We introduce an efficient gradient based algorithm to minimize the peak sidelobe level (PSL) for binary sequence designs with or without low correlation zone requirements. The proposed algorithm calculates the effective step sizes by leveraging fast Fourier transform operations and employing low-complexity updates, and its local convergence is proved. Numerical examples are provided to demonstrate that our approach can outperform the state-of-the-art algorithms in generating binary sequences with lower PSL values.

We propose a novel mixed analog-to-digital converter (ADC) architecture for direction-of-arrival (DOA) estimation using a uniform linear array, where the in-phase and quadrature-phase channels can be independently sampled by different ADCs. We derive the Cramér-Rao bound (CRB) and utilize its lower bound to optimize the placement of different ADCs via a swap-based method. Numerical examples are provided to demonstrate the superiority of the optimized placement of different ADCs over existing schemes.

To overcome the dynamic range problems that conventional coarse quantized analog-to-digital converters (ADCs) suffer from, we consider the modulo ADCs with known folding-count (Mod-ADC-K). Two Cramér-Rao bounds (CRBs) are derived for signal parameter estimation from data generated by Mod-ADC-K, for both quantized and unquantized cases. Then we analyze their characteristics, and compare them to the conventional ADCs. Numerical examples are presented to verify the characteristics of Mod-ADC-K, and show that the low-bit Mod-ADC-K can mitigate the dynamic range problems.

In this paper, a simple Doppler-range processing (DRP) algorithm was first presented to mitigate two well-known problems encountered in high-speed moving target detection using automotive radar, i.e., range/Doppler migration and velocity ambiguity. DRP algorithm can achieve full range and velocity resolutions, as well as attaining coherent integration gains, while requiring a computational complexity comparable to that of the conventional range-Doppler processing (RDP) approach. Moreover, it can also automatically resolve the velocity ambiguity problems. We then introduce a data-adaptive spotlighting (DAS) algorithm to detect weak targets buried by shadow sidelobes of nearby strong targets with folded velocities. The effectiveness of the proposed algorithms are demonstrated by numerical examples.

Periodic binary sequences with good autocorrelation properties are useful for phase-modulated continuous wave (PMCW) automotive radar systems. The optimization problem encountered in the periodic binary sequence designs is NP-hard, and most of the existing algorithms are not suitable for designing long periodic sequences due to their heavy computational burdens. We consider an FFT-based algorithm for the efficient designs of long periodic binary sequences with arbitrary period lengths and ample diversity. Several numerical examples are provided to demonstrate the performance of the proposed algorithm.

In this work, we consider target parameter estimation of phase-modulated continuous-wave (PMCW) multiple-input multiple-output (MIMO) radars with few-bit analog-to-digital converters (ADCs). We formulate the estimation problem as a sparse signal recovery problem and modify the fast iterative shrinkage-thresholding algorithm (FISTA) to solve it. The ℓ2,1-norm is adopted to promote the sparsity in the range-Doppler-angle domain. Simulation results show that using few-bit ADCs can achieve comparable performance to many-bit ADCs when targets are widely separated. However, if targets are spaced closely, performance losses can occur when 1-bit ADCs are applied.

We consider herein the case of two vehicles equipped with multi-input multi-output (MIMO) automotive radars driving next to each other. We assume that 5G communications allow us to coordinate the radar probing waveforms for the vehicles. Then the binary sequence sets transmitted by different vehicles should meet the requirement that the cross-correlations of the sequence sets between vehicles are as low as possible for all time lags, while the auto-correlation sidelobes and cross-correlations within a low correlation zone (LCZ) of the binary sequence sets transmitted by each vehicle are lower than a desired level. We establish an optimization problem to realize these goals. We consider the coordinate-descent (CD) framework and we solve the optimization problem efficiently by taking full advantage of the fast Fourier transforms (FFTs) and introducing computationally efficient updating procedures within the CD iterations. Numerical examples are provided to demonstrate that the proposed algorithms can be used to effectively and efficiently design binary sequence sets, including long sequence sets, useful for MIMO automotive radar applications.

We consider the problem of phase modulated continuous wave (PMCW) radar signal processing when the receiver utilizes one-bit sampling with known time-varying thresholds. We formulate the target parameter estimation problem as a sparse signal recovery problem and use the alternating direction method of multipliers (ADMM) to solve it efficiently. Specifically, the log-norm approximation is used to replace the `0-norm to make the optimization problem more tractable. We then judiciously design the detailed updating steps of ADMM for the log-norm approximation, so that all updating steps involve computationally efficient closed-form solutions. Numerical examples are provided to demonstrate the effectiveness of our algorithm.

Abstract Defects of hesitant fuzzy set (HFS) manifest in actual decision‐making process, so adding probabilities to the values in HFS is necessary. The probabilistic HFS (PHFS) is a useful tool to describe the uncertainty of elements in HFS by introducing occurrence probabilities. However, some important issues in PHFS utilization remain to be addressed. In this study, an outranking method for multicriteria decision making (MCDM) with probabilistic hesitant information is presented. First, the binary relations between two probabilistic hesitant fuzzy elements (PHFEs) are defined on the basis of the elimination and choice translating reality method. Some outranking relations between the alternatives are then introduced. Second, we provide a Hausdorff distance between two PHFEs. The main characteristic of the proposed Hausdorff distance is that it does not require the same length and arrangement of the PHFEs. Third, a maximizing Hausdorff distance deviation method is developed to obtain the evaluation criteria weights under a probabilistic hesitant fuzzy environment. Finally, an illustrative example in conjunction with comparative analysis is used to demonstrate that the proposed method is feasible for practical MCDM problems.

This study addresses the high‐resolution time delay estimation (TDE) via sparse parameter estimation methods. Two representative algorithms, Sparse Asymptotic Minimum Variance (SAMV) and SParse Iterative Covariance‐based Estimation are devised in both the time and frequency domains for application to the TDE of spread‐spectrum signals and their performances are analysed in various multipath environments. The authors also proposes the combined approach of SAMV and weighted RELAX, referred to as SAMV‐WRELAX, to reduce the computational load. Numerical examples demonstrate that the frequency‐domain approaches with a proper type of snapshots not only outperform the corresponding time‐domain approaches but also mitigate the problem of the noise correlation encountered in time‐domain processing. They also show that the computational load of SAMV‐WRELAX with a grid size of decreases up to a few tenths of that of SAMV with a fine grid, e.g. a size of , without any performance degradations.

This study addresses the problem of direction‐of‐arrival (DOA) estimation of coherent signals via sparse parameter estimation. Since many sparse methods provide good performances regardless of signal correlations and array geometry, they can be considered as candidates for DOA estimation of coherent signals impinging on a sensor array with arbitrary geometry. However, their straightforward applications require high computational loads especially for two‐dimensional (2D) DOA estimation. Two efficient methods based on sparse parameter estimation are herein presented; one is a combined approach of sparse estimation and the RELAX algorithm extended for 2D DOA estimation and the other relies on the adaptive 2D grid refinement and power update control. Numerical simulations are performed to demonstrate the efficiency of the proposed methods using a uniform circular array for both 1D and 2D DOA estimation cases. It is shown that sparse asymptotic minimum variance (SAMV)‐RELAX, a combined approach of SAMV and RELAX, outperforms SAMV and multi‐stage SAMV in 2D scenarios without suffering from plateau effects for off‐grid signals and that its computational load is significantly lower than those of SAMV and multi‐stage SAMV. In addition, SAMV‐RELAX does not require the difficult selection of grid parameters for fine DOA estimation unlike the multi‐stage approach.

This paper proposes two methods for robust Capon beamforming. One is for the doubly constrained robust Capon beamforming problem, where the unit modular constraints on the elements of the steering vector of interest are enforced to circumvent the look direction error or phase perturbations of the signal-of-interest; and another addresses robust beamforming in impulsive noise environment, where we consider the lp-norm minimization (0 < p < 2) of the output while constraining the mainlobe response ripple term. We apply the splitting technique to simplify the resultant nonconvex optimization problem and solve it using alternating direction method of multipliers. The performance of the proposed methods is demonstrated via numerical examples.

We consider the problem of direction-of-arrival (DOA) and waveform estimation from coarsely quantized measurement samples obtained with an array of sensors. We introduce a majorization minimization based algorithm to cyclically maximize the likelihood function of the quantized array data. We also use the Bayesian information criterion (BIC) to determine the number of incident signals. Numerical examples are provided to demonstrate the effectiveness of our approaches.

We consider the problem of sinusoidal parameter estimation from signed measurement samples. We formulate the sinusoidal parameter estimation problem as a sparse signal recovery problem and apply the alternating direction method of multipliers (ADMM) to efficiently solve it. The ℓ1-norm and log-norm approximations are used to replace the ℓ0-norm. We then judiciously design the detailed update steps of ADMM for the two approximations, so that most or all update steps involve computationally efficient closed-form solutions. Numerical examples are provided to demonstrate the effectiveness of our approaches.

Radio frequency interference (RFI) causes serious problems to ultrawideband (UWB) radar operations due to severely degrading radar imaging capability and target detection performance. This paper formulates proper data models and proposes novel methods for effective RFI mitigation. We first apply the single-snapshot Sparse Iterative Covariance-based Estimation (SPICE) algorithm to data from each pulse repetition interval for RFI mitigation and discuss the connection of SPICE to the l1-penalized least absolute deviation (l1-PLAD) approach. Then, we devise a modified group SPICE algorithm and we prove that it is equivalent to a special case of the l1,2-PLAD method. The modified group SPICE algorithm can be applied to data from a coherent processing interval for effective RFI mitigation. Both the single-snapshot SPICE and the modified group SPICE methods simultaneously exploit the sparsity properties of both RFI spectrum and UWB radar target echoes. Unlike the existing sparsity-based RFI suppression methods, such as the robust principal component analysis algorithm, the proposed methods are hyperparameter-free and therefore easier to use in practical applications. Furthermore, the fast implementation of the SPICE methods is considered by exploiting the special structures of both single-snapshot and multiple-snapshot covariance matrices. Finally, the results obtained from applying the SPICE methods to simulated data as well as measured data collected by the U.S. Army Research Laboratory synthetic aperture radar system are presented to demonstrate the effectiveness of the proposed methods.

The mutual interference between similar radar systems can result in reduced radar sensitivity and increased false alarm rates. To address the interference mitigation problems in similar radar systems, we propose herein two slow-time coding schemes to modulate the pulses within a coherent processing interval (CPI). Specifically, the first coding scheme is designed through Doppler shifting and the second is devised via an optimization method. The proposed coding schemes are very easy to implement in practice and the incorporation of the coding schemes only requires slight modification of the existing systems. Our numerical examples indicate that the proposed coding schemes can reduce the interference power level in a desired area of the cross-ambiguity function significantly.

Multiple-input multiple-output forward-looking ground-penetrating radar (GPR) systems can be used to detect landmines. To enhance its performance, two data-dependent imaging algorithms, based on the sparse learning via iterative minimization (SLIM) and sparse covariance-based estimation (SPICE) techniques for high-resolution imaging, applied to the time-domain GPR data, were previously developed. Time-domain SLIM (TD-SLIM) and time-domain SPICE (TD-SPICE) yield higher resolution and lower sidelobe compared with data-independent approaches such as delay-and-sum and recursive sidelobe minimization. However, the two data-dependent imaging algorithms are computationally expensive. To provide both improved landmine detection performance and significantly reduced computational time compared with the TD-SLIM and TD-SPICE algorithms, we propose herein the frequency-domain SLIM algorithm.

The problem of model order selection from signed measurements obtained via 1-bit sampling is considered. The extension of the Bayesian information criterion (BIC) to the case of 1-bit sampling, referred to as 1bBIC, is proposed to determine the signal model order. A detailed analysis of and an application to sinusoidal signals are presented to demonstrate the performance of 1bBIC when the One-Bit RELAX algorithm is used to estimate the parameters of sinusoidal signals.

We derive a phase retrieval algorithm using the alternating direction method of multipliers. For the cost function obtained from the maximum likelihood criterion, we introduce auxiliary amplitude and phase variables to avoid the absolute value operator and decouple the determination of the auxiliary phase variables from that of the auxiliary amplitude variables. As a result, a phase retrieval algorithm consisting only of two least-squares steps is derived. The performance of the proposed algorithm is investigated via numerical examples, as well as an application to flat-spectrum periodic unimodular sequence design.

This paper considers the problem of reconstructing true targets in a single-channel synthetic aperture radar (SAR) imaging system, which has been disturbed by deceptive jammings. Since the deceptive jammings are usually confined to the main lobe of an SAR antenna, their time-frequency distributions are different from those of the true echoes. This enables us to utilize a dynamic synthetic aperture (DSA) scheme to extract the characteristics of the true and false targets. Dictionaries about the true and false targets are constructed by taking interactions between scatterers into account. Then a sparsity-driven optimization problem is solved to reconstruct the true and false targets separately with super-resolution. Moreover, the deceptively jammed SAR data are divided into different areas to handle various scenarios efficiently, and strategies for DSA selection are addressed as well. Simulations are provided to verify the effectiveness of the proposed algorithm.

This paper proposes a compressive pulse-Doppler radar that works through one-bit quantization of the received noisy signal. The one-bit quantization is performed by comparing the signal with a time-varying reference level. Considering the sparsity of the targets in the range-Doppler domain, the problem is dealt with by a sparse recovery method. The proposed method leads to an optimization problem that can be tackled by a convex approximation. Numerical examples show that the proposed method has a promising performance in the detection/estimation of the target parameters. Moreover, it is seen that in low signal to noise ratio, increasing the sampling rate at the receiver side is a compensating factor that effectively improves the performance.

This letter focuses on the local ambiguity function shaping through unimodular sequence design. An accelerated iterative sequential optimization (AISO) algorithm is proposed to minimize the average value of the weighted integrated sidelobe level (WISL) over specific Doppler bins and range bins of interest. We evaluate the effectiveness of the AISO algorithm in terms of its achieved WISL and computational complexity in comparison with the gradient method via numerical examples. The capability of using the design to detect high-speed targets is also evaluated.

The detection of ground moving targets with arbitrary linear motion from an airborne multi-channel radar via a long coherent processing interval is considered. A reparameterization of the target's linear motion is developed which allows for maximizing the target signal energy in synthetic aperture radar images, and decouples the array processing from the image formation process. The algorithm genrates estimates of the target's along-track and cross-track velocity components, making a unique determination of the target's motion parameters possible.

The detection of ground moving targets with arbitrary linear motion from an airborne multichannel radar via a long coherent processing interval is considered. The technique maximizes the target signal energy in synthetic aperture radar (SAR) images by matching to the target's linear motion profile. A reparameterization of the target's linear motion is developed that decouples the array processing from the image formation process. An explicit approach to forming SAR images focused with respect to a particular along-track velocity is presented. The ground clutter is canceled via an adaptive array technique, which also yields an estimate of the target radial velocity. Because the algorithm generates estimates of the target's along-track and cross-track velocity components, a unique determination of the target's motion parameters is possible. The approach is derived and investigated via simulated point spread functions. Algorithm performance is demonstrated on the GOTCHA SAR ground moving target indication data set.

The use of distances based on optimal transportation has recently shown promise for discrimination of power spectra. In particular, spectral estimation methods based on ℓ1regularization as well as covariance based methods can be shown to be robust with respect to such distances. These transportation distances provide a geometric framework where geodesics corresponds to smooth transition of spectral mass, and have been useful for tracking. In this paper we investigate the use of these distances for automatic target recognition. We study the use of the Monge-Kantorovich distance compared to the standard ℓ2distance for classifying civilian vehicles based on SAR images. We use a version of the Monge-Kantorovich distance that applies also for the case where the spectra may have different total mass, and we formulate the optimization problem as a minimum flow problem that can be computed using efficient algorithms.

The adaptive spectral estimation method IAA provides better performance than the periodogram at the cost of higher computational complexity. Current fast IAA algorithms reduce the computational complexity using Toeplitz/Vandermonde structures, but are not efficient for missing data cases when the number of missing samples is small. We considerably reduce the computational complexity compared to the state-of-the-art by using a low rank completion to transform the problem to a Toeplitz/Vandermonde structured problem.

This paper focuses on two signal processing aspects of multistatic active sonar systems, namely enhanced range-Doppler imaging and improved target parameter estimation. The main contributions of this paper are: i) a hybrid dense-sparse method is proposed to generate range-Doppler images with both low sidelobe levels and high accuracy; ii) a generalized K-Means clustering (GKC) method for target association is developed to associate the range measurements from different transmitter-receiver pairs; iii) the extended invariance principle-based weighted least-squares (EXIP-WLS) method is developed for accurate target position and velocity estimation. The effectiveness of the proposed multistatic active sonar system is verified using numerical examples.

Due to its long-standing importance, the problem of designing the receive filter and transmit sequence for clutter/interference rejection in active sensing has been studied widely in the last decades. In this letter, we propose a cyclic optimization of the transmit sequence and the receive filter. The proposed approach can handle arbitrary peak-to-average-power ratio (PAR) constraints on the transmit sequence, and can be used for large dimension designs (with ~ 103variables) even on an ordinary PC.

A novel forensic tool used for assessing the authenticity of digital audio recordings is known as the electric network frequency (ENF) criterion. It involves extracting the embedded power line (utility) frequency from said recordings and matching it to a known database to verify the time the recording was made, and its authenticity. In this paper, a nonparametric, adaptive, and high resolution technique, known as the time-recursive iterative adaptive approach, is presented as a tool for the extraction of the ENF from digital audio recordings. A comparison is made between this data dependent (adaptive) filter and the conventional short-time Fourier transform (STFT). Results show that the adaptive algorithm improves the ENF estimation accuracy in the presence of interference from other signals. To further enhance the ENF estimation accuracy, a frequency tracking method based on dynamic programming will be proposed. The algorithm uses the knowledge that the ENF is varying slowly with time to estimate with high accuracy the frequency present in the recording.

The cross ambiguity function (CAF) arises in many areas such as radar/sonar and communications when correlation processing is performed in the presence of a Doppler frequency shift. In this paper, the CAF synthesis problem is tackled: a pair of waveforms are jointly designed so that their CAF approximates a desired one. The so-generated waveforms have relatively low peak-to-average power ratios and in certain cases can be constant modulus. Numerical examples are provided to show the effectiveness of the proposed algorithm in synthesizing different types of CAF.

In this paper we present a new sparse iterative covariance-based estimation approach, called SPICE, to the direction of arrival estimation problem. SPICE is obtained by the minimization of a statistically well motivated covariance matrix fitting criterion and can be used in both single and multiple-snapshot cases. Some of the unique features enjoyed by SPICE are: it takes account of the noise in the data in a natural manner, it does not require selection of any hyper-parameters, and it has global convergence properties.

We consider a fast implementation of the weighted least-squares based iterative adaptive approach (IAA) for spectral estimation of uniformly sampled sequences. IAA is a robust, user parameter-free and nonparametric adaptive algorithm that can work with a single data sequence or snapshot. Compared with the conventional periodogram, IAA can be used to significantly increase the resolution and suppress the sidelobe levels. However, due to its high computational complexity, IAA can only be used in applications with short data sequences. We present herein a novel fast implementation of IAA using a Gohberg-Semencul (G-S)-type factorization of the IAA covariance matrix. By exploiting the Toeplitz structure of the said matrix, we are able to reduce the computational cost by two orders of magnitudes even for sequences with moderate lengths.

Two computationally efficient approaches are proposed for aeroacoustic source power estimation, under the assumption of a single dominant source contaminated by uncorrelated noise. The proposed methods are evaluated using both simulated and measured data. The numerical examples show that the proposed algorithms yield good power estimates even under low signal-to-noise ratio (SNR) conditions, and the experimental results show that the power estimates obtained via the proposed approaches are consistent with each other. Furthermore, the approaches are computationally much more efficient than the existing nonlinear least-squares (NLS) algorithm.

We consider moving target detection and velocity estimation for multichannel synthetic-aperture-radar (SAR)-based ground moving target indication (GMTI). Via forming velocity versus cross-range images, we show that small moving targets can be detected even in the presence of strong stationary ground clutter. Furthermore, the velocities of the moving targets can be estimated, and the misplaced moving targets can be placed back to their original locations based on the estimated velocities. An iterative adaptive approach, which is robust and user parameter free, is used to form velocity versus cross-range images for each range bin of interest. Moreover, we discuss calibration techniques to estimate the relative antenna distances and antenna gains in practical systems. Furthermore, we present a simple algorithm for stationary clutter cancelation. We conclude by demonstrating the effectiveness of our approaches by using the Air Force Research Laboratory publicly released Gotcha airborne SAR-based GMTI data set.

This paper presents an in-depth analysis of the zero forcing (ZF) and minimum mean squared error (MMSE) equalizers applied to wireless multiinput multioutput (MIMO) systems with no fewer receive than transmit antennas. In spite of much prior work on this subject, we reveal several new and surprising analytical results in terms of output signal-to-noise ratio (SNR), uncoded error and outage probabilities, diversity-multiplexing (D-M) gain tradeoff and coding gain. Contrary to the common perception that ZF and MMSE are asymptotically equivalent at high SNR, we show that the output SNR of the MMSE equalizer (conditioned on the channel realization) is$\rho_{\rm mmse} = \rho_{\rm zf}+\eta_{\ssr snr}$, where$\rho_{\rm zf}$is the output SNR of the ZF equalizer and that the gap$\eta_{\ssr snr}$is statistically independent of$\rho_{\rm zf}$and is a nondecreasing function of input SNR. Furthermore, as${\ssr snr}\ura{} \infty$,$\eta_{\ssr snr}$converges with probability one to a scaled${\cal F}$random variable. It is also shown that at the output of the MMSE equalizer, the interference-to-noise ratio (INR) is tightly upper bounded by${{\eta_{\ssr snr}}\over {\rho_{\rm zf}}}$. Using the decomposition of the output SNR of MMSE, we can approximate its uncoded error, as well as outage probabilities through a numerical integral which accurately reflects the respective SNR gains of the MMSE equalizer relative to its ZF counterpart. The$\epsilon$-outage capacities of the two equalizers, however, coincide in the asymptotically high SNR regime. We also provide the solution to a long-standing open problem: applying optimal detection ordering does not improve the D-M tradeoff of the vertical Bell Labs layered Space-Time (V-BLAST) architecture. It is shown that optimal ordering yields a SNR gain of$10\log_{10}N$dB in the ZF-V-BLAST architecture (where$N$is the number of transmit antennas) whereas for the MMSE-V-BLAST architecture, the SNR gain due to ordered detection is even better and significantly so.

Sparse Bayesian learning (SBL) has been used as a signal recovery algorithm for compressed sensing. It has been shown that SBL is easy to use and can recover sparse signals more accurately than the well-known Basis Pursuit (BP) algorithm. However, the computational complexity of SBL is quite high, which limits its use in large-scale problems. We propose herein an efficient Gibbs sampling approach, referred to as GS-SBL, for compressed sensing. Numerical examples show that GS-SBL can be faster and perform better than the existing SBL approaches.

With the advent of high-throughput technologies, ℓ1 regularized learning algorithms have attracted much attention recently. Dozens of algorithms have been proposed for fast implementation, using various advanced optimization techniques. In this paper, we demonstrate that ℓ1 regularized learning problems can be easily solved by using gradient-descent techniques. The basic idea is to transform a convex optimization problem with a non-differentiable objective function into an unconstrained non-convex problem, upon which, via gradient descent, reaching a globally optimum solution is guaranteed. We present detailed implementation of the algorithm using ℓ1 regularized logistic regression as a particular application. We conduct large-scale experiments to compare the new approach with other state-of-the-art algorithms on eight medium and large-scale problems. We demonstrate that our algorithm, though simple, performs similarly or even better than other advanced algorithms in terms of computational efficiency and memory usage.

In this paper, we show that Sudoku puzzles can be formulated and solved as a sparse linear system of equations. We begin by showing that the Sudoku ruleset can be expressed as an underdetermined linear system: Ax = b, where A is of size m times n and n > m. We then prove that the Sudoku solution is the sparsest solution of Ax = b, which can be obtained by lo norm minimization, i.e. min ||x:||0s.t. Ax = b. Instead of this minimization SB problem, inspired by the sparse representation literature, we solve the much simpler linear programming problem of minimizing the l1norm of x, i.e. min ||x||1s.t. Ax = b, and show numerically that this approach solves representative Sudoku puzzles.

We present a new derivation of a lower bound for anaperiodiccorrelation metric: the integrated sidelobe level (ISL) of a set of sequences under the energy constraint. Sequences (or sequence sets) with low aperiodic correlations are widely demanded in many applications, including radar/sonar range compression, medical imaging, channel estimation and multi-user spread-spectrum communications. While the lower bound has been implicitly discussed in the literature before, here we adopt a different framework to derive the bound. In particular, we make use in the derivation of our recently proposed cyclic algorithm framework, which can also be used to efficiently synthesize unimodular sequences with low correlations. We also show that by relaxing the unimodular constraint, the ISL lower bound can be approached closely.

Sequence sets with low periodic correlations are used in many areas, such as asynchronous code-division multiple access (CDMA) systems, medical imaging, radar and sonar. Lower bounds on the integrated sidelobe level (ISL) and the peak sidelobe level (PSL) of periodic sequence sets, under a power constraint, have been previously derived in the literature. In this letter, we obtain the ISL and PSL lower bounds using a different framework. The main contribution of the letter consists in using this framework to derive closed-form expressions forallpower constrained periodic sequence sets that meet the ISL lower bound.

Unimodular (i.e., constant modulus) sequences with good autocorrelation properties are useful in several areas, including communications, radar and sonar. The integrated sidelobe level (ISL) is often used to express the goodness of the autocorrelation properties of a given sequence. In this paper, we present several cyclic algorithms for the local minimization of ISL-related metrics. 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 introduce a missing data recovery methodology based on a weighted least squares iterative adaptive approach (IAA). The proposed method is referred to as the missing-data IAA (MIAA) and it can be used for uniform or non-uniform sampling as well as for arbitrary data missing patterns. MIAA uses the IAA spectrum estimates to retrieve the missing data, based on a spectral least squares criterion similar to that used by IAA. Numerical examples are presented to show the effectiveness of MIAA for missing data recovery. We also show that MIAA can outperform an existing competitive approach, and this at a much lower computational cost.

Sequences with impulse-like correlations are at the core of several radar and communication applications. Two criteria that can be used to design such sequences, and which lead to rather different results in the aperiodic correlation case, are shown to be identical in the periodic case. Furthermore, two simplified versions of these two criteria, which similarly yield completely different sequences in the aperiodic case, are also shown to be equivalent. A corollary of these unexpected equivalences is that the periodic correlations of an arbitrary sequence must satisfy an intriguing identity, which is also presented in this letter.

We introduce a missing data recovery methodology based on a weighted least squares iterative adaptive approach (IAA). The proposed method is referred to as the missing-data IAA (MIAA) and it can be used for uniform or nonuniform sampling as well as for arbitrary data missing patterns. MIAA uses the IAA spectrum estimates to retrieve the missing data, by means of either a frequency domain or a time domain approach. Numerical examples are presented to show the effectiveness of MIAA for missing data reconstruction. In particular, we show that MIAA can outperform an existing competitive approach, and this at a much lower computational cost.

One of the most well-known robust adaptive beamforming approaches is diagonal loading. However, there are usually no clear guidelines on how to choose the diagonal loading level reliably. In this paper, we present algorithms that can compute the diagonal loading level fully automatically from the given data without the need of specifying any user parameters. The proposed diagonal loading algorithms use shrinkage-based covariance matrix estimates, instead of the conventional sample covariance matrix, in the standard Capon beamforming formulation. The performance of the resulting beamformers is illustrated via numerical examples and compared with other adaptive beamforming techniques.

Pulse compression radar systems make use of transmit code sequences and receive filters that are specially designed to achieve good range resolution and target detection capability at practically acceptable transmit peak power levels. The present paper is a contribution to the literature on the problem of designing transmit codes and receive filters for radar. In a nutshell: the main goal of this paper, which considers the cases of both negligible and non-negligible Doppler shifts, is to show how to design the receive filter (including its length) and the transmit code sequence via the optimization of a number of relevant metrics considered separately or in combination. The paper also contains several numerical studies whose aim is to illustrate the performance of the proposed designs.

In array processing, when the available snapshot number is comparable with or even smaller than the sensor number, the sample covariance matrix R is a poor estimate of the true covariance matrix R. To estimate R more accurately, we can make use of prior environmental knowledge, which is manifested as knowing an a priori covariance matrix R0. In this paper, we consider both modified general linear combinations (MGLC) and modified convex combinations (MCC) of the a priori covariance matrix R0, the sample covariance matrix R, and an identity matrix I to get an enhanced estimate of R, denoted as R. Numerical examples are provided to demonstrate the type of achievable performance by using R instead of R in the standard Capon beamformer.

We consider feature selection in the semi-supervised learning setting. This problem is rarely addressed in the literature. We propose a new algorithm as a natural extension of the recently developed Logistic I-RELIEF algorithm. The basic idea of the proposed algorithm is to modify the objective function of Logistic I-RELIEF to include the margins of unlabeled samples by following the large margin principle. Experimental results on artificial and benchmark datasets are presented to demonstrate the viability of the newly proposed method.

The so-called merit factor approach (MFA) to radar binary sequence design has led to several theoretical contributions in fairly diverse research areas including information theory, computer science, combinatorial optimization, and analytical number theory. However, the MFA-which basically aims at minimizing the clutter effect on radar performance-implicitly assumes the use of a least squares (LS) receiver that is optimal only when there is no clutter. This problem can be eliminated by using a more general optimal instrumental-variables (IV) receiver in lieu of the LS receiver. The IV receiver can reject clutter more efficiently than the LS receiver. Additionally, the binary sequence design problem associated with the IV approach has an interesting form.

We present new array beampattern synthesis approaches via semidefinite relaxation (SDR) for arbitrary array. Compared to the conventional approaches of using weight vectors at the array output for array pattern synthesis, which we refer to as the vector weighting approaches (VWA), weight matrices are used at the array output by MWA for much improved flexibility for optimal array pattern synthesis, and globally optimal solutions can be determined efficiently due to convex optimization formulations. Numerical examples are presented to show the excellent performance of MWA.

A MIMO (multi-input multi-output) radar system, unlike standard phased-array radar, can transmit via its antennas multiple probing signals. This waveform diversity offered by MIMO radar enables superior capabilities compared with a standard phased-array radar. We consider MIMO radar waveform optimization for parameter estimation for the general case of multiple targets in the presence of spatially colored interference and noise. Numerical examples are provided to demonstrate the effectiveness of the approaches we consider herein.

The so-called merit factor approach (MFA) to radar binary sequence design has led to several theoretical contributions in fairly diverse research areas including information theory, computer science, combinatorial optimization, and analytical number theory. However, the pragmatic motivation of this approach is shown here to be questionable. Specifically, the MFA - which basically aims at minimizing thecluttereffect on radar performance - implicitly assumes the use of a least-squares (LS) receiver that is optimal only when there isno clutter. This apparent inconsistency in the problem formulation can be eliminated by using a more general optimal instrumental-variables (IV) receiver in lieu of the LS receiver. The IV receiver proposed here is shown to reject clutter much more efficiently than the LS receiver. Additionally, the binary sequence design problem associated with the IV receiver is shown to have an interesting form that is likely to attract the attention of the readers previously interested in the MFA.

MOTIVATION: Accurate prognosis of breast cancer can spare a significant number of breast cancer patients from receiving unnecessary adjuvant systemic treatment and its related expensive medical costs. Recent studies have demonstrated the potential value of gene expression signatures in assessing the risk of post-surgical disease recurrence. However, these studies all attempt to develop genetic marker-based prognostic systems to replace the existing clinical criteria, while ignoring the rich information contained in established clinical markers. Given the complexity of breast cancer prognosis, a more practical strategy would be to utilize both clinical and genetic marker information that may be complementary. METHODS: A computational study is performed on publicly available microarray data, which has spawned a 70-gene prognostic signature. The recently proposed I-RELIEF algorithm is used to identify a hybrid signature through the combination of both genetic and clinical markers. A rigorous experimental protocol is used to estimate the prognostic performance of the hybrid signature and other prognostic approaches. Survival data analyses is performed to compare different prognostic approaches. RESULTS: The hybrid signature performs significantly better than other methods, including the 70-gene signature, clinical makers alone and the St. Gallen consensus criterion. At the 90% sensitivity level, the hybrid signature achieves 67% specificity, as compared to 47% for the 70-gene signature and 48% for the clinical makers. The odds ratio of the hybrid signature for developing distant metastases within five years between the patients with a good prognosis signature and the patients with a bad prognosis is 21.0 (95% CI:6.5-68.3), far higher than either genetic or clinical markers alone. AVAILABILITY: The breast cancer dataset is available at www.nature.com and Matlab codes are available upon request.

A multi-input multi-output (MIMO) radar system, unlike a standard phased-array radar, can transmit multiple linearly independent probing signals via its antennas. We show herein that this waveform diversity enables the MIMO radar to significantly improve its parameter identifiability. Specifically, we show that the maximum number of targets that can be uniquely identified by the MIMO radar is up to$M_{t}$times that of its phased-array counterpart, where$M_{t}$is the number of transmit antennas.

We present two improved Multi-static Adaptive Microwave Imaging (MAMI) methods: MAMI-2 and MAMI-C, for early breast cancer detection. MAMI is one of the microwave imaging modalities based the significant contrast between the di-electric properties of normal and malignant breast tissues and employs multiple antennas that take turns to transmit ultra wideband (UWB) pulses while all antennas are used to receive the reflected signals. The MAMI methods we investigate herein utilize the data-adaptive robust Capon beamformer (RCB) to achieve high resolution and interference suppression. We will demonstrate the effectiveness of our proposed methods for breast cancer detection via numerical examples with data simulated using the finite difference time domain (FDTD) method based on a 3-D realistic breast model.

We consider Signal Waveform's Optimal-under-Restriction Design (SWORD) for active sensing. In the presence of colored interference and noise with known statistical properties, waveform optimization for active sensors such as radar can significantly increase the signal-to-interference-plus-noise ratio needed for much improved target detection. However, the so-obtained optimal waveforms can result in significant modulus variation, poor range resolution, and/or high peak sidelobe levels. To mitigate these problems, we can constrain the waveform optimization problem by restricting the sought-after waveform to be similar to a desired waveform, which is known to have, for example, constant modulus as well as reasonable range resolution and peak sidelobe level. One example of the desired waveform is the widely used linear frequency modulated waveform or chirp. We will provide a detailed solution to the constrained optimization problem and explain how it is related with the existing waveform optimization methods

We consider improving the performance of orthogonal frequency-division multiplexing (OFDM)-based mobile broadband wireless communication (MBWC) systems. We show that a recently approved packet-based MBWC standard can cause the resulting systems to suffer from severe performance degradations for time-varying channels due to the lack of a mechanism for tracking the time-varying channels needed for coherent detection. We consider both packet design and signal processing to deal with time-varying channels. For the packet design, we segment an entire packet into multiple subpackets - with each subpacket having zero tail bits to reset the convolutional channel encoder - so that the detection/decoding result of each subpacket can be used to update the channel response for this subpacket. For signal processing, we use weighted polynomial fitting and prediction at the receiver to improve the channel tracking accuracy. Simulation results show that the coherent detection based on our new scheme can significantly outperform the commonly suggested differential modulation/detection methods

In this paper, we present an asymptotic analysis of the V-BLAST scheme at high signal-to-noise ratio (SNR) region. We consider point-to-point MIMO communications over an i.i.d. Rayleigh flat fading channel with n transmitting antennas and m (m /spl ges/ n) receiving antennas. Both the zero-forcing V-BLAST (ZF-V-BLAST) and minimum mean-squared-error V-BLAST (MMSE-V-BLAST) are analyzed with respect to their diversity gains and BER performances. We show that the diversity gain of V-BLAST, including ZF-V-BLAST and MMSE-V-BLAST, with optimal ordering is m - n + 1, i.e. applying the optimal ordering technique does not improve the diversity gain. Contrary to the common perception that the MMSE and ZF estimators have asymptotically the same post-processing SNR for high input SNR, we show that the difference between the post-processing SNRs of the two estimators does not vanish for high SNR. We also quantify the remarkable BER performance advantage of the MMSE-V-BLAST over the ZF-V-BLAST for high SNR.

Assuming the availability of the channel state information at the transmitter (CSIT) and receiver (CSIR), we consider the joint optimal transceiver design for multi-input multi-output (MIMO) communication systems. Using our recently developed generalized triangular decomposition (GTD), we propose a scheme, which we refer to as adaptable channel decomposition (ACD), to decompose a MIMO channel into multiple subchannels with prescribed capacities, or equivalently, signal-to-interference-and-noise ratios (SINR). We also determine the subchannel capacity region such that the channel decomposition is capacity lossless. This scheme is particularly relevant to the applications where independent data streams with different quality-of-services (QoS) share the same MIMO channel.

The expectation-maximization (EM) algorithm is often used in maximum likelihood (ML) estimation problems with missing data. However, EM can be rather slow to converge. In this paper, we introduce a new algorithm for parameter estimation problems with missing data, which we call equalization-maximization (EqM) (for reasons to be explained later). We derive the EqM algorithm in a general context and illustrate its use in the specific case of a Gaussian autoregressive time series with a varying amount of missing observations. In the presented examples, EqM outperforms EM in terms of computational speed, at a comparable estimation performance.

We consider two-dimensional (2D) nonparametric complex spectral estimation (with its 1D counterpart as a special case) of data matrices with missing samples occurring in arbitrary patterns. Previously, the MAPES-EM algorithms were developed for the general 1D missing-data problem and shown to have excellent spectral estimation performance. In this paper, we present 2D extensions of MAPES-EM and develop another 2D MAPES algorithm, referred to as MAPES-CM, which solves a maximum likelihood problem iteratively via cyclic maximization (CM). Compared with MAPES-EM, MAPES-CM has similar spectral estimation performance but is computationally much more efficient.

We consider the relationship between several single-symbol detectors for double differential modulation. We have shown in a previous paper that a simple heuristic detector is identical to the generalized likelihood ratio test (GLRT) detector. In this correspondence, we introduce a maximum a posteriori probability (MAP) detector and show that it is identical to the heuristic and GLRT detectors. Consequently, neither GLRT nor MAP can offer any gain over the simple heuristic detector, which means that the latter should be the detector of choice.

Currently, the nonadaptive delay-and-sum (DAS) beamformer is extensively used for ultrasound imaging, despite the fact that it has lower resolution and worse interference suppression capability than the adaptive standard Capon beamformer (SCB) if the steering vector corresponding to the signal of interest (SOI) is accurately known. The main problem which restricts the use of SCB, however, is that SCB lacks robustness against steering vector errors that are inevitable in practice. Whenever this happens, the performance of SCB may hecome worse than that of DAS. Therefore, a robust adaptive beamformer is desirable to maintain the robustness of DAS and adaptivity of SCB. In this paper we consider a recent promising robust Capon beamformer (RCB) for ultrasound imaging. We propose two ways of implementing RCB, one based on time delay and the other based on time reversal. RCB extends SCB by allowing the array steering vector to be within an uncertainty set. Hence, it restores the appeal of SCB including its high resolution and superb interference suppression capabilities, and also retains the attractiveness of DAS including its robustness against steering vector errors. The time-delay-based RCB can tolerate the misalignment of data samples and the time-reversal-based RCB can withstand the uncertainty of the Green's function. Both time-delay-based RCB and time-reversal-based RCB can be efficiently computed at a comparable cost to SCB. The excellent performances of the proposed robust adaptive beamforming approaches are demonstrated via a number of simulated and experimental examples.

We consider improving the overall system performance of an orthogonal frequency-division multiplexing-based multiple-input multiple-output (MIMO) wireless local area network system. We use a combined iterative detection/decoding and channel updating method, referred to herein as turbo processing, to improve performance. First, we improve a recently proposed list sphere decoder-based iterative MIMO soft-detector by constraining the value of the a priori information from a soft-in soft-out channel decoder. Second, we propose a channel updating scheme using the decoded packet data to improve the channel estimation accuracy. Simulation results show that turbo processing can be used to significantly improve the performance of the system considered.

We consider the problem of soft-detection for communication systems employing double differential modulation and forward error correction codes, for example, a convolutional code. We propose a soft-detector (based on the multiple symbol heuristic detector) with low computational complexity. Simulation results are provided to show the superior performance of the new soft-detector.

AdaBoost rarely suffers from overfitting problems in low noise data cases. However, recent studies with highly noisy patterns clearly showed that overfitting can occur. A natural strategy to alleviate the problem is to penalize the distribution skewness in the learning process to prevent several hardest examples from spoiling decision boundaries. In this paper, we describe in detail how a penalty scheme can be pursued in the mathematical programming setting as well as in the Boosting setting. By using two smooth convex penalty functions, two new soft margin concepts are defined and two new regularized AdaBoost algorithms are proposed. The effectiveness of the proposed algorithms is demonstrated through a large scale experiment. Compared with other regularized AdaBoost algorithms, our methods can achieve at least the same or much better performances.

We present a multi-input multi-output (MIMO) transceiver design that combines the geometric mean decomposition (GMD) with either the conventional zero-forcing VBLAST decoder (ZF-VBLAST), or the zero-forcing dirty paper precoder (ZF-DP). Our approach decomposes a MIMO channel into multiple identical subchannels, which obviates the need of bit allocation and simplifies the design of modulation/demodulation and coding/decoding schemes. Moreover, we prove that our scheme is asymptotically optimal for high signal-to-noise ratio (SNR) in terms of both the channel throughput and the bit-error-rate (BER) performance.

The information criterion (IC) rule and the generalized likelihood ratio test (GLRT) have been usually considered to be two rather different approaches to model order selection. However, we show here that a natural implementation of the GLRT is, in fact, equivalent to the IC rule. A consequence of this equivalence is that a specific IC rule, such as Akaike IC or Bayesian IC, can be viewed as a more direct way of implementing a GLRT with a specific threshold. Another consequence of the equivalence, which is emphasized herein, is a possibly original way of exploiting the information provided by the local behavior of an IC for selecting the structure of sparse models (the parameter vectors of which comprise "many" elements equal to zero).

Two algorithms for double-differential detection of multiple phase-shift keying modulation are proposed, based on a least-squares criterion and a generalized-likelihood ratio test, respectively. While both algorithms take advantage of the performance gain obtained by observing the received signal over an observation interval longer than that required for symbol-by-symbol detection, the former has the important advantage of reduced implementation complexity, whereas the latter offers better performance.

The maximum-likelihood detector (MLD), also called the generalized likelihood ratio test (GLRT) detector, for single differential modulation is easy to derive. On the other hand, the MLD problem associated with double differential modulation is much more complicated and solving it was deemed to require a computationally unattractive nonlinear search. Consequently, a simple heuristic detector was usually preferred to the MLD, on computational grounds. In this correspondence, we prove the somewhat unexpected result that the aforementioned heuristic detector coincides with the exact MLD.

We consider parameter estimation and error reduction for orthogonal frequency-division multiplexing (OFDM) based high-speed wireless local area networks (WLANs). We devise or select algorithms that can provide benefit to the overall system performance and can be efficiently implemented in real-time. In particular, first, we give a channel model which is especially useful for assessing the channel parameter estimation methods devised for OFDM-based WLANs. Second, we provide a sequential method for the estimation of carrier frequency offset (CFO), symbol timing, and channel response by exploiting the structure of the packet preamble specified by the IEEE 802.11a standard. Finally, to correct the residue CFO induced phase error using the pilot tones, we consider maximum-likelihood phase tracking and least-squares phase fitting approaches; to improve the channel estimation accuracy using the decoded data, we present a semiblind channel estimation method; to mitigate the sampling clock induced time delay error, we provide a sampling clock synchronization approach that obviates the need of an automatic frequency control clock recovery circuit. The overall system performance of using our algorithms is demonstrated via several numerical examples.

The amplitude estimation of a signal whose waveform is known (up to an unknown scaling factor) in the presence of interference and noise is of interest in several applications including using the emerging quadrupole resonance (QR) technology for explosive detection. In such applications a sensor array is often deployed for interference suppression. This paper considers the complex amplitude estimation of a known waveform signal whose array response is also known a priori. We study a practical scenario where the interference and noise is both spatially and temporally correlated. We model the interference and noise vector as a multichannel autoregressive (AR) random process. A cyclic iterative ML (IML) method is presented. We show that in most cases the IML method is superior to its simple ML counterpart that ignores the temporal correlation of the interference and noise.

Whenever the knowledge of the array steering vector is imprecise (as is often the case in practice), the performance of the Capon beamformer may become worse than that of the standard beamformer. Diagonal loading (including its extended versions) has been a popular approach to improve the robustness of the Capon beamformer. In this paper we show that a natural extension of the Capon beamformer to the case of uncertain steering vectors also belongs to the class of diagonal loading approaches but the amount of diagonal loading can be precisely calculated based on the uncertainty set of the steering vector. The proposed robust Capon beamformer can be efficiently computed at a comparable cost with that of the standard Capon beamformer. Its excellent performance is demonstrated via a number of numerical examples.

In radar applications, adaptive beampatterns with low sidelobes and stable mainlobe shapes are desired to suppress pulsed deceptive jammers or sidelobe targets and to accurately measure the direction-of-arrival (DOA) of a target using monopulse techniques. In practice, all kinds of errors exist, such as signal pointing errors, array calibration errors and array covariance matrix estimation errors. In the presence of these errors, adaptive beamformers can suffer from severe performance degradations, including poor interference rejection, distorted mainlobes, and high sidelobes. In this paper, we investigate how a quadratic constraint based adaptive beamformer with peak sidelobe control, referred to as the PPSC (precise peak sidelobe control) method, can be combined with a signal removal scheme to achieve desired adaptive beampatterns and interference rejection performance for a uniform linear array. Numerical results are provided to demonstrate the performance of the proposed method.

The Capon beamformer has better resolution and much better interference rejection capability than the standard (data-independent) beamformer, provided that the array steering vector corresponding to the signal of interest (SOI) is accurately known. However, whenever the knowledge of the SOI steering vector is imprecise (as is often the case in practice), the performance of the Capon beamformer may become worse than that of the standard beamformer. We present a natural extension of the Capon beamformer to the case of uncertain steering vectors. The proposed robust Capon beamformer can no longer be expressed in a closed form, but it can be efficiently computed. Its excellent performance is demonstrated via a number of numerical examples.

We describe the so-called time-reversal space-time block coding (TR-STBC) transmission scheme for communication systems with multiple transmit antennas operating over frequency-selective channels. TR-STBC can be seen as an extension of the orthogonal space-time block codes for flat fading channels. We show that using TR-STBC, a linear filtering at the receiver can achieve an approximate decoupling of the space-time channel into scalar and independent frequency-selective channels and hence any standard maximum-likelihood sequence detector (MLSD) can be used for equalization. Numerical examples are provided to illustrate the performance of the TR-STBC transmission scheme.

Stoica, Li and Li, (see IEEE Trans. Signal Processing, vol.48, p.338-52, 2000) introduced an amplitude estimation based scheme for one-dimensional (1-D) system identification that overcomes several drawbacks (e.g., computational complexity, local convergence, and statistical inefficiency when spectrally colored noise is present) suffered by the conventional output error method (OEM). Along the same line, we herein propose a two-dimensional (2-D) system identification scheme that makes use of 2-D amplitude estimation. In particular, we consider the recently introduced 2-D amplitude and phase estimation (APES) amplitude estimator, which has been shown to yield superior performance over its competitors. To benchmark the proposed scheme, we also derive the Cramer-Rao bound (CRB) for the 2-D system identification problem.

Abstract Differential space–time modulation (DSTM) schemes were recently proposed to fully exploit the transmit and receive antenna diversities without the need for channel state information. DSTM is attractive in fast flat fading channels since accurate channel estimation is difficult to achieve. In this paper, we propose a new modulation scheme to improve the performance of DS‐CDMA systems in fast time‐dispersive fading channels. This scheme is referred to as the differential space–time modulation for DS‐CDMA (DST‐CDMA) systems. The new modulation and demodulation schemes are especially studied for the fast fading down‐link transmission in DS‐CDMA systems employing multiple transmit antennas and one receive antenna. We present three demodulation schemes, referred to as the differential space–time Rake (DSTR) receiver, differential space–time deterministic (DSTD) receiver, and differential space–time deterministic de‐prefix (DSTDD) receiver, respectively. The DSTD receiver exploits the known information of the spreading sequences and their delayed paths deterministically besides the Rake‐type combination; consequently, it can outperform the DSTR receiver, which employs the Rake‐type combination only, especially for moderate‐to‐high SNR. The DSTDD receiver avoids the effect of intersymbol interference and hence can offer better performance than the DSTD receiver. Copyright © 2001 John Wiley & Sons, Ltd.

We previously studied amplitude estimation of one-dimensional (1D) sinusoidal signals from measurements corrupted by possibly colored observation noise (see Stoica, P. et al., IEEE Trans. on Sig. Proc., vol. 48, p.338-52, 2000). We extend those results for two-dimensional (2D) amplitude estimation. In particular, we investigate the 2D sinusoidal amplitude estimation within the general frameworks of least squares (LS), weighted least squares (WLS), and MAtched FIlterbank (MAFI) estimation. A variety of 2D amplitude estimators are presented, which are all asymptotically statistically efficient. The performances of these estimators in finite samples are compared numerically with one another. Making use of amplitude estimation techniques, we introduce a new scheme for 2D system identification, which is shown to be computationally simpler and statistically more accurate than the conventional output error method (OEM), when the observation noise is colored.

We propose a method for estimating the amplitude spectrum of a 2D-signal from frequency domain (or phase history) data that contain gaps. This is a key problem in synthetic aperture radar (SAR) imaging with angular diversity. Our method is an extension of the well-known amplitude and phase estimation (APES) algorithm to the incomplete data case, and is called gapped-data APES (GAPES). It has recently been shown that APES minimizes a certain least-squares (LS) criterion, and our extension of APES is based on minimizing this criterion with respect to the missing data as well. We provide an example of the algorithm applied to SAR imaging from phase history data with angular diversity; and we also show the advantages of 2D data processing over 1D (row or column-wise) data processing that are enabled by our new algorithm.

The so-called orthogonal frequency division multiplexing (OFDM) technique has received considerable interest, especially in the area of wireless local area networks (WLANs). One way of meeting the demands for increased data rates in WLANs is to provide the transmitter and receiver with multiple antennas. In this letter, we consider the estimation of the channel and the design of optimal preambles (training sequences) for an OFDM system with two transmit and multiple receive antennas.

We present an efficient carrier frequency offset (CFO) estimation algorithm for the orthogonal frequency-division multiplexing (OFDM)-based wireless local area networks (WLANs). The packet preamble information we use is based on the high rate WLAN standards adopted by the IEEE 802.11 standardization group. Numerical results are presented to demonstrate the effectiveness of the proposed algorithm.

We present herein a decoupled multiuser acquisition (DEMA) algorithm for code-timing estimation in asynchronous code-division multiple-access (CDMA) communication systems. The DEMA estimator is an asymptotic (for large data samples) maximum-likelihood method that models the channel parameters as deterministic unknowns. By evoking the mild assumption that the transmitted data bits for all users are independently and identically distributed, we show that the multiuser timing estimation problem that usually requires a search over a multidimensional parameter space decouples into a set of noniterative one-dimensional problems. Hence, the proposed algorithm is computationally efficient. DEMA has the desired property that, in the absence of noise, it obtains the exact parameter estimates even with a finite number of data samples which can be heavily correlated. Another important feature of DEMA is that it exploits the structure of the receiver vectors and, therefore, is near-far resistant. Numerical examples are included to demonstrate and compare the performances of DEMA and a few other standard code-timing estimators.

We investigate herein the problem of amplitude estimation of sinusoidal signals from observations corrupted by colored noise. A relatively large number of amplitude estimators are described which encompass least squares (LS) and weighted least squares (WLS) methods. Additionally, filterbank approaches, which are widely used for spectral analysis, are extended to amplitude estimation. Specifically, we consider the matched-filterbank (MAFI) approach and show that, by appropriately designing the prefilters, the MAFI approach includes the WLS approach. The amplitude estimation techniques discussed in this paper do not model the noise, and yet they are all asymptotically statistically efficient. It is their different finite-sample properties that are of particular interest to this study. Numerical examples are provided to illustrate the differences among the various estimators. Though amplitude estimation applications are numerous, we focus on system identification using sinusoidal probing signals.

We show that the main result on eigenpolynomials for two-dimensional (2-D) sinusoidal signals in a recent letter by Li and Cheng (see ibid., vol.5, p.71-3, March 1998) is incorrect, and hence the characterization of 2-D eigenpolynomials is still an open problem. Furthermore, we state a related problem that is also open and hence awaiting a (satisfactory) solution.

We introduce a novel design criterion for data-dependent narrowband filters that are of interest in temporal or spatial spectral analysis applications. The solution to the design problem considered is shown to coincide with the previously introduced amplitude and phase estimation (APES) filter. The new derivation of APES in this article sheds more light on the properties of APES and provides some intuitive explanation of the performance superiority of the APES filter over the Capon filter.

A computationally efficient method for structured covariance matrix estimation is presented. The proposed method provides an asymptotic (for large samples) maximum likelihood estimate of a structured covariance matrix and is referred to as AML. A closed-form formula for estimating Hermitian Toeplitz covariance matrices is derived which makes AML computationally much simpler than most existing Hermitian Toeplitz matrix estimation algorithms. The AML covariance matrix estimator can be used in a variety of applications. We focus on array processing and show that AML enhances the performance of angle estimation algorithms, such as MUSIC, by making them attain the corresponding Cramer-Rao bound (CRB) for uncorrelated signals.

In this paper, an efficient Weighted Fourier transform and RELAXation based algorithm (referred to as WRELAX) is first proposed for the well-known time delay estimation problem. WRELAX involves only a sequence of weighted Fourier transforms. Its resolution is much higher than that of the conventional matched filter approach. One disadvantage associated with WRELAX is that it converges slowly when the signals are spaced very closely. To overcome this problem, the well-known high resolution MODE (method of direction estimation) algorithm, which was originally proposed for angle estimation in array processing, is modified and used with WRELAX for super resolution time delay estimation. The latter method is referred to as MODE-WRELAX. MODE-WRELAX provides better accuracy than MODE and higher resolution than WRELAX. Moreover, it applies to both complex- and real-valued signals (including those with highly oscillatory correlation functions). Numerical results show that the MODE-WRELAX estimates can approach the corresponding the Cramer-Rao bounds.

We propose a receiver diversity based code-timing estimator for DS-CDMA systems. The systems are assumed to work in a flat fading and near-far environment, where an arbitrary antenna array is used at the receiver of the system to achieve the spatial diversity. The algorithm is derived by modeling the known training sequence as the desired signal and all other signals including the multiuser interfering signals and the additive noise as unknown colored Gaussian noise so that a knowledge of the number of active users is not required. We show that by utilizing the information collected via multiple antenna sensors, the length of the training sequences can be greatly reduced. We also show that the algorithm is an asymptotic maximum Likelihood estimator. As a result, the mean-squared error of the code-timing estimates obtained by the algorithm approaches the Cramer-Rao lower bound (CRB) as the length of the training sequence increases. Moreover, the algorithm does not require the search over a parameter space and the code-timing is obtained by rooting a second-order polynomial, which is computationally very efficient. Simulation results show that the algorithm is quite robust against the near-far problem and requires a much shorter training sequence than the existing estimators.

We propose an efficient algorithm for estimating the code timing of direct-sequence code-division multiple-access (DS-CDMA) systems that consist of an arbitrary antenna array at the receiver and work in a flat-fading and near-far environment. The algorithm is an asymptotic (for large number of data samples) maximum-likelihood (ML) estimator that is derived by modeling the known training sequence as the desired signal and all other signals including the interfering signals and the additive noise as unknown colored Gaussian noise. The algorithm does not require the search over a parameter space and the code timing is obtained by rooting a second-order polynomial, which is computationally very efficient. Simulation results show that the algorithm is quite robust against the near-far problem and channel fading. It requires a shorter training sequence than the single-antenna-based estimators.

We present an adaptive finite impulse response (FIR) filtering approach, which is referred to as the Amplitude and Phase EStimation (APES) algorithm, for interferometric synthetic aperture radar (SAR) imaging. We compare the APES algorithm with other FIR filtering approaches including the Capon and fast Fourier transform (FFT) methods. We show via both numerical and experimental examples that the adaptive FIR filtering approaches such as Capon and APES can yield more accurate spectral estimates with much lower sidelobes and narrower spectral peaks than the FFT method. We show that although the APES algorithm yields somewhat wider spectral peaks than the Capon method, the former gives more accurate overall spectral estimates and SAR images than the latter and the FFT method.

We present a comparative study of using the IQML (iterative quadratic maximum likelihood) algorithm and the MODE (method of direction estimation) algorithm for direction-of-arrival estimation with a uniform linear array. The consistent condition and the theoretical mean-squared error for the parameter estimates of IQML are presented. The computational complexities of both algorithms are also compared. We show that the frequency estimates obtained via MODE are asymptotically statistically efficient, while those obtained via IQML are almost always inconsistent and hence inefficient. We also show that the amount of computations required by IQML is usually much larger than that required by MODE, especially for low signal-to-noise ratio and large number of snapshots.

As one of the key steps in the feature extraction of targets consisting of both trihedral and dihedral corner reflectors via synthetic aperture radar, this paper studies the problem of estimating the parameters of a single dihedral corner reflector. The data model of the problem and the Cramer-Rao bounds (CRBs) for the parameter estimates of the data model are presented. Two algorithms, the FFTB (fast Fourier transform based) algorithm and the NLS (non-linear least squares) algorithm, are devised to estimate the model parameters. Numerical examples show that the parameter estimates obtained with both algorithms approach the CRBs as the signal-to-noise ratio increases. The parameter estimates obtained with the NLS algorithm start to achieve the CRB at a lower SNR than those with the FFTB algorithm, while the latter algorithm is computationally more efficient.

This paper describes how the computationally efficient one-dimensional MODE (1D-MODE) algorithm can be used to estimate the frequencies of two-dimensional complex sinusoids. We show that the 1D-MODE algorithm is computationally more efficient than the asymptotically statistically efficient 2D-MODE algorithm, especially when the numbers of spatial measurements are large. We find that the 1D-MODE algorithm is asymptotically statistically efficient for high signal-to-noise ratio. We also show that although the 1D-MODE is no longer statistically efficient when the number of temporal snapshots is large, the performance of the 1D-MODE can still be very close to that of the 2D-MODE under mild conditions. Numerical examples comparing the performance of the 1D-MODE and 2D-MODE algorithms are also presented.

We introduce a new method for determining the number of straight lines, line angles, offsets, widths, and discontinuities in complicated images. In this method, line angles are obtained by searching the peaks of a hybrid discrete Fourier and bilinear transformed line angle spectrum. Numerical advantages and performance are demonstrated.

In this paper, we present an efficient algorithm for estimating the propagation delay of a known training sequence in an asynchronous direct-sequence code division multiple access (DS-CDMA) system. The algorithm is a large sample maximum likelihood (LSML) estimator that is derived by modeling the known training sequence as the desired signal and all other signals including the interfering signals and thermal noise as unknown colored Gaussian noise that are uncorrelated with the desired signal. LSML is asymptotically statistically efficient as the length of the training sequence goes to infinity. We shall show that LSML is robust against the near-far problem. The performance of the LSML estimator is compared with that of the MUSIC estimator via numerical examples and is shown to be better than that of the latter method in the sense of having lower root-mean-squared errors, lower computational complexity, and tolerating more users.

For a data model consisting of deterministic signals in additive Gaussian noise, we prove that the Cramer-Rao bound (CRB) corresponding to the signal parameters decreases as the number of data samples increases provided that the number of new observations is larger than the number of additional unknowns required to parameterize these observations. We also show that the CRB theory is not applicable whenever the aforementioned condition does not hold true.

This paper examines the modeling of synthetic aperture radar (SAR) phase histories with 2-D damped exponential models of low order. The use of a low order model is warranted when the radar returns are attributable to a small number of point scatterers. We show that the fit of the widely used damped exponential model is highly dependent on the image scene. Specifically, current high resolution methods have limited applicability due to mismatch between the assumed model and observed data.

This paper addresses the problem of combining adaptive polarization processing and space-time processing for further performance improvement of radar target detection in clutter and jammer environments. Since the most straightforward cascade combinations have quite limited performance improvement potentials, we focus on the development of adaptive processing in the joint polarization-space-time domain. Unlike a direct extension of some existing space-time processing algorithms to the joint domain, the processing algorithm developed in this paper does not need a potentially costly polarization filter bank to cover the unknown target polarization parameter. The performance of the new algorithm is derived and evaluated in terms of the probability of detection and the probability of false alarm, and it is compared with other algorithms that do not utilize the polarization information or assume that the target polarization is known. Es wird eine Kombination von adaptiver Polarisations- und Raum-Zeit-Signalverarbeitung für die Verbesserung bei der Radardetektion von Objekten in stark gestörtem, unübersichtlichem Umfeld behandelt. Da eine Kaskadenstruktur zur Nutzung von Polarisations- und Raum-Zeit-Analyse nur ein geringes Verbesserungspotential beinhaltet, konzentrieren wir uns auf die Entwicklung adaptiver Verfahren zur zusammenhängenden Analyse im Polarisations-Raum-Zeitbereich. Im Gegensatz zu einer naheliegenden Erweiterung von existierenden Raum-Zeit-Analyse-Algorithmen durch die Polarisationsinformation, benötigt der in diesem Artikel entwickelte Algorithmus keine aufwandsintensive Filterbank zur Bestimmung der unbekannten Polarisationsinformation eines Objektes. Die Leistungsfähigkeit des neuen Algorithmus wird hergeleitet und anhand von Detektionswahrscheinlichkeiten, bzw. Wahrscheinlichkeiten für Fehlalarm bestätigt. Ferner wird der Algorithmus mit anderen, die die Polarisationsinformation nicht nutzen oder sie als bekannt voraussetzen, verglichen. Le sujet de cet article est le problème de la combinaison d'un traitement adaptatif de la polarisation et du traitement espace-temps à des fins d'amélioration des performances de la détection radar de cibles dans des environnements présentant fouillis et encombrement. Du fait que les combinaisons en cascade les plus directes ont des potentiels d'amélioration de performances fort limités, nous nous focalisons sur le développement d'un traitement adaptatif dans le domaine conjoint polarisation-espace-temps. A l'invers d'une extension directe de certains algorithmes espace-temps au domaine conjoint, l'algorithme de traitement développé dans cet article ne nécessite pas un banc de filtres de polarisation potentiellement coûteux pour gérer le paramètre inconnu de polarisation de la cible. Les performances de cet algorithme sont dérivées et évaluées en termes de probabilité de détection et probabilité de fausse alarme, et sont comparées à celles d'autres algorithmes n'utilisant pas l'information de polarisation ou supposant la polarisation de la cible connue.

This paper considers the problem of statistically efficient estimation of the parameters of partially polarized electromagnetic (EM) waves with a uniform linear array of crossed dipoles. We consider the maximum likelihood (ML) estimation of incident angles and the degrees of polarization. We present a computationally efficient large sample ML estimator that avoids the multidimensional search over the parameter space required by the exact ML estimator.>

The statistical performance of using ESPRIT to estimate both the arrival directions and the polarizations of incoming plane waves with a uniform linear array of crossed dipoles is studied. Compact formulae for the mean-squared errors of both direction and polarization estimates are provided for both the case of large data samples and the case of high signal-to-noise ratio. Numerical results are presented to compare the theoretical analysis and the Monte-Carlo simulation results.>