Adaptive transmit and receive design for array radar

This dissertation aims to apply adaptive processing for both the receiver and transmitter of a radar system, to address challenges such as the requirement of excessive training signals and high computational complexity in the conventional adaptive processing techniques for practical applications. The first part of this dissertation deals with an adaptive reduced-rank detector, referred to as the CG-AMF detector, at the receiver of radar systems. The CG-AMF detector is obtained by using the conjugate gradient algorithm to solve for the weight vector of the adaptive matched filter (AMF). The CG is a computationally efficient iterative algorithm which finds the projection of the AMF weight vector to the Krylov subspace with a dimension growing with the CG iterations. This effectively leads to a family of reduced-rank detectors indexed by the number of CG iterations. We examine the output signal-to-interference-and-noise ratio (SINR) of the CG-AMF detector in the presence of strong clutter/interference. Specifically, by exploiting a connection between the CG algorithm and the Lanczos algorithm, we show the output SINR can be asymptotically expressed in a simple form involving a Ritz vector of the sample covariance. The probability density function (PDF) of the output SINR is then obtained based on this approximation. Our theoretical analysis of the CG-AMF detector is verified by computation simulation. Numerical comparisons are also made with several popular reduced-rank detectors using either data-independent or data-dependent rank reduction approaches. Our results show that for a fixed training size, the CG-AMF detector often reaches its peak output SINR with a lower rank compared with the other reduced-rank detectors, which implies that the CG-AMF detector has lower computational complexity requirement. In the second part, we consider adaptive transmit and receive beampattern design for array radar systems. While adaptive processing is primarily employed at the receiver in conventional beamforming techniques, we also use it for adaptive transmit beamforming, which involves adaptively selecting the transmit correlation matrix by maximizing the output SINR at the receiver. One motivation of utilizing adaptive processing at the transmitter is that with imprecise knowledge of the interferences, only relying on adaptive receive beamforming may be inadequate for interference cancellation, whereas joint adaptive transmit and receive beamforming can potentially afford a stronger ability to handle the interferences. Simulations are provided to demonstrate the performance of the proposed joint adaptive transmit and receive beamforming approach. Given a correlation matrix obtained in the previous optimal beampattern design stage, the next problem becomes that of determining the probing waveforms which is the ultimate goal of the designing exercise. The third part of the dissertation deals with the synthesis of transmit waveform matrix whose correlation matrix is equal or close to the pre-specified correlation matrix, and which also satisfies some practically motivated constraints. We consider the signal synthesis problem with a desired correlation matrix and a constant modulus constraint as well as a similarity constraint involving a known radar waveform with some desire properties. The proposed optimization algorithm based on cyclic algorithm and iterative algorithm yields solutions with good accuracy. Numerical simulations are also presented to demonstrate the effectiveness of the proposed algorithm.