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The optimal power law for the detection of a Gaussian burst in a background of Gaussian noise

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2 Author(s)
Fawcett, J.A. ; Defense Res. Establ. Pacific, Victoria, BC, Canada ; Maranda, B.H.

The optimal power law is analyzed using characteristic function techniques. For a signal occupying more than about λ=0.5 of the integration time, the standard square-law energy detector is close to optimal (among the class of power-law detectors). The optimal power is ν*=3 for λ≈0.3, increasing rapidly as λ decreases below this value. The SNR advantage of the optimal processor is not significant for λ>0.5, but exceeds 1 dB for λ<0.1. It is further shown that a cube-law processor yields close-to-optimal results over a wide range of λ. For the representative values of probability of false alarm (Pfa) and probability of detection (Pd) chosen in the performance analysis, the results do not depend strongly on the number of points N that are integrated. Calculations performed for other values of P d and Pfa also show that the results do not depend strongly on the value of these two parameters

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Information Theory, IEEE Transactions on  (Volume:37 ,  Issue: 1 )