An Analysis of Mutually Dispersive Brown Symbols for Non-Linear Ambiguity Suppression

Abstract

This thesis significantly advances research towards the implementation of optimal Non-linear Ambiguity Suppression (NLS) waveforms by analyzing the Brown theorem. The Brown theorem is reintroduced with the use of simplified linear algebraic notation. A methodology for Brown symbol design and digitization is provided, and the concept of dispersive gain is introduced. Numerical methods are utilized to design, synthesize, and analyze Brown symbol performance. The theoretical performance in compression and dispersion of Brown symbols is demonstrated and is shown to exhibit significant improvement compared to discrete codes. As a result of this research a process is derived for the design of optimal mutually dispersive symbols for any sized family. In other words, the limitations imposed by conjugate LFM are overcome using NLS waveforms that provide an effective-fold increase in radar unambiguous range. This research effort has taken a theorem from its infancy, validated it analytically, simplified it algebraically, tested it for realizability, and now provides a means for the synthesis and digitization of pulse coded waveforms that generate an N-fold increase in radar effective unambiguous range. Peripherally, this effort has motivated many avenues of future research