Radars use coherence to increase the signal-processing gain. In electronic support, that same coherence can be exploited to accurately estimate carrier frequency when measured modulo the pulse repetition frequency. Such estimates can be used for passive emitter geolocation, for example. In the pioneering work of Howard & Lavoie on this topic [1], [2], results are demonstrated only where the pulse repetition interval (PRI) is an integer and where pulses are sinusoidal. In this paper, we show how the results can be generalised to a broad class of pulse shapes, without needing to know the pulse shape in advance. We also show how the signals may be efficiently processed when the PRI is non-integer.

Eigenvalues of the Gram matrix formed from received data frequently appear in sufficient detection statistics for multi-channel detection with Generalized Likelihood Ratio (GLRT) and Bayesian tests. In a frequently presented model for passive radar, in which the null hypothesis is that the channels contain only complex white Gaussian noise and the alternative hypothesis is that the channels contain a common rank-one signal in the mean, the GLRT statistic is the largest eigenvalue λ1of the Gram matrix formed from data, which has a Wishart distribution. Although exact expressions for the distribution of λ1are known under both hypotheses, numerically calculating values of these distribution functions presents difficulties in cases where the dimension of the data vectors is large. Following on recent work addressing this issue under the null hypothesis, this paper presents a method to calculate values of this distribution under the alternative hypothesis, allowing tractable computation of receiver operating characteristic curves.

In multi-channel detection, sufficient statistics for Generalized Likelihood Ratio and Bayesian tests are often functions of the eigenvalues of the Gram matrix formed from data vectors collected at the sensors. When the null hypothesis is that the channels contain only independent complex white Gaussian noise, the distributions of these statistics arise from the joint distribution of the eigenvalues of a complex Wishart matrix G. This paper considers the particular case of the largest eigenvalue λ1of G, which arises in passive radar detection of a rank-one signal. Although the distribution of λ1is known analytically, calculating its values numerically has been observed to present formidable difficulties. This is particularly true when the dimension of the data vectors is large, as is common in passive radar applications, making computation of accurate detection thresholds intractable. This paper presents results that significantly advance the state of the art for this problem.

Sidelobe suppression has always been an important part of crafting communications signals to keep interference with users of adjacent spectrum to a minimum. Systems based on the discrete Fourier transform, such as orthogonal frequency-division multiplexing (OFDM) and single-carrier frequency-division multiple access (SC-FDMA) are especially prone to out-of-band power leakage. Although many techniques have been proposed to suppress sidelobes in DFT-based systems, a satisfactory balance between computational complexity and out-of-band power leakage has remained elusive. Orthogonal precoding is a promising, linear technique in which the nullspace of a precoding matrix with orthonormal columns is designed to suppress the sidelobes. In particular, Xu and Chen [1], van de Beek [2] and Ma et al. [3] have proposed orthogonal precoders that yield excellent out-of-band suppression. However, they suffer from high arithmetic complexity-quadratic in the number of active subcarriers-which has limited their application. In this paper, we find that the arithmetic complexity can be made linear instead of quadratic if a block reflector is used to perform the precoding instead of an otherwise unstructured unitary transformation. There is no penalty to be paid in achieved bit-error rate. We show by numerical simulation that the penalty in peak-to-average power ratio is also very small for OFDM.

A method inspired by Generalised Canonical Correlation (GCC) has been proposed as a detection statistic for multistatic passive radar when a noise-free reference signal is unavailable [1]. The GCC statistic can be expressed as the largest eigenvalue of the Gram matrix of the received signals. It is derived from a suitably formulated generalised likelihood ratio test (GLRT). The Gram matrix is drawn from a Wishart distribution: a central Wishart distribution in the target-absent case and a non-central Wishart distribution when the target is present. Numerical computation using the eigenvalue distribution is fraught with difficulties [2]. Exact theoretical expressions involve ratios of products of factorials which soon defeat attempts at straightforward implementation in double-precision floating point. On the other hand, standard approximations, such as the Tracy-Widom distribution [3], are inaccurate when a low false-alarm rate is required. In this paper, we present a new method to accurately compute probabilities using standard double-precision floating-point arithmetic. This allows practical application of the GCC statistic to CFAR detection in passive radar scenarios where the number of samples is large (104–107), and the number of receivers is small (2–5).

The problem of estimating the period of a point process from observations that are both sparse and noisy is considered. By sparse it is meant that only a potentially small unknown subset of the process is observed. By noisy it is meant that the subset that is observed, is observed with error, or noise. Existing accurate algorithms for estimating the period require O(N2) operations where is the number of observations. By quantizing the observations we produce an estimator that requires only O(N log N) operations by use of the chirp z-transform or the fast Fourier transform. The quantization has the adverse effect of decreasing the accuracy of the estimator. This is investigated by Monte-Carlo simulation. The simulations indicate that significant computational savings are possible with negligible loss in statistical accuracy.

We present practical, experimental results for a system, driven by a particle filter, that dynamically steers a space surveillance sensor to track and search for resident space objects. In contrast to traditional Kalman-filter-based trackers, this system can exploit scheduled observations where the target is not found within the field of view. Furthermore, real-time observation-evaluation enables the system to immediately respond to these events by conducting a limited search. We describe the system and report the results of a recent field trial using a computer-controlled Raven-class electro-optical sensor to track objects using two-line element sets (TLEs) of various ages. Even for quite old TLEs - in some cases over six months old - the system demonstrates successful, automatic reacquisition.

We show that for those lattices of Voronoi's first kind with known obtuse superbasis, a closest lattice point can be computed in $O(n^4)$ operations, where $n$ is the dimension of the lattice. To achieve this a series of relevant lattice vectors that converges to a closest lattice point is found. We show that the series converges after at most $n$ terms. Each vector in the series can be efficiently computed in $O(n^3)$ operations using an algorithm to compute a minimum cut in an undirected flow network.

We consider least squares estimators of carrier phase and amplitude from a noisy communications signal. We focus on signaling constellations that have symbols evenly distributed on the complex unit circle, i.e., M-ary phase shift keying. We show, under reasonably mild conditions on the distribution of the noise, that the least squares estimator of carrier phase is strongly consistent and asymptotically normally distributed. However, the amplitude estimator is not consistent, but converges to a positive real number that is a function of the true carrier amplitude, the noise distribution and the size of the constellation. The results of Monte Carlo simulations are provided and these corroborate the theoretical results.

We consider the root lattice$A_{n}$and derive explicit recursive formulas for the moments of its Voronoi cell. These formulas enable accurate prediction of the error probability of lattice codes constructed from$A_{n}$.

Estimating the coefficients of a noisy polynomial phase signal is important in many fields including radar, biology and radio communications. One approach to estimation 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 therefore must be unwrapped before the regression can be performed. A recent approach suggested by the authors is to perform the unwrapping in a least squares manner. It was shown by Monte Carlo simulation that this produces a remarkably accurate estimator. In this paper we describe the asymptotic properties of this estimator, showing that it is strongly consistent and deriving its central limit theorem. We hypothesise that the estimator produces very near maximum likelihood performance.

The Coxeter lattices are a family of lattices containing many of the important lattices in low dimensions. This includesAn,E7,E8and their dualsAn*,E7*, andE8*. We consider the problem of finding a nearest point in a Coxeter lattice. We describe two new algorithms, one with worst case arithmetic complexityO(nlogn) and the other with worst case complexityO(n) wherenis the dimension of the lattice. We show that for the particular latticesAnandAn* the algorithms are equivalent to nearest point algorithms that already exist in the literature.

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.

Block crosstalk cancellation techniques in practical multi-user digital subscriber line (DSL) environments may involve a high computational complexity as the channel and noise statistics can vary over time. We follow an adaptive approach by designing a structurally consistent significance-test feature within the normalized least-mean-square (NLMS) adaptive crosstalk canceller, aimed to detect significant crosstalkers within a DSL binder. The proposed detection-guided NLMS adaptive partial crosstalk canceller for DSL targets the dominant crosstalkers across user lines and tones, has low run-time complexity, demonstrates significantly faster convergence, and requires smaller training sequences when compared via simulation to the equivalent standard NLMS adaptive crosstalk canceller.

This paper considers the problem of beamforming in multiple-input multiple-output (MIMO) wireless systems. Assuming perfect channel state information at the receiver, the choice of the beamforming vector is made possible through a noiseless limited-rate feedback of one or more bits per coefficient to the transmitter. This paper proposes the use of beamforming codebooks based on quadrature amplitude modulation (QAM) and phase-shift keying (PSK) constellations, which essentially eliminates the need for storage of the codebook. We show that such codebooks perform arbitrarily close to the perfect feedback case as the constellation size increases, and that full diversity order is achieved. We demonstrate an equivalence between the beamforming codebook search problem with that of noncoherent sequence detection. Based on this we propose fast beamforming vector search algorithms. Monte-Carlo simulations are presented to show that the performance is comparable to the best known codebooks, and that the search complexity can be reduced by several orders of magnitude.

This paper considers the multiuser multiple-input multiple-output (MIMO) Rayleigh fading broadcast channel. We consider the case where the multiple transmit antennas are used to deliver independent data streams to multiple users via a multiuser technique known as vector perturbation. We propose lattice-theoretic and rate-distortion based approaches to analyze the performance of these systems, taking into account the practical restrictions imposed by limited feedback and training. We show that performance is primarily determined by the ratio between the number of users and the number of transmit antennas. We then propose a new practical low-complexity low-rate feedback scheme, and show that the performance approaches the ideal rate-distortion based scheme.

It has been well known for at least twenty years that computing the maximizer of the periodogram, in order to estimate the unknown frequency in a noisy sinusoid, is problematic. In particular, because the periodogram is highly nonlinear, a grid size of order o (T-1) is needed to find the maximizer reliably, where T is the sample size, and that Newton's method may fail to find the zero of the first derivative of the periodogram closest to the maximizer of the periodogram calculated, for example, using the FFT. In this paper, we show that Newton's method does, in fact, work if it is applied to an appropriately chosen monotonic function of the periodogram.

The problem of estimating the period of a periodic point process is considered when the observations are sparse and noisy. There is a class of estimators that operate by maximizing an objective function over an interval of possible periods, notably the periodogram estimator of Fogel & Gavish and the line-search algorithms of Sidiropoulos et al. and Clarkson. For numerical calculation, the interval is sampled. However, it is not known how fine the sampling must be in order to ensure statistically accurate results. In this paper, a new estimator is proposed which eliminates the need for sampling. For the proposed statistical model, it calculates a maximum- likelihood estimate. It is shown that the expected arithmetic complexity of the algorithm is O(n3log n) where n is the number of observations. Numerical simulations demonstrate the superior statistical performance of the new estimator.

This paper considers the use of multiple transmit antennas to deliver independent data streams to multiple users. In particular, we examine a multi-user technique known as vector perturbation. We provide a new lattice-theoretic approach to analyze its performance in the presence of Rayleigh fading. Vector perturbation is based on performing a channel inversion, with the additional step of perturbing the data signal prior to linear preceding to significantly reduce the required transmit power. To analyze such systems it is necessary to calculate the resulting average energy of the sphere-encoded signal vector, as this determines the signal-to-noise ratio (SNR) at the output of the demodulator. Previous results presented in the literature were partially analytic, requiring further numerical evaluation. Here, we derive a concise approximation to the output SNR. We also provide tight upper and lower bounds on the bit error rate for the reception of QAM symbols using the required modulo demodulator, as a function of the average energy of the sphere- encoded signal vector.

The latticeAn*is an important lattice because of its covering properties in low dimensions. Clarkson described an algorithm to compute the nearest lattice point inAn*that requiresO(nlogn) arithmetic operations. In this correspondence, we describe a new algorithm. While the complexity is stillO(nlogn), it is significantly simpler to describe and verify. In practice, we find that the new algorithm also runs faster.

This paper proposes a new QAM based codebook for beamforming in multiple-input multiple-output (MIMO) wireless systems with a limited-rate feedback channel. We show that such codebooks perform arbitrarily close to the perfect feedback case as the constellation size increases, and that full diversity order is achieved. We demonstrate an equivalence between the problems of beamforming codebook search and noncoherent sequence detection. Based on this we propose a fast beamforming vector search algorithm. Monte-Carlo simulations are presented to show that the performance is comparable to the best known codebooks, and that the search complexity can be reduced by several orders of magnitude.

Fundamental matrix estimation is a central problem in computer vision and forms the basis of tasks such as stereo imaging and structure from motion. Existing algorithms typically analyze the relative geometries of matched feature points identified in both projected views. Automated feature matching is itself a challenging problem. Results typically have a large number of false matches. Traditional fundamental matrix estimation methods are very sensitive to matching errors, which led naturally to the application of robust statistical estimation techniques to the problem. In this work, an entirely novel approach is proposed to the fundamental matrix estimation problem. Instead of analyzing the geometry of matched feature points, the problem is recast in the frequency domain through the use of Integral Projection, showing how this is a reasonable model for orthographic cameras. The problem now reduces to one of identifying matching lines in the frequency domain which, most importantly, requires no feature matching or correspondence information. Experimental results on both real and synthetic data are presented that demonstrate the algorithm is a practical technique for fundamental matrix estimation. The behavior of the proposed algorithm is additionally characterized with respect to input noise, feature counts, and other parameters of interest.

We consider the optimal performance of noncoherent channel estimation, that is, where the codebook is known to the receiver but the actual transmitted data is not. It is well known that when training data is known to the receiver, the minimum variance of the channel estimation error for unbiased channel estimation is bounded by the Cramer-Rao lower bound. However, in the noncoherent case, where joint estimation of both a continuous channel and discrete data is required, the Cramer- Rao bound is not applicable. We derive a new bound for this mixed multiple parameter estimation problem for flat fading channels, based on the Hammersley-Chapman-Robbins bound for restricted parameters. We show that the new noncoherent bound asymptotically approaches the Cramer-Rao bound with increasing SNR and sequence length. As an example we consider channel estimation for BPSK over a positive real-valued channel. We show that the noncoherent ML detector is asymptotically unbiased and achieves the lower bound with increasing SNR. We also observe that for moderate SNR the noncoherent ML estimator can actually outperform the optimal coherent ML estimator.

One of the key problems in computer vision is the recovery of epipolar geometry constraints between different camera views. The majority of existing techniques rely on point correspondences, which are typically perturbed by mismatches and noise, hence limiting the accuracy of these techniques. To overcome these limitations, we propose a novel approach that estimates epipolar geometry constraints based on a statistical model in the RADON domain. The method requires no correspondences, explicit constraints on the data or assumptions regarding the scene structure. Results are presented on both synthetic and real data that show the method's robustness to noise and outliers.

We present a novel, maximum-likelihood (ML), lattice-decoding algorithm for noncoherent block detection of QAM signals. The computational complexity is polynomial in the block length; making it feasible for implementation compared with the exhaustive search ML detector. The algorithm works by enumerating the nearest neighbor regions for a plane defined by the received vector; in a conceptually similar manner to sphere decoding. Simulations show that the new algorithm significantly outperforms existing approaches.

In this paper we present a novel maximum-likklihood polynomial-time algorithm for noncoherent detection of PAM over fading channels. The algorithm is based on a geometric interpretation of the noncoherent detection metric. This interpretation leads to a novel low complexity decoder based on an angular criterion, rather than the usual Euclidean distance sense. We prove that the ML estimate of the data must lie in a reduced search space which is of log-linear complexity with the block length. We then provide an algorithm that enumerates the codewords and their corresponding metrics in an efficient, recursive manner. We also consider detection of ASK, by combining the maximum-likelihood algorithm with a simple phase estimator.

The accurate fitting of a circle to noisy measurements of circumferential points is a much studied problem in the literature. In this paper, we present an interpretation of the maximum-likelihood estimator (MLE) and the Delogne-Kåsa estimator (DKE) for circle-center and radius estimation in terms of convolution on an image which is ideal in a certain sense. We use our convolution-based MLE approach to find good estimates for the parameters of a circle in digital images. In digital images, it is then possible to treat these estimates as preliminary estimates into various other numerical techniques which further refine them to achieve subpixel accuracy. We also investigate the relationship between the convolution of an ideal image with a "phase-coded kernel" (PCK) and the MLE. This is related to the "phase-coded annulus" which was introduced by Atherton and Kerbyson who proposed it as one of a number of new convolution kernels for estimating circle center and radius. We show that the PCK is an approximate MLE (AMLE). We compare our AMLE method to the MLE and the DKE as well as the Cramér-Rao Lower Bound in ideal images and in both real and synthetic digital images.

This correspondence considers block detection for blind wireless digital transmission. At high signal-to-noise ratio (SNR), block detection errors are primarily due to the received sequence having multiple possible decoded sequences with the same likelihood. We derive analytic expressions for the probability of detection ambiguity written in terms of a Dedekind zeta function, in the zero noise case with large constellations. Expressions are also provided for finite constellations, which can be evaluated efficiently, independent of the block length. Simulations demonstrate that the analytically derived error floors exist at high SNR

We examine the problem of fitting a circle to a set of noisy measurements of points from the circle's circumference, assuming independent, identically distributed Gaussian measurement errors. We propose an algorithm based on branch and bound to obtain the maximum likelihood estimate and show that this algorithm obtains the optimal estimate. We examine the rate of convergence and determine the computational complexity of the proposed algorithm. We also provide timings and compare them to those of existing techniques for circle fitting proposed in the literature. Finally, we demonstrate that our algorithm is statistically efficient by comparing our results to the Cramer-Rao lower bound.

This paper presents performance bounds for block-based detection of PAM and QAM transmitted over non-coherent channels. Such channels give rise to inherent detection ambiguities since multiple possible transmit sequences can have the same likelihood. The number of ambiguous sequences is a function of the block length. In this paper, we derive the probability of detection error in terms of a Dedekind zeta function of the block length, for infinite-sized constellations and zero noise. We also provide expressions for finite constellations which can be evaluated in polynomial time with the constellation size, as opposed to checking all possible sequences

This paper presents a new low-complexity multicarrier modulation (MCM) technique based on lattices which achieves a peak-to-average power ratio (PAR) as low as three. The scheme can be viewed as a "drop in" replacement for the discrete multitone (DMT) modulation of an asymmetric digital subscriber line modem. We show that the lattice-MCM retains many of the attractive features of sinusoidal-MCM, and does so with lower implementation complexity, O(N), compared with DMT, which requires O(NlogN) operations. We also present techniques for narrowband interference rejection and power profiling. Simulation studies confirm that performance of the lattice-MCM is superior, even compared with recent techniques for PAR reduction in DMT.

The paper presents a new multicarrier modulation (MCM) technique based on lattices which achieves a peak-to-average power ratio (PAR) as low as 3. The scheme can be viewed as a 'drop in' replacement for the discrete multitone (DMT) modulation of an ADSL modem. Performance is up to 8.5 dB better than standard DMT in amplifier-clipped conditions. Moreover, the new technique has a lower implementation complexity, O(N), compared with DMT which requires O(N log N) operations. Simulation studies confirm that the performance of the lattice-MCM is superior even compared to recent techniques for PAR-reduction in DMT.

In this paper, we examine the relationship between frequency estimation and phase unwrapping and a problem in algorithmic number theory known as the nearest lattice point problem. After briefly reviewing the theory of these three topics, we introduce an interpretation of the maximum likelihood frequency estimation problem as a nearest lattice point problem. We develop an algorithm based on this approach and present numerical results to compare its performance with other estimation techniques. We find that the algorithm has good powers of estimation.

Prospective authors are requested to submit new, unpublished manuscripts for inclusion in the upcoming event described in this call for papers.

A good radar warning receiver should observe a radar very soon after it begins transmitting, so in designing our radar warning receiver we would like to ensure that the intercept time is low or the probability of intercept after a specified time is high. We consider a number of problems concerning the overlaps or coincidences of two periodic pulse trains. We show that the first intercept time of two pulse trains started in phase is a homogeneous Diophantine approximation problem which can be solved using the convergents of the simple continued fraction (s.c.f.) expansion of the ratio of their pulse repetition intervals (PRIs). We find that the intercept time for arbitrary starting phases is an inhomogeneous Diophantine approximation problem which can be solved in a similar manner. We give a recurrence equation to determine the times at which subsequent coincidences occur. We then demonstrate how the convergents of the s.c.f. expansion can be used to determine the probability of intercept of the two pulse trains after a specified time when one or both of the initial phases are random. Finally, we discuss how the probability of intercept varies as a function of the PRIs and its dependence on the Farey points.