An experimental evaluation of the Neyman–Pearson detector

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Abstract
Several aspects of the discrete time Neyman–Pearson detector are investigated using experimental acoustic data. The problem considered is the detection of a known signal in a surface reverberant environment. The Neyman–Pearson detector is formulated with a given noise ensemble, and then employed to detect a known signal in that noise field. The noise background consists of sonar returns obtained by directing the transmitter and receiver array toward the wind driven surface of a freshwater lake. The noise process is assumed Gaussian with a known covariance matrix, which is estimated with an ensemble average over the reverberation events. Data for the known signal consist of a single echo from a Styrofoam sphere recorded with no measurable reverberation present. Signal plus noise returns are created by adding samples of the target return to samples of the reverberation returns at specified signal-to-noise ratios (S/N). The performance of the detector is obtained experimentally and compared to the performance predicted from theoretical considerations based on the Gaussian assumption and the empirical covariance matrix. The performance is investigated as a function of S/N, number of channels, and transmission type. Two types of transmission are employed, a 1.0-ms pulsed continuous wave (cw) signal at a carrier frequency of 80 kHz, and a 1.0-ms pulsed linear frequency modulated (LFM) signal with a 10-kHz sweep centered at 80 kHz. The degradation of the detector’s performance due to simplifying assumptions that have been placed on the noise process is investigated. The Neyman–Pearson detector using the experimental data displays the following improvements in performance over the simple matched filter: 12 dB for the cw data and 9 dB for the LFM data.

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