I. Vaughan L. Clarkson

Analysis of the variance threshold of Kay's weighted linear predictor frequency estimator

A theoretical approximation for the variance of Kays weighted linear predictor frequency estimator is derived. From this expression, an inequality describing the variance threshold of the estimator is found. The window weights are then optimized to improve the variance. Numerical simulations demonstrate that the variance approximations are valid for medium to high signal-to-noise ratios or for large numbers of samples. >

Generalized canonical correlation for passive multistatic radar detection

In this paper, we consider the problem of target detection in passive multistatic radar. In passive radar, we make use of illuminators of opportunity. As the illuminators are not under our direct control, the illuminating signal itself is unknown. We propose a signal model which reflects this. In deriving a maximum-likelihood estimator for the unknown parameters, including the illumination, we find that the maximum value of the likelihood is a monotonic function of the largest eigenvalue of the Gram matrix of the received signals. The generalised likelihood ratio test turns out to be equivalent to comparison of the largest eigenvalue against a threshold, so we propose its use as a target detection statistic. The proposed detector is similar to generalised canonical correlation in multivariate statistics. The benefit of using this statistic over others such as generalised variance is demonstrated through numerical simulations in the context of passive radar using DVB-T signals.

Polynomial Phase Estimation by Least Squares Phase Unwrapping

Estimating the coefficients of a noisy polynomial phase signal is important in fields including radar, biology and radio communications. One approach attempts to perform polynomial regression on the phase of the signal. This is complicated by the fact that the phase is wrapped modulo 2π and must be unwrapped before regression can be performed. In this paper, we consider an estimator that performs phase unwrapping in a least squares manner. We call this the least squares unwrapping (LSU) estimator. The LSU estimator can be computed in a reasonable amount of time for data sets of moderate size using existing general purpose algorithms from algebraic number theory. Under mild conditions on the distribution of the noise we describe the asymptotic properties of this estimator, showing that it is strongly consistent and asymptotically normally distributed. A key feature is that the LSU estimator is accurate over a far wider range of parameters than many popular existing estimators. Monte-Carlo simulations support our theoretical results and demonstrate the excellent statistical performance of the LSU estimator when compared with existing state-of-the-art estimators.

A statistical analysis of the Delogne-Kasa method for fitting circles

Abstract In this paper, we examine the problem of fitting a circle to a set of noisy measurements of points on the circles circumference. Delogne [Proc. IMEKO-Symp. Microwave Measurements, 1972, pp. 117–123] has proposed an estimator which has been shown by Kasa [IEEE Trans. Instrum. Meas. 25 (1976) 8–14] to be convenient for its ease of analysis and computation. Using Chans circular functional model to describe the distribution of points, we perform a statistical analysis of the estimate of the circles centre, assuming independent, identically distributed Gaussian measurement errors. We examine the existence of the mean and variance of the estimator for fixed sample sizes. We find that the mean exists when the number of sample points is greater than 3 and the variance exists when this number is greater than 4. We also derive approximations for the mean and variance for fixed sample sizes when the noise variance is small. We find that the bias approaches zero as the noise variance diminishes and that the variance approaches the Cramer–Rao lower bound.

An improved algorithm for optimal noncoherent QAM detection

Ryan et at. recently described two polynomial time algorithms for noncoherent detection of square QAM in block fading channels with additive white Gaussian noise (AWGN). The first algorithm is optimal with respect to the generalized likelihood ratio test (GLRT) and requires O(T3) arithmetic computations, where T is the block length of the noncoherent receiver. The second algorithm requires only O(T2 logT) arithmetic computations but is statistically suboptimal. This paper derives a new algorithm that is optimal yet requires only O(T2 logT) arithmetic computations. The new algorithm has the geometric interpretation of finding the nearest codeword to a plane (2 dimensional subspace). The nearest codeword is found by testing codewords that are near a finite number of lines formed by the intersection of the plane and the nearest neighbour boundaries of the codewords.

Passive radar signal processing in single frequency networks

In this paper, we consider the problem of target detection in passive multistatic radar with multiple transmitters. Passive radar makes use of illuminators of opportunity, such as television and radio broadcast towers. As the illuminators do not cooperate with the receivers, the illuminating signal itself is unknown. The system considered is the DVB-T standard, which is often operated as part of single frequency network (SFN).

Late-Time Estimation for Resonance-Based Radar Target Identification

This communication presents a novel method for determining the commencement of the late-time resonant response of a radar target, without a priori knowledge of the target geometry or orientation. Insights from Kroneckers theorem for Hankel matrices are used to determine the offset for the processing window for extraction of the true complex natural resonances by exploiting characteristic changes in the Hankel matrix, including the matrix rank and the distribution of eigenvalues. Results are presented for both simulated and measured targets.

Linear-time block noncoherent detection of PSK

We propose a new algorithm for noncoherent sequence detection of M-ary phase-shift-keying (M-PSK) symbols transmitted over a block fading channel. The algorithm is of complexity O(T), where T is the sequence length, and is therefore computationally superior to existing maximum-likelihood (ML) detectors of complexity O(T logT). Our detector is based on a new approximation we propose to the noncoherent ML function. We show that by using this close approximation, the detection problem reduces to a nearest lattice point problem for the lattice An*, from which we derive our O(T) approach. Simulation results are provided that show the difference in bit error rate is negligibly small for a wide range of signal-to-noise ratios.

Polynomial-phase estimation, phase unwrapping and the nearest lattice point problem

Polynomial-phase signals have attracted significant interest due to their applicability to radar, sonar, geophysics, and radio communication. In this paper we introduce a new technique for estimating the parameters of polynomial phase signals. The parameters are estimated by performing phase unwrapping in a least squares manner. The least squares problem is formulated as a nearest lattice point problem that can be solved using existing techniques. The statistical performance of the new estimator is excellent when compared with popular existing estimators such as those based on the discrete polynomial phase transform.

Finding a closest point in a lattice of Voronoi's first kind

We show that for those lattices of Voronois first kind with known obtuse superbasis, a closest lattice point can be computed in