Grid selection for sparse estimation of spectral-line parameters is a critical problem that was in need of a satisfactory solution: assuming the usual case of a uniform spectral grid how should one select the number of grid points, K? We first present a simple practical rule for choosing an initial value (or initial values) of K in a given situation. Then, we go on to explain how the estimation results corresponding to different values of K can be compared with one another and therefore how to select the "best" value of K among those considered. Furthermore, we introduce a method for detecting when a grid is "too rough" and for obtaining refined parameter estimates in such a case.
This paper presents a novel SParse Iterative Covariance-based Estimation approach, abbreviated as SPICE, to array processing. The proposed approach is obtained by the minimization of a covariance matrix fitting criterion and is particularly useful in many-snapshot cases but can be used even in single-snapshot situations. SPICE has several unique features not shared by other sparse estimation methods: it has a simple and sound statistical foundation, it takes account of the noise in the data in a natural manner, it does not require the user to make any difficult selection of hyperparameters, and yet it has global convergence properties.
Unimodular (i.e., constant modulus) sequences with good autocorrelation properties are useful in several areas, including communications and radar. The integrated sidelobe level (ISL) of the correlation function is often used to express the goodness of the correlation properties of a given sequence. In this paper, we present several cyclic algorithms for the local minimization of ISL-related metrics. These cyclic algorithms can be initialized with a good existing sequence such as a Golomb sequence, a Frank sequence, or even a (pseudo)random sequence. To illustrate the performance of the proposed algorithms, we present a number of examples, Including the design of sequences that have virtually zero autocorrelation sidelobes In a specified lag interval and of long sequences that could hardly be handled by means of other algorithms previously suggested in the literature.
We begin by revisiting the periodogram to explain why arguably the plain least-squares periodogram (LSP) is preferable to the "classical" Fourier periodogram, from a data-fitting viewpoint, as well as to the frequently-used form of LSP due to Lomb and Scargle, from a computational standpoint. Then we go on to introduce a new enhanced method for spectral analysis of nonuniformly sampled data sequences. The new method can be interpreted as an iteratively weighted LSP that makes use of a data-dependent weighting matrix built from the most recent spectral estimate. Because this method is derived for the case of real-valued data (which is typically more complicated to deal with in spectral analysis than the complex-valued data case), it is iterative and it makes use of an adaptive (i.e., data-dependent) weighting, we refer to it as the real-valued iterative adaptive approach (RIAA). LSP and RIAA are nonparametric methods that can be used for the spectral analysis of general data sequences with both continuous and discrete spectra. However, they are most suitable for data sequences with discrete spectra (i.e., sinusoidal data), which is the case we emphasize in this paper. AB We begin by revisiting the periodogram to explain why arguably the plain least-squares periodogram (LSP) is preferable to the "classical" Fourier periodogram, from a data-fitting viewpoint, as well as to the frequently-used form of LSP due to Lomb and Scargle, from a computational standpoint. Then we go on to introduce a new enhanced method for spectral analysis of nonuniformly sampled data sequences. The new method can be interpreted as an iteratively weighted LSP that makes use of a data-dependent weighting matrix built from the most recent spectral estimate. Because this method is derived for the case of real-valued data (which is typically more complicated to deal with in spectral analysis than the complex-valued data case), it is iterative and it makes use of an adaptive (i.e., data-dependent) weighting, we refer to it as the real-valued iterative adaptive approach (RIAA). LSP and RIAA are nonparametric methods that can be used for the spectral analysis of general data sequences with both continuous and discrete spectra. However, they are most suitable for data sequences with discrete spectra (i.e., sinusoidal data), which is the case we emphasize in this paper.
This paper makes use of the Pisarenko framework, originally devised for temporal power spectrum estimation, to introduce a method for spatial power estimation that outperforms the beamforming method (except in extreme cases with serious calibration errors) as well as the Capon method (except in idealized situations with plentiful data and no miscalibration). An important feature of the proposed method is that it is user parameter-free, unlike most previous proposals with a similar character. Throughout the paper we emphasize a covariance matrix fitting approach to spatial power estimation, which provides clear intuitive explanations of the typical performance of the methods in the class under discussion. In a somewhat separated analysis, of interest for signal estimation applications, we derive the beamformer that passes a signal of interest in an undistorted manner, has minimum white-noise gain, and whose output power equals a given value (that should be larger than the Capon beamformer output power, which is known to have the smallest possible value). The given power value, referred to above, can be either obtained with a spatial power estimation method or perhaps provided directly by the user.
A multiple-input multiple-output (MIMO) radar system, unlike a standard phased-array radar, can choose freely the probing signals transmitted via its antennas to maximize the power around the locations of the targets of interest, or more generally to approximate a given transmit beampattern, and also to minimize the cross-correlation of the signals reflected back to the radar by the targets of interest. In this paper, we show how the above desirable features can be achieved by designing the covariance matrix of the probing signal vector transmitted by the radar. Moreover, in a numerical study, we show that the proper choice of the probing signals can significantly improve the performance of adaptive MIMO radar techniques. Additionally, we demonstrate the advantages of several MIMO transmit beampattern designs, including a beampattern matching design and a minimum sidelobe beampattern design, over their phased-array counterparts.
Transmit beampattern design is a critically important task in many fields including defense and homeland security as well as biomedical applications. Flexible transmit beampattern designs can be achieved by exploiting the waveform diversity offered by an array of sensors that transmit probing signals chosen at will. Unlike a standard phased-array, which transmits scaled versions of a single waveform, a waveform diversity-based system offers the flexibility of choosing how the different probing signals are correlated with one another. Recently proposed techniques for waveform diversity-based transmit beampattern design have focused on the optimization of the covariance matrix R of the waveforms, as optimizing a performance metric directly with respect to the waveform matrix is a more complicated operation. Given an R, obtained in a previous optimization stage or simply pre-specified, the problem becomes that of determining a signal waveform matrix X whose covariance matrix is equal or close to R, and which also satisfies some practically motivated constraints (such as constant-modulus or low peak-to-average-power ratio constraints). We propose a cyclic optimization algorithm for the synthesis of such an X, which (approximately) realizes a given optimal covariance matrix R under various practical constraints. A numerical example is presented to demonstrate the effectiveness of the proposed algorithm.
In space-time adaptive processing (STAP), the clutter covariance matrix is routinely estimated from secondary "target-free" data. Because this type of data is, more often than not, rather scarce, the so-obtained estimates of the clutter covariance matrix are typically rather poor. In knowledge-aided (KA) STAP, an a priori guess of the clutter covariance matrix (e.g., derived from knowledge of the terrain probed by the radar) is available. In this note, we describe a computationally simple and fully automatic method for combining this prior guess with secondary data to obtain a theoretically optimal (in the mean-squared error sense) estimate of the clutter covariance matrix. The authors apply the proposed method to the KASSPER data set to illustrate the type of achievable performance.
This paper discusses the joint design of receive filters and transmit signals for active sensing applications such as radar and active sonar. The goal is to minimize the mean-square error (MSE) of target's scattering coefficient estimate in the presence of clutter and interference, which is equivalent to maximizing the signal-to-clutter-plus-interference ratio. A discrete-time signal model is assumed and practical constant-modulus or low peak-to-average-power ratio (PAR) constraints are imposed on the transmit signal. Several optimization methods are proposed for this joint design. Furthermore, the MSE criterion is expressed in the frequency domain and a corresponding MSE lower bound is derived. Numerical examples for different types of interferences are included to demonstrate the effectiveness of the proposed designs.
The identification of multi-input multi-output (MIMO) linear systems has previously received a new impetus with the introduction of the state-space (SS) approach based on subspace approximations. This approach has immediately gained popularity, owing to the fact that it avoids the use of canonical forms, requires the determination of only one structural parameter, and has been empirically shown to yield MIMO models with good accuracy in many cases, However, the SS approach suffers from several drawbacks: there is no well-established rule tied to this approach for determining the structural parameter, and, perhaps more important the SS parameter estimates depend on the data in a rather complicated way, which renders almost futile any attempt to analyze and optimize the performance of the estimator. In this paper, we consider a transfer function (TF) approach based on instrumental variables (IV), as an alternative to the SS approach. We use the simplest canonical TF parameterization in which the denominator is equal to a scalar polynomial times the identity matrix. The analysis and optimization of the statistical accuracy of the TF approach is straightforward. Additionally, a simple test tailored to this approach is devised for estimating the single structural parameter needed. A simulation study, in which we compare the performances of the SS and the TF approaches, shows that the latter can provide more accurate models than the former at a lower computational cost.
The authors comment that an interesting attempt was made to simplify the derivation of the Cramer-Rao bound (CRB) for the principal parameters in the so-called superimposed-signals-in-noise models. Here, we streamline the derivation in question and then go on to show how it relates to other possible derivations of the CRB. We show that the new derivation can be neatly interpreted as performing a block diagonalization of the CRB matrix, which is a sensible thing to do in the presence of nuisance parameters. Gu (see ibid., vol.48, p.543-545, Feb. 2000) replies that the interesting problem of de-coupling in Cramer-Rao bounds is algebraically and neatly approached in this article, whereas the linearization method is geometrical, with statistical interpretations.
The results and interpretations obtained in the above referred paper are shown to be well known or obvious. Additionally, corrections to some misleading statements in the aforementioned paper are presented.
High-performance signal parameter estimation from sensor array data is a problem which has received much attention. A number of so-called eigenvector (EV) techniques such as MUSIC, ESPRIT, WSF, and MODE have been proposed in the literature. The EV techniques for array processing require knowledge of the spatial noise correlation matrix that constitutes a significant drawback. A novel instrumental variable (IV) approach to the sensor array problem is proposed. The IV technique relies on the same basic geometric properties as the EV methods to obtain parameter estimates. However, by exploiting the temporal correlation of the source signals, no knowledge of the spatial noise covariance is required. The asymptotic properties of the IV estimator are examined and an optimal IV method is derived. Computer simulations are presented to study the properties of the IV estimators in samples of practical length. The proposed algorithm is also shown to perform better than MUSIC on a full-scale passive sonar experiment.
High-performance signal parameter estimation from sensor array data is a problem which has received much attention. A number of so-called eigenvector (EV) techniques such as MUSIC, ESPRIT, WSF, and MODE have been proposedin the literature. The EV techniques for array processing require knowledge of the spatial noise correlation matrix that constitutes a significant drawback. A novel instrumental variable (IV) approach to the sensor array problem is proposed. The IV technique relies on the same basic geometric properties as the EV methods to obtain parameter estimates. However, by exploiting the temporal correlation of the source signals, no knowledge of the spatial noisecovariance is required. The asymptotic properties of the IV estimator are examined and an optimal IV method is derived. Computer simulations are presented to study the properties of the IV estimators in samples of practical length. The proposed algorithm is also shown to perform better than MUSIC on a full-scale passive sonar experiment
We develop Bayesian learning methods for low-rank matrix reconstruction and completion from linear measurements. For under-determined systems, the developed methods reconstruct low-rank matrices when neither the rank nor the noise power is known a priori. We derive relations between the proposed Bayesian models and low-rank promoting penalty functions. The relations justify the use of Kronecker structured covariance matrices in a Gaussian-based prior. In the methods, we use expectation maximization to learn the model parameters. The performance of the methods is evaluated through extensive numerical simulations on synthetic and real data.
We consider a distributed compressed sensing scenario where many sensors measure correlated sparse signals and the sensors are connected through a network. Correlation between sparse signals is modeled by a partial common support-set. For such a scenario, the main objective of this paper is to develop a greedy pursuit algorithm. We develop a distributed parallel pursuit (DIPP) algorithm based on exchange of information about estimated support-sets at sensors. The exchange of information helps to improve estimation of the partial common support-set, that in turn helps to gradually improve estimation of support-sets in all sensors, leading to a better quality reconstruction performance. We provide restricted isometry property (RIP) based theoretical analysis on the algorithm's convergence and reconstruction performance. Under certain theoretical requirements (i.e., under certain assumptions) on the quality of information exchange over the network and RIP parameters of sensor nodes, we show that the DIPP algorithm converges to a performance level that depends on a scaled additive measurement noise power (convergence in theory) where the scaling coefficient is a function of RIP parameters and information processing quality parameters. Using simulations, we show practical reconstruction performance of DIPP vis-a-vis amount of undersampling, signal-to-measurement-noise ratios and network-connectivity conditions.
A Bayesian approach to estimate parameters of signals embedded in complex Gaussian noise with unknown color is presented. The study specifically focuses on a Bayesian treatment of the unknown noise covariance matrix making up a nuisance parameter in such problems. By integrating out uncertainties regarding the noise color, an enhanced ability to estimate both the signal parameters as well as properties of the error is exploited. Several noninformative priors for the covariance matrix, such as the reference prior, the Jeffreys prior, and modifications to this, are considered. Some of the priors result in analytical solutions, whereas others demand numerical approximations. In the linear signal model, connections are made between the standard Adaptive Maximum Likelihood (AML) estimate and a Bayesian solution using the Jeffreys prior. With adjustments to the Jeffreys prior, correspondence to the regularized solution is also established. This in turn enables a formal treatment of the regularization parameter. Simulations indicate that significant improvements, compared to the AML estimator, can be obtained by considering both the derived regularized solutions as well as the one obtained using the reference prior. The simulations also indicate the possibility of enhancing the predictions of properties of the error as uncertainties in the noise color are acknowledged.
The paper derives the reference prior for complex covariance matrices. The reference prior is a noninformative prior that circumvents some of the weaknesses of common alternatives in multidimensional settings. As a consequence, inference based on this prior renders well-behaving solutions that in many cases outperform traditionally used approaches. The main obstacle is that inference based on this prior require integration over high-dimensional spaces which have no closed form solutions. A focus of the paper is therefore to discuss efficient implementation strategies based on Markov chain Monte Carlo methods. It is identified that certain structures can be treated analytically both for the case where the parameter of interest is the covariance matrix itself but also for cases in which the covariance matrix is a nuisance parameter that characterizes noise color. Evaluation in both these settings also verify the superior performance obtained by using the proposed prior as compared to traditional techniques to treat unknown covariance matrices.
This paper describes several new techniques for direction of arrival (DOA) estimation using arrays composed of multiple translated and uncalibrated subarrays. The new algorithms can be thought of as generalizations of the MUSIC, Root-MUSIC, and MODE techniques originally developed for fully calibrated arrays. The advantage of these new approaches is that the DOAs can be estimated using either a simple one-dimensional (I-D) search or by rooting a polynomial, as opposed to the multidimensional search required by multiple invariance (MI)-ESPRIT. When it can be applied, the proposed MI-MODE algorithm shares the statistical optimality of MI-ESPRIT. While MI-MUSIC and Root-MI-MUSIC are only optimal for uncorrelated sources, they perform better than a single invariance implementation of ESPRIT and are thus better suited for finding the initial conditions required by the MI-ESPRIT search.
A subspace-fitting formulation of the ESPRIT problem is presented that provides a framework for extending the algorithm to exploit arrays with multiple invariances. In particular, a multiple invariance (MI) ESPRIT algorithm is developed and the asymptotic distribution of the estimates is obtained. Simulations are conducted to verify the analysis and to compare the performance of MI ESPRIT with that of several other approaches. The excellent quality of the MI ESPRIT estimates is explained by recent results which state that, under certain conditions, subspace-fitting methods of this type are asymptotically efficient.
ESPIRIT is a recently developed technique for high-resolution signal parameter estimation with applications to direction-of-arrival estimation and time series analysis. By exploiting invariances designed into the sensor array, parameter estimates are obtained directly, without knowledge of the array response and without computation or search of some spectral measure. The original formulation of ESPIRIT assumes there is only one invariance in the array associated with each dimension of the parameter space. However, in many applications, arrays that possess multiple invariances (e.g., uniform linear arrays, uniformly sampled time series) are employed, and the question of which invariance to use naturally arises. More importantly, it is desirable to exploit the entire invariance structure simultaneously in estimating the signal parameters. Herein, a subspace-fitting formulation of the ESPIRIT problem is presented that provides a framework for extending the algorithm to exploit arrays with multiple invariances. In particular, a multiple invariance (MI) ESPIRIT algorithm is developed and the asymptotic distribution of the estimates obtained. Simulations are conducted to verify the analysis and to compare the performance of MI ESPIRIT with that of several other approaches. The excellent quality of the MI ESPIRIT estimates is explained by recent results which state that, under certain conditions, subspace-fitting methods of this type are asymptotically efficient.
We consider range-Doppler imaging via transmitting a train of probing pulses. We present two methods for range-Doppler imaging. The first one is based on the instrumental variables (IV) filter and the second one is based on the iterative adaptive approach (IAA). Numerical results show that both methods can suppress interference from neighboring range and Doppler bins. An attractive feature of the IV filter is that it can be computed offline. IAA has better performance than IV and has super resolution, but at the cost of a higher computational complexity.
This paper studies the detection performance of a multiple-input-multiple-output (MIMO) multifunction radio frequency (MFRF) system, which simultaneously supports radar, communication, and jamming. We show that the detection performance of the MIMO MFRF system improves as the transmit signal-to-interference-plus-noise-ratio (SINR) increases. To analyze the achievable SINR of the system, we formulate an SINR maximization problem under the communication and jamming functionality constraint as well as a transmit energy constraint. We derive a closed-form solution of this optimization problem for energy-constrained waveforms and present a detailed analysis of the achievable SINR. Moreover, we analyze the SINR for systems transmitting constant-modulus waveforms, which are often used in practice. We propose an efficient constant-modulus waveform design algorithm to maximize the SINR. Numerical results demonstrate the capability of a MIMO array to provide multiple functions, and also show the tradeoff between radar detection and the communication/jamming functionality.
We consider the design of polyphase waveforms for ground moving target detection with airborne multiple-input-multiple-output (MIMO) radar. Due to the constant-modulus and finite-alphabet constraint on the waveforms, the associated design problem is non-convex and in general NP-hard. To tackle this problem, we develop an efficient algorithm based on relaxation and cyclic optimization. Moreover, we exploit a reparameterization trick to avoid the significant computational burden and memory requirement brought about by relaxation. We prove that the objective values during the iterations are guaranteed to converge. Finally, we provide an effective randomization approach to obtain polyphase waveforms from the relaxed solution at convergence. Numerical examples show the effectiveness of the proposed algorithm for designing polyphase waveforms.
This paper examines the statistical properties of the narrowband Doppler volume backscattering process and analyzes its evolutionary spectrum. After clarifying the mechanism of both the finite duration Doppler effect and the continuously space-shifted integration process, the first two order time-varying statistics under a more general assumption, i.e., von Mises distribution, of random phase are derived. The generalization permits nonuniform phase tendency, which occurs in layered medium scattering. Based on the locally stationary process model, the evolutionary spectrum of the signal is derived. It is shown that the variation of the backscattering strength enters the spectrum as an amplitude modulation, whereas the variation of the random phase distribution acts as both the amplitude modulation and the frequency modulation. Finally, the observability of the average flow speed using spectral centroid estimate is discussed.
This paper proposes a novel algorithm to estimate the time-varying spectral centroid of the narrowband Doppler volume backscattering signal. It is constructed in a semi-parametric way, that is, modeling parametrically the local narrowband evolutionary spectrum using an AR(2) and nonparametrically adapting its time-varying coefficients using the wavelet shrinkage. The improved performance is gained by the underlying linear prediction function of the AR(2) and the minimax optimality of the unknown smoothness adaptation of the wavelet shrinkage procedure.
We consider the problem of decentralized hypothesis testing in a network of energy harvesting sensors, where sensors make noisy observations of a phenomenon and send quantized information about the phenomenon towards a fusion center. The fusion center makes a decision about the present hypothesis using the aggregate received data during a time interval. We explicitly consider a scenario under which the messages are sent through parallel access channels towards the fusion center. To avoid limited lifetime issues, we assume each sensor is capable of harvesting all the energy it needs for the communication from the environment. Each sensor has an energy buffer (battery) to save its harvested energy for use in other time intervals. Our key contribution is to formulate the problem of decentralized detection in a sensor network with energy harvesting devices. Our analysis is based on a queuing-theoretic model for the battery and we propose a sensor decision design method by considering long term energy management at the sensors. We show how the performance of the system changes for different battery capacities. We then numerically show how our findings can be used in the design of sensor networks with energy harvesting sensors.
We consider the problem of decentralized hypothesis testing under communication constraints in a topology where several peripheral nodes are arranged in tandem. Each node receives an observation and transmits a message to its successor, and the last node then decides which hypothesis is true. We assume that the observations at different nodes are, conditioned on the true hypothesis, independent and the channel between any two successive nodes is considered error-free but rate-constrained. We propose a cyclic numerical design algorithm for the design of nodes using a person-by-person methodology with the minimum expected error probability as a design criterion, where the number of communicated messages is not necessarily equal to the number of hypotheses. The number of peripheral nodes in the proposed method is in principle arbitrary and the information rate constraints are satisfied by quantizing the input of each node. The performance of the proposed method for different information rate constraints, in a binary hypothesis test, is compared to the optimum rate-one solution due to Swaszek and a method proposed by Cover, and it is shown numerically that increasing the channel rate can significantly enhance the performance of the tandem network. Simulation results for $M$-ary hypothesis tests also show that by increasing the channel rates the performance of the tandem network significantly improves.
We consider the problem of distributed binary hypothesis testing in a parallel network topology where sensors independently observe some phenomenon and send a finite rate summary of their observations to a fusion center for the final decision. We explicitly consider a scenario under which (integer) rate messages are sent over an error free multiple access channel, modeled by a sum rate constraint at the fusion center. This problem was previously studied by Chamberland and Veeravalli, who provided sufficient conditions for the optimality of one bit sensor messages. Their result is however crucially dependent on the feasibility of having as many one bit sensors as the (integer) sum rate constraint of the multiple access channel, an assumption that can often not be satisfied in practice. This prompts us to consider the case of an a-priori limited number of sensors and we provide sufficient condition under which having no two sensors with rate difference more than one bit, so called rate balancing, is an optimal strategy with respect to the Bhattacharyya distance between the hypotheses at the input to the fusion center. We further discuss explicit observation models under which these sufficient conditions are satisfied.
© 2015 IEEE. This paper presents optimal parameter selection and preconditioning of the alternating direction method of multipliers (ADMM) algorithm for a class of distributed quadratic problems, which can be formulated as equality-constrained quadratic programming problems. The parameter selection focuses on the ADMM step-size and relaxation parameter, while the preconditioning corresponds to selecting the edge weights of the underlying communication graph. We optimize these parameters to yield the smallest convergence factor of the iterates. Explicit expressions are derived for the step-size and relaxation parameter, as well as for the corresponding convergence factor. Numerical simulations justify our results and highlight the benefits of optimal parameter selection and preconditioning for the ADMM algorithm.
This paper presents optimal parameter selection and preconditioning of the alternating direction method of multipliers (ADMM) algorithm for a class of distributed quadratic problems, which can be formulated as equality-constrained quadratic programming problems. The parameter selection focuses on the ADMM step-size and relaxation parameter, while the preconditioning corresponds to selecting the edge weights of the underlying communication graph. We optimize these parameters to yield the smallest convergence factor of the iterates. Explicit expressions are derived for the step-size and relaxation parameter, as well as for the corresponding convergence factor. Numerical simulations justify our results and highlight the benefits of optimal parameter selection and preconditioning for the ADMM algorithm.
This paper considers coordinated multicast beamforming in a multicell multigroup multiple-input single-output system. Each base station (BS) serves multiple groups of users by forming a single beam with common information per group. We propose centralized and distributed beamforming algorithms for two different optimization targets. The first objective is to minimize the total transmission power of all the BSs while guaranteeing the user-specific minimum quality-of-service targets. The semidefinite relaxation (SDR) method is used to approximate the nonconvex multicast problem as a semidefinite program (SDP), which is solvable via centralized processing. Subsequently, two alternative distributed methods are proposed. The first approach turns the SDP into a two-level optimization via primal decomposition. At the higher level, intercell interference powers are optimized for fixed beamformers, whereas the lower level locally optimizes the beamformers by minimizing BS-specific transmit powers for the given intercell interference constraints. The second distributed solution is enabled via an alternating direction method of multipliers, where the intercell interference optimization is divided into a local and a global optimization by forcing the equality via consistency constraints. We further propose a centralized and a simple distributed beamforming design for the signal-to-interference-plus-noise ratio (SINR) balancing problem in which the minimum SINR among the users is maximized with given per-BS power constraints. This problem is solved via the bisection method as a series of SDP feasibility problems. The simulation results show the superiority of the proposed coordinated beamforming algorithms over traditional noncoordinated transmission schemes, and illustrate the fast convergence of the distributed methods. Index Terms—Alternating direction method of multipliers, distributed optimization, multi-cell coordination, physical layer multigroup multicasting, primal decomposition, SINR balancing, sum power minimization.
This paper studies the energy efficiency and sum rate tradeoff for coordinated beamforming in multicell multiuser multigroup multicast multiple-input single-output systems. We first consider a conventional network energy efficiency maximization (EEmax) problem by jointly optimizing the transmit beamformers and antennas selected to be used in transmission. We also account for per-antenna maximum power constraints to avoid nonlinear distortion in power amplifiers and user-specific minimum rate constraints to guarantee certain service levels and fairness. To be energy efficient, transmit antenna selection is employed. It eventually leads to a mixed-Boolean fractional program. We then propose two different approaches to solve this difficult problem. The first solution is based on a novel modeling technique that produces a tight continuous relaxation. The second approach is based on sparsity-inducing method, which does not require the introduction of any Boolean variable. We also investigate the tradeoff between the energy efficiency and sum rate by proposing two different formulations. In the first formulation, we propose a new metric, that is, the ratio of the sum rate and the so-called weighted power. Specifically, this metric reduces to EEmax when the weight is 1, and to sum rate maximization when the weight is 0. In the other method, we treat the tradeoff problem as a multiobjective optimization for which a scalarization approach is adopted. Numerical results illustrate significant achievable energy efficiency gains over the method where the antenna selection is not employed. The effect of antenna selection on the energy efficiency and sum rate tradeoff is also demonstrated.
We describe an efficient technique analyzing signals that comprise a number of polynomial-phase components, The technique is based on a recently proposed "multiple frequency tracker," which is an algorithm for recursive estimation of parameters of multiple sine waves in noise, It has a relatively low SNR threshold and moderate computational complexity.
Two algorithms for tracking parameters of slowly varying multiple complex sine waves (cisoids) in noise (the multiple frequency tracker and the adaptive notch filter) are described, For high signal-to-noise ratio (SNR), the properties of the algorithms (i.e., stability, noise rejection, and tracking speed) are studied analytically using a linear filter approximation technique, The tradeoff between noise rejection and tracking error for both algorithms is shown to be similar, Different choices of the design variables are discussed, namely i) minimal mean-square estimation error for random walk modeled frequency variations and ii) minimal stationary estimation variance subject to a given tracking delay.
A class of computationally efficient DOA estimators under the Partial Relaxation (PR) framework has recently been proposed. Conceptually different from conventional DOA estimation methods in the literature, the estimators under the PR framework rely on the non-complete relaxation of the array manifold while performing a spectral-search in the field of view. This particular type of relaxation essentially implies a modified signal model with partial information loss due to the relaxation. The information loss and its impact on the DOA estimation performance have not yet been analytically quantified in the literature. In this paper, the information loss induced by the relaxation of the array manifold is investigated through the Cramér-Rao Bound (CRB). The closed-form expression of the CRB for DOA estimation under the PR model, on the one hand, provides insight on the information loss in the asymptotic region where the number of snapshots tends to infinity. On the other hand, the proposed CRB characterizes the lower bound for the DOA estimation performance of all PR estimators. We prove that, under the assumptions of Gaussian source signal and noise, the CRB of the PR signal model is lower-bounded by the conventional stochastic CRB. We also prove that the previously proposed Weighted Subspace Fitting estimator under the PR framework asymptotically achieves the CRB of the PR signal model. Furthermore, it is shown that the asymptotic mean-squared errors of all Weighted Subspace Fitting estimators under the PR framework for any positive definite weighting matrix are identical. © 1991-2012 IEEE.
In this paper, the partial relaxation approach is introduced and applied to the direction-of-arrival estimation problem using spectral search. Unlike existing spectral-based methods such as conventional beamformer, Capon beamformer, or MUSIC that can be considered as single source approximation of multisource estimation criteria, the proposed approach accounts for the existence of multiple sources. At each considered direction, the manifold structure of the remaining interfering signals impinging on the sensor array is relaxed, which results in closed form estimates for the "interference" parameters. Thanks to this relaxation, the conventional multi-source optimization problem reduces to a simple spectral search. Following this principle, we propose estimators based on the deterministic maximum likelihood, weighted subspace fitting, and covariance fitting methods. To calculate the null-spectra efficiently, an iterative rooting scheme based on the rational function approximation is applied to the partial relaxation methods. Simulation results show that, irrespective of any specific structure of the sensor array, the performance of the proposed estimators is superior to the conventionalmethods, especially in the case of low signal-to-noise-ratio and low number of snapshots, while maintaining a computational cost that is comparable to MUSIC.
The problem of finding the least squares solution to a system of equations Hs = y is considered, when is a vector of binary variables and the coefficient matrix H is unknown but of bounded uncertainty. Similar to previous approaches to robust binary least squares, we explore the potential of a min-max design with the aim to provide solutions that are less sensitive to the uncertainty in H . We concentrate on the important case of ellipsoidal uncertainty, i.e., the matrix H is assumed to be a deterministic unknown quantity which lies in a given uncertainty ellipsoid. The resulting problem is NP-hard, yet amenable to convex approximation techniques: Starting from a convenient reformulation of the original problem, we propose an approximation algorithm based on semidefinite relaxation that explicitly accounts for the ellipsoidal uncertainty in the coefficient matrix. Next, we show that it is possible to construct a tighter relaxation by suitably changing the description of the feasible region of the problem, and formulate an approximation algorithm that performs better in practice. Interestingly, both relaxations are derived as Lagrange bidual problems corresponding to the two equivalent problem reformulations. The strength of the proposed tightened relaxation is demonstrated by pertinent simulations.
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 Cramer-Rao Lower Bound (CRLB), and ML consistency conditions for the proposed sparse nonlinear model. The proposed ML approach lends itself naturally to l(1)-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.
We consider the problem of tracking the time-varying (TV) parameters of a harmonic or chirp signal using particle filtering (PF) tools. Similar to previous PF approaches to TV spectral analysis, we assume that the model parameters (complex amplitude, frequency, and frequency rate in the chirp case) evolve according to a Gaussian AR(1) model; but we concentrate on the important special case of a single TVharmonic or chirp.We show that the optimal importance function that minimizes the variance of the particle weights can be computed in closed form, and develop procedures to draw samples from it. We further employ Rao–Blackwellization to come up with reduced-complexity versions of the optimal filters. The end result is custom PF solutions that are considerably more efficient than generic ones, and can be used in a broad range of important applications that involve a single TV harmonic or chirp signal, e.g., TV Doppler estimation in communications, and radar.
The problem of tracking a frequency-hopped signal without knowledge of its hopping pattern is considered. The problem is of interest in military communications, where, in addition to frequency, hop timing can also be randomly shifted to guard against unauthorized reception and jamming. A conceptually simple nonlinear and non-Gaussian stochastic state-space model is proposed to capture the randomness in carrier frequency and hop timing. This model is well-suited for the application of particle filtering tools: it is possible to compute the optimal (weight variance-minimizing) importance function in closed-form. A convenient mixture representation of the latter is employed together with Rao-Blackwellization to derive a very simple optimal sampling procedure. This is representative of the state-of-art in terms of systematic design of particle filters. A heuristic design approach is also developed, using the mode of the spectrogram to localize hop particles. Performance is assessed in a range of experiments using both simulated and measured data. Interestingly, the results indicate that the heuristic design approach can outperform the systematic one, and both are robust to model assumptions.
We present the joint likelihood (ML) symbol-time and carrier-frequency offset estimator in orthogonal frequency-division multiplexing (OFDM) systems. Redundant information contained within the cyclic prefix enables this estimation without additional pilots. Simulations show that the frequency estimator may be used in tracking mode and the time estimator in an acquisition mode.
Based on a generative model (GM) and beliefs over hidden states, the free energy principle (FEP) enables an agent to sense and act by minimizing a free energy bound on Bayesian surprise, i.e., the negative logarithm of the marginal likelihood. Inclusion of desired states in the form of prior beliefs in the GM leads to active inference (ActInf). In this work, we aim to reveal connections between ActInf and stochastic optimal control. We reveal that, in contrast to standard cost and constraint-based solutions, ActInf gives rise to a minimization problem that includes both an information-theoretic surprise term and a model-predictive control cost term. We further show under which conditions both methodologies yield the same solution for estimation and control. For a case with linear Gaussian dynamics and a quadratic cost, we illustrate the performance of ActInf under varying system parameters and compare to classical solutions for estimation and control.
Massive MIMO is a compelling wireless access concept that relies on the use of an excess number of base-station antennas, relative to the number of active terminals. This technology is a main component of 5G New Radio and addresses all important requirements of future wireless standards: a great capacity increase, the support of many simultaneous users, and improvement in energy efficiency. Massive MIMO requires the simultaneous processing of signals from many antenna chains, and computational operations on large matrices. The complexity of the digital processing has been viewed as a fundamental obstacle to the feasibility of Massive MIMO in the past. Recent advances on system-algorithm-hardware co-design have led to extremely energy-efficient implementations. These exploit opportunities in deeply-scaled silicon technologies and perform partly distributed processing to cope with the bottlenecks encountered in the interconnection of many signals. For example, prototype ASIC implementations have demonstrated zero-forcing precoding in real time at a 55 mW power consumption (20 MHz bandwidth, 128 antennas, and multiplexing of 8 terminals). Coarse and even errorprone digital processing in the antenna paths permits a reduction of consumption with a factor of 2 to 5. This article summarizes the fundamental technical contributions to efficient digital signal processing for Massive MIMO. The opportunities and constraints on operating on low-complexity RF and analog hardware chains are clarified. It illustrates how terminals can benefit from improved energy efficiency. The status of technology and real-life prototypes discussed. Open challenges and directions for future research are suggested.