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Spectrum sensing constitutes a key ingredient in many cognitive radio paradigms in order to detect and protect primary transmissions. Most sensing schemes in the literature assume a time-invariant channel. However, when operating in low Signal-to-Noise Ratio (SNR) conditions, observation times are necessarily long and may become larger than the coherence time of the channel. In this paper the problem of detecting an unknown constant-magnitude waveform in frequency-flat time-varying channels with noise background of unknown variance is considered. The channel is modeled using a Basis Expansion Model (BEM) with random coefficients.
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