Transmit beamforming and waveforms for random, sparse array radar

We address the design of radar waveforms, transmit and receive beamforming, and signal processing in moving, sparse array antennas with randomly positioned elements. We are motivated by a concept for less expensive space based radar consisting of a formation of small, autonomous, identical satellites in nearly the same low earth orbits. The satellites operate collaboratively as a coherent, large aperture radar to detect and locate slowly moving targets near the earth surface. Limited fuel mandates that the satellites navigate only to avoid collision within array aperture limits and not necessarily to maintain any ideal array antenna configuration. Sensitive, coherent cancellation of ground reflections implies that the transmit and receive beamforming and waveforms create highly correlated space-time samples of the reflected ground clutter. Using an electromagnetic model for the ground reflected signals, we determine general, displaced phase center conditions on the transmit waveform and transmit/receive beamforming to create the highly correlated samples. The random array element positions are assumed to be known from independent measurement. We then describe a novel, iterative approach to the design of transmit and receive beamforming weights that maximizes the ratio of the output target signal to interference when the waveform conditions for signal correlation are satisfied. A constraint on the total radiated energy is implicit in the design. Results of the optimization for specific random array realizations reveal interesting conclusions: 1) The displaced phase center condition requires that the phase center of the transmit and/or receive arrays translate backwards, against the direction of array motion, with nearly identical patterns between successive pulses. When applied to the random, sparse array, we find that we may use only the complete array (without translation) and/or individual array elements, with backward translation between the elements dictated by the inter-pulse time and radar speed along the array; 2) The inter-pulse times are selected based on the random but known transmit and/or receive inter-element spacings. Criteria for selection include (1) emphasis on longer inter-pulse times to increase radar sensitivity to slowly moving targets and (2) use of multiple inter-pulse times to minimize blind speeds in the beamforming; 3) Iterative optimization of the transmit/receive beamforming with total energy constraint results in (1) nearly uniform transmit array illumination and (2) emphasis on individual receive array elements satisfying the displaced phase center condition and forming two pulse cancellers of the ground clutter. The canceller outputs are combined linearly to provide the detection statistic. Negligible loss (<; 0.2 dB) results when optimization is constrained by the use of uniform, maximum gain transmit weights and only those receive elements satisfying the displaced center condition 4) Losses due to the lack of ground clutter cancellation in the displaced phase center elements are caused in part by random (and unknown) timing and element position errors. This suggests using overlapped sub-arrays in the physical element (satellite) arrays to compensate adaptively for these errors. Monte Carlo simulations reveal that with half wavelength separation between the sub-arrays, position errors on the order of one wavelength are allowable by appropriate linear combination of sub-array outputs.