Trade-Off between Bandwidth and Number of Array Elements in the Performance Enhancement of Passive Fathometer

Jahangir Alam, E. H. Huntington, M. R. Frater

School of Engineering and Information Technology, University College, University of New South Wales, Canberra, Australia.

DOI: 10.4236/oja.2013.32A003                

Abstract

Improved signal to noise ratio (SNR) and resolution of the ambient noise cross-correlation function (NCF) between two points help in the estimation of bottom profile of the ocean. One of the main requirements of the improvement of the SNR and resolution is collection of a large amount of data. These large amounts of data can be achieved by recording a large bandwidth ambient noise or using an array of hydrophones. This paper evaluates the performance of the array processing and compares it to the large bandwidth technique in terms of SNR and resolution of NCF. It is shown that the large bandwidth technique gives better SNR and resolution compared to the array processing technique under certain conditions. The outcome of this article finds application in the enhanced estimation of the passive fathometer.

Keywords

Passive Fathometer; Cross-Correlation; SNR; Resolution; Bandwidth; Array Processing

1. Introduction

Time domain cross-correlation between two ambient noise fields plays an important role in the various estimation applications such as bottom profiling of the ocean [1,2], geoacoustic inversion [3] and finding critical angle at the water sediment interface [4]. Improved signal to noise ratio (SNR) and resolution of the ambient noise cross-correlation function (NCF) enhances all these estimations because it helps in the estimation of the Green’s function (GF) [2]. A large collection of data is an important requirement for the better estimation of the GF and thus improvement of the SNR and resolution of the NCF [2,5].

There have been significant numbers of work [4-7] related to the collection of coherent signals during the estimation of GF. Previous literature [4] shows that achieving the requirement of a sufficient amount of data using only two sensors requires a long observation time. The use of an array of hydrophones solves the problem of time constraints by averaging the results of each pair of hydrophones in the array [1,4,8,9]. The SNR and resolution are improved in the array processing but at the cost of complex signal processing and increased expenses [1]. Recent work [2] shows that increase of the bandwidth of the ambient noise field coming from the end-fire region improves SNR and resolution of the NCF even if noise fields are recorded at only two sensors.

In this paper, it is shown theoretically that the large bandwidth technique gives better SNR and resolution compared to the array processing technique under a wide range of circumstances. A mathematical derivation of the cross-correlation function in the array processing is presented here. Delay and sum (DS) beam-forming technique described in [1] is applied in the array processing of this paper, which leads to the derivation of the SNR and resolution of the NCF in array processing. A relationship between the two techniques is shown in this paper in which the resources required to achieve a desired SNR and resolution are defined.

This article is divided into six sections. Section two presents the background of array processing technique and section three provides the mathematics of the SNR and resolution of the cross-correlation function in array processing. Section four shows the numerical simulation of array processing technique to justify the mathematics of section three. Section five presents the comparison between the large bandwidth and array processing technique and finally section six summarises the findings and conclusions drawn from this study.

2. Array Processing

An array in the underwater signal processing is a collection of vertically or horizontally spaced hydrophones, that is used to acquire data at all the hydrophones simultaneously. The array is used in data acquisition applica tions to make use of beam-forming. Beam-forming is a signal processing technique that superimposes a number of time delayed signals by proper delay adjustment so that the SNR of the resultant signal increases [1,9]. Figure 1 shows an equispaced 4-hydrophone vertical array where hydrophones are noted by and. is placed in the top (towards ocean surface) and is placed in the bottom (towards seabed) of the hydrophone chain.

In this paper, it is assumed that the array is placed underwater and a noise signal coming from a surface noise source N which is placed in the end-fire region of the array. Each hydrophone of the array receives a direct path signal and a bottom reflected signal from A with corresponding time delays. Beam-forming the crosscorrelation of each pair of hydrophones, a strong correlation function can be achieved [1]. In the first stage of beam-forming, each hydrophone is taken as reference and cross-correlation is performed with all other hydrophones. All of these correlations are averaged together after proper delay adjustment so that desired peak of each correlation function coincides in the same position [1]. Figure 2 shows the conceptual diagram of the positions of correlation peaks in every correlation steps of the first stage of beam-forming.

Figure 2(a) shows that the cross-correlations between the reference hydrophone and all other hydrophones generate correlation peaks in different positions. First row of Figure 2(a) shows the autocorrelation of the noise field received by where the leftmost and rightmost peaks are generated at distance from the correlation centre (0 position) due to the cross-correlation between

Conflicts of Interest

The authors declare no conflicts of interest.

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