Code Optimisation Framework for Multicode Sonar Systems

<p>The ocean is a temporally and spatially varying environment, the characteristics of which pose significant challenges to the development of effective underwater wireless communications and sensing systems. An underwater sensing system such as a sonar detects the presence of a known signal through correlation. It is advantageous to use multiple transducers to increase surveying area with reduced surveying costs and time. Each transducers is assigned a dedicated code. When using multiple codes, the sidelobes of auto- and crosscorrelations are restricted to theoretical limits known as bounds. Sets of codes must be optimised in order to achieve optimal correlation properties, and, achieve Sidelobe Level (SLL)s as low as possible. In this thesis, we present a novel code-optimisation method to optimise code-sets with any number of codes and up to any length of each code. We optimise code-sets for a matched filter for application in a multi-code sonar system. We first present our gradient-descent based algorithm to optimise sets of codes for flat and low crosscorrelations and autocorrelation sidelobes, including conformance of the magnitude of the samples of the codes to a target power profile. We incorporate the transducer frequency response and the channel effects into the optimisation algorithm. We compare the correlations of our optimised codes with the well-known Welch bound. We then present a method to widen the autocorrelation mainlobe and impose monotonicity. In many cases, we are able to achieve SLLs beyond the Welch bound. We study the Signal to Noise Ratio (SNR) improvement of the optimised codes for an Underwater Acoustic (UWA) channel. During its propagation, the acoustic wave suffers non-constant transmission loss which is compensated by the application of an appropriate Time Variable Gain (TVG). The effect of the TVG modifies the noise received with the signal. We show that in most cases, the matched filter is still the optimum filter. We also show that the accuracy in timing is very important in the application of the TVG to the received signal. We then incorporate Doppler tolerance into the existing optimisation algorithm. Our proposed method is able to optimise sets of codes for multiple Doppler scaling factors and non-integer delays in the arrival of the reflection, while still conforming to other constraints. We suggest designing mismatched filters to further reduce the SLLs, firstly using an existing Quadratically Constrained Qaudratic Program (QCQP) formulation and secondly, as a local optimisation problem, modifying our basic optimisation algorithm.</p>

Code Optimisation Framework for Multicode Sonar Systems

<p>The ocean is a temporally and spatially varying environment, the characteristics of which pose significant challenges to the development of effective underwater wireless communications and sensing systems. An underwater sensing system such as a sonar detects the presence of a known signal through correlation. It is advantageous to use multiple transducers to increase surveying area with reduced surveying costs and time. Each transducers is assigned a dedicated code. When using multiple codes, the sidelobes of auto- and crosscorrelations are restricted to theoretical limits known as bounds. Sets of codes must be optimised in order to achieve optimal correlation properties, and, achieve Sidelobe Level (SLL)s as low as possible. In this thesis, we present a novel code-optimisation method to optimise code-sets with any number of codes and up to any length of each code. We optimise code-sets for a matched filter for application in a multi-code sonar system. We first present our gradient-descent based algorithm to optimise sets of codes for flat and low crosscorrelations and autocorrelation sidelobes, including conformance of the magnitude of the samples of the codes to a target power profile. We incorporate the transducer frequency response and the channel effects into the optimisation algorithm. We compare the correlations of our optimised codes with the well-known Welch bound. We then present a method to widen the autocorrelation mainlobe and impose monotonicity. In many cases, we are able to achieve SLLs beyond the Welch bound. We study the Signal to Noise Ratio (SNR) improvement of the optimised codes for an Underwater Acoustic (UWA) channel. During its propagation, the acoustic wave suffers non-constant transmission loss which is compensated by the application of an appropriate Time Variable Gain (TVG). The effect of the TVG modifies the noise received with the signal. We show that in most cases, the matched filter is still the optimum filter. We also show that the accuracy in timing is very important in the application of the TVG to the received signal. We then incorporate Doppler tolerance into the existing optimisation algorithm. Our proposed method is able to optimise sets of codes for multiple Doppler scaling factors and non-integer delays in the arrival of the reflection, while still conforming to other constraints. We suggest designing mismatched filters to further reduce the SLLs, firstly using an existing Quadratically Constrained Qaudratic Program (QCQP) formulation and secondly, as a local optimisation problem, modifying our basic optimisation algorithm.</p>

Low Correlation Codes for Sonar Systems

<p>Sonar is a vital technology for the detection of objects in the water. Sonarsystems have been redefined over many decades, but research is still beingconducted into optimal detection methods. Codes, and the filters thatprocess the codes, have been at the forefront of this research. An importantobjective has been the minimization of interference caused by reflections.Matched filters are commonly used in sonar systems. They are equivalent tocorrelation filters, which are bound by the Welch bound. The Welch boundgoverns the minimum peak correlation for points outside of detection.This thesis investigated matched filters and their bounds, and it wasfound that by relaxing the condition for detection, properties beyond theWelch bound could be achieved. By relaxing these conditions, the Welchbound no longer applies, and so a modified Welch bound was developedto accurately investigate the nature of these codes. In this thesis, methodsto generate codes for these new codes were investigated. Generating codesfor a matched filter is a non-convex problem, so gradient based methodswere utilised. Methods to improve correlation and power characteristicswere developed, along with methods for mapping a sequence for use witha digital transmitter having particular limitations. Mis-matched filters wereused to improve signal characteristics that may be lost due to this mapping.The performance of the generated codes was evaluated, and the rela-tionships between input parameters and output properties of the resultingsignal were observed. These performance assessments demonstrate thattradeoffs are required between various properties, and a balance is neededto obtain codes useful for sonar. The optimization was parametrized by anexample 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 correlationproperties. Furthermore, compared to the general bounds for the propertiesof 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 toverify their feasibility. There were several additional considerations whichlimit codes that can be tested, and once these are taken into account thetest provided a robust method to verify the design process. Initial testsshowed results that differed from simulations, but after the inclusion ofzero padding before upscaling, the results from empirical testing agreewith simulation.Summarizing the research in this thesis, a new set of codes were devel-oped using a gradient based optimization method. The codes were mappedto a digital transmitter, and the filter adjusted using a mis-matched filter. The optimization was shown to generate near optimal codes which met allthe given sonar system requirements</p>

Low Correlation Codes for Sonar Systems

<p>Sonar is a vital technology for the detection of objects in the water. Sonarsystems have been redefined over many decades, but research is still beingconducted into optimal detection methods. Codes, and the filters thatprocess the codes, have been at the forefront of this research. An importantobjective has been the minimization of interference caused by reflections.Matched filters are commonly used in sonar systems. They are equivalent tocorrelation filters, which are bound by the Welch bound. The Welch boundgoverns the minimum peak correlation for points outside of detection.This thesis investigated matched filters and their bounds, and it wasfound that by relaxing the condition for detection, properties beyond theWelch bound could be achieved. By relaxing these conditions, the Welchbound no longer applies, and so a modified Welch bound was developedto accurately investigate the nature of these codes. In this thesis, methodsto generate codes for these new codes were investigated. Generating codesfor a matched filter is a non-convex problem, so gradient based methodswere utilised. Methods to improve correlation and power characteristicswere developed, along with methods for mapping a sequence for use witha digital transmitter having particular limitations. Mis-matched filters wereused to improve signal characteristics that may be lost due to this mapping.The performance of the generated codes was evaluated, and the rela-tionships between input parameters and output properties of the resultingsignal were observed. These performance assessments demonstrate thattradeoffs are required between various properties, and a balance is neededto obtain codes useful for sonar. The optimization was parametrized by anexample 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 correlationproperties. Furthermore, compared to the general bounds for the propertiesof 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 toverify their feasibility. There were several additional considerations whichlimit codes that can be tested, and once these are taken into account thetest provided a robust method to verify the design process. Initial testsshowed results that differed from simulations, but after the inclusion ofzero padding before upscaling, the results from empirical testing agreewith simulation.Summarizing the research in this thesis, a new set of codes were devel-oped using a gradient based optimization method. The codes were mappedto a digital transmitter, and the filter adjusted using a mis-matched filter. The optimization was shown to generate near optimal codes which met allthe given sonar system requirements</p>

Constructions of asymptotically optimal codebooks with respect to Welch bound and Levenshtein bound

<p style='text-indent:20px;'>Codebooks with small maximum cross-correlation amplitudes are used to distinguish the signals from different users in code division multiple access communication systems. In this paper, several classes of codebooks are introduced, whose maximum cross-correlation amplitudes asymptotically achieve the corresponding Welch bound and Levenshtein bound. Specially, a class of optimal codebooks with respect to the Levenshtein bound is obtained. These classes of codebooks are constructed by selecting certain rows deterministically from circulant matrices, Fourier matrices and Hadamard matrices, respectively. The construction methods and parameters of some codebooks provided in this paper are new.</p>

New Constructions of Codebooks Nearly Meeting the Welch Bound

Optimal codebooks meeting the Welch bound with equality are desirable in many areas, such as direct spread code division multiple access communications, compressed sensing and so on. However, it is difficult to construct such optimal codebooks. There have been a number of attempts to construct codebooks nearly meeting the Welch bound. In this paper, we introduce a generic construction of codebooks using generalized bent functions from [Formula: see text] to [Formula: see text], where [Formula: see text] is a prime and [Formula: see text] is a positive integer with [Formula: see text]. With this construction, we obtain two new families of codebooks nearly meeting the Welch bound. These codebooks have new parameters and could have a small alphabet size. In particular, a class of regular generalized bent functions from [Formula: see text] to [Formula: see text] is presented.