Investigation of topics in radar signal processing

In the first topic, we investigate a promising image reconstruction algorithm proposed by W. Lawton for spotlight-mode synthetic aperture radar (SAR). The spatial domain image is produced through a series of convolutions and DFTs, all performed using FFTs. We show that the algorithm implements a form of trapezoidal-to-Cartesian interpolation followed by an FFT.In the second topic, we propose a simplified back-projection algorithm for spotlight-mode SAR in which the filtered projections are obtained automatically by choosing the radar waveform to be the impulse response of the desired filter. The filtering is accomplished through the physical mechanism of the waveform reflecting off the target, which is described by a convolution. We then describe a parallel architecture for the back-projection of the filtered projections and analyze its computational and memory requirements.In the third topic, we give a basic derivation of bistatic spotlight-mode SAR (BSSAR). We show that BSSAR can be explained using the projection-slice theorem from computed tomography. We find the locations of the Fourier domain samples and examine the shape of the Fourier grid for several special cases of transmitter and receiver motions.In the fourth topic, we consider the chirp-z interpolation algorithm which is a promising approach to interpolation between two uniform grids with arbitrary spacings. We derive an expression for the total mean-squared error between the chirp-z interpolated samples and the actual samples. We extend the chirp-z interpolation algorithm to multiple dimensions for the general case of periodic sampling with arbitrary sampling geometries.In the last topic, we investigate the least-squares ambiguity function synthesis problem, which has applications in range-Doppler radar imaging and time-frequency signal analysis. We present the solution for least-squares ambiguity function synthesis both in the continuous and discrete time-frequency domains. We then propose a design algorithm and present designs obtained by employing the proposed algorithm. Also, we give the relation between discrete Wigner distributions obtained using samples taken at the Nyquist rate and at twice the Nyquist rate. Finally, we show that discrete Wigner distribution synthesis can be performed using essentially the same algorithm proposed for ambiguity function synthesis. (Abstract shortened with permission of author.)U of I OnlyETDs are only available to UIUC Users without author permissio