The LLRT detector for a known deterministic signal in the presence of multiplicative noise is studied. An interesting property of this `multiplicative' detector is discovered. For the exponential class of noise covariances, it is shown that an unrestricted increase of output SNR (detection index) can be achieved when increasing the sampling rate. Such effect does not occur in the case of LLRT detector in the presence of additive noise, where the detection index is limited by the noise correlation time.
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