Detecting the presence of a white Gaussian signal distorted by a\ noisy time-varying channel is addressed by means of three different\ detectors. First, the generalized likelihood ratio test (GLRT) is\ found for the case where the channel has no temporal structure, resulting\ in the well-known Bartlett{\textquoteright}s test. Then it is shown that, under\ the transformation group given by scaling factors, a locally most\ powerful invariant test (LMPIT) does not exist. Two alternative approaches\ are explored in the low signal-to-noise ratio (SNR) regime:\ the first assigns a prior probability density function (pdf) to the channel\ (hence modeled as random), whereas the second assumes an underlying\ basis expansion model (BEM) for the (now deterministic)\ channel and obtains the maximum likelihood (ML) estimates of the\ parameters relevant for the detection problem. The performance of\ these detectors is evaluated via Monte Carlo simulation.

},
keywords = {cognitive radio, dynacs, spectrum sensing},
doi = {10.1109/SSP.2012.6319858},
author = {Daniel Romero and Javier V{\'\i}a and R. L{\'o}pez-Valcarce and Ignacio Santamar{\'\i}a}
}