Quickest Detection of a Random Signal in Background Noise Using a Sensor Array
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Quickest Detection of a Random Signal in Background Noise Using a Sensor Array Taragay Oskiper Zargis Medical Corp., Princeton, NJ 08540, USA Email: [email protected]
H. Vincent Poor Department of Electrical Engineering, Princeton University, Princeton, NJ 08544, USA Email: [email protected] Received 2 December 2003; Revised 21 June 2004 The problem of detecting the onset of a signal impinging at an unknown angle on a sensor array is considered. An algorithm based on parallel CUSUM tests matched to each of a set of discrete beamforming angles is proposed. Analytical approximations are developed for the mean time between false alarms, and for the detection delay of this algorithm. Simulations are included to verify the results of this analysis. Keywords and phrases: sensor array, quickest detection, angle-of-arrival estimation.
1.
INTRODUCTION
In this paper, we consider the problem of detecting, as soon as possible, a target that appears abruptly and at an unknown angle in a sensor array. This is a problem that arises in a number of applications including radar, sonar, and communications. For a fixed angle of incidence and known signal and noise distributions, this is a classical problem in statistical change detection, and can be solved, for example, by the Page’s CUSUM algorithm. However, here we consider the situation in which the angle of incidence and the signal and noise statistics are unknown. In this case, alternatives to the classic CUSUM must be considered, and a number of such methods have been developed for such problems [1, 2, 3, 4, 5]. Here, we use an approach motivated by Nikiforov [4] in which we discretize the set of incidence angles and run parallel change-detection algorithms, each one matched to a beamformer pointed at a particular angle. The presence of a signal is announced the first time the test statistic associated with any of these parallel algorithms crosses a threshold. The angle of incidence is then estimated as the pointing angle corresponding to the first test to detect. This test can be analyzed by adapting the methodology of Lorden [6], and we do so by deriving expressions for the mean time between false alarms and the asymptotic mean detection delay for our test. We include a number of simulation results to verify these expressions and to illustrate further properties of the proposed
algorithm, including the effects on the performance of increasing the number of array elements. This paper is organized as follows. In Section 2, we describe a model for the problem of interest, including relevant performance criteria. In Section 3, we review briefly the action and properties of the classic Page’s CUSUM test to provide a framework for our algorithm. Section 4 develops our parallel beamformer-based CUSUM algorithm, while Section 5 contains an analysis of the algorithm under the assumption of Gaussian noise. We also measure the performance of the proposed method against the optimal algorithm that has perfect knowledge of the signal and noise distributions together with the direction
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