Space-time reduced rank methods and CFAR signal detection algorithms with applications to HPRF radar

In radar applications, the statistical properties (covariance matrix) of the interference are typically unknown a priori and are estimated from a dataset with limited sample support. Often, the limited sample support leads to numerically ill-conditioned radar detectors. Under such circumstances, classical interference cancellation methods such as sample matrix inversion (SMI) do not perform satisfactorily. In these cases, innovative reduced-rank space-time adaptive processing (STAP) techniques outperform full-rank techniques. The high pulse repetition frequency (HPRF) radar problem is analyzed and it is shown that it is in the class of adaptive radar with limited sample support. Reduced-rank methods are studied for the HPRF radar problem. In particular, the method known as diagonally loaded covariance matrix SMI (L-SMI) is closely investigated. Diagonal loading improves the numerical conditioning of the estimated covariance matrix, and hence, is well suited to be applied in a limited sample support environment. The performance of L-SMI is obtained through a theoretical distribution of the output conditioned signal-to-noise ratio of the space-time array. Reduced-rank techniques are extended to constant false alarm rate (CFAR) detectors based on the generalized likelihood ratio test (GLRT). Two new modified CFAR GLRT detectors are considered and analyzed. The first is a subspace-based GLRT detector where subspace-based transformations are applied to the data prior to detection. A subspace transformation adds statistical stability which tends to improve performance at the expense of an additional SNR loss. The second detector is a modified GLRT detector that incorporates a diagonally loaded covariance matrix. Both detectors show improved performance over the traditional GLRT

An adaptive detection of spread targets in locally Gaussian clutter using a long integration time

This paper deals with the problem of detecting a collision target in ground clutter, using a long integration time. A single reception channel being available, classical space time adaptive processing (STAP) cannot be used. After range processing, ground clutter can be modeled as a known interference subspace in the Doppler domain depending on its radial and orthoradial speeds. We exploit this a priori knowledge to perform an adpative detection of a collision target supposed to lie in a known and different subspace. A GLRT detector is first derived for known clutter covariance matrix. Then, the unknown covariance matrix is adaptively estimated from the projection of the data onto the modeled clutter subspace, and is plugged in the GLRT to form a suboptimal detector. The proposed scheme can be viewed as a synthetic STAP, for which the space domain is replaced by a clutter orthoradial information and longer integration time

Adaptive detection of a signal known only to lie on a line in a known subspace, when primary and secondary data are partially homogeneous

This paper deals with the problem of detecting a signal, known only to lie on a line in a subspace, in the presence of unknown noise, using multiple snapshots in the primary data. To account for uncertainties about a signal's signature, we assume that the steering vector belongs to a known linear subspace. Furthermore, we consider the partially homogeneous case, for which the covariance matrix of the primary and the secondary data have the same structure but possibly different levels. This provides an extension to the framework considered by Bose and Steinhardt. The natural invariances of the detection problem are studied, which leads to the derivation of the maximal invariant. Then, a detector is proposed that proceeds in two steps. First, assuming that the noise covariance matrix is known, the generalized-likelihood ratio test (GLRT) is formulated. Then, the noise covariance matrix is replaced by its sample estimate based on the secondary data to yield the final detector. The latter is compared with a similar detector that assumes the steering vector to be known

Space/time/frequency methods in adaptive radar

Radar systems may be processed with various space, time and frequency techniques. Advanced radar systems are required to detect targets in the presence of jamming and clutter. This work studies the application of two types of radar systems. It is well known that targets moving along-track within a Synthetic Aperture Radar field of view are imaged as defocused objects. The SAR stripmap mode is tuned to stationary ground targets and the mismatch between the SAR processing parameters and the target motion parameters causes the energy to spill over to adjacent image pixels, thus hindering target feature extraction and reducing the probability of detection. The problem can be remedied by generating the image using a filter matched to the actual target motion parameters, effectively focusing the SAR image on the target. For a fixed rate of motion the target velocity can be estimated from the slope of the Doppler frequency characteristic. The problem is similar to the classical problem of estimating the instantaneous frequency of a linear FM signal (chirp). The Wigner-Ville distribution, the Gabor expansion, the Short-Time Fourier transform and the Continuous Wavelet Transform are compared with respect to their performance in noisy SAR data to estimate the instantaneous Doppler frequency of range compressed SAR data. It is shown that these methods exhibit sharp signal-to-noise threshold effects. The space-time radar problem is well suited to the application of techniques that take advantage of the low-rank property of the space-time covariance matrix. It is shown that reduced-rank methods outperform full-rank space-time adaptive processing when the space-time covariance matrix is estimated from a dataset with limited support. The utility of reduced-rank methods is demonstrated by theoretical analysis, simulations and analysis of real data. It is shown that reduced-rank processing has two effects on the performance: increased statistical stability which tends to improve performance, and introduction of a bias which lowers the signal-to-noise ratio. A method for evaluating the theoretical conditioned SNR for fixed reduced-rank transforms is also presented

Matched direction detectors and estimators for array processing with subspace steering vector uncertainties

In this paper, we consider the problem of estimating and detecting a signal whose associated spatial signature is known to lie in a given linear subspace but whose coordinates in this subspace are otherwise unknown, in the presence of subspace interference and broad-band noise. This situation arises when, on one hand, there exist uncertainties about the steering vector but, on the other hand, some knowledge about the steering vector errors is available. First, we derive the maximum-likelihood estimator (MLE) for the problem and compute the corresponding Cramer-Rao bound. Next, the maximum-likelihood estimates are used to derive a generalized likelihood ratio test (GLRT). The GLRT is compared and contrasted with the standard matched subspace detectors. The performances of the estimators and detectors are illustrated by means of numerical simulations

Adaptive detection of distributed targets in compound-Gaussian noise without secondary data: A Bayesian approach

In this paper, we deal with the problem of adaptive detection of distributed targets embedded in colored noise modeled in terms of a compound-Gaussian process and without assuming that a set of secondary data is available.The covariance matrices of the data under test share a common structure while having different power levels. A Bayesian approach is proposed here, where the structure and possibly the power levels are assumed to be random, with appropriate distributions. Within this framework we propose GLRT-based and ad-hoc detectors. Some simulation studies are presented to illustrate the performances of the proposed algorithms. The analysis indicates that the Bayesian framework could be a viable means to alleviate the need for secondary data, a critical issue in heterogeneous scenarios