Nathan A. Goodman

Adaptive Waveform Design and Sequential Hypothesis Testing for Target Recognition With Active Sensors

Cognitive radar is a recently proposed approach in which a radar system may adaptively and intelligently interrogate a propagation channel using all available knowledge including previous measurements, task priorities, and external databases. A distinguishing characteristic of cognitive radar is that it operates in a closed loop, which enables constant optimization in response to its changing understanding of the channel. In this paper, we compare two different waveform design techniques for use with active sensors operating in a target recognition application. We also propose the integration of waveform design with a sequential-hypothesis-testing framework that controls when hard decisions may be made with adequate confidence. The result is a system that updates multiple target hypotheses/classes based on measured data, customizes waveforms as the class probabilities change, and draws conclusions when sufficient understanding of the propagation channel is achieved

Processing of multiple-receiver spaceborne arrays for wide-area SAR

The instantaneous area illuminated by a single-aperture synthetic aperture radar (SAR) is fundamentally limited by the minimum SAR antenna area constraint. This limitation is due to the fact that the number of illuminated resolution cells cannot exceed the number of collected data samples. However, if spatial sampling is added through the use of multiple-receiver arrays, then the maximum unambiguous illumination area is increased because multiple beams can be formed to reject range-Doppler ambiguities. Furthermore, the maximum unambiguous illumination area increases with the number of receivers in the array. One spaceborne implementation of multiple-aperture SAR that has been proposed is a constellation of formation-flying satellites. In this implementation, several satellites fly in a cluster and work together as a single coherent system. There are many advantages to the constellation implementation including cost benefits, graceful performance degradation, and the possibility of performing in multiple modes. The disadvantage is that the spatial samples provided by such a constellation will be sparse and irregularly spaced; consequently, traditional matched filtering produces unsatisfactory results. We investigate SAR performance and processing of sparse, multiple-aperture arrays. Three filters are evaluated: the matched filter, maximum-likelihood filter, and minimum mean-square error filter.

Theory and Application of SNR and Mutual Information Matched Illumination Waveforms

A comprehensive theory of matched illumination waveforms for both deterministic and stochastic extended targets is presented. Design of matched waveforms based on maximization of both signal-to-noise ratio (SNR) and mutual information (MI) is considered. In addition the problem of matched waveform design in signal-dependent interference is extensively addressed. New results include SNR-based waveform design for stochastic targets, SNR-based design for a known target in signal-dependent interference, and MI-based design in signal-dependent interference. Finally we relate MI and SNR in the context of waveform design for stochastic targets.

Optimum and decentralized detection for multistatic airborne radar

The likelihood ratio test (LRT) for multistatic detection detection is derived for the case where each sensor platform is a coherent space-time radar. Due to the geometric separation of the platforms, target statistics are modeled as independent from platform to platform but constant over the local data on a single platform. Clutter statistics are also assumed independent from platform to platform but have a local space-time correlation structure typical of monostatic space-time adaptive processing (STAP). Moreover, the target Doppler hypothesis varies from platform to platform due to multiple viewing perspectives. Previous published work has investigated the detection improvement obtained by multiple input, multiple output (MIMO) radar. This prior work, however, has only considered white noise. When clutter is considered, the diversity benefit of a MIMO or multistatic radar system is strongly dependent on geometry. We investigate the relationship between geometry and diversity gain for multistatic airborne space-time radar and the effects of this relationship on decentralized and centralized detection.

Source Estimation Using Coprime Array: A Sparse Reconstruction Perspective

Direction-of-arrival (DOA), power, and achievable degrees-of-freedom (DOFs) are fundamental parameters for source estimation. In this paper, we propose a novel sparse reconstruction-based source estimation algorithm by using a coprime array. Specifically, a difference coarray is derived from a coprime array as the foundation for increasing the number of DOFs, and a virtual uniform linear subarray covariance matrix sparse reconstruction-based optimization problem is formulated for DOA estimation. Meanwhile, a modified sliding window scheme is devised to remove the spurious peaks from the reconstructed sparse spatial spectrum, and the power estimation is enhanced through a least squares problem. Simulation results demonstrate the effectiveness of the proposed algorithm in terms of DOA estimation and power estimation as well as the achievable DOFs.

Spectral-domain covariance estimation with a priori knowledge

A knowledge-aided spectral-domain approach to estimating the interference covariance matrix used in space-time adaptive processing (STAP) is proposed. Prior knowledge of the range-Doppler clutter scene is used to identify geographic regions with homogeneous scattering statistics. Then, minimum-variance spectral estimation is used to arrive at a spectral-domain clutter estimate. Finally, space-time steering vectors are used to transform the spectral-domain estimate into a data-domain estimate of the clutter covariance matrix. The proposed technique is compared with ideal performance and to the fast maximum likelihood technique using simulated results. An investigation of the performance degradation that can occur due to various inaccurate knowledge assumptions is also presented

On Clutter Rank Observed by Arbitrary Arrays

This paper analyzes the rank and eigenspectrum of the clutter covariance matrix observed by space-time radar systems with arbitrarily configured arrays and varying look geometry. Motivated by recent applications that suggest use of nonuniform antenna arrays, a generalized theory of clutter rank is derived and demonstrated. First, a one-dimensional effective random process is defined by projecting the measurements obtained by an arbitrary space-time radar system into an equivalent one-dimensional sampling structure. Then, this projection and the Karhunen-Loeve representation of random processes are used to predict clutter rank based on effective aperture-bandwidth product. Simulated results are used to confirm the theory over a wide range of scenarios, and along the way, the well-known Brennans rule for clutter rank is shown to be a special case of the proposed aperture-bandwidth product

Cognitive Radar Network: Cooperative Adaptive Beamsteering for Integrated Search-and-Track Application

Cognitive radar (CR) is a paradigm shift from a traditional radar system in that previous knowledge and current measurements obtained from the radar channel are used to form a probabilistic understanding of its environment. Moreover, CR incorporates this probabilistic knowledge into its task priorities to form illumination and probing strategies, thereby rendering it a closed-loop system. Depending on the hardwares capabilities and limitations, there are various degrees of freedom that a CR may utilize. Here we concentrate on spatial illumination as a resource, where adaptive beamsteering is used for search-and-track functions. We propose a multiplatform cognitive radar network (CRN) for integrated search-and-track application. Specifically, two radars cooperate in forming a dynamic spatial illumination strategy, where beamsteering is matched to the channel uncertainty to perform the search function. Once a target is detected and a track is initiated, track information is integrated into the beamsteering strategy as part of CRs task prioritization.

Superresolution of Coherent Sources in Real-Beam Data

In this work we study the unique problems associated with resolving the direction of arrival (DOA) of coherent signals separated by less than an antenna beamwidth when the data are collected in the beamspace domain with, for example, electronically or holographically scanned antennas. We also propose a technique that is able to resolve these coherent signals. The technique is based on interpolation of the data measured by an element-space virtual array. Although the data are collected in the beamspace domain, the coherence structure can be broken by interpolating multiple shifted element-space virtual arrays. The efficacy of this technique depends on a fundamental tradeoff that arises due to a nonuniform signal-to-noise ratio (SNR) profile across the elements of the virtual array. This profile is due to the structure imposed by the specific beam pattern of the antenna. In addition to describing our technique and studying the SNR profile tradeoff, we also incorporate a strategy for improving performance through a subswath technique that improves covergence of covariance estimates.

Optically multiplexed imaging with superposition space tracking

We describe a novel method to track targets in a large field of view. This method simultaneously images multiple, encoded sub-fields of view onto a common focal plane. Sub-field encoding enables target tracking by creating a unique connection between target characteristics in superposition space and the target’s true position in real space. This is accomplished without reconstructing a conventional image of the large field of view. Potential encoding schemes include spatial shift, rotation, and magnification. We discuss each of these encoding schemes, but the main emphasis of the paper and all examples are based on one-dimensional spatial shift encoding. System performance is evaluated in terms of two criteria: average decoding time and probability of decoding error. We study these performance criteria as a function of resolution in the encoding scheme and signal-to-noise ratio. Finally, we include simulation and experimental results demonstrating our novel tracking method.