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We propose two computationally efficient residual Doppler shift estimation methods for underwater acoustic multicarrier communication. The first method is based on computing the phase of the root of a low order polynomial. The second method is a closed-form least squares estimate given the unwrapped phases of the minimal eigenvector of a small data matrix. The complexities of both estimates are significantly lower compared to the methods commonly used in underwater acoustic multicarrier communication, which result in nonlinear least squares estimators and thus require a fine grid search in the frequency domain. Numerical simulations show that the mean square errors of the proposed methods have similar performance as the common estimation techniques, achieve the Cramer–Rao lower bounds at low noise levels, and agree with their theoretically derived variances. Pool experiments and sea trial results further demonstrate that the suggested estimates yield similar results as the common nonlinear least squares estimates but at a lower complexity. [ABSTRACT FROM PUBLISHER]

We consider the problem of estimating the fundamental initial frequency and frequency rate of a linear chirp with random amplitudes harmonic components. We develop an iterative nonlinear least squares estimator, which involves a large number of computations as it requires high resolution search in the initial frequency and frequency rate parameter space. As an alternative, we suggest two suboptimal low-complexity estimators. The first is based on the high-order ambiguity function, which reduces the problem to a one-dimensional search. The second method applies our recently published harmonic separate-estimate method, which was used for constant-amplitude harmonic chirps. We present modifications of both methods for harmonic chirps with random amplitudes. We also provide a framework for estimating the number of harmonic components. Numerical simulations show that the iterative nonlinear least-squares estimator achieves its asymptotic accuracy in medium to high signal-to-noise ratio, while the two sub-optimal low-complexity estimators perform well in high signal-to-noise ratio. Real data examples demonstrate the performance of the harmonic separate-estimate method on random amplitude real-life signals. [ABSTRACT FROM AUTHOR]

We present a closed-form least squares algorithm for estimating the position and velocity of a source, asynchronously transmitting known dual linear chirp signals, given times of arrival measurements obtained by spatially distributed sensors. The estimates involve less computational load compared to the optimal maximum likelihood estimates. Simulations show that the proposed estimates have similar mean square errors as the optimal estimates, and are close to the lower bound for small and moderate measurement noise. [ABSTRACT FROM AUTHOR]

We suggest an adaptive blind interference suppression (BIS) beamformer that synthesizes a desired beampattern. For a strong interference, the principal eigenvector of the data sample covariance matrix approaches the array response at the interference direction. The beamformer weight vector minimizes the distance from a desired beampattern subject to a zero response to this principal eigenvector. For a strong interference, uncorrelated with the desired signal, the asymptotic array gain (AG) of the BIS beamformer achieves the AG of the minimum power distortionless response (MPDR) beamformer. Simulations demonstrate that, for a finite number of samples, the AG of the BIS beamformer outperforms that of the MPDR beamformer and that it is not sensitive to sensor gain and phase errors. [ABSTRACT FROM PUBLISHER]

Consider the problem of estimating the parameters of multiple polynomial phase signals observed by a sensor array. In practice, it is difficult to maintain a precisely calibrated array. The array manifold is then assumed to be unknown, and the estimation is referred to as blind estimation. To date, only an approximated maximum likelihood estimator (AMLE) was suggested for blindly estimating the polynomial coefficients of each signal. However, this estimator requires a multidimensional search over the entire coefficient space. Instead, we propose an estimation approach which is based on two steps. First, the signals are separated using a blind source separation technique, which exploits the constant modulus property of the signals. Then, the coefficients of each polynomial are estimated using a least squares method applied to the unwrapped phase of the estimated signal. This estimator does not involve any search in the coefficient spaces. The computational complexity of the proposed estimator increases linearly with respect to the polynomial order, whereas that of the AMLE increases exponentially. Simulation results show that the proposed estimator achieves the Cramér-Rao lower bound at moderate or high signal to noise ratio. [ABSTRACT FROM PUBLISHER]

The parameters of interest of a polynomial phase signal observed by a sensor array include the direction of arrival and the polynomial coefficients. The direct maximum likelihood estimation of these parameters requires a nonlinear multidimensional search. In this paper, we present a two-step estimation approach. The estimation requires only a one-dimensional search in the direction of arrival space and involves a simple least squares solution for the polynomial coefficients. The efficiency of the estimates is corroborated by Monte Carlo simulations. [ABSTRACT FROM AUTHOR]

Several techniques for emitter localization based on the Doppler effect have been described in the literature. One ex- ample is the differential Doppler (DD) method in which the signal of a stationary emitter is intercepted by at least two moving receivers. The frequency difference between the receivers is measured at several locations along their trajectories and the emitter's position is then estimated based on these measurements. This two-step approach is suboptimal since each frequency difference measurement is performed independently, although all measurements correspond to a common emitter position. Instead, a single-step approach based on the maximum likelihood criterion is proposed here for both known and unknown waveforms. The position is determined directly from all the observations by a search in the position space. The method can only be used for narrowband signals, that is, under the assumption that the signal bandwidth must be small compared to the inverse of the propagation time between the receivers. Simulations show that the proposed method outperforms the DD method for weak signals while both methods converge to the Cramér-Rao bound for strong known signals. Finally, it is shown that in some cases of interest the proposed method inherently selects reliable observations while ignoring unreliable data. [ABSTRACT FROM AUTHOR]

We exploit results from detection theory for deriving fundamental limitations on resolution. The results are general and are not based on any specific resolution technique and therefore hold for any method and for any resolution success rate. We show that for signals with additive white Gaussian noise the resolution limit is approximated by a simple expression related to the signal to noise ratio, the signal waveform and the resolution success rate. As an example, we discuss the resolution of two complex exponentials with closely spaced frequencies. The theoretical result is compared with the empirical performance of model order selection methods such as the Akaike information criterion and the minimum description length. [ABSTRACT FROM AUTHOR]

We derive conditions for unique geolocation of multiple radio-frequency emitters using a general observation model. These conditions specify the maximum number of emitters that can be uniquely located by a geolocation system, often referred to as the resolution capacity (RC). Our derivations extend previously published results for geolocation based on angle-of-arrival (AOA) estimation. We show that with no prior information, the RC is upper bounded by the total number of antenna elements in the system, i.e., LM, where M is the number of elements in each array and L is the number of arrays. In contrast, the RC of geolocation based on AOA is upper bounded by M. In addition, if the signals are known to be uncorrelated, and the arrays are uniform and linear, the RC is upper bounded by (LM)2-L(M-1)2-1. However, more emitters can be resolved using different types of arrays. Our results lead to the inevitable conclusion that geolocation based on AOA is suboptimal, and new methods should be developed that can jointly exploit the information collected by all the antenna arrays [ABSTRACT FROM PUBLISHER]

Given time and frequency differences of arrival measurements, we estimate the position and velocity of an emitter by jointly eliminating nonlinear nuisance parameters with an orthogonal projection matrix. Although simulation results show that this estimator does not always perform as well as the two-step estimator, the benefit is its computational simplicity. Whereas the complexity of the two-step estimator increases cubically with respect to the number of sensors, the complexity of the proposed estimator increases quadratically. [ABSTRACT FROM PUBLISHER]