Frank C. Robey

MIMO radar theory and experimental results

The continuing progress of Moores law has enabled the development of radar systems that simultaneously transmit and receive multiple coded waveforms from multiple phase centers and to process them in ways that have been unavailable in the past. The signals available for processing from these multiple-input multiple-output (MIMO) radar systems appear as spatial samples corresponding to the convolution of the transmit and receive aperture phase centers. The samples provide the ability to excite and measure the channel that consists of the transmit/receive propagation paths, the target and incidental scattering or clutter. These signals may be processed and combined to form an adaptive coherent transmit beam, or to search an extended area with high resolution in a single dwell. Adaptively combining the received data provides the effect of adaptively controlling the transmit beamshape and the spatial extent provides improved track-while-scan accuracy. This paper describes the theory behind the improved surveillance radar performance and illustrates this with measurements from experimental MIMO radars.

MIMO Radar Ambiguity Functions

Multiple-Input Multiple-Output (MIMO) radar has been shown to provide enhanced performance in theory and in practice. MIMO radars are equipped with the ability to choose freely their transmitted waveforms at each aperture. In conventional radar systems Woodwards ambiguity function is used to characterize waveform resolution performance. In this paper we extend the idea of waveform ambiguity functions to MIMO radars. MIMO ambiguity functions are developed that simultaneously characterize the effects of array geometry and transmitted waveforms on resolution performance. Overall resolution performance is shown to be governed by a space-time covariance function that can be controlled by the system on transmit using waveform diversity. Visual examples are provided to illustrate the resolution enhancement possible using MIMO technology

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.

Distributed Coherent Aperture Measurements for Next Generation BMD Radar

This paper describes the distributed coherent aperture work being carried out at MIT Lincoln Laboratory in support of the next generation radar (NGR) program under the direction of the Radar Systems Technology (RST) group within the Missile Defense Agency/Advanced Systems (MDA/AS) Directorate. The NGR concept achieves transportability and high-radar sensitivity by coherently combining multiple distributed radar apertures in a building block manner. The operational concept uses orthogonal noise-like waveforms and multiple-input multiple-output (MIMO) techniques for cohere-on-receive operation and for adaptively estimating the transmit coherence parameters. In cohere-on-transmit mode, like waveforms are used and the relative phase and transmit time of each transmit pulse is adaptively adjusted so that the transmitted pulses arrive at the target in-phase and at the same time. In cohere-on-receive mode, an N2 signal-to-noise ratio (SNR) gain is achieved over a single aperture when the orthogonal waveforms are combined coherently. In cohere-on-transmit mode, full coherence is achieved on both transmit and receive for an N2 SNR gain over a single radar. The NGR concept and recent highly-successful distributed aperture measurement campaigns are described. These measurements were carried out at the white sands missile range (WSMR) using the Lincoln Laboratory Wideband MIMO Distributed Aperture Test System in July 2005 and at the Air Force Research Laboratory (AFRL) Ipswich Antenna Range Facility in August 2004. Wideband coherence on transmit and receive was demonstrated at X-band in real time against live targets. A performance analysis, including comparison to the Cramer-Rao bounds, is given for the coherence parameter estimators during the presentation. Future plans are briefly discussed, including experiments with more radar channels and plans to demonstrate additional benefits of using MIMO techniques with distributed apertures and through spatial diversity

Array Calibration Utilizing Clutter Scattering

A method of calibrating airborne radar arrays using scattering from the surface of the earth is proposed. The method uses the mapping of clutter azimuth and elevation to Doppler frequency to separate the energy that is arriving from different azimuths and elevations. Calibration is then accomplished using the clutter data. Range and Doppler ambiguities are examined to predict the adverse impact these will have on the resulting calibration. The necessarily limited data collection time duration limits the resolution of the clutter scattering to some angular extent: the impact of this resolution on the calibration results are also examined.

Array calibration and modeling of steering vectors

The use of structure in estimating covariance matrices has shown great promise for adaptive arrays when the data for estimating a covariance matrix is limited. When applied to adaptive beamforming or detection the result is a significant gain in effective signal-to-noise ratio when compared to unstructured estimates. In practice, the array steering vectors are not as predicted in the ideal models and the covariance is mis-modeled by the assumed structure. This mis-modeling can severely limit the performance in the presence of jamming or strong background clutter. The impact of the mis-modeling is examined and array manifold calibration is shown to reduce the impact while retaining the benefits of structured covariance estimation.

Vector antenna and maximum likelihood imaging for radio astronomy

Radio astronomy using frequencies less than ~100 MHz provides a window into non-thermal processes in objects ranging from planets to galaxies. Observations in this frequency range are also used to map the very early history of star and galaxy formation in the universe. Much effort in recent years has been devoted to highly capable low frequency ground-based interferometric arrays such as LOFAR, LWA, and MWA. Ground-based arrays, however, cannot observe astronomical sources below the ionospheric cut-off frequency of ~10 MHz, so the sky has not been mapped with high angular resolution below that frequency. The only space mission to observe the sky below the ionospheric cut-off was RAE-2, which achieved an angular resolution of ~60 degrees in 1973. This work presents alternative sensor and algorithm designs for mapping the sky both above and below the ionospheric cutoff. The use of a vector sensor, which measures the full electric and magnetic field vectors of incoming radiation, enables reasonable angular resolution (~5 degrees) from a compact sensor (~4 m) with a single phase center. A deployable version of the vector sensor has been developed to be compatible with the CubeSat form factor. Results from simulation as well as ground testing of the vector sensor are presented. A variety of imaging algorithms, including expectation-maximization (EM), space-alternating generalized expectation-maximization (SAGE), projected gradient ascent maximum likelihood (PGAML), and non-negative least squares (NNLS), have been applied to the data. The results indicate that the vector sensor can map the astronomical sky even in the presence of strong interfering signals. A conceptual design for a spacecraft to map the sky at frequencies below the ionospheric cut-off is presented. Finally, the possibility of using multiple vector sensors to form an interferometer is discussed.

Full space-time clutter covariance estimation

For an airborne radar array, beamforming and detection are problems in both space and time. To null clutter, it is necessary to exploit both dimensions, and to do so optimally requires knowledge of the full space-time covariance matrix and the array steering vectors. This paper derives an expectation-maximization (EM) algorithm for the estimation of full space-time covariance matrices while simultaneously estimating array steering vectors. The EM approach iterates between estimating the spatial steering vectors and power associated with clutter scattering from different angles and the formation of a full space-time covariance matrix. The final result is an estimate of the set of array steering vectors and an estimate of the space-time covariance matrix. In practice, one would never need to form this covariance since all calculations could be performed using the SVD of the appropriately weighted clutter space-time steering vector matrix. The technique is capable of providing a positive definite estimate of the space-time covariance and complete array calibration with only a single space-time data sample.

Covariance estimation in terms of Stokes parameters with application to vector sensor imaging

Vector sensor imaging presents a challenging problem in covariance estimation when allowing arbitrarily polarized sources. We propose a Stokes parameter representation of the source covariance matrix which is both qualitatively and computationally convenient. Using this formulation, we adapt the proximal gradient and expectation maximization (EM) algorithms and apply them in multiple variants to the maximum likelihood and least squares problems. We also show how EM can be cast as gradient descent on the Riemannian manifold of positive definite matrices, enabling a new accelerated EM algorithm. Finally, we demonstrate the benefits of the proximal gradient approach through comparison of convergence results from simulated data.

Design and characterization of a fiberoptic RF remoting link

This paper describes the design and characterization of a fiber optic link developed to route received RF signals from remotely located S-band telemetry systems to a central processing and recording facility. This fiber optic system demonstrates for the first time the feasibility of linking RF data from multiple antennas via a single fiber and over a nearly 100-km distance. Measured data of key link parameters such as gain, bit-error-rate, crosstalk, phase and gain stability, dynamic range, and noise figure are presented.