Ben A. Johnson

MUSIC, G-MUSIC, and Maximum-Likelihood Performance Breakdown

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.

Recent results in MIMO over-the-horizon radar

A demonstration of multiple-input multiple-output over-the-horizon radar is presented. Transmitter signal beam- forming on a multi-element array has been created, not conventionally before transmission at the transmitter facility, but, after radar signal transmission, skywave propagation, target scattering, return signal propagation, and reception using an over-the-horizon radar receiver. Transmitter beam-patterns have been created simultaneously from the signal received at two widely separated locations. The first is within line-of-sight propagation of the end-point of the one-hop ionospheric transmitter to target path, and the second from the signal received at the end-point of the two-hop ionospheric transmitter to target to receiver propagation path. These beampatterns are shown to be practically identical. They reveal the target radar return signal direction-of-departure at the transmitter. This example of a-posteriori transmitter beamforming suggests that it will be possible to create multiple simultaneous adaptive range dependent transmitter beams with an appropriately designed over-the-horizon radar. This has several applications including for the mitigation of Doppler-spread clutter.

Noncausal Adaptive Spatial Clutter Mitigation in Monostatic MIMO Radar: Fundamental Limitations

The problem of a point target detection masked by clutter distributed over range and Doppler, including the range and Doppler of the target, is considered for a multimode propagation scenario commonly encountered in quasimonostatic HF over-the-horizon radars (OTHR). Here, a clutter signal spread in Doppler frequency due to propagation via a disturbed ionospheric layer competes with a target and narrowband clutter returns propagating via a stable ionospheric layer with the same group delay (radar range). Mitigation over all ranges of spread clutter propagating via a ¿mixed mode¿ path with indistinguishable direction-of-arrival (DoA) relative to the target requires (potentially adaptive) transmit beamforming to exploit the direction-of-departure (DoD) difference, which varies as a function of radar range. This range-dependent beamforming can be implemented only via the use of multiple-input multiple-output radar technology. In this paper, we explore the fundamental limitations that exist for the maximal dimension of the area in range-Doppler space occupied by spread clutter and the required properties (cardinality) of the orthogonal waveform set for efficient spread clutter mitigation.

Orthogonal waveform support in MIMO HF OTH radars

HF skywave radar performance and flexibility can benefit from transmission of multiple orthogonal waveforms in a multiple-input, multiple-output (MIMO) radar architecture. Several practical limitations need to be considered in such a design. One issue is that many HF radar transmit arrays are over-sampled spatially to allow for operation over a significant portion of the HF band. Transmission of orthogonal waveforms in this case can result in large reactive power and consequent equipment damage. Another issue is the ability to generate orthogonal waveform sets with sufficient cardinality at the low time-bandwidth products typical of aircraft surveillance operation. There are likely to be fewer waveforms than transmit elements and so some form of spatial rank expansion, from waveform to radiated signal, is required. Both of these issues are examined using Maric-Titlebaum frequency-hop codes as one example of an orthogonal waveform set.

GLRT-Based Detection-Estimation for Undersampled Training Conditions

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.

Use of adaptive non-causal transmit beamforming in OTHR: Experimental results

We report results from an experiment that applied multiple-input multiple-output (MIMO) waveform techniques to over-the-horizon radar (OTHR). The experiment objective was to demonstrate that adaptive transmitter beamforming could be used to reject spatially discrete radar clutter. In MIMO radar architectures, conventional or adaptive transmitter beamforming occurs following waveform transmission, propagation, scatter from targets and clutter sources, return propagation and finally signal reception. We have successfully rejected spatially discrete clutter 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 this we estimated the transmitted waveform direction-of-departure from the transmitter array to the target and used the estimate as the preserved steer direction in the adaptive beamformer. The direction-of-departure estimates agreed well with the true values.

Principles of Mode-Selective MIMO OTHR

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.

Two-Dimensional Multivariate Parametric Models for Radar Applications—Part II: Maximum-Entropy Extensions for Hermitian-Block Matrices

In a series of two papers, a new class of parametric models for two-dimensional multivariate (matrix-valued, space-time) adaptive processing is introduced. This class is based on the maximum-entropy extension and/or completion of partially specified matrix-valued Hermitian covariance matrices in both the space and time dimensions. The first paper considered the more restricted class of Hermitian Toeplitz-block covariance matrices that model stationary clutter. This second paper deals with the more general class of Hermitian-block covariance matrices that model nonstationary clutter. For our recently proposed 2-D time-varying autoregressive (TVAR) model, we derive optimal and computationally practical suboptimal methods for calculating such parametric models. The maximum-likelihood covariance matrix estimate for the 2-D TVAR model is also derived. The efficacy of the introduced models is illustrated by signal-to-interference-plus-noise ratio (SINR) degradation results obtained when applying the covariance matrix models to space-time adaptive processing filter design, compared with the true clutter covariance matrix provided by the DARPA KASSPER dataset.

Iterative Adaptive Kronecker MIMO Radar Beamformer: Description and Convergence Analysis

We introduce an iterative procedure for design of adaptive KL-variate linear beamformers that are structured as the Kronecker product of K-variate (transmit) and L-variate (receive) beamformers. We focus on MIMO radar applications for scenarios where only joint transmit and receive adaptive beamforming can efficiently mitigate multi-mode propagated backscatter interference. This is because the direction-of-departure (DoD) on one interference mode, and the direction-of-arrival (DoA) on the other, coincide with those of a target, respectively. We introduce a Markov model for the adaptive iterative routine, specify its convergence condition, and derive final (stable) signal-to-interference-plus-noise ratio (SINR) performance characteristics. Simulation results demonstrate high accuracy of the analytical derivations. In addition, we demonstrate, that for the considered class of multiple-input multiple-output (MIMO) radar interference scenarios, the diagonally loaded sample matrix inversion (SMI) algorithm provides additional performance improvement and convergence rate for this iterative adaptive Kronecker beamformer.

DOA estimator performance assessment in the pre-asymptotic domain using the likelihood principle

Performance assessment of algorithms for direction of arrival (DOA) estimation are typically done using large-sample justified asymptotic constructs such as consistency, efficiency, and the Cramer-Rao lower bound. The performance in parameter accuracy (usually the mean square error of the DOA estimate) of the algorithm relative to the true parameters of the sources is evaluated to determine if the algorithm is accurate, robust, computationally efficient, etc. However, performance assessment of the algorithm in practical circumstances with limited data sample volume cannot use these methods, because asymptotic statistical behavior is no longer met and the true location of the sources is in general unknown. This paper reviews the application of an performance assessment technique referred to as expected likelihood in such practical small-sample circumstances, and provides simulation and real-world examples of the capabilities provided by expected likelihood which does not rely on knowledge of the true source locations. Uses of the approach in other areas such aiding of numerical optimization, model order determination, and determination of appropriate diagonal loading in LSMI applications is also reviewed.