Can addition of noise improve distributed detection performance? Hao Chen, Pramod K. Varshney Department of EECS 335 Link Hall, Syracuse University Syracuse, NY 13244 hchen21{varshney}@syr.edu James H. Michels JHM Technologies P.O. Box 4142 Ithaca, NY 14852 jmichels@americu.net Steven M. Kay ECE Department University of Rhode Island Kingston, RI 02881 kay@ele.uri.edu Abstract - Stochastic resonance (SR), a nonlinear physical phenomenon in which the performance of some nonlinear systems can be enhanced by adding suitable noise, has been observed and applied in many areas. However, it has not been shown whether or not this phenomenon plays a role in distributed detection. It seems counterintuitive that adding ad- ditional noise to the received decisions at the fusion center can improve detection performance. How- ever, in this paper, we demonstrate the existence of the SR phenomenon in decision fusion by examples. An explanation for its existence is provided. Keywords: Stochastic resonance, distributed detection, decision fusion. 1 Introduction Stochastic Resonance (SR) is a nonlinear phenomenon first reported and analyzed in [1] in terms of a nonlinear dynamic effect where the system performance can be enhanced by adding suitable noise under certain condi- tions. Since then, the SR effect has been observed and applied in a wide range of applications [2] including audio systems, neural networks, hyperspectral imag- ing, neuroscience, medical imaging, and visual percep- tion. The classic SR signature is the signal-to-noise ratio (SNR) gain of certain nonlinear systems, i.e, the output SNR is significantly higher than the input SNR when an appropriate amount of noise is added [3, 2]. Some approaches have been proposed to tune the SR system by maximizing SNR [4, 5, 6, 7]. SR was also found to enhance the mutual information (MI) between input and output signals [8, 9]. Although it has been shown that the capacity of a SR channel can not exceed the actual capacity at the input, Mitaim and Kosko [9] showed that almost all noise probability density func- tions produce some SR effect in threshold neurons and a new statistically robust learning law was proposed to find the optimal noise level. Compared to SNR, MI is more directly correlated with the transferred input signal information. In signal detection theory, SR also plays a very im- portant role in improving the signal detectability. In [10] and [11], improvement of detection performance of a weak sinusoidal signal is reported. To detect a DC signal in a Gaussian mixture noise background, Kay [12] showed that under certain conditions, perfor- mance of the sign detector can be enhanced by adding some white Gaussian noise. For a more general two hypotheses detection problem, the underlying mecha- nism of the stochastic resonance phenomenon is being explored [13]. The signal detection optimization prob- lem involving the determination of the stochastic res- onance probability density function (pdf) for a fixed detector was solved and reported in [14]. Despite the progress achieved over the past two decades, it has not been shown whether this phenom- enon plays a role in distributed detection. In this pa- per, we investigate the existence of the SR effect in dis- tributed detection systems for the two hypotheses de- tection problem. We restrict ourselves to binary local sensor outputs, denoted by U k , and assume conditional independence among sensor observations. The perfor- mance degradation of detection performance caused by transmission errors between local sensor outputs and the fusion center is assessed. The relationship between the additive SR noise and system performance is ex- plored. For the traditional two-stage approach using the Chair-Varshney fusion rule [15], the role of additive SR noise at both the decoding stage and the decision stage is discussed. We show that the SR phenomenon exists under certain circumstances, for both cases. The paper is organized as follows. In Section 2, the detection framework using stochastic resonance is briefly discussed. The channel model used in this pa- per is discussed in Section 3. The existence of SR effect is demonstrated by two constructive distributed detec- tion examples in Section 4. Conclusions and further