Journals: Frequency-Domain GLR Detection of a Second-Order Cyclostationary Signal Over Fading Channels
J. Riba Sagarra, Font Segura, J. Villares Piera and G. Vázquez Grau


Cyclostationary processes exhibit a form of frequency diversity. Based
on that, we show that a digital waveform with symbol period $T$ can
be asymptotically represented as a rank-1 frequency-domain vector
process which exhibits uncorrelation at different frequencies inside
the Nyquist spectral support of $1/T$. By resorting to the fast Fourier
transform (FFT), this formulation obviates the need of estimating
a cumbersome covariance matrix to characterize the likelihood function.
We then derive the generalized likelihood ratio test (GLRT) for the
detection of a cyclostationary signal in unknown white noise without
the need of a assuming a synchronized receiver. This provides a sound
theoretical basis for the exploitation of the cyclostationary feature
and highlights an explicit link with classical square timing recovery
schemes, which appear implicitly in the core of the GLRT. Moreover,
to avoid the well-known sensitivity of cyclostationary-based detection
schemes to frequency-selective fading channels, a parametric channel
model based on a lower bound on the coherence bandwidth is adopted
and incorporated into the GLRT. By exploiting the rank-1 structure
of small spectral covariance matrices, the obtained detector outperforms
the classical spectral correlation magnitude detector.

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