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  • 1. Alodeh, Maha
    et al.
    Chatzinotas, Symeon
    Ottersten, Björn E.
    KTH, School of Electrical Engineering (EES), Signal Processing.
    Spatial DCT-Based Channel Estimation in Multi-Antenna Multi-Cell Interference Channels2015In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 63, no 6, p. 1404-1418Article in journal (Refereed)
    Abstract [en]

    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.

  • 2. Ambat, Sooraj K.
    et al.
    Chatterjee, Saikat
    KTH, School of Electrical Engineering (EES), Communication Theory.
    Hari, K. V. S.
    A Committee Machine Approach for Compressed Sensing Signal Reconstruction2014In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 62, no 7, p. 1705-1717Article in journal (Refereed)
    Abstract [en]

    Although many sparse recovery algorithms have been proposed recently in compressed sensing (CS), it is well known that the performance of any sparse recovery algorithm depends on many parameters like dimension of the sparse signal, level of sparsity, and measurement noise power. It has been observed that a satisfactory performance of the sparse recovery algorithms requires a minimum number of measurements. This minimum number is different for different algorithms. In many applications, the number of measurements is unlikely to meet this requirement and any scheme to improve performance with fewer measurements is of significant interest in CS. Empirically, it has also been observed that the performance of the sparse recovery algorithms also depends on the underlying statistical distribution of the nonzero elements of the signal, which may not be known a priori in practice. Interestingly, it can be observed that the performance degradation of the sparse recovery algorithms in these cases does not always imply a complete failure. In this paper, we study this scenario and show that by fusing the estimates of multiple sparse recovery algorithms, which work with different principles, we can improve the sparse signal recovery. We present the theoretical analysis to derive sufficient conditions for performance improvement of the proposed schemes. We demonstrate the advantage of the proposed methods through numerical simulations for both synthetic and real signals.

  • 3. Ambat, Sooraj K.
    et al.
    Chatterjee, Saikat
    KTH, School of Electrical Engineering (EES), Communication Theory.
    Hari, K. V. S.
    Fusion of Algorithms for Compressed Sensing2013In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 61, no 14, p. 3699-3704Article in journal (Refereed)
    Abstract [en]

    For compressed sensing (CS), we develop a new scheme inspired by data fusion principles. In the proposed fusion based scheme, several CS reconstruction algorithms participate and they are executed in parallel, independently. The final estimate of the underlying sparse signal is derived by fusing the estimates obtained from the participating algorithms. We theoretically analyze this fusion based scheme and derive sufficient conditions for achieving a better reconstruction performance than any participating algorithm. Through simulations, we show that the proposed scheme has two specific advantages: 1) it provides good performance in a low dimensional measurement regime, and 2) it can deal with different statistical natures of the underlying sparse signals. The experimental results on real ECG signals shows that the proposed scheme demands fewer CS measurements for an approximate sparse signal reconstruction.

  • 4.
    Astély, David
    et al.
    KTH, Superseded Departments, Signals, Sensors and Systems.
    Ottersten, Björn
    KTH, Superseded Departments, Signals, Sensors and Systems.
    The effects of local scattering on direction of arrival estimation with MUSIC1999In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 47, no 12, p. 3220-3234Article in journal (Refereed)
    Abstract [en]

    In wireless communication scenarios, multipath propagation may cause angular spreading as seen from a base station antenna array. Environments where most energy incident on the array is from scatterers local to the mobile transmitters are considered, and the effects on direction of arrival (DOA) estimation with the MUSIC algorithm are studied. Previous work has studied rapidly time-varying channels and concluded that local scattering has a minor effect on DOA estimation in such scenarios. In this work, a channel that is time-invariant during the observation period is considered, and under the assumption of small angular spread, an approximate distribution for the DOA estimates is derived. The results show that local scattering has a significant impact on DOA estimation in the time invariant case. Numerical examples are included to illustrate the analysis and to demonstrate that the results may be used to formulate a simple estimator of angular spread. An extension to more general Rayleigh and Ricean fading channels is also included, In addition, results from processing experimental data collected in suburban environments are presented. Good agreement with the derived distributions is obtained.

  • 5.
    Astély, David
    et al.
    KTH, Superseded Departments, Signals, Sensors and Systems.
    Swindlehurst, Andrew Lee
    Department of Electrical and Computer Engineering, Brigham Young University, Provo, UT 84602 USA.
    Ottersten, Björn
    KTH, Superseded Departments, Signals, Sensors and Systems.
    Spatial signature estimation for uniform linear arrays with unknown receiver gains and phases1999In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 47, no 8, p. 2128-2138Article in journal (Refereed)
    Abstract [en]

    The problem of spatial signature estimation using a uniform linear array (ULA) with unknown receiver gain and phase responses is studied. Sufficient conditions for identifying the spatial signatures are derived, and a closed-Form ESPRIT-like estimator is proposed, The performance of the method is investigated by means of simulations and on experimental data collected with an antenna array in a suburban environment. The results show that the absence of receiver calibration is not critical for uplink signal waveform estimation using a plane wave model.

  • 6.
    Bao, Lei
    et al.
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Skoglund, Mikael
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Fischione, Carlo
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Johansson, Karl Henrik
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Rate Allocation for Quantized Control Over Binary Symmetric Channels2012In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 60, no 6, p. 3188-3202Article in journal (Refereed)
    Abstract [en]

    Utility maximization in networked control systems (NCSs) is difficult in the presence of limited sensing and communication resources. In this paper, a new communication rate optimization method for state feedback control over a noisy channel is proposed. Linear dynamic systems with quantization errors, limited transmission rate, and noisy communication channels are considered. The most challenging part of the optimization is that no closed-form expressions are available for assessing the performance and the optimization problem is nonconvex. The proposed method consists of two steps: (i) the overall NCS performance measure is expressed as a function of rates at all time instants by means of high-rate quantization theory, and (ii) a constrained optimization problem to minimize a weighted quadratic objective function is solved. The proposed method is applied to the problem of state feedback control and the problem of state estimation. Monte Carlo simulations illustrate the performance of the proposed rate allocation. It is shown numerically that the proposed method has better performance when compared to arbitrarily selected rate allocations. Also, it is shown that in certain cases nonuniform rate allocation can outperform the uniform rate allocation, which is commonly considered in quantized control systems, for feedback control over noisy channels.

  • 7.
    Bengtsson, Mats
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing.
    Ottersten, Björn
    KTH, School of Electrical Engineering (EES), Signal Processing.
    A generalization of weighted subspace fitting to full-rank models2001In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 49, no 5, p. 1002-1012Article in journal (Refereed)
    Abstract [en]

    The idea of subspace fitting provides a popular framework for different applications of parameter estimation and system identification. Previously, some algorithms have been suggested based on similar ideas, for a sensor array processing problem where the underlying data model is not low rank. We show that two of these algorithms (DSPE and DISPARE) fail to give consistent estimates and introduce a general class of subspace fitting-like algorithms for consistent estimation of parameters from a possibly full-rank data model. The asymptotic performance is analyzed, and an optimally weighted algorithm is derived. The result gives a lower bound on the estimation performance for any estimator based on a low-rank approximation of the linear space spanned by the sample data. We show that in general, for full-rank data models, no subspace-based method can reach the Cramer-Rao lower bound (CRB)

  • 8.
    Bengtsson, Mats
    et al.
    KTH, Superseded Departments, Signals, Sensors and Systems.
    Ottersten, Björn
    KTH, Superseded Departments, Signals, Sensors and Systems.
    Low-complexity estimators for distributed sources2000In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 48, no 8, p. 2185-2194Article in journal (Refereed)
    Abstract [en]

    In antenna array applications, the propagation environment is often more complicated than the ordinarily assumed model of plane wavefronts. Here, a low-complexity algorithm is suggested for estimating both the DOA and the spread angle of a source subject to local scattering, using a uniform linear array. The parameters are calculated from the estimates obtained using a standard algorithm such as root-MUSIC to fit a two-ray model to the data. The algorithm is shown to give consistent estimates, and the statistical performance is studied analytically and through simulations

  • 9.
    Bergman, Svante
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Ottersten, Björn
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Lattice-based linear precoding for MIMO channels with transmitter CSI2008In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 56, no 7, p. 2902-2914Article in journal (Refereed)
    Abstract [en]

    Herein, the design of linear dispersion codes for multiple-input multiple-output communication systems is investigated. The receiver as well as the transmitter are assumed to have perfect knowledge of the channel, and the receiver is assumed to employ maximum likelihood detection. We propose to use linear precoding and lattice invariant operations to transform the channel matrix into a lattice generator matrix with large minimum distance separation. With appropriate approximations, it is shown that this corresponds to selecting lattices with good sphere-packing properties. Lattice invariant transformations are then used to minimize the power consumption. An algorithm for this power minimization is presented along with a lower bound on the optimization. Numerical results indicate significant gains by using the proposed method compared to channel diagonalization with adaptive bit loading.

  • 10.
    Bergman, Svante
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Palomar, Daniel P.
    Department of Electronic and Computer Engineering, Hong Kong University of Science and Technology.
    Ottersten, Björn
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Joint Bit Allocation and Precoding for MIMO Systems With Decision Feedback Detection2009In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 57, no 11, p. 4509-4521Article in journal (Refereed)
    Abstract [en]

    This paper considers the joint design of bit loading, precoding and receive filters for a multiple-input multiple-output (MIMO) digital communication system employing decision feedback (DF) detection at the receiver. Both the transmitter as well as the receiver are assumed to know the channel matrix perfectly. It is well known that, for linear MIMO transceivers, a diagonal transmission (i.e., orthogonalization of the channel matrix) is optimal for some criteria. Surprisingly, it was shown five years ago that for the family of Schur-convex functions an additional rotation of the symbols is necessary. However, if the bit loading is optimized jointly with the linear transceiver, then this rotation is unnecessary. Similarly, for DF MIMO optimized transceivers a rotation of the symbols is sometimes needed. The main result of this paper shows that for a DF MIMO transceiver where the bit loading is jointly optimized with the transceiver filters, the rotation of the symbols becomes unnecessary, and because of this, also the DF part of the receiver is not required. The proof is based on a relaxation of the available bit rates on the individual substreams to the set of positive real numbers. In practice, the signal constellations are discrete and the optimal relaxed bit loading has to be rounded. It is shown that the loss due to rounding is small, and an upper bound on the maximum loss is derived. Numerical results are presented that confirm the theoretical results and demonstrate that orthogonal transmission and the truly optimal DF design perform almost equally well.

  • 11.
    Björnson, Emil
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Bengtsson, Mats
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Ottersten, Björn
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Pareto characterization of the multicell MIMO performance region with simple receivers2012In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 60, no 8, p. 4464-4469Article in journal (Refereed)
    Abstract [en]

    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).

  • 12.
    Björnson, Emil
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Hammarwall, David
    Ericsson Research, Stockholm, Sweden.
    Ottersten, Björn
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Exploiting Quantized Channel Norm Feedback Through Conditional Statistics in Arbitrarily Correlated MIMO Systems2009In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 57, no 10, p. 4027-4041Article in journal (Refereed)
    Abstract [en]

    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 multi-plexing 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.

  • 13.
    Björnson, Emil
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Jaldén, Niklas
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Bengtsson, Mats
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Ottersten, Björn
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Optimality Properties, Distributed Strategies, and Measurement-Based Evaluation of Coordinated Multicell OFDMA Transmission2011In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 59, no 12, p. 6086-6101Article in journal (Refereed)
    Abstract [en]

    The throughput of multicell systems is inherently limited by interference andthe available communication resources. Coordinated resource allocation is the key to efficient performance, but the demand on backhaul signaling andcomputational resources grows rapidly with number of cells, terminals, andsubcarriers. 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) optimalityof 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 measuredmulticell 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.

  • 14.
    Björnson, Emil
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Kountouris, Marios
    Bengtsson, Mats
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Ottersten, Björn
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Receive Combining vs. Multi-Stream Multiplexing in Downlink Systems With Multi-Antenna Users2013In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 61, no 13, p. 3431-3446Article in journal (Refereed)
    Abstract [en]

    In downlink multi-antenna systems with many users, the multiplexing gain is strictly limited by the number of transmit antennas and the use of these antennas. Assuming that the total number of receive antennas at the multi-antenna users is much larger than, 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 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.

  • 15.
    Björnson, Emil
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Ottersten, Björn
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    A Framework for Training-Based Estimation in Arbitrarily Correlated Rician MIMO Channels With Rician Disturbance2010In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 58, no 3, p. 1807-1820Article in journal (Refereed)
    Abstract [en]

    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.

  • 16.
    Björnson, Emil
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Zakhour, Randa
    Mobile Communications Department, EURECOM.
    Gesbert, David
    Mobile Communications Department, EURECOM.
    Ottersten, Björn
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Cooperative Multicell Precoding: Rate Region Characterization and Distributed Strategies With Instantaneous and Statistical CSI2010In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 58, no 8, p. 4298-4310Article in journal (Refereed)
    Abstract [en]

    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.

  • 17.
    Björnson, Emil
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Zheng, Gan
    Interdisciplinary Centre for Security, Reliability and Trust, University of Luxembourg.
    Bengtsson, Mats
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Ottersten, Björn
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Robust Monotonic Optimization Framework for Multicell MISO Systems2012In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 60, no 5, p. 2508-2523Article in journal (Refereed)
    Abstract [en]

    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 robustness 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.

  • 18.
    Blasco-Serrano, Ricardo
    et al.
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. Ericsson Research.
    Zachariah, Dave
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. Division of Systems and Control. Division of Systems and Control. Uppsala University.
    Sundman, Dennis
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Thobaben, Ragnar
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Skoglund, Mikael
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    A Measurement Rate-MSE Tradeoff for Compressive Sensing Through Partial Support Recovery2014In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 62, no 18, p. 4643-4658Article in journal (Refereed)
    Abstract [en]

    We study the fundamental relationship between two relevant quantities in compressive sensing: the measurement rate, which characterizes the asymptotic behavior of the dimensions of the measurement matrix in terms of the ratio m/ log n (m being the number of measurements and n the dimension of the sparse signal), and the mean square estimation error. First, we use an information-theoretic approach to derive sufficient conditions on the measurement rate to reliably recover a part of the support set that represents a certain fraction of the total signal power when the sparsity level is fixed. Second, we characterize the mean square error of an estimator that uses partial support set information. Using these two parts, we derive a tradeoff between the measurement rate and the mean square error. This tradeoff is achievable using a two-step approach: first support set recovery, then estimation of the active components. Finally, for both deterministic and random signals, we perform a numerical evaluation to verify the advantages of the methods based on partial support set recovery.

  • 19.
    Blomqvist, Anders
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Wahlberg, Bo
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    On the relation between weighted frequency-domain maximum-likelihood power spectral estimation and the prefiltered covariance extension approach2007In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 55, no 1, p. 384-389Article in journal (Refereed)
    Abstract [en]

    The aim of this correspondence is to study the connection between weighted frequency-domain maximum-likelihood power spectral estimation and the time-domain prefiltered covariance extension approach. Weighting and prefiltering are introduced to emphasize the model fit in a certain frequency range. The main result is that these two methods are very closely related for the case of autoregressive (AR) model estimation, which implies that both can be formulated as convex optimization problems. Examples illustrating the methods and the effect of prefiltering/weighting are provided.

  • 20.
    Byrnes, Christopher
    et al.
    KTH, Superseded Departments, Mathematics.
    Enqvist, Per
    KTH, Superseded Departments, Mathematics.
    Lindquist, Anders
    KTH, Superseded Departments, Mathematics.
    Cepstral coefficients, covariance lags, and pole-zero models for finite data strings2001In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 49, no 4, p. 677-693Article in journal (Refereed)
    Abstract [en]

    One of the most widely used methods of spectral estimation in signal and speech processing is linear predictive coding (LPC). LPC has some attractive features, which account for its popularity, including the properties that the resulting modeling filter i) matches a finite window of n + 1 covariance lags, ii) is rational of degree at most n, and iii) has stable zeros and poles. The only limiting factor of this methodology is that the modeling filter is "all-pole," i.e., an autoregressive (AR) model. In this paper, we present a systematic description of all autoregressive moving-average (ARMA) models of processes that have properties i)-iii) in the context of cepstral analysis and homomorphic filtering. Indeed, we show that each such ARMA model determines and is completely determined by its finite windows of cepstral coefficients and covariance lags. This characterization has an intuitively appealing interpretation of a characterization by using measures of the transient and the steady-state behaviors of the signal, respectively. More precisely, we show that these nth-order windows form local coordinates for all ARMA models of degree n and that the pole-zero model can be determined from the windows as the unique minimum of a convex objective function. We refine this optimization method by first noting that the maximum entropy design of an LPC filter is obtained by maximizing the zeroth cepstral coefficient, subject to the constraint i). More generally, we modify this scheme to a more well-posed optimization problem where the covariance data enters as a constraint and the linear weights of the cepstral coefficients are "positive"-in a sense that a certain pseudo-polynomial is positive-rather succinctly generalizing the maximum entropy method. This new problem is a homomorphic filter generalization of the maximum entropy method, providing a procedure for the design of any stable, minimum-phase modeling filter of degree less or equal to n that interpolates the given covariance window We conclude the paper by presenting an algorithm for realizing these biters in a lattice-ladder form, given the covariance window and the moving average part of the model. While we also show how to determine the moving average part using cepstral smoothing, one can make use of any good a priori estimate for the system zeros to initialize the algorithm. Indeed, we conclude the paper with an example of this method, incorporating an example from the literature on ARMA modeling.

  • 21.
    Cao, Phuong
    et al.
    KTH, School of Electrical Engineering (EES), Communication Theory.
    Oechtering, Tobias
    KTH, School of Electrical Engineering (EES), Communication Theory.
    Schaefer, Rafael
    The Information Theory and Applications Chair, Technische Universitat Berlin.
    Mikael, Skoglund
    KTH, School of Electrical Engineering (EES), Communication Theory.
    Optimal Transmit Strategy for MISO Channels with Joint Sum and Per-antenna Power Constraints2016In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476Article in journal (Refereed)
    Abstract [en]

    In this paper, we study an optimal transmit strategy for multiple-input single-output (MISO) Gaussian channels with joint sum and per-antenna power constraints. We study in detail the interesting case where the sum of the per-antenna power constraints is larger than sum power constraint. A closed-form characterization of an optimal beamforming strategy is derived.It is shown that we can always find an optimal beamforming transmit strategy that allocates the maximal sum power with phases matched to the complex channel coefficients. The main result is a simple recursive algorithm to compute the optimal power allocation. Whenever the optimal power allocation of the corresponding problem with sum power constraint only exceeds per-antenna power constraints, it is optimal to allocate maximal per-antenna power to those antennas to satisfy the per-antenna power constraints. The remaining power is divided amongst the other antennas whose optimal allocation follows from a reduced joint sum and per-antenna power constraints problem of smaller channel coefficient dimension and reduced sum power constraint. Finally, the theoretical results are illustrated by numerical examples.

  • 22.
    Chatterjee, Saikat
    et al.
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Flåm, John T.
    NTNU - Norwegian University of Science and Technology.
    Kansanen, Kimmo
    NTNU - Norwegian University of Science and Technology.
    Ekman, Tobjorn
    NTNU - Norwegian University of Science and Technology.
    On MMSE estimation: A linear model under Gaussian mixture statistics2012In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 60, no 7, p. 3840-3845Article in journal (Refereed)
    Abstract [en]

    In a Bayesian linear model, suppose observation y = Hx + n stems from independent inputs x and n which are Gaussian mixture (GM) distributed. With known matrix H, the minimum mean square error (MMSE) estimator for x , has analytical form. However, its performance measure, the MMSE itself, has no such closed form. Because existing Bayesian MMSE bounds prove to have limited practical value under these settings, we instead seek analytical bounds for the MMSE, both upper and lower. This paper provides such bounds, and relates them to the signal-to-noise-ratio (SNR).

  • 23.
    Chatterjee, Saikat
    et al.
    KTH, School of Electrical Engineering (EES), Communication Theory.
    Sundman, Dennis
    KTH, School of Electrical Engineering (EES), Communication Theory.
    Vehkaperä, Mikko
    KTH, School of Electrical Engineering (EES), Communication Theory.
    Skolglund, Mikael
    KTH, School of Electrical Engineering (EES), Communication Theory.
    Projection-based and look ahead strategies for atom selection2012In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 60, no 2, p. 634-647Article in journal (Refereed)
    Abstract [en]

    In this paper, we improve iterative greedy search algorithms in which atoms are selected serially over iterations, i.e., one-by-one over iterations. For serial atom selection, we devise two new schemes to select an atom from a set of potential atoms in each iteration. The two new schemes lead to two new algorithms. For both the algorithms, in each iteration, the set of potential atoms is found using a standard matched filter. In case of the first scheme, we propose an orthogonal projection strategy that selects an atom from the set of potential atoms. Then, for the second scheme, we propose a look-ahead strategy such that the selection of an atom in the current iteration has an effect on the future iterations. The use of look-ahead strategy requires a higher computational resource. To achieve a tradeoff between performance and complexity, we use the two new schemes in cascade and develop a third new algorithm. Through experimental evaluations, we compare the proposed algorithms with existing greedy search and convex relaxation algorithms.

  • 24. Christopoulos, D.
    et al.
    Chatzinotas, S.
    Ottersten, Björn
    Weighted fair multicast multigroup beamforming under per-antenna power constraints2014In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 62, no 19, p. 5132-5142Article in journal (Refereed)
    Abstract [en]

    A multiantenna transmitter that conveys independent sets of common data to distinct groups of users is considered. This model is known as physical layer multicasting to multiple cochannel groups. In this context, the practical constraint of a maximum permitted power level radiated by each antenna is addressed. The per-antenna power constrained system is optimized in a maximum fairness sense with respect to predetermined quality of service weights. In other words, the worst scaled user is boosted by maximizing its weighted signal-to-interference plus noise ratio. A detailed solution to tackle the weighted max-min fair multigroup multicast problem under per-antenna power constraints is therefore derived. The implications of the novel constraints are investigated via prominent applications and paradigms. What is more, robust per-antenna constrained multigroup multicast beamforming solutions are proposed. Finally, an extensive performance evaluation quantifies the gains of the proposed algorithm over existing solutions and exhibits its accuracy over per-antenna power constrained systems.

  • 25.
    de Fréin, Ruairí
    et al.
    Sparse Signal Processing Group, University College Dublin.
    Rickard, Scott
    Sparse Signal Processing Group, University College Dublin.
    The Synchronized Short-Time-Fourier-Transform: Properties and Definitions for Multichannel Source Separation2011In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, ISSN 1053-587X, Vol. 59, no 1, p. 91-103Article in journal (Refereed)
    Abstract [en]

    This paper proposes the use of a synchronized linear transform, the synchronized short-time-Fourier-transform (sSTFT), for time-frequency analysis of anechoic mixtures. We address the short comings of the commonly used time-frequency linear transform in multichannel settings, namely the classical short-time-Fourier-transform (cSTFT). We propose a series of desirable properties for the linear transform used in a multichannel source separation scenario: stationary invertibility, relative delay, relative attenuation, and finally delay invariant relative windowed-disjoint orthogonality (DIRWDO). Multisensor source separation techniques which operate in the time-frequency domain, have an inherent error unless consideration is given to the multichannel properties proposed in this paper. The sSTFT preserves these relationships for multichannel data. The crucial innovation of the sSTFT is to locally synchronize the analysis to the observations as opposed to a global clock. Improvement in separation performance can be achieved because assumed properties of the time-frequency transform are satisfied when it is appropriately synchronized. Numerical experiments show the sSTFT improves instantaneous subsample relative parameter estimation in low noise conditions and achieves good synthesis.

  • 26.
    del Aguila, Pol
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Information Science and Engineering.
    Jaldén, Joakim
    KTH, School of Electrical Engineering and Computer Science (EECS), Information Science and Engineering.
    Cell detection by functional inverse diffusion and non-negative group sparsity – Part I: Modeling and Inverse Problems2018In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 66, no 20, p. 5407-5421Article in journal (Refereed)
    Abstract [en]

    In this two-part paper, we present a novel framework and methodology to analyze data from certain image-based biochemical assays, e.g., ELISPOT and Fluorospot assays. In this first part, we start by presenting a physical partial differential equations (PDE) model up to image acquisition for these biochemical assays. Then, we use the PDEs' Green function to derive a novel parametrization of the acquired images. This parametrization allows us to propose a functional optimization problem to address inverse diffusion. In particular, we propose a non-negative group-sparsity regularized optimization problem with the goal of localizing and characterizing the biological cells involved in the said assays. We continue by proposing a suitable discretization scheme that enables both the generation of synthetic data and implementable algorithms to address inverse diffusion. We end Part I by providing a preliminary comparison between the results of our methodology and an expert human labeler on real data. Part II is devoted to providing an accelerated proximal gradient algorithm to solve the proposed problem and to the empirical validation of our methodology.

  • 27.
    del Aguila, Pol
    et al.
    KTH, School of Electrical Engineering and Computer Science (EECS), Information Science and Engineering.
    Jaldén, Joakim
    KTH, School of Electrical Engineering and Computer Science (EECS), Information Science and Engineering.
    Cell detection by functional inverse diffusion and non-negative group sparsity – Part II: Proximal optimization and Performance evaluation2018In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 66, no 20, p. 5422-5437Article in journal (Refereed)
    Abstract [en]

    In this two-part paper, we present a novel framework and methodology to analyze data from certain image-based biochemical assays, e.g., ELISPOT and Fluorospot assays. In this second part, we focus on our algorithmic contributions. We provide an algorithm for functional inverse diffusion that solves the variational problem we posed in Part I. As part of the derivation of this algorithm, we present the proximal operator for the non-negative group-sparsity regularizer, which is a novel result that is of interest in itself, also in comparison to previous results on the proximal operator of a sum of functions. We then present a discretized approximated implementation of our algorithm and evaluate it both in terms of operational cell-detection metrics and in terms of distributional optimal-transport metrics.

  • 28.
    Do, Tan Tai
    et al.
    KTH, School of Electrical Engineering (EES), Communication Theory.
    Oechtering, Tobias J.
    KTH, School of Electrical Engineering (EES), Communication Theory.
    Skoglund, Mikael
    KTH, School of Electrical Engineering (EES), Communication Theory.
    Optimal Transmission for the MIMO Bidirectional Broadcast Channel in the Wideband Regime2013In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 61, no 20, p. 5103-5116Article in journal (Refereed)
    Abstract [en]

    This paper considers a transmit strategy for an AWGN MIMO bidirectional broadcast channel in the wideband regime. In order to characterize the boundaries of the wideband capacity and energy per bit regions, the transmit strategy at the relay is designed to maximize the weighted wideband rate sum. A closed form of the optimal transmit covariance matrix is derived, which shows that a single beam transmit strategy is optimal. The transmit strategies for some special cases are also analyzed. The fairness versus energy efficiency tradeoff is then discussed. In addition, an extension to multipair MIMO bidirectional broadcast channel is studied in which we show that serving a certain pair with full power is optimal in the sense of maximizing the achievable weighted wideband rate sum. Finally, a discussion on the conjecture of the minimum energy per bit for multi-pair systems is provided.

  • 29.
    Elvander, Filip
    et al.
    Lund Univ, Ctr Math Sci, SE-22100 Lund, Sweden..
    Jakobsson, Andreas
    Lund Univ, Ctr Math Sci, SE-22100 Lund, Sweden..
    Karlsson, Johan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Interpolation and Extrapolation of Toeplitz Matrices via Optimal Mass Transport2018In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 66, no 20, p. 5285-5298Article in journal (Refereed)
    Abstract [en]

    In this work, we propose a novel method for quantifying distances between Toeplitz structured covariance matrices. By exploiting the spectral representation of Toeplitz matrices, the proposed distance measure is defined based on an optimal mass transport problem in the spectral domain. This may then be interpreted in the covariance domain, suggesting a natural way of interpolating and extrapolating Toeplitz matrices, such that the positive semidefiniteness and the Toeplitz structure of these matrices are preserved. The proposed distance measure is also shown to be contractive with respect to both additive and multiplicative noise and thereby allows for a quantification of the decreased distance between signals when these are corrupted by noise. Finally, we illustrate how this approach can be used for several applications in signal processing. In particular, we consider interpolation and extrapolation of Toeplitz matrices, as well as clustering problems and tracking of slowly varying stochastic processes.

  • 30. Fertl, Peter
    et al.
    Jaldén, Joakim
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Matz, Gerald
    Performance Assessment of MIMO-BICM Demodulators Based on Mutual Information2012In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 60, no 3, p. 1366-1382Article in journal (Refereed)
    Abstract [en]

    We provide a comprehensive performance comparison of soft-output and hard-output demodulators in the context of non-iterative multiple-input multiple-output bit-interleaved coded modulation (MIMO-BICM). Coded bit error rate (BER), widely used in literature for demodulator comparison, has the draw-back of depending strongly on the error correcting code being used. This motivates us to propose the mutual information of the equivalent modulation channel (comprising modulator, wireless channel, and demodulator) as a code-independent performance measure. We present extensive numerical results for spatially independent identically distributed (i.i.d.) ergodic and quasi-static fading channels under perfect and imperfect channel state information. These results reveal that the performance ranking of MIMO demodulators is rate-dependent and provide new insights regarding MIMO-BICM system design, i.e., the choice of antenna configuration, symbol constellation, and demodulator for a given target rate.

  • 31. Flam, J. T.
    et al.
    Zachariah, Dave
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Vehkaperä, mikko
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Chatterjee, Saikat
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    The linear model under mixed gaussian inputs: Designing the transfer matrix2013In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 61, no 21, p. 5247-5259Article in journal (Refereed)
    Abstract [en]

    Suppose a linear model Y = Hx+n, where inputs x, n are independent Gaussian mixtures. The problem is to design the transfer matrix so as to minimize the mean square error (MSE) when estimating x from . This problem has important applications, but faces at least three hurdles. Firstly, even for a fixed H, the minimum MSE (MMSE) has no analytical form. Secondly, theMMSE is generally not convex in . Thirdly, derivatives of the MMSEw.r.t. are hard to obtain. This paper casts theproblemas a stochastic program and invokes gradient methods. The study is motivated by two applications in signal processing. One concerns the choice of error-reducing precoders; the other deals with selection of pilot matrices for channel estimation. In either setting, our numerical results indicate improved estimation accuracy-markedly better than those obtained by optimal design based on standard linear estimators. Some implications of the non-convexities of the MMSE are noteworthy, yet, to our knowledge, not well known. For example, there are cases in which more pilot power is detrimental for channel estimation. This paper explains why.

  • 32.
    Georgiou, Tryphon T.
    et al.
    Department of Electrical Engineering, University of Minnesota.
    Karlsson, Johan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
    Takyar, Mir Shahrouz
    Department of Electrical Engineering, University of Minnesota.
    Metrics for Power Spectra: An Axiomatic Approach2009In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 57, no 3, p. 859-867Article in journal (Refereed)
    Abstract [en]

    We present an axiomatic framework for seeking distances between power spectral density functions. The axioms require that the sought metric respects the effects of additive and multiplicative noise in reducing our ability to discriminate spectra, as well as they require continuity of statistical quantities with respect to perturbations measured in the metric. We then present a particular metric which abides by these requirements. The metric is based on the Monge-Kantorovich transportation problem and is contrasted with an earlier Riemannian metric based on the minimum-variance prediction geometry of the underlying time-series. It is also being compared with the more traditional Itakura-Saito distance measure, as well as the aforementioned prediction metric, on two representative examples.

  • 33. Gezici, Sinan
    et al.
    Bayram, Suat
    Kurt, Mehmet Necip
    Gholami, Mohammad Reza
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Optimal Jammer Placement in Wireless Localization Systems2016In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 64, no 17, p. 4534-4549Article in journal (Refereed)
    Abstract [en]

    In this study, the optimal jammer placement problem is proposed and analyzed for wireless localization systems. In particular, the optimal location of a jammer node is obtained by maximizing the minimum of the Cramer-Rao lower bounds (CRLBs) for a number of target nodes under location related constraints for the jammer node. For scenarios with more than two target nodes, theoretical results are derived to specify conditions underwhich the jammer node is located as close to a certain target node as possible, or the optimal location of the jammer node is determined by two of the target nodes. Also, explicit expressions are provided for the optimal location of the jammer node in the presence of two target nodes. In addition, in the absence of distance constraints for the jammer node, it is proved, for scenarios with more than two target nodes, that the optimal jammer location lies on the convex hull formed by the locations of the target nodes and is determined by two or three of the target nodes, which have equalized CRLBs. Numerical examples are presented to provide illustrations of the theoretical results in different scenarios.

  • 34.
    Ghadimi, Euhanna
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Shames, Iman
    Johansson, Mikael
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Multi-Step Gradient Methods for Networked Optimization2013In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 61, no 21, p. 5417-5429Article in journal (Refereed)
    Abstract [en]

    We develop multi-step gradient methods for network-constrained optimization of strongly convex functions with Lipschitz-continuous gradients. Given the topology of the underlying network and bounds on the Hessian of the objective function, we determine the algorithm parameters that guarantee the fastest convergence and characterize situations when significant speed-ups over the standard gradient method are obtained. Furthermore, we quantify how uncertainty in problem data at design-time affects the run-time performance of the gradient method and its multi-step counterpart, and conclude that in most cases the multi-step method outperforms gradient descent. Finally, we apply the proposed technique to three engineering problems: resource allocation under network-wide budget constraint, distributed averaging, and Internet congestion control. In all cases, our proposed algorithms converge significantly faster than the state-of-the art.

  • 35.
    Ghauch, Hadi
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Communication Theory.
    Kim, Taejoon
    City University of Hong Kong.
    Bengtsson, Mats
    KTH, School of Electrical Engineering (EES), Signal Processing.
    Skoglund, Mikael
    KTH, School of Electrical Engineering (EES), Communication Theory.
    Distributed Low-Overhead Schemes for Multi-stream MIMO Interference Channels2015In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 63, no 7, p. 1737-1749Article in journal (Refereed)
    Abstract [en]

    Our aim in this work is to propose fully distributed schemes for transmit and receive filter optimization. The novelty of the proposed schemes is that they only require a few forward-backward iterations, thus causing minimal communication overhead. For that purpose, we relax the well-known leakage minimization problem, and then propose two different filter update structures to solve the resulting non-convex problem: though one leads to conventional full-rank filters, the other results in rank-deficient filters, that we exploit to gradually reduce the transmit and receive filter rank, and greatly speed up the convergence. Furthermore, inspired from the decoding of turbo codes, we propose a turbo-like structure to the algorithms, where a separate inner optimization loop is run at each receiver (in addition to the main forward-backward iteration). In that sense, the introduction of this turbo-like structure converts the communication overhead required by conventional methods to computational overhead at each receiver (a cheap resource), allowing us to achieve the desired performance, under a minimal overhead constraint. Finally, we show through comprehensive simulations that both proposed schemes hugely outperform the relevant benchmarks, especially for large system dimensions.

  • 36. Ghayem, Fateme
    et al.
    Sadeghi, Mostafa
    Babaie-Zadeh, Massoud
    Chatterjee, Saikat
    KTH, School of Electrical Engineering and Computer Science (EECS), Information Science and Engineering.
    Skoglund, Mikael
    KTH, School of Electrical Engineering and Computer Science (EECS), Information Science and Engineering.
    Jutten, Christian
    Sparse Signal Recovery Using Iterative Proximal Projection2018In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 66, no 4, p. 879-894Article in journal (Refereed)
    Abstract [en]

    This paper is concerned with designing efficient algorithms for recovering sparse signals from noisy underdetermined measurements. More precisely, we consider minimization of a nonsmooth and nonconvex sparsity promoting function subject to an error constraint. To solve this problem, we use an alternating minimization penalty method, which ends up with an iterative proximal-projection approach. Furthermore, inspired by accelerated gradient schemes for solving convex problems, we equip the obtained algorithm with a so-called extrapolation step to boost its performance. Additionally, we prove its convergence to a critical point. Our extensive simulations on synthetic as well as real data verify that the proposed algorithm considerably outperforms some well-known and recently proposed algorithms.

  • 37.
    Göransson, Bo
    et al.
    KTH, Superseded Departments, Signals, Sensors and Systems.
    Ottersten, Björn
    KTH, Superseded Departments, Signals, Sensors and Systems.
    Direction estimation in partially unknown noise fields1999In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 47, no 9, p. 2375-2385Article in journal (Refereed)
    Abstract [en]

    The problem of direction of arrival estimation in the presence of colored noise with unknown covariance is considered, The unknown noise covariance is assumed to obey a linear parametric model. Using this model, the maximum likelihood directions parameter estimate is derived, and a large sample approximation is formed. It is shown that a priori information on the source signal correlation structure is easily incorporated into this approximate ML (AML) estimator. Furthermore, a closed-form expression of the Cramer-Rao bound on the direction parameter is provided. A perturbation analysis with respect to a small error in the assumed noise model is carried out, and an expression of the asymptotic bias due to the model mismatch is given. Computer simulations and an application of the proposed technique to a full-scale passive sonar experiment is provided to illustrate the results.

  • 38.
    Hammarwall, David
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Bengtsson, Mats
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Ottersten, Björn
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Acquiring partial CSI for spatially selective transmission by instantaneous channel norm feedback2008In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 56, no 3, p. 1188-1204Article in journal (Refereed)
    Abstract [en]

    In the design of next-generation multiuser communication systems, multiple-antenna transmission is an essential part providing additional spatial degrees of freedom 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. Herein, we show that the Euclidean norm of the instantaneous channel, when combined with long-term channel statistics provides sufficient information for the transmitter to efficiently utilize multiuser diversity in time, frequency, and space. We consider the downlink of a communication system where the base station has multiple transmit antennas whereas each user terminal has a single receive antenna. The CSI provided by channel statistics and feedback of the norm of the instantaneous channel vector is studied in depth for correlated Rayleigh and Ricean fading channels, within a minimum mean-square error (MMSE) estimation framework. An asymptotic analysis (high instantaneous SNR) is presented which shows that channel realizations with large channel norm provide additional spatial CSI at the transmitter. This makes the proposed scheme ideal for multiuser diversity transmission schemes, where resources are only allocated to users experiencing favorable channel conditions.

  • 39.
    Hammarwall, David
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Bengtsson, Mats
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Ottersten, Björn
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    On downlink beamforming with indefinite shaping constraints2006In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 54, no 9, p. 3566-3580Article in journal (Refereed)
    Abstract [en]

    Beamforming schemes have been proposed to exploit the spatial characteristics of multiple-input single-output (MISO) wireless radio channels. Several algorithms are available for optimal joint beamforming and power control for the downlink. Such optimal beamforming minimizes the total transmission power, while ensuring an individual target quality of service (QoS) for each user; alternatively the weakest QoS is maximized, subject to a power constraint. Herein, we consider both formulations and some of the available algorithms are generalized to enable indefinite quadratic shaping constraints on the beamformers. By imposing such additional constraints, the QoS measure can be extended to take other factors than the customary signal-to-interference-and-noise ratio (SINR) into account. Alternatively, other limitations such as interference requirements or physical constraints may be handled within the optimization. We also consider a more general SINR expression than previously analyzed, which allows for more accurate modeling, e.g., of nonzero self-interference in code-division multiple-access (CDMA) systems. Several applications for indefinite equality or inequality constraints are suggested and evaluated. For example, it is shown how such constraints may be used to ensure a minimum level of path diversity in a CDMA system. Other applications include limiting intercell interference in decentralized systems

  • 40.
    Hammarwall, David
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Bengtsson, Mats
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Ottersten, Björn
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Utilizing the spatial information provided by channel norm feedback in SDMA systems2008In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 56, no 7, p. 3278-3293Article in journal (Refereed)
    Abstract [en]

    To achieve high performance, in terms of reliability and throughput, in future multiple-antenna communication systems, it is essential to fully exploit the spatial dimensions of the wireless propagation channel. In multiuser communication systems, the throughput can be significantly increased by simultaneously transmitting to several users in the same time-frequency slot by means of spatial-division multi-access (SDMA). A major limiting factor for downlink SDMA transmission is the amount of channel-state information (CSI) that is available at the transmitter. In most cases, CSI can be measured/estimated only at the user terminals and must be fed back to the base station. This procedure typically constrains the amount of CSI that can be conveyed to the base station. Herein, we develop several low-complexity, as well as optimized, SDMA downlink resource-allocation schemes that are particularly suitable for systems utilizing statistical channel information and partial CSI feedback. A framework is proposed for combining statistical channel information with a class of instantaneous channel norms. It is shown that, in wide-area scenarios, the feedback of such a scalar norm provides sufficient information for the proposed resource-allocation algorithms to perform efficient SDMA beamforming (BF) and scheduling.

  • 41. Han, Duo
    et al.
    Mo, Yilin
    Wu, Junfeng
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Automatic Control.
    Shi, Ling
    An Opportunistic Sensor Scheduling Solution to Remote State Estimation Over Multiple Channels2016In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 64, no 18, p. 4905-4917Article in journal (Refereed)
    Abstract [en]

    We consider a sensor scheduling problem where the sensors have multiple choices of communication channel to send their local measurements to a remote state estimator for state estimation. Specifically, the sensors can transmit high-precision data packets over an expensive channel or low-precision data packets, which are quantized in several bits, over some cheap channels. The expensive channel, though being able to deliver more accurate data which leads to good estimation quality at the remote estimator, can only be used scarcely due to its high cost (e.g., high energy consumption). On the other hand, the cheap channel, though having a small cost, delivers less accurate data which inevitably deteriorates the remote estimation quality. In this work we propose a new framework in which the sensors switch between the two channels to achieve a better tradeoff among the communication cost, the estimation performance and the computational complexity, where the two-channel case can be easily extended to a multiple-channel case. We propose an opportunistic sensor schedule which reduces the communication cost by randomly switching among the expensive and cheap channels, and in the meantime maintains low computational complexity while introducing data quantization into the estimation problem. We present a minimum mean square error (MMSE) estimator in a closed-form under the proposed opportunistic sensor schedule. We also formulate an optimization problem to search the best opportunistic schedule with a linear quantizer. Furthermore, we show that the MMSE estimator in the limiting case becomes the standard Kalman filter.

  • 42. Han, Duo
    et al.
    You, Keyou
    Xie, Lihua
    Wu, Junfeng
    KTH, School of Electrical Engineering (EES), Automatic Control.
    Shi, Ling
    Optimal Parameter Estimation Under Controlled Communication Over Sensor Networks2015In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 63, no 24, p. 6473-6485Article in journal (Refereed)
    Abstract [en]

    This paper considers parameter estimation of linear systems under sensor-to-estimator communication constraint. Due to the limited battery power and the traffic congestion over a large sensor network, each sensor is required to reduce the rate of communication between the estimator and itself. We propose an observation-driven sensor scheduling policy such that the sensor transmits only the important measurements to the estimator. Unlike the existing deterministic scheduler, our stochastic scheduling is smartly designed to well compensate for the loss of the Gaussianity of the system. This results in a nice feature that the maximum-likelihood estimator (MLE) is still able to be recursively computed in a closed form, and the resulting estimation performance can be explicitly evaluated. Moreover, an optimization problem is formulated and solved to obtain the best parameters of the scheduling policy under which the estimation performance becomes comparable to the standard MLE with full measurements under a moderate transmission rate. Finally, simulations are included to validate the theoretical results.

  • 43. He, Shiwen
    et al.
    Huang, Yongming
    Yang, Luxi
    Ottersten, Björn
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Coordinated Multicell Multiuser Precoding for Maximizing Weighted Sum Energy Efficiency2014In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 62, no 3, p. 741-751Article in journal (Refereed)
    Abstract [en]

    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.

  • 44. He, Shiwen
    et al.
    Wang, Jiaheng
    Huang, Yongming
    Ottersten, Björn
    KTH, School of Electrical Engineering (EES). Univ Luxembourg, Luxembourg.
    Hong, Wei
    Codebook-Based Hybrid Precoding for Millimeter Wave Multiuser Systems2017In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 65, no 20, p. 5289-5304Article in journal (Refereed)
    Abstract [en]

    In millimeter-wave (mmWave) systems, antenna architecture limitations make it difficult to apply conventional fully digital precoding techniques but call for low-cost analog radio frequency (RF) and digital baseband hybrid precoding methods. This paper investigates joint RF-baseband hybrid precoding for the downlink of multiuser multiantenna mmWave systems with a limited number of RF chains. Two performance measures, maximizing the spectral efficiency and the energy efficiency of the system, are considered. We propose a codebook-based RF precoding design and obtain the channel state information via a beam sweep procedure. Via the codebook-based design, the original system is transformed into a virtual multiuser downlink system with the RF chain constraint. Consequently, we are able to simplify the complicated hybrid precoding optimization problems to joint codeword selection and precoder design (JWSPD) problems. Then, we propose efficient methods to address the JWSPD problems and jointly optimize the RF and baseband precoders under the two performance measures. Finally, extensive numerical results are provided to validate the effectiveness of the proposed hybrid precoders.

  • 45. Host-Madsen, A.
    et al.
    Händel, Peter
    KTH, Superseded Departments, Signals, Sensors and Systems.
    Effects of sampling and quantization on single-tone frequency estimation2000In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 48, no 3, p. 650-662Article in journal (Refereed)
    Abstract [en]

    The effects of sampling and quantization on frequency estimation for a single sinusoid are investigated. Cramer-Rao bound for I-bit quantization is derived and compared with the limit of infinite quantization. It is found that I-bit quantization gives a slightly worse performance, however, with a dramatic increase of variance at certain frequencies. This can be avoided by using four times ol oversampling. The effect of sampling when using nonideal antialiasing lowpass filters is therefore investigated through derivation of the Cramer-Rao lower bounds. Finally, fast estimators for 1-bit quantization, in particular, correlation-based estimators, are derived,and their performance is investigated. The paper is concluded with simulation results for fourtimes oversampled I-bit quantization.

  • 46.
    Huang, Yongming
    et al.
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Yang, Luxi
    School of Information Science and Engineering, Southeast University, Nanjing, China.
    Bengtsson, Mats
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Signal Processing.
    Ottersten, Björn
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    A Limited Feedback Joint Precoding for Amplify-and-Forward Relaying2010In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 58, no 3, p. 1347-1357Article in journal (Refereed)
    Abstract [en]

    This paper deals with the practical precoding design for a dual hop downlink with multiple-input multiple-output (MIMO) amplify-and-forward relaying. First, assuming that full channel state information (CSI) of the two hop channels is available, a suboptimal dual hop joint precoding scheme, i.e., precoding at both the base station and relay station, is investigated. Based on its structure, a scheme of limited feedback joint precoding using joint codebooks is then proposed, which uses a distributed codeword selection to concurrently choose two joint precoders such that the feedback delay is considerably decreased. Finally, the joint codebook design for the limited feedback joint precoding system is analyzed, and results reveal that independent codebook designs at the base station and relay station using the conventional Grassmannian subspace packing method is able to guarantee that the overall performance of the dual hop joint precoding scheme improves with the size of each of the two codebooks. Simulation results show that the proposed dual hop joint precoding system using distributed codeword selection scheme exhibits a rate or BER performance close to the one using the optimal centralized codeword selection scheme, while having lower computational complexity and shorter feedback delay.

  • 47.
    Huang, Yongming
    et al.
    School of Information Science and Engineering, Southeast University, Nanjing.
    Yang, Luxi
    School of Information Science and Engineering, Southeast University, Nanjing.
    Bengtsson, Mats
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Signal Processing.
    Ottersten, Björn
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Exploiting Long-Term Channel Correlation in Limited Feedback SDMA Through Channel Phase Codebook2011In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 59, no 3, p. 1217-1228Article in journal (Refereed)
    Abstract [en]

    Improving channel information quality at the base station (BS) is crucial for the optimization of frequency division duplexed (FDD) multi-antenna multiuser downlink systems with limited feedback. To this end, this paper proposes to estimate a particular representation of channel state information (CSI) at the BS through channel norm feedback and a newly developed channel phase codebook, where the long-term channel correlation is efficiently exploited to improve performance. In particular, the channel representation is decomposed into a gain-related part and a phase-related part, with each of them estimated separately. More specifically, the gain-related part is estimated from the channel norm and channel correlation matrix, while the phase-related part is determined using a channel phase codebook, constructed with the generalized Lloyd algorithm. Using the estimated channel representation, joint optimization of multiuser precoding and opportunistic scheduling is performed to obtain an SDMA transmit scheme. Computer simulation results confirm the advantage of the proposed scheme over state of the art limited feedback SDMA schemes under correlated channel environment.

  • 48.
    Huang, Yongming
    et al.
    School of Information Science and Engineering, Southeast University, Nanjing.
    Zheng, Gan
    Interdisciplinary Centre for Security, Reliability and Trust (SnT), University of Luxembourg.
    Bengtsson, Mats
    KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering (EES), Signal Processing.
    Wong, Kai-Kit
    Yang, Luxi
    School of Information Science and Engineering, Southeast University, Nanjing, China.
    Ottersten, Björn
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Distributed Multicell Beamforming With Limited Intercell Coordination2011In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 59, no 2, p. 728-738Article in journal (Refereed)
    Abstract [en]

    This paper studies distributed optimization schemes for multicell joint beamforming and power allocation in time-division-duplex (TDD) multicell downlink systems where only limited-capacity intercell information exchange is permitted. With an aim to maximize the worst-user signal-to-interference-and-noise ratio (SINR), we devise a hierarchical iterative algorithm to optimize downlink beamforming and intercell power allocation jointly in a distributed manner. The proposed scheme is proved to converge to the global optimum. For fast convergence and to reduce the burden of intercell parameter exchange, we further propose to exploit previous iterations adaptively. Results illustrate that the proposed scheme can achieve near-optimal performance even with a few iterations, hence providing a good tradeoff between performance and backhaul consumption. The performance under quantized parameter exchange is also examined.

  • 49. Hyberg, P.
    et al.
    Jansson, Magnus
    KTH, Superseded Departments, Signals, Sensors and Systems.
    Ottersten, Björn
    KTH, Superseded Departments, Signals, Sensors and Systems.
    Array interpolation and bias reduction2004In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 52, no 10, p. 2711-2720Article in journal (Refereed)
    Abstract [en]

    Interpolation (mapping) of data from a given antenna array onto the output of a virtual array of more suitable configuration is well known in array signal processing. This operation allows arrays of any geometry to be used with fast direction-of-arrival (DOA) estimators designed for linear arrays. Conditions for preserving DOA error variance under such mappings have been derived by several authors. However, in many cases, such as omnidirectional signal surveillance over multiple octaves, systematic mapping errors will dominate over noise effects and cause significant bias in the DOA estimates. To prevent mapping errors from unduly affecting the DOA estimates, this paper uses a geometrical interpretation of a Taylor series expansion of the DOA estimator criterion function to derive an alternative design of the mapping matrix. Verifying simulations show significant bias reduction in the DOA estimates compared with previous designs. The key feature of the proposed design is that it takes into account the orthogonality between the manifold mapping errors and certain gradients of the estimator criterion function. With the new design, mapping of narrowband signals between dissimilar array geometries over wide sectors and large frequency ranges becomes feasible.

  • 50.
    Hyberg, Per
    et al.
    Swedish Defence Research Agency (FOI), SE-172 90, Stockholm, Sweden.
    Jansson, Magnus
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Ottersten, Björn
    KTH, School of Electrical Engineering (EES), Signal Processing. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Array interpolation and DOA MSE reduction2005In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 53, no 12, p. 4464-4471Article in journal (Refereed)
    Abstract [en]

    Interpolation or mapping of data from a given real array to data from a virtual array of more suitable geometry is well known in array signal processing. This operation allows arrays of any geometry to be used with fast direction-of-arrival (DOA) estimators designed for linear arrays. In an earlier companion paper [21], a first-order condition for zero DOA bias under such mapping was derived and was also used to construct a design algorithm for the mapping matrix that minimized the DOA estimate bias. This bias-minimizing theory is now extended to minimize not only bias, but also to consider finite sample effects due to noise and reduce the DOA mean-square error (MSE). An analytical first-order expression for mapped DOA MSE is derived, and a design algorithm for the transformation matrix that minimizes this MSE is proposed. Generally, DOA MSE is not reduced by minimizing the size of the mapping errors but instead by rotating these errors and the associated noise subspace into optimal directions relative to a certain gradient of the DOA estimator criterion function. The analytical MSE expression and the design algorithm are supported by simulations that show not only conspicuous MSE,improvements in relevant scenarios, but also a more robust preprocessing for low signal-to-noise ratios (SNRs) as compared with the pure bias-minimizing design developed in the previous paper.

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