Lee K. Patton

Modulus constraints in adaptive radar waveform design

Within the taxonomy of adaptive waveform generation methodologies is the family of arbitrary waveform design algorithms, which are capable of designing both the modulus and phase of a complex-valued waveform in response to changes in the operational environment of the sensor. Algorithms of this kind have been the subject of renewed research interest as a consequence of the relatively recent advances in linear RF power amplifiers, arbitrary waveform generators, and computational capability. In this paper, we use hardware considerations to argue that constraints on the maximum waveform modulus will generally supersede the total energy constraint commonly found in the literature. In order to illustrate the deleterious effects on system performance that can arise when these modulus constraints are not accounted for, we subjected recently published waveform design algorithms to maximum modulus limitations in simulation, and we present the results here. We also propose a novel arbitrary waveform design algorithm that accounts for both maximum modulus constraints and constraints on the waveformpsilas autocorrelation function. Simulation results that demonstrate the efficacy of this algorithm are presented.

Centralized Passive MIMO Radar Detection Without Direct-Path Reference Signals

This work addresses the problem of target detection in passive multiple-input multiple-output (MIMO) radar networks without utilization of direct-path reference signals. A generalized likelihood ratio test for this problem is derived, and the distribution of the test statistic is identified under both hypotheses. Equivalence is established between passive MIMO radar networks without references and passive source localization networks. Numerical examples demonstrate important characteristics of the detector, namely, the asymmetric contributions to detection performance from transmitters and receivers, and non-coherent integration gain as a function of signal length. The ambiguity properties of this detector are also investigated, and it is shown that the salient ambiguities can be explained in terms of the time-difference of arrival, frequency-difference of arrival, and angle-of-arrival of the target signals.

Radar-centric design of waveforms with disjoint spectral support

Radar designers seek transmit waveforms that have an acceptable time envelope (modulus), power spectral density, and ambiguity function. However, these three waveform properties are often derived from different sources, which can result in requirement inconsistency. This paper re-examines the design of radar waveforms with disjoint spectral support (also known as sparse frequency or thinned spectrum waveform design) from the perspective of these waveform properties. The conventional multi-objective optimization approach is discarded in favor of constrained nonlinear programming, which can accommodate firm constraints on the waveform modulus and ambiguity function when minimizing transmission energy in specified stop-bands. A novel autocorrelation sequence masking method is used to satisfy the ambiguity constraints. This affords more precise control over range sidelobes than does the more common approach of penalizing integrated sidelobe level. Numeric examples are presented that demonstrate the efficacy of the approach.

Phase Retrieval for Radar Waveform Optimization

An important problem in radar waveform optimization is the synthesis of discrete time constant modulus signals from Fourier magnitude data. Iterative algorithms for solving this problem have been proposed in the literature, but the algorithms are only applicable in limited cases, and the convergent behavior of these algorithms has not been established. We connect waveform design to the well-studied problem of phase retrieval. This is useful for explaining the success of the proposed iterative methods. We generalize and extend the existing algorithms to handle the case in which the dimensions of the time domain waveform and the frequency domain data are unequal, and we provide a convergence analysis. We also relate the phase retrieval problem to the problem of synthesizing discrete time constant modulus signals from power spectral density (PSD) data, which is different and more appropriate for the waveform design problem. We compare the iterative methods to direct search gradient methods for both problems, and establish that the proposed algorithms can provide comparable performance with reduced computational complexity.

Multichannel Detection of an Unknown Rank-N Signal Using Uncalibrated Receivers

This letter addresses the problem of detecting an unknown rank-N signal using multiple receivers that are uncalibrated in the sense that each applies an unknown scaling to the received signal and the (possibly unequal) receiver noise powers are unknown. This problem has been addressed for the case in which the signal can be modeled as a linear combination of N Gaussian random vectors. We consider the alternative approach of modeling the signal as a deterministic unknown. We derive an approximate generalized likelihood ratio test (GLRT) for low signal-to-noise ratios (SNRs). The resulting detector is invariant to relative scalings of the data, and is therefore constant false alarm rate (CFAR) with respect to the unknown noise powers. Numerical examples show this low-SNR GLRT performs well at all SNRs and can outperform other CFAR detectors when N = 1. However, CFAR detectors derived assuming unknown Gaussian signals appear to perform better for N > 1.

Autocorrelation and modulus constraints in radar waveform optimization

Two methods of constraining the waveform auto-correlation sequence (ACS) in a radar waveform optimization problem are compared. The first method directly constrains the envelope of the waveform ACS, whereas the second method indirectly constrains the waveform ACS through the imposition of a similarity constraint. Both methods are imposed in conjunction with constraints on the waveform modulus. The resulting nonlinear programming problems were formulated for a specific example, and solved using standard numerical algorithms. The results indicate that the similarity constraint may not be a useful means of constraining the waveform ACS when the waveform modulus is simultaneously constrained. The results also demonstrate that phase-only optimization can provide a significant decrease in computation time while providing near optimal results.

Multichannel detection of an unknown rank-one signal with uncalibrated receivers

This paper addresses the problem of detecting an unknown rank-one signal using multiple receivers that are uncalibrated in the sense that they each apply an unknown scaling to the received signal, and their respective noise powers are unknown. This problem has been addressed for the case in which the unknown signal can be modeled as a Gaussian random vector. However, that assumption is not applicable to some signal types, such as the constant modulus signals found in radar and communications. For these problems, the signal can be modeled as a deterministic unknown, which is the approach taken here. We derive a generalized likelihood ratio test for this problem under a low signal-to-noise ratio (SNR) assumption. The resulting detector is invariant to relative scalings of the data, and therefore possesses the constant false alarm rate (CFAR) property with respect to the unknown noise powers. Numerical examples show the proposed detector can outperform CFAR detectors derived under the Gaussian assumption.

Detection in passive MIMO radar networks

This paper considers detection in passive multiple-input multiple-output (MIMO) radar sensor networks. Multiple centralized and decentralized detection architectures are surveyed and compared via Monte Carlo simulation. A recently proposed generalized likelihood ratio test (GLRT) detector, termed the reference-surveillance GLRT, is shown to have superior detection performance because it maximally exploits the correlations in the measured data. Specifically, it exploits inter-receiver reference-surveillance correlations and inter-receiver surveillance-surveillance correlations, two concepts that are explained in this paper. In this way, the reference-surveillance GLRT achieves better sensitivity under all direct-path-to-noise ratio conditions than more conventional matched filter-inspired detection approaches, which exploit only some of the correlations within the measured data.

Rapid waveform adaptation for nearly optimal detection in colored interference

A cognitive radar can dynamically design its transmit waveform in response to changing environmental knowledge, which may be obtained a priori, estimated online, or both. We consider the detection of targets in wide-sense stationary additive colored Gaussian noise. Cognitive radar has been shown to provide potentially significant improvements for this problem. However, existing algorithms may be too computationally demanding for some scenarios. We present an approach that can be implemented in the most demanding scenarios. This approach trades optimality for reduced computational complexity by computing a large library of nearly optimal waveforms before operation, and retrieving them rapidly at runtime.

On the applicability of source localization techniques to passive multistatic radar

The source localization problem concerns the detection and localization of an emitter whose transmission is observed by geographically separated receivers. The passive multistatic radar (PMR) problem concerns the detection and localization of a target that scatters an illumination signal to geographically separated receivers. By modeling the scattering target as an emitter, the techniques of source localization can be applied to the PMR problem. Indeed, this approach has recently been introduced in the literature. However, the exact relationship between the two problems has not been made explicit. In this work, we derive a centralized generalized likelihood ratio test (GLRT) detector that performs the processing characteristic of both source localization and PMR. This detector is used to assess the relative detection benefit provided by source localization in PMR. We show that source localization techniques are of limited utility in PMR due to the SNR regimes of the target-scattered and direct-path signals typical of the PMR signal environment.