channel state information (CSI) is necessary to achieve high throughput and low outage probability in multiuser multi antenna systems. There are two types of CSI: directional and quality ... [more ▼]

Feedback of channel state information (CSI) is necessary to achieve high throughput and low outage probability in multiuser multi antenna systems. There are two types of CSI: directional and quality information. Many papers have analyzed the importance of these in asymptotic regimes. However, we show that such results should be handled with care, as very different conclusions can be drawn depending on the spatial correlation and number of users. There fore, we propose a quantization framework and evaluate the tradeoff between directional and quality feedback under practical conditions. [less ▲]

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See detailComputational Framework for Optimal Robust Beamforming in Coordinated Multicell Systems
Björnson, Emil; Bengtsson, Mats; Zheng, Gan UL et al

in Computational Framework for Optimal Robust Beamforming in Coordinated Multicell Systems (2011)

Coordinated beamforming can significantly improve the performance of cellular systems through joint interference management. Unfortunately, such beamforming optimization problems are typically NP-hard in ... [more ▼]

Coordinated beamforming can significantly improve the performance of cellular systems through joint interference management. Unfortunately, such beamforming optimization problems are typically NP-hard in multicell scenarios, making heuristic beamforming the only feasible choice in practice. This paper proposes a new branch-reduce-and-bound algorithm that solves such optimization problems globally, with a complexity suitable for benchmarking and analysis. Compared to prior work, the framework handles robustness to uncertain intercell interference and numerical analysis shows higher efficiency. [less ▲]

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See detailImpact of Spatial Correlation and Precoding Design in OSTBC MIMO Systems
Björnson, Emil; Eduard, Jorswieck; Ottersten, Björn UL

in IEEE Transactions on Wireless Communications (2010), 9(11), 3578-3589

The impact of transmission design and spatial correlation on the symbol error rate (SER) is analyzed for multi-antenna communication links. The receiver has perfect channel state information (CSI), while ... [more ▼]

The impact of transmission design and spatial correlation on the symbol error rate (SER) is analyzed for multi-antenna communication links. The receiver has perfect channel state information (CSI), while the transmitter has either statistical or no CSI. The transmission is based on orthogonal space-time block codes (OSTBCs) and linear precoding. The precoding strategy that minimizes the worst-case SER is derived for the case when the transmitter has no CSI. Based on this strategy, the intuitive result that spatial correlation degrades the SER performance is proved mathematically. In the case when the transmitter knows the channel statistics, the correlation matrix is assumed to be jointly-correlated (a generalization of the Kronecker model). The eigenvectors of the SER-optimal precoding matrix are shown to originate from the correlation matrix and the remaining power allocation is a convex problem. Equal power allocation is SER-optimal at high SNR. Beamforming is SER-optimal at low SNR, or for increasing constellation sizes, and its optimality range is characterized. A heuristic low-complexity power allocation is proposed and evaluated numerically. Finally, it is proved analytically that receive-side correlation always degrades the SER. Transmit-side correlation will however improve the SER at low to medium SNR, while its impact is negligible at high SNR. [less ▲]

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See detailCooperative Multicell Precoding : Rate Region Characterization and Distributed Strategies with Instantaneous and Statistical CSI
Björnson, Emil; Randa, Zakhour; David, Gesbert et al

in IEEE Transactions on Signal Processing (2010), 58(8), 4298-4310

Base station cooperation is an attractive way of increasing the spectral efficiency in multiantenna communication. By serving each terminal through several base stations in a given area, intercell ... [more ▼]

Base station cooperation is an attractive way of increasing the spectral efficiency in multiantenna communication. By serving each terminal through several base stations in a given area, intercell interference can be coordinated and higher performance achieved, especially for terminals at cell edges. Most previous work in the area has assumed that base stations have common knowledge of both data dedicated to all terminals and full or partial channel state information (CSI) of all links. Herein, we analyze the case of distributed cooperation where each base station has only local CSI, either instantaneous or statistical. In the case of instantaneous CSI, the beamforming vectors that can attain the outer boundary of the achievable rate region are characterized for an arbitrary number of multiantenna transmitters and single-antenna receivers. This characterization only requires local CSI and justifies distributed precoding design based on a novel virtual signal-to-interference noise ratio (SINR) framework, which can handle an arbitrary SNR and achieves the optimal multiplexing gain. The local power allocation between terminals is solved heuristically. Conceptually, analogous results for the achievable rate region characterization and precoding design are derived in the case of local statistical CSI. The benefits of distributed cooperative transmission are illustrated numerically, and it is shown that most of the performance with centralized cooperation can be obtained using only local CSI. [less ▲]

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See detailA Framework for Training-Based Estimation in Arbitrarily Correlated Rician MIMO Channels with Rician Disturbance
Björnson, Emil; Ottersten, Björn UL

in IEEE Transactions on Signal Processing (2010), 58(3), 1807-1820

In this paper, we create a framework for training-based channel estimation under different channel and interference statistics. The minimum mean square error (MMSE) estimator for channel matrix estimation ... [more ▼]

In this paper, we create a framework for training-based channel estimation under different channel and interference statistics. The minimum mean square error (MMSE) estimator for channel matrix estimation in Rician fading multi-antenna systems is analyzed, and especially the design of mean square error (MSE) minimizing training sequences. By considering Kronecker-structured systems with a combination of noise and interference and arbitrary training sequence length, we collect and generalize several previous results in the framework. We clarify the conditions for achieving the optimal training sequence structure and show when the spatial training power allocation can be solved explicitly. We also prove that spatial correlation improves the estimation performance and establish how it determines the optimal training sequence length. The analytic results for Kronecker-structured systems are used to derive a heuristic training sequence under general unstructured statistics. The MMSE estimator of the squared Frobenius norm of the channel matrix is also derived and shown to provide far better gain estimates than other approaches. It is shown under which conditions training sequences that minimize the non-convex MSE can be derived explicitly or with low complexity. Numerical examples are used to evaluate the performance of the two estimators for different training sequences and system statistics. We also illustrate how the optimal length of the training sequence often can be shorter than the number of transmit antennas. [less ▲]

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See detailOptimality Properties and Low-Complexity Solutions to Coordinated Multicell Transmission
Björnson, Emil; Bengtsson, Mats; Ottersten, Björn UL

in Global Telecommunications Conference (GLOBECOM 2010), 2010 IEEE (2010)

Base station cooperation can theoretically improve the throughput of multicell systems by coordinating interference and serving cell edge terminals through multiple base stations. In practice, the extent ... [more ▼]

Base station cooperation can theoretically improve the throughput of multicell systems by coordinating interference and serving cell edge terminals through multiple base stations. In practice, the extent of cooperation is limited by the increase in backhaul signaling and computational demands. To address these concerns, we propose a novel distributed cooperation structure where each base station has responsibility for the interference towards a set of terminals, while only serving a subset of them with data. Weighted sum rate maximization is considered, and conditions for beamforming optimality and the optimal transmission structure are derived using Lagrange duality theory. This leads to distributed low-complexity transmission strategies, which are evaluated on measured multiantenna channels in a typical urban multicell environment. [less ▲]

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See detailExploiting Quantized Channel Norm Feedback Through Conditional Statistics in Arbitrarily Correlated MIMO Systems
Björnson, Emil; Hammarwall, David; Ottersten, Björn UL

in IEEE Transactions on Signal Processing (2009), 57(10), 4027-4041

In the design of narrowband multi-antenna systems, a limiting factor is the amount of channel state information (CSI) available at the transmitter. This is especially evident in multi-user systems, where ... [more ▼]

In the design of narrowband multi-antenna systems, a limiting factor is the amount of channel state information (CSI) available at the transmitter. This is especially evident in multi-user systems, where the spatial user separability determines the multiplexing gain, but it is also important for transmission-rate adaptation in single-user systems. To limit the feedback load, the unknown and multi-dimensional channel needs to be represented by a limited number of bits. When combined with long-term channel statistics, the norm of the channel matrix has been shown to provide substantial CSI that permits efficient user selection, linear precoder design, and rate adaptation. Herein, we consider quantized feedback of the squared Frobenius norm in a Rayleigh fading environment with arbitrary spatial correlation. The conditional channel statistics are characterized and their moments are derived for both identical, distinct, and sets of repeated eigenvalues. These results are applied for minimum mean square error (MMSE) estimation of signal and interference powers in single- and multi-user systems, for the purpose of reliable rate adaptation and resource allocation. The problem of efficient feedback quantization is discussed and an entropy-maximizing framework is developed where the post-user-selection distribution can be taken into account in the design of the quantization levels. The analytic results of this paper are directly applicable in many widely used communication techniques, such as space-time block codes, linear precoding, space division multiple access (SDMA), and scheduling. [less ▲]

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See detailOn the Impact of Spatial Correlation and Precoder Design on the Performance of MIMO Systems with Space-Time Coding
Björnson, Emil; Ottersten, Björn UL; Jorswieck, Eduard

in Acoustics, Speech and Signal Processing, 2009. ICASSP 2009. IEEE International Conference on (2009)

The symbol error performance of spatially correlated multi-antenna systems is analyzed herein. When the transmitter only has statistical channel information, the use of space-time block codes still ... [more ▼]

The symbol error performance of spatially correlated multi-antenna systems is analyzed herein. When the transmitter only has statistical channel information, the use of space-time block codes still permits spatial multiplexing and mitigation of fading. The statistical information can be used for precoding to optimize some quality measure. Herein, we analyze the performance in terms of the symbol error rate (SER). It is shown analytically that spatial correlation at the receiver decreases the performance both without precoding and with an SER minimizing precoder. Without precoding, correlation should also be avoided at the transmitter side, but with an SER minimizing precoder the performance is actually improved by increasing spatial correlation at the transmitter. The structure of the optimized precoder is analyzed and the asymptotic properties at high and low SNRs are characterized and illustrated numerically. [less ▲]

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See detailDistributed Multicell and Multiantenna Precoding: Characterization and Performance Evaluation
Björnson, Emil; Zakhour, Randa; Gesbert, David et al

in Global Telecommunications Conference, 2009. GLOBECOM 2009. IEEE (2009)

This paper considers downlink multiantenna communication with base stations that perform cooperative precoding in a distributed fashion. Most previous work in the area has assumed that transmitters have ... [more ▼]

This paper considers downlink multiantenna communication with base stations that perform cooperative precoding in a distributed fashion. Most previous work in the area has assumed that transmitters have common knowledge of both data symbols of all users and full or partial channel state information (CSI). Herein, we assume that each base station only has local CSI, either instantaneous or statistical. For the case of instantaneous CSI, a parametrization of the beamforming vectors used to achieve the outer boundary of the achievable rate region is obtained for two multi-antenna transmitters and two single-antenna receivers. Distributed generalizations of classical beamforming approaches that satisfy this parametrization are provided, and it is shown how the distributed precoding design can be improved using the so-called virtual SINR framework. Conceptually analog results for both the parametrization and the beamforming design are derived in the case of local statistical CSI. Heuristics on the distributed power allocation are provided in both cases, and the performance is illustrated numerically. [less ▲]

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See detailOn the Principles of Multicell Precoding with Centralized and Distributed Cooperation Björnson, Emi Ottersten, Björn
Björnson, Emil; Ottersten, Björn UL

in Wireless Communications & Signal Processing, 2009. WCSP 2009. International Conference on (2009)

Cooperative precoding is an attractive way of improving the performance in multicell downlink scenarios. By serving each terminal through multiple surrounding base stations, inter-cell interference can be ... [more ▼]

Cooperative precoding is an attractive way of improving the performance in multicell downlink scenarios. By serving each terminal through multiple surrounding base stations, inter-cell interference can be coordinated and higher spectral efficiency achieved, especially for terminals at cell edges. The optimal performance of multicell precoding is well-known as it can be treated as a single cell with distributed antennas. However, the requirements on backhaul signaling and computational power scales rapidly in large and dense networks, which often makes such fully centralized approaches impractical. In this paper, we review and generalize some recent work on multicell precoding with both centralized and distributed cooperation. We propose practical precoding strategies under Rician channel conditions, and illustrate how the major gain of multicell precoding originates from having good base station synchronization and not from making centralized precoding decisions. [less ▲]

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See detailTraining-Based Bayesian MIMO Channel and Channel Norm Estimation
Björnson, Emil; Ottersten, Björn UL

in Acoustics, Speech and Signal Processing, 2009. ICASSP 2009. IEEE International Conference on (2009)

Training-based estimation of channel state information in multi-antenna systems is analyzed herein. Closed-form expressions for the general Bayesian minimum mean square error (MMSE) estimators of the ... [more ▼]

Training-based estimation of channel state information in multi-antenna systems is analyzed herein. Closed-form expressions for the general Bayesian minimum mean square error (MMSE) estimators of the channel matrix and the squared channel norm are derived in a Rayleigh fading environment with known statistics at the receiver side. When the second-order channel statistics are available also at the transmitter, this information can be exploited in the training sequence design to improve the performance. Herein, mean square error (MSE) minimizing training sequences are considered. The structure of the general solution is developed, with explicit expressions at high and low SNRs and in the special case of uncorrelated receive antennas. The optimal length of the training sequence is equal or smaller than the number of transmit antennas. [less ▲]

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See detailExploiting Long-term Statistics in Spatially Correlated Multi-user MIMO Systems with Quantized Channel Norm Feedback
Björnson, Emil; Ottersten, Björn UL

in Proceedings IEEE International Conference on Acoustics, Speech, and Signal (ICASSP) (2008)

In wireless multiple antenna and multi-user systems, the spatial dimensions may be exploited to increase the performance by means of antenna gain, spatial diversity, and multi-user diversity. A limiting ... [more ▼]

In wireless multiple antenna and multi-user systems, the spatial dimensions may be exploited to increase the performance by means of antenna gain, spatial diversity, and multi-user diversity. A limiting factor in such systems is the channel information required by the transmitter to control the intra-cell interference. Herein, the properties of spatially correlated channels with longterm statistical information at the transmitter and fixed-rate feedback of the quantized Euclidean channel norm are analyzed using a spectral subspace decomposition framework. A spatial division multiple access scheme is proposed with interference suppression at the receiver and joint scheduling and zero-forcing beamforming at the transmitter. Closed-form expressions for first and second moments of the feedback conditional channel statistics are derived. It is shown that only a few bits of feedback are required to achieve reliable rate estimation and weighted sum-rate maximization. [less ▲]

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See detailFeedback design in multiuser MIMO systems using quantization splitting and hybrid instantaneous/statistical channel information
Björnson, Emil; Hammarwall, David; Zakhour, Randa et al

in Proceedings ICT Mobile and Wireless Communications Summit (2008)

In the design of next generation multiuser communication systems, multiple antenna transmission is an essential part providing spatial multiplexing gain and allowing efficient use of resources. A major ... [more ▼]

In the design of next generation multiuser communication systems, multiple antenna transmission is an essential part providing spatial multiplexing gain and allowing efficient use of resources. A major limiting factor in the resource allocation is the amount of channel state information (CSI) available at the transmitter, particularly in multiuser systems where the feedback from each user terminal must be limited. To this effect we propose two independent approaches for an efficient representation of the channel in multiuser MIMO systems. In the first approach, channel quantization is considered where the total number of feedback bits is limited. A resource allocation scheme is proposed where the available rate is split between the scheduling phase, where all users feed back a coarse CSI quantization, and the precoding phase where the selected receivers refine their CSI. The optimum splitting of the available feedback rate provides a large increase in performance and even simple heuristic splitting gives a noticeable advantage. In the second approach, we exploit a combination of instantaneous and statistical channel information. For spatially correlated Rayleigh and Ricean channels, it is shown that the CSI to large extent can be represented by the channel norm when the long-term channel statistics are known. Within a minimum mean square error (MMSE) estimation framework, feedback of a few bits of the quantized channel norm is sufficient to perform efficient resource allocation and achieve performance close to that of full CSI. [less ▲]

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