Frequency-Domain GLR Detection of a Second-Order Cyclostationary Signal Over Fading Channels

• Published in: IEEE transactions on signal processing 2014-04, Vol.62 (8), p.1899-1912
• Main Authors: Riba, Jaume, Font-Segura, Josep, Villares, Javier, Vazquez, Gregori
• Format: Article
• Language: English
• Subjects: Algorithms; Applied sciences; Asymptotic properties; Channels; Cognitive radio; Cognitive radio networks; Component; Correlation; Covariance matrices; Cyclostationarity based detection; Detection, estimation, filtering, equalization, prediction; Detectors; Digital modulation; Enginyeria de la telecomunicació; Estimating; Exact sciences and technology; Fading; Fourier transforms; Frequency-domain analysis; Frequency-smoothed cyclic periodogram; GLRT; Information, signal and communications theory; LMPIT; Mathematical models; Maximum-likelyhood; Noise; Processament del senyal; Ràdio cognitiva; Signal and communications theory; Signal processing; Signal representation. Spectral analysis; Signal, noise; Spectra; Spectral correlation; Telecommunications and information theory; Tests; Timing synchronization; Tractament del senyal; Vectors; Àrees temàtiques de la UPC
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2014.2303433

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.