For sensors where the number of available independent identically distributed training samples T is less than the number of antenna array elements M , we propose nondegenerate properly normalized ...likelihood ratio (LR) tests (both standard and scale-invariant) to support detection-estimation of m point sources (m < T) in white noise, based on a generalized likelihood-ratio test (GLRT) approach. We demonstrate that these tests can detect MUSIC-specific ldquooutliersrdquo in the direction-of-arrival (DOA) estimation of closely spaced independent sources caused by insufficient training volume and/or signal-to-noise ratio (SNR). We then compare the performance of the introduced LRs to other test statistics available in this undersampled regime. We show that a search for solutions that increase the introduced LR allows us to replace the detected outliers by proper DOA estimates. This ldquopredict and curerdquo process leverages the SNR ldquogaprdquo between MUSIC breakdown and breakdown of maximum-likelihood estimation itself. The resultant LR maximization makes the associated covariance model statistically ldquoas likelyrdquo as the true covariance matrix and removes the vast percentage of outliers in certain scenarios.
The well-known general problem of signal detection in background interference is addressed for situations where a certain statistical description of the interference is unavailable, but is replaced ...by the observation of some secondary (training) data that contains only the interference. For the broad class of interferences that have a large separation between signal-and noise-subspace eigenvalues, we demonstrate that adaptive detectors which use a diagonally loaded sample covariance matrix or a fast maximum likelihood (FML) estimate have significantly better detection performance than the traditional generalized likelihood ratio test (GLRT) and adaptive matched filter (AMI') detection techniques, which use a maximum likelihood (ML) covariance matrix estimate. To devise a theoretical framework that can generate similarly efficient detectors, two major modifications are proposed for Kelly's traditional GLRT and AMF detection techniques. First, a two-set GLRT decision rule takes advantage of an a priori assignment of different functions to the primary and secondary data, unlike the Kelly rule that was derived without this. Second, instead of ML estimates of the missing parameters in both GLRT and AMF detectors, we adopt expected likelihood (EL) estimates that have a likelihood within the range of most probable values generated by the actual interference covariance matrix. A Gaussian model of fluctuating target signal and interference is used in this study. We demonstrate that, even under the most favorable loaded sample-matrix inversion (LSMI) conditions, the theoretically derived EL-GLRT and FL-AMF techniques (where the loading factor is chosen from the training data using the EL matching principle) gives the same detection performance as the loaded AMF technique with a proper a priori data-invariant loading factor. For the least favorable conditions, our EL-AMF method is still superior to the standard AMF detector, and may be interpreted as an intelligent (data-dependent) method for selecting the loading factor.
The results from an experiment that applied one class of multiple-input multiple-output waveform techniques to over-the-horizon radar (OTHR) are reported. The experiment aimed to demonstrate that ...adaptive transmitter beamforming could be used in an appropriately design radar to reject spatially discrete Doppler-spread clutter. In this report, spatially discrete clutter was successfully rejected to the noise floor of the radar return with rejection in excess of 35 dB, achieved using common adaptive algorithms and straightforward training data selection. As part of the rejection algorithm, the transmitted waveform direction-of-departure (DOD) from the transmitter array to the target was estimated and used as the preserved steer direction in the adaptive beamformer. The DOD estimates agree well with the geometrically determined true values. The demonstration of non-causal transmit beamforming suggests that it will be possible to create multiple simultaneous adaptive range-dependent transmitter beams with an appropriately designed OTHR. This has several applications including for the mitigation of Doppler-spread clutter.
We consider the adaptive radar problem where the properties of the (nonstationary) clutter signals can be estimated using multiple observations of radar returns from a number of sufficiently ...homogeneous range/azimuth resolution cells. We derive a method for approximating an arbitrary Hermitian covariance matrix by a time-varying autoregressive model of order m, TVAR(m), that is based on the Dym-Gohberg band-matrix extension technique which gives the unique TVAR(m) model for any nondegenerate covariance matrix. We demonstrate that the Dym-Gohberg transformation of the sample covariance matrix gives the maximum-likelihood (ML) estimate of the TVAR(m) covariance matrix. We introduce an example of TVAR(m) clutter modeling for high-frequency over-the-horizon radar that demonstrates its practical importance
The problem of estimating the number of independent Gaussian sources and their parameters impinging upon an antenna array is addressed for scenarios that are problematic for standard techniques, ...namely, under "threshold conditions" (where subspace techniques such as MUSIC experience an abrupt and dramatic performance breakdown). We propose an antenna geometry-invariant method that adopts the generalized-likelihood-ratio test (GLRT) methodology, supported by a maximum-likelihood-ratio lower-bound analysis that allows erroneous solutions ("outliers") to be found and rectified. Detection-estimation performance in both uniform circular and linear antenna arrays is shown to be significantly improved compared with conventional techniques but limited by the performance-breakdown phenomenon that is intrinsic to all such maximum-likelihood (ML) techniques
The multiple hypothesis testing problem of the detection-estimation of an unknown number of independent Gaussian point sources is adequately addressed by likelihood ratio (LR) maximization over the ...set of admissible covariance matrix models. We introduce nonasymptotic lower and upper bounds for the maximum LR. Since LR optimization is generally a nonconvex multiextremal problem, any practical solution could now be tested against these bounds, enabling a high probability of recognizing nonoptimal solutions. We demonstrate that in many applications, the lower bound is quite tight, with approximate maximum likelihood (ML) techniques often unable to approach this bound. The introduced lower bound analysis is shown to be very efficient in determining whether or not performance breakdown has occurred for subspace-based direction-of-arrival (DOA) estimation techniques. We also demonstrate that by proper LR maximization, we can extend the range of signal-to-noise ratio (SNR) values and/or number of data samples wherein accurate parameter estimates are produced. Yet, when the SNR and/or sample size falls below a certain limit for a given scenario, we show that ML estimation suffers from a discontinuity in the parameter estimates: a phenomenon that cannot be eliminated within the ML paradigm.
This work addresses the problem of direction-of-arrival (DOA) estimation using spatial compressive sensing (SCS) with bias mitigation via an expected likelihood (EL) approach. Compressive sensing ...(CS)-based estimation approaches such as SCS suffer from two main bias sources: a) a grid-bias resulting from the discretization of the azimuth bearing space and b) an inherent-bias which is the result of regularized L 1 optimization underpinning sparse signal recovery. This work investigates the SCS bias sources and proposes a novel application of the EL approach to mitigate both SCS bias sources to produce two competitive maximum likelihood (ML) surrogate algorithms for DOA estimation. The DOA estimation performance and practical suitability of the proposed approaches are demonstrated via simulation. Simulations demonstrate that SCS with the EL-based bias mitigation is able to provide improved DOA estimation accuracy without the need for intensive regularization parameter tuning.
This paper considers the problem of direction-of-arrival (DOA) estimation for multiple uncorrelated plane waves incident on so-called `fully augmentable' sparse linear arrays. In situations where a ...decision is made on the number of existing signal sources (m) prior to the estimation stage, we investigate the conditions under which DOA estimation accuracy is effective (in the maximum-likelihood sense). In the case where m is less than the number of antenna sensors (M), a new approach called `MUSIC-maximum-entropy equalization' is proposed to improve DOA estimation performance in the `preasymptotic region' of finite sample size (N) and signal-to-noise ratio. A full-sized positive definite (p.d.) Toeplitz matrix is constructed from the MxM direct data covariance matrix, and then, alternating projections are applied to find a p.d. Toeplitz matrix with m-variate signal eigensubspace (`signal subspace truncation'). When m greater than or equal to M, Cramer-Rao bound analysis suggests that the minimal useful sample size N is rather large, even for arbitrarily strong signals. It is demonstrated that the well-known direct augmentation approach (DAA) cannot approach the accuracy of the corresponding Cramer-Rao bound, even asymptotically (as N arrow right infinity ) and, therefore, needs to he improved. We present a new estimation method whereby signal subspace truncation of the DAA augmented matrix is used for initialization and is followed by a local maximum-likelihood optimization routine. The accuracy of this method is demonstrated to be asymptotically optimal for the various superior scenarios (m greater than or equal to M) presented.
Direction-of-arrival estimation performance of MUSIC and maximum-likelihood estimation in the so-called ldquothresholdrdquo area is analyzed by means of general statistical analysis (GSA) (also known ...as random matrix theory). Both analytic predictions and direct Monte Carlo simulations demonstrate that the well-known MUSIC-specific ldquoperformance breakdownrdquo is associated with the loss of resolution capability in the MUSIC pseudo-spectrum, while the sample signal subspace is still reliably separated from the actual noise subspace. Significant distinctions between (MUSIC/G-MUSIC)-specific and MLE-intrinsic causes of ldquoperformance breakdown,rdquo as well as the role of ldquosubspace swaprdquo phenomena, are specified analytically and supported by simulation.
Principles of Mode-Selective MIMO OTHR Abramovich, Y. I.; Frazer, G. J.; Johnson, B. A.
IEEE transactions on aerospace and electronic systems,
07/2013, Letnik:
49, Številka:
3
Journal Article
Recenzirano
In over-the-horizon radar (OTHR) the need to preferentially select propagation mode arises when one or more modes are perturbed by ionospheric disturbances. Due to mixed-mode propagation and ...range-elevation coupling, such control is only implementable using noncausal beamforming via MIMO radar architectures. We introduce three key principles that govern mode-selective multiple-input multiple-output (MIMO) OTHR design. Numerical examples illustrate the high potential efficiency of mode-selective MIMO OTHR, while field trials support the introduced main principles.
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