On the identifiability of multipath parameters

Consider a received signal consisting of noise and an unknown wave-form 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 suucient conditions for the afore-mentioned model to be identiiable 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 coeecient, nor the waveform power, nor the noise power can be unambiguously determined.