HOS-based noise models for signal-detection optimization in non-Gaussian environments A. Tesei, and C.S. Regazzoni DIBE, University of Genoa, Genoa, Italy Abstract - Two pdf models suitable for describing non-Gaussian iid noise are introduced. The models are used in the design of a LOD test for detecting weak signals in real non-Gaussian noise. Results obtained in the context of an underwater acoustic application are encouraging. 1. INTRODUCTION 1 Conventional signal processing and detection criteria, optimised in presence of Gaussian noise, may decay in non-Gaussian environments. Higher Order Statistics (HOS) [1] is a powerful means to analyse non-Gaussian noise and build robust detectors. This work focuses attention on the problem of optimizing detection in presence of additive, iid, stationary, non-Gaussian noise under the conditions of weak signals (i.e., for low Signal-to-Noise Ratio - SNR). In order to optimize the Probability of Detection P det for low SNR values, the selected binary statistical test consists in a Locally Optimum Detector (LOD) [2], whose test rule is computed on the basis of new models of noise univariate probability density function (pdf) [3]. The investigated models are expressed in terms of the HOS parameters skewness (of the 3rd-order) which quantifies the deviation from shape symmetry, and kurtosis (of the 4th order) which quantifies the sharpness of a shape. The detector has been tested in the case of deterministic signals corrupted by real shipping-traffic noise, acquired during a sea campaign, in the context of CEC MAST-I SNECOW project (May 1993) [4]. 2. DESCRIPTION OF THE APPROACH The proposed method is based on the statistical analysis of channel noise. As LOD requires the analytical model of noise pdf, attention is focused on this aspect. The first model is a generic pdf introduced by Champernowne and used in [3]. It can be applied if the N noise components have an hyperbolic distribution of power. In this acoustic application, in which noise main components are the ship, from which the sensor was dropped (strong source), and the surrounding traffic ships (which can be considered equally distributed on the sea, and contribute weakly to noise), this pdf model is reasonable. It depends on β 2 , the ratio between the 4th and the square of the 2nd moments [3]. A second new model is presented, the "asymmetric Gaussian" pdf, consisting of two Gaussian parts, and depending on two second-order parameters (deriving from the definition of variance), i.e., the "left and right variances", which together maintain the same information provided by the skewness. The non-linear function g lo ( . ), in terms of which the likelihood-ratio of the LOD rule is expressed [2], is easily expressed in terms of these two models. Information added by HOS-based description is contained in simple parameters (β 2 or σ l and σ r ), and no constraint has to be satisfied about signal characteristics. 3. EXPERIMENTAL RESULTS AND FUTURE WORK 1 This work was partially supported by the Commission of European Community in the context of MAST-I SNECOW Project An extensive test phase was carried out. Noise was acquired in a coastal shallow-water area. The presence of a lot of traffic and of reflection and refraction makes the detector work in critical conditions. The LOD performances are summarized in Fig. 1 in terms of P det vs. SNR. A comparison among the results of the two proposed pdfs and the Gaussian model is presented. The tests were carried out by fixing the Probability of False Alarm P FA =α=5%. Non Gaussian real underwater acoustic ship-traffic noise was characterized by μ=0, β 2 =2.84, σ l = 1860, σ r =1500. The proposed models appear approximately equivalent, as noise presents deviation from both Gaussian sharpness and symmetry. The next investigation step, concerning the model of propagation through a real shallow-water channel, is going to be carried out. SNR (dB) Detection Probability 0 0,2 0,4 0,6 0,8 1 -26 -24 -22 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 (a) SNR (dB) Detection Probability 0 0.2 0.4 0.6 0.8 1 -32 -30 -28 -26 -24 -22 -20 -18 -16 -14 -12 -10 -8 -6 (b) SNR (dB) Detection Probability 0 0,2 0,4 0,6 0,8 1 -26 -24 -22 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 (c) Fig. 1 Results of the LO detector under the Champernowne (a), the asymmetric-Gaussian (b) and the Gaussian (c) hypotheses. REFERENCES [1] C. Nikias, J. Mendel, "Signal Processing with Higher-Order Spectra", IEEE SP Mag. , pp. 10-37, July 1993. [2] S.A. Kassam, Signal Detection in Non-Gaussian Noise, Springer Verlag, Berlin, 1988. [3] R.J. Webster, "Ambient Noise Statistics", IEEE Trans. SP, Vol. 41 (6), pp. 2249-53, 1993. [4] DIBE, SNECOW Project-MAST 0029-C(A) Final Report- Task 5: Ship traffic noise statistical evaluation, Dec. 1993.