A NEW HOS-BASED MODEL FOR SIGNAL DETECTION IN NON-GAUSSIAN NOISE: AN APPLICATION TO UNDERWATER ACOUSTIC COMMUNICATIONS G. Tacconi, A. Tesei, and C.S. Regazzoni Dept. of Biophysical and Electronic Engineering (DIBE) - University of Genoa Via Opera Pia 11A - 16145 Genova - ITALY. Phone: +39 10 3532792. Fax: +39 10 3532134. E-mail: tale@dibe.unige.it Abstract - In the context of digital signal processing addressed to underwater acoustic communications, this work focuses attention on the optimization of detection of weak signals in presence of additive independent stationary non-Gaussian noise. In order to detect signals in the case of low SNR values, the selected binary statistical testing approach consists in a Locally Optimum Detector (LOD), designed on the basis of a new proposed HOS-based model of non-Gaussian noise probability density function (pdf). In particular, an "asymmetric Gaussian" pdf model is introduced, in order to describe realistically non-Gaussian noise in a very simple way. The resulting test has been compared with the Gaussian- hypothesis LOD test. Experimental results have shown significant advantages in modelling noise pdf on the basis of the proposed pdf function; they derive from the application of the LOD test for detecting known deterministic signals corrupted by real acoustic ship-traffic-radiated noise. 1. INTRODUCTION * Conventional digital signal processing algorithms and detection criteria, based on the Second Order Statistics (SOS), and optimised in presence of Gaussian noise, may degrade their performances in non-Gaussian environments. In this case, Higher Order Statistics (HOS) [1][2] is selected for analysing noise and building efficient detection tests. This paper presents an innovative HOS-based noise pdf model applied for detection in presence of additive, independent and identically distributed (iid), stationary, non-Gaussian noise, under the critical conditions of weak signals (e.g., for values of the Signal-to-Noise Ratio - SNR - belonging to the range [-20÷-5] dB). The detection problem is faced with reference to a general digital communication system, as shown in Fig. 1. * This work was partially supported by CEC in the context of the MAST-I Project SNECOW (Shipping Noise Evaluation in COastal Waters). Source s(k) Channel Hc(.) + n(k) y(k) s'(k) detect. result Receiver Fig. 1. Mathematical block diagram of a general communication system. The system is made up of three main blocks: a. a source of deterministic or stochastic signals, {s(k), k=1, .., K}; b. a propagation channel that uses an input/output function, H c ( . ), and adds to the transmitted signal independent, stationary, generally non- Gaussian noise, {n(k), k=1, .., K}, consisting of iid samples; c. a receiver of the resulting observation, {y(k), k=1, .., K}, on the basis of which to decide between the two hypotheses of presence (hypothesis H1) and absence (hypothesis H0) of a transmitted signal {s(k)} [3][4]. Attention is focused on the receiver block; the other modules are simplified: a) the signals emitted are deterministic and have simple known shapes (e.g., impulses, sinusoids, etc.); b) the transfer function can only attenuate the signals transmitted (H c (w)=G, G is constant, G≤ 1). Detection is dealt with as binary hypothesis testing in the context of statistical inference [3]. Under the aforesaid assumptions, detection optimization can be reached by selecting the most suitable: 1. binary hypothesis statistical detection criteria, 2. signal processing techniques for noise characterization as a basis for designing detection algorithms. For improving detection performances with generalized noise environments and low SNR values, the Locally Optimum Detection class is selected [3];