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See detailCodebook-Based Hybrid Precoding for Millimeter Wave Multiuser Systems
He, S.; Wang, J.; Huang, Y. et al

in IEEE Transactions on Signal Processing (2017), 65(20), 5289-5304

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See detailPer-antenna constant envelope precoding and antenna subset selection: A geometric approach
Zhang, J.; Huang, Y.; Wang, J. et al

in IEEE Transactions on Signal Processing (2016), 64(23), 6089-6104

Constant envelope (CE) precoding can efficiently control the peak-to-average power ratio (PAPR) and improve the power efficiency of power amplifiers in large-scale antenna array systems. Antenna subset ... [more ▼]

Constant envelope (CE) precoding can efficiently control the peak-to-average power ratio (PAPR) and improve the power efficiency of power amplifiers in large-scale antenna array systems. Antenna subset selection (ASS), combined with CE precoding, can further improve power efficiency by using a part of antennas to combine the desired signal. However, due to the inherent nonlinearity, the joint optimization of CE precoding and ASS is very challenging and satisfactory solutions are yet not available. In this paper, we present new methods for CE precoding and ASS optimization from a geometric perspective. First, we show the equivalence between the CE precoder design and a polygon construction problem in the complex plane, thus transforming the algebraic problem into a geometric problem. Aiming to minimize the computational complexity, we further transform the CE precoder design into a triangle construction problem, and propose a novel algorithm to achieve the optimal CE precoder with only linear complexity in the number of used antennas. Then, we investigate the joint optimization of ASS and CE precoding to minimize the total transmit power while satisfying the QoS requirement. Based on the geometric interpretation, we develop an efficient ASS algorithm, which, using only addition and comparison operations, is guaranteed to find the globally optimal solution and provides robustness to channel uncertainty. The complexity of the proposed ASS algorithm is at most quadratic in the number of antennas in the worst case. The optimality and superiority of the proposed geometric methods are demonstrated via numerical results. [less ▲]

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See detailA parallel decomposition method for nonconvex stochastic multi-agent optimization problems
Yang, Yang UL; Scutari, Gesualdo; Palomar, Daniel et al

in IEEE Transactions on Signal Processing (2016), 64(11), 2949-2964

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See detailMultiantenna GLR Detection of Rank-One Signals With Known Power Spectral Shape Under Spatially Uncorrelated Noise
Sala, Josep; Vázquez-Vilar;, Gonzalo; López-Valcarce, Roberto et al

in IEEE Transactions on Signal Processing (2016), 64(23), 6269-6283

We establish the generalized likelihood ratio (GLR) test for a Gaussian signal of known power spectral shape and unknown rank-one spatial signature in additive white Gaussian noise with an unknown ... [more ▼]

We establish the generalized likelihood ratio (GLR) test for a Gaussian signal of known power spectral shape and unknown rank-one spatial signature in additive white Gaussian noise with an unknown diagonal spatial correlation matrix. This is motivated by spectrum sensing problems in dynamic spectrum access, in which the temporal correlation of the primary signal can be assumed known up to a scaling, and where the noise is due to an uncalibrated receive array. For spatially independent identically distributed (i.i.d.) noise, the corresponding GLR test reduces to a scalar optimization problem, whereas the GLR detector in the general non-i.i.d. case yields a more involved expression, which can be computed via alternating optimization methods. Low signal-to-noise ratio (SNR) approximations to the detectors are given, together with an asymptotic analysis showing the influence on detection performance of the signal power spectrum and SNR distribution across antennas. Under spatial rank-P conditions, we show that the rank-one GLR detectors are consistent with a statistical criterion that maximizes the output energy of a beamformer operating on filtered data. Simulation results support our theoretical findings in that exploiting prior knowledge on the signal power spectrum can result in significant performance improvement. [less ▲]

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See detailConstructive Multiuser Interference in Symbol Level Precoding for the MISO Downlink Channel
Alodeh, Maha UL; Chatzinotas, Symeon UL; Ottersten, Björn UL

in IEEE Transactions on Signal Processing (2015)

This paper investigates the problem of interference among the simultaneous multiuser transmissions in the downlink of multiple-antenna systems. Using symbol-level precoding, a new approach to exploit the ... [more ▼]

This paper investigates the problem of interference among the simultaneous multiuser transmissions in the downlink of multiple-antenna systems. Using symbol-level precoding, a new approach to exploit the multiuser interference is discussed. The concept of exploiting the interference between spatial multiuser transmissions by jointly utilizing data information (DI) and channel state information (CSI), in order to design symbol-level precoders, is proposed. To this end, the interference between data streams is transformed under certain conditions into useful signal that can improve the signal to interference noise ratio (SINR) of the downlink transmissions. We propose a maximum ratio transmission (MRT) based algorithm that jointly exploits DI and CSI to glean the benefits from constructive multiuser interference. Subsequently, a relation between the constructive interference downlink transmission and physical layer multicasting is established. In this context, novel constructive interference precoding techniques that tackle the transmit power minimization (min-power) with individual SINR constraints at each user's receivers is proposed. Furthermore, fairness through maximizing the weighted minimum SINR (max-min SINR) of the users is addressed by finding the link between the min power and max min SINR problems. Moreover, heuristic precoding techniques are proposed to tackle the weighted sum rate problem. Finally, extensive numerical results show that the proposed schemes outperform other state of the art techniques. [less ▲]

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See detailOn the Performance of Hadamard Ratio Detector-based Spectrum Sensing for Cognitive Radios
Sedighi, Saeid UL; Taherpour, Abbas; Sala, Josep et al

in IEEE Transactions on Signal Processing (2015), 63(14), 38093824

—We consider the problem of multiantenna spectrum sensing (SS) in cognitive radios (CRs) when the receivers are assumed to be uncalibrated across the antennas. The performance of the Hadamard Ratio ... [more ▼]

—We consider the problem of multiantenna spectrum sensing (SS) in cognitive radios (CRs) when the receivers are assumed to be uncalibrated across the antennas. The performance of the Hadamard Ratio Detector (HRD) is analyzed in such a scenario. Specifically, we first derive the exact distribution of the HRD statistic under the null hypothesis, which leads to an elaborate but closed-form expression for the false-alarm probability. Then, we derive a simpler and tight closed-form approximation for both the false-alarm and detection probabilities by using a moment-based approximation of the HRD statistical distribution under both hypotheses. Finally, the accuracy of the obtained results is verified by simulations. [less ▲]

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See detailSpatial DCT-Based Channel Estimation in Multi-Antenna Multi-Cell Interference Channels
Alodeh, Maha UL; Chatzinotas, Symeon UL; Ottersten, Björn UL

in IEEE Transactions on Signal Processing (2015)

This work addresses channel estimation in multiple antenna multicell interference-limited networks. Channel state information (CSI) acquisition is vital for interference mitigation. Wireless networks ... [more ▼]

This work addresses channel estimation in multiple antenna multicell interference-limited networks. Channel state information (CSI) acquisition is vital for interference mitigation. Wireless networks often suffer from multicell interference, which can be mitigated by deploying beamforming to spatially direct the transmissions. The accuracy of the estimated CSI plays an important role in designing accurate beamformers that can control the amount of interference created from simultaneous spatial transmissions to mobile users. Therefore, a new technique based on the structure of the spatial covariance matrix and the discrete cosine transform (DCT) is proposed to enhance channel estimation in the presence of interference. Bayesian estimation and Least Squares estimation frameworks are introduced by utilizing the DCT to separate the overlapping spatial paths that create the interference. The spatial domain is thus exploited to mitigate the contamination which is able to discriminate across interfering users. Gains over conventional channel estimation techniques are presented in our simulations which are also valid for a small number of antennas. [less ▲]

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See detailData Predistortion for Multicarrier Satellite Channels Based on Direct Learning
Piazza, Roberto UL; Shankar, Bhavani UL; Ottersten, Björn UL

in IEEE Transactions on Signal Processing (2014), 62(22),

Satellite communication is facing the urgent need of improving data rate and efficiency to compete with the quality of service offered by terrestrial communication systems. An imminent gain, achievable ... [more ▼]

Satellite communication is facing the urgent need of improving data rate and efficiency to compete with the quality of service offered by terrestrial communication systems. An imminent gain, achievable without the need of upgrading current satellite technology, can be obtained by exploiting multicarrier operation at the transponder and using highly efficient modulation schemes. However, on-board multicarrier joint amplification of high order modulation schemes is a critical operation as it brings severe non-linear distortion effects. These distortions increase as the on-board High Power Amplifier (HPA) is operated to yield higher power efficiencies. In this work, we propose novel techniques to implement on ground predistortion that enable multicarrier transmission of highly efficient modulation schemes over satellite channels without impacting infrastructure on the downlink. [less ▲]

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See detailStatistical Framework for Optimization in the Multi-User MIMO Uplink With ZF-DFE
Järmyr, Simon; Ottersten, Björn UL; Jorswieck, Eduard A.

in IEEE Transactions on Signal Processing (2014), 62(10), 2730-2745

We consider performance optimization in the uplink of a multiuser multiantenna communication system. Each user multiplexes data onto several independently encoded data streams, which are spatially ... [more ▼]

We consider performance optimization in the uplink of a multiuser multiantenna communication system. Each user multiplexes data onto several independently encoded data streams, which are spatially precoded and conveyed over a fading narrowband multiple-input multiple-output (MIMO) channel. All users' data streams are decoded successively at the receiving base station using zero-forcing decision feedback equalization (ZF-DFE). We target the joint optimization of a decoding order and linear precoders for all users based on long-term channel information. For a class of general MIMO channel models, including the separable-correlation and double-scattering models, we show that the choice of precoder for a certain user does not affect the performance of the others. This leads to a particularly straightforward characterization of general user utility regions as a polyblock, or a convex polytope if time-sharing is allowed. We formulate the decoding-ordering problem under transmit-correlated Rayleigh fading as a linear assignment problem, enabling the use of existing efficient algorithms. Combining decoding ordering with single-user precoder optimization by means of alternating optimization, we propose an efficient iterative scheme that is verified numerically to converge fast and perform close to optimally, successfully reaping the benefits of both precoding and ordering in the MIMO uplink. [less ▲]

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See detailCoordinated Multicell Multiuser Precoding for Maximizing Weighted Sum Energy Efficiency
He, Shiwen; Huang, Yongming; Yang, Luxi et al

in IEEE Transactions on Signal Processing (2014), 62(3), 741-751

Energy efficiency optimization of wireless systems has become urgently important due to its impact on the global carbon footprint. In this paper we investigate energy efficient multicell multiuser ... [more ▼]

Energy efficiency optimization of wireless systems has become urgently important due to its impact on the global carbon footprint. In this paper we investigate energy efficient multicell multiuser precoding design and consider a new criterion of weighted sum energy efficiency, which is defined as the weighted sum of the energy efficiencies of multiple cells. This objective is more general than the existing methods and can satisfy heterogeneous requirements from different kinds of cells, but it is hard to tackle due to its sum-of-ratio form. In order to address this non-convex problem, the user rate is first formulated as a polynomial optimization problem with the test conditional probabilities to be optimized. Based on that, the sum-of-ratio form of the energy efficient precoding problem is transformed into a parameterized polynomial form optimization problem, by which a solution in closed form is achieved through a two-layer optimization. We also show that the proposed iterative algorithm is guaranteed to converge. Numerical results are finally provided to confirm the effectiveness of our energy efficient beamforming algorithm. It is observed that in the low signal-to-noise ratio (SNR) region, the optimal energy efficiency and the optimal sum rate are simultaneously achieved by our algorithm; while in the middle-high SNR region, a certain performance loss in terms of the sum rate is suffered to guarantee the weighed sum energy efficiency. [less ▲]

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See detailCompressive Sparsity Order Estimation for Wideband Cognitive Radio Receiver
Sharma, Shree Krishna UL; Chatzinotas, Symeon UL; Ottersten, Björn UL

in IEEE Transactions on Signal Processing (2014)

Compressive Sensing (CS) has been widely investigated in the Cognitive Radio (CR) literature in order to reduce the hardware cost of sensing wideband signals assuming prior knowledge of the sparsity ... [more ▼]

Compressive Sensing (CS) has been widely investigated in the Cognitive Radio (CR) literature in order to reduce the hardware cost of sensing wideband signals assuming prior knowledge of the sparsity pattern. However, the sparsity order of the channel occupancy is time-varying and the sampling rate of the CS receiver needs to be adjusted based on its value in order to fully exploit the potential of CS-based techniques. In this context, investigating blind Sparsity Order Estimation (SOE) techniques is an open research issue. To address this, we study an eigenvalue-based compressive SOE technique using asymptotic Random Matrix Theory. We carry out detailed theoretical analysis for the signal plus noise case to derive the asymptotic eigenvalue probability distribution function (aepdf) of the measured signal’s covariance matrix for sparse signals. Subsequently, based on the derived aepdf expressions, we propose a technique to estimate the sparsity order of the wideband spectrum with compressive measurements using the maximum eigenvalue of the measured signal’s covariance matrix. The performance of the proposed technique is evaluated in terms of normalized SOE Error (SOEE). It is shown that the sparsity order of the wideband spectrum can be reliably estimated using the proposed technique for a variety of scenarios. [less ▲]

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See detailMulti-portfolio optimization: A potential game approach
Yang, Yang UL; Rubio, Francisco; Scutari, Gesualdo et al

in IEEE Transactions on Signal Processing (2013)

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See detailTransceiver design for distributed STBC based AF cooperative networks in the presence of timing and frequency offsets
Nasir, A.A.; Mehrpouyan, H.; Durrani, S. et al

in IEEE Transactions on Signal Processing (2013), 12(61), 3143-3158

In multi-relay cooperative systems, the signal at the destination is affected by impairments such as multiple channel gains, multiple timing offsets (MTOs), and multiple carrier frequency offsets (MCFOs ... [more ▼]

In multi-relay cooperative systems, the signal at the destination is affected by impairments such as multiple channel gains, multiple timing offsets (MTOs), and multiple carrier frequency offsets (MCFOs). In this paper we account for all these impairments and propose a new transceiver structure at the relays and a novel receiver design at the destination in distributed space-time block code (DSTBC) based amplify-and-forward (AF) cooperative networks. The Cramér-Rao lower bounds and a least squares (LS) estimator for the multi-parameter estimation problem are derived. In order to significantly reduce the receiver complexity at the destination, a differential evolution (DE) based estimation algorithm is applied and the initialization and constraints for the convergence of the proposed DE algorithm are investigated. In order to detect the signal from multiple relays in the presence of unknown channels, MTOs, and MCFOs, novel optimal and sub-optimal minimum mean-square error receiver designs at the destination node are proposed. Simulation results show that the proposed estimation and compensation methods achieve full diversity gain in the presence of channel and synchronization impairments in multi-relay AF cooperative networks. [less ▲]

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See detailCooperative cognitive networks: Optimal, distributed and low-complexity algorithms
Zheng, Gan UL; Song, Shenghui; Wong, Kai-Kit et al

in IEEE Transactions on Signal Processing (2013), 11(61), 2778-2790

This paper considers the cooperation between a cognitive system and a primary system where multiple cognitive base stations (CBSs) relay the primary user's (PU) signals in exchange for more opportunity to ... [more ▼]

This paper considers the cooperation between a cognitive system and a primary system where multiple cognitive base stations (CBSs) relay the primary user's (PU) signals in exchange for more opportunity to transmit their own signals. The CBSs use amplify-and-forward (AF) relaying and coordinated beamforming to relay the primary signals and transmit their own signals. The objective is to minimize the overall transmit power of the CBSs given the rate requirements of the PU and the cognitive users (CUs). We show that the relaying matrices have unity rank and perform two functions: Matched filter receive beamforming and transmit beamforming. We then develop two efficient algorithms to find the optimal solution. The first one has a linear convergence rate and is suitable for distributed implementation, while the second one enjoys superlinear convergence but requires centralized processing. Further, we derive the beamforming vectors for the linear conventional zero-forcing (CZF) and prior zero-forcing (PZF) schemes, which provide much simpler solutions. Simulation results demonstrate the improvement in terms of outage performance due to the cooperation between the primary and cognitive systems. [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 detailA Bayesian Monte Carlo Markov Chain Method for Parameter Estimation of Fractional Differenced Gaussian Processes
Olivares Pulido, German UL; Teferle, Felix Norman UL

in IEEE Transactions on Signal Processing (2013), 61(9), 2405-2412

We present a Bayesian Monte Carlo Markov Chain method to simultaneously estimate the spectral index and power amplitude of a fractional differenced Gaussian process at low frequency, in presence of white ... [more ▼]

We present a Bayesian Monte Carlo Markov Chain method to simultaneously estimate the spectral index and power amplitude of a fractional differenced Gaussian process at low frequency, in presence of white noise, and a linear trend and periodic signals. This method provides a sample of the likelihood function and thereby, using Monte Carlo integration, all parameters and their uncertainties are estimated simultaneously. We test this method with simulated and real Global Positioning System height time series and propose it as an alternative to optimization methods currently in use. Furthermore, without any mathematical proof, the results from the simulations suggest that this method is unaffected by the stationary regime and hence, can be used to check whether or not a time series is stationary. [less ▲]

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See detailSparse conjoint analysis through maximum likelihood estimation
Tsakonas, Efthymios; Jalden, J.; Sidiropoulos, N.D et al

in IEEE Transactions on Signal Processing (2013), 22

Conjoint analysis (CA) is a classical tool used in preference assessment, where the objective is to estimate the utility function of an individual, or a group of individuals, based on expressed preference ... [more ▼]

Conjoint analysis (CA) is a classical tool used in preference assessment, where the objective is to estimate the utility function of an individual, or a group of individuals, based on expressed preference data. An example is choice-based CA for consumer profiling, i.e., unveiling consumer utility functions based solely on choices between products. A statistical model for choice-based CA is investigated in this paper. Unlike recent classification-based approaches, a sparsity-aware Gaussian maximum likelihood (ML) formulation is proposed to estimate the model parameters. Drawing from related robust parsimonious modeling approaches, the model uses sparsity constraints to account for outliers and to detect the salient features that influence decisions. Contributions include conditions for statistical identifiability, derivation of the pertinent Cramér-Rao Lower Bound (CRLB), and ML consistency conditions for the proposed sparse nonlinear model. The proposed ML approach lends itself naturally to ℓ1-type convex relaxations which are well-suited for distributed implementation, based on the alternating direction method of multipliers (ADMM). A particular decomposition is advocated which bypasses the apparent need for outlier communication, thus maintaining scalability. The performance of the proposed ML approach is demonstrated by comparing against the associated CRLB and prior state-of-the-art using both synthetic and real data sets. [less ▲]

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See detailImproving Physical Layer Secrecy Using Full-Duplex Jamming Receivers
Zheng, Gan UL; Krikidis, Ioannis; Jiangyuan, Li et al

in IEEE Transactions on Signal Processing (2013), 20(61), 4962-4974

This paper studies secrecy rate optimization in a wireless network with a single-antenna source, a multi-antenna destination and a multi-antenna eavesdropper. This is an unfavorable scenario for secrecy ... [more ▼]

This paper studies secrecy rate optimization in a wireless network with a single-antenna source, a multi-antenna destination and a multi-antenna eavesdropper. This is an unfavorable scenario for secrecy performance as the system is interference-limited. In the literature, assuming that the receiver operates in half duplex (HD) mode, the aforementioned problem has been addressed via use of cooperating nodes who act as jammers to confound the eavesdropper. This paper investigates an alternative solution, which assumes the availability of a full duplex (FD) receiver. In particular, while receiving data, the receiver transmits jamming noise to degrade the eavesdropper channel. The proposed self-protection scheme eliminates the need for external helpers and provides system robustness. For the case in which global channel state information is available, we aim to design the optimal jamming covariance matrix that maximizes the secrecy rate and mitigates loop interference associated with the FD operation. We consider both fixed and optimal linear receiver design at the destination, and show that the optimal jamming covariance matrix is rank-1, and can be found via an efficient 1-D search. For the case in which only statistical information on the eavesdropper channel is available, the optimal power allocation is studied in terms of ergodic and outage secrecy rates. Simulation results verify the analysis and demonstrate substantial performance gain over conventional HD operation at the destination. [less ▲]

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See detailRobust MIMO precoding for several classes of channel uncertainty
Wang, J.; Bengtsson, M.; Ottersten, Björn UL et al

in IEEE Transactions on Signal Processing (2013), 12(61), 3056-3070

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 ... [more ▼]

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. [less ▲]

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See detailIterative Precoder Design and User Scheduling for Block-Diagonalized Systems
Tran, Le-Nam; Bengtsson, Mats; Ottersten, Björn UL

in IEEE Transactions on Signal Processing (2012), 60(7), 3726-3739

The block diagonalization (BD) scheme is a low-complexity suboptimal precoding technique for multiuser multiple input-multiple output (MIMO) downlink channels, which completely precancels the multiuser ... [more ▼]

The block diagonalization (BD) scheme is a low-complexity suboptimal precoding technique for multiuser multiple input-multiple output (MIMO) downlink channels, which completely precancels the multiuser interference. Accordingly, the precoder of each user lies in the null space of other users' channel matrices. In this paper, we propose an iterative algorithm using QR decompositions (QRDs) to compute the precoders. Specifically, to avoid dealing with a large concatenated matrix, we apply the QRD to a sequence of matrices of lower dimensions. One problem of BD schemes is that the number of users that can be simultaneously supported is limited due to zero interference constraints. When the number of users is large, a set of users must be selected, and selection algorithms should be designed to exploit the multiuser diversity gain. Finding the optimal set of users requires an exhaustive search, which has too high computational complexity to be practically useful. Based on the iterative precoder design, this paper proposes a low-complexity user selection algorithm using a greedy method, in which the precoders of selected users are recursively updated after each selection step. The selection metric of the proposed scheduling algorithm relies on the product of the squared row norms of the effective channel matrices, which is related to the eigenvalues by the Hadamard and Schur inequalities. An asymptotic analysis is provided to show that the proposed algorithm can achieve the optimal sum rate scaling of the MIMO broadcast channel. The numerical results show that the proposed algorithm achieves a good trade-off between sum rate performance and computational complexity. When users suffer different channel conditions, providing fairness among users is of critical importance. To address this problem, we also propose two fair scheduling (FS) algorithms, one imposing fairness in the approximation of the data rate, and another directly imposing fairness in the product of the sq- ared row norms of the effective channel matrices. [less ▲]

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