Weak signal detection in a noisy environment

Increased probability of tone detection even when SNR drops below −10 dB

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Army researchers have developed a novel algorithm – the adjacent conjugate convolution (ACC) – to compute the fast Fourier transform of an array of time domain samples of a particular frequency. The outcome is a power spectral density (PSD) array describing the relative power as a function of frequency.

A variety of digital signal processing algorithms are used for detecting the presence of an expected signal within a received noisy signal. When the expected signal is a single tone (pure sine wave at a particular frequency), the PSD algorithm is commonly used. The presence of a single tone is revealed by a single spike in PSD at the tone frequency when PSD is plotted versus frequency.

The probability of detection depends on the signal-to-noise ratio (SNR) of the received signal, with the typical probability of tone detection dropping rapidly when SNR drops below −10 dB. Therefore, improvements to tone detection are needed.

The PSD of an array has improved gain compared to a conventional PSD calculation because the ACC algorithm divides the input array into multiple segments, and coherently integrates uncorrelated noise from adjacent segments. As a result, the ACC algorithm has the desirable behavior of compensating for frequency drift and producing a PSD array with improved gain. Tones can be detected in the output of the ACC algorithm by the PSD array as input to a Constant False Alarm Rate (CFAR) detector.

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