Design of energy efficient pulse trains for radar

The work presented in this thesis is concerned with the design of discrete coded waveforms for improving range resolution and clutter performance of radar systems. This approach to signal design offers many advantages in terms of waveform shaping and digital implementation of processors. Assuming a matched filter receiver, the bulk of the work is concentrated on studying the autocorrelation function properties of these waveforms, which are directly related to the range resolution. The main objective is to synthesize pulse trains subject to a fixed amplitude constraint, whose autocorrelation sidelobes are as low as possible. Constant amplitude waveforms are attractive for a number of reasons; the principal one being the optimum utilization of transmitter power. Pulse .train signals can be synthesized directly by factorizing the spectrum of specified autocorrelation functions. The problems which arise if the autocorrelation function is only given in magnitude are considered and a design method is presented. For some applications, especially digital implementation, the design objective may be to approximate the response characteristics of a given analogue waveform. It is shown that virtually all the desired properties of analogue signals can be retained if the sampling interval is chosen properly. In addition various suggestions for reducing the range sidelobes of the autocorrelation function are discussed. An attempt is made to solve the signal design problem using numerical optimization methods that incorporate the fixed amplitude constraint. In particular, a constrained optimization technique is developed for synthesizing binary sequences with good autocorrelation function properties. Moreover, the problem of designing pairs of phase coded pulse trains with low autocorrelation sidelobes and small mutual crosscorrelation is considered. In the case of impulse-equivalent sequences known as Huffman codes, a synthesis method based on uniform pulse trains is shown to yield sequences with good energy efficiency. Furthermore, a new approach to the signal design problem using Huffman codes and parameter variational techniques is presented. Although the range sidelobes can be reduced quite effectively by numerical methods, for some applications they might still be too large. Thus optimum sidelobe reduction filters, which minimize the detection loss subject to a set of sidelobe constraints, are derived by mismatching the receiver filter. Finally, in the case where significant target velocity is encountered, it becomes necessary to consider not only the range but also the velocity resolution properties of the transmitted waveform. This is done for the various types of pulse trains using the standard range-doppler ambiguity description of Woodward.