Low Correlation Codes for Sonar Systems

Abstract

Sonar is a vital technology for the detection of objects in the water. Sonar systems have been redefined over many decades, but research is still beingconducted into optimal detection methods. Codes, and the filters that process the codes, have been at the forefront of this research. An important objective has been the minimization of interference caused by reflections. Matched filters are commonly used in sonar systems. They are equivalent to correlation filters, which are bound by the Welch bound. The Welch bound governs the minimum peak correlation for points outside of detection.This thesis investigated matched filters and their bounds, and it was found that by relaxing the condition for detection, properties beyond the Welch bound could be achieved. By relaxing these conditions, the Welch bound no longer applies, and so a modified Welch bound was developed to accurately investigate the nature of these codes. In this thesis, methods to generate codes for these new codes were investigated. Generating codes for a matched filter is a non-convex problem, so gradient based methods were utilised. Methods to improve correlation and power characteristics were developed, along with methods for mapping a sequence for use witha digital transmitter having particular limitations. Mis-matched filters were used to improve signal characteristics that may be lost due to this mapping. The performance of the generated codes was evaluated, and the relationships between input parameters and output properties of the resultingsignal were observed. These performance assessments demonstrate that tradeoffs are required between various properties, and a balance is needed to obtain codes useful for sonar. The optimization was parametrized by an example set of requirements for sonar. The signals were found to meet the given requirements, and when compared to codes typically used in sonar, the optimized signals were shown to have significantly better correlation properties. Furthermore, compared to the general bounds for the properties of codes, it was found that the new codes had nearly optimal properties, and performed better than equivalent codes bounded by the Welch bound. The performance of codes were also investigated in a water tank to verify their feasibility. There were several additional considerations which limit codes that can be tested, and once these are taken into account the test provided a robust method to verify the design process. Initial tests showed results that differed from simulations, but after the inclusion of zero padding before upscaling, the results from empirical testing agree with simulation. Summarizing the research in this thesis, a new set of codes were developed using a gradient based optimization method. The codes were mapped to a digital transmitter, and the filter adjusted using a mismatched filter. The optimization was shown to generate near optimal codes which met all the given sonar system requirements.