Consider a received signal consisting of noise and an unknown waveform that arrives at a sensor through both a direct path and an attenuated and delayed specular path. We show that a commonly used frequency-domain model for such a signal is valid essentially only under the assumption that the waveform that underwent multipath propagation is band-limited. Furthermore, we derive sufficient conditions for the aforementioned model to be identifiable from second-order statistics (i.e., its parameters can be uniquely determined from the spectral density of the received signal). We also show that in the frequently considered case of a white waveform, neither the attenuation coefficient, nor the waveform power, nor the noise power can be unambiguously determined.
Stoica, P., Jakobsson, A., & Swindlehurst, A. L. (1999). On the identifiability of multipath parameters. Signal Processing, 74(3), 327–330. https://doi.org/10.1016/S0165-1684(99)00027-4