Sub-Nyquist Cyclostationary Detection for Cognitive Radio

Abstract

Abstract-Cognitive Radio requires efficient and reliable spectrum sensing of wideband signals. In order to cope with the sampling rate bottleneck, new sampling methods have been proposed that sample below the Nyquist rate. However, such techniques decrease the signal to noise ratio (SNR), deteriorating the performance of subsequent energy detection. Cyclostationary detection, which exploits the periodic property of communication signal statistics, absent in stationary noise, is a natural candidate for this setting. In this work, we consider cyclic spectrum recovery from sub-Nyquist samples, in order to achieve both efficiency and robustness to noise. To that end, we propose a structured compressed sensing algorithm, that extends orthogonal matching pursuit to account for the structure imposed by cyclostationarity. Next, we derive a lower bound on the sampling rate required for perfect cyclic spectrum recovery in the presence of stationary noise and show that it can be reconstructed from samples obtained below Nyquist, without any sparsity constraints on the signal. In particular, in non sparse settings, the cyclic spectrum can be recovered at 4/5 of the Nyquist rate. If the signal of interest is sparse, then the sampling rate may be further reduced to 8/5 of the Landau rate. Once the cyclic spectrum is recovered, we estimate the number of transmissions that compose the input signal, along with their carrier frequencies and bandwidths. Simulations show that cyclostationary detection outperforms energy detection in low SNRs in the sub-Nyquist regime. This was already known in the Nyquist regime, but is even more pronounced at sub-Nyquist sampling rates.

20 Years of Evolution From Cognitive to Intelligent Communications

“…It is also able to recover the power spectra of stationary signals, which makes the approach applicable even for non-sparse signals. It has been further proved that cyclic spectrum can be reconstructed from sub-Nyquist samples without sparsity constraint on the signals [39].…”

Compressed cyclostationary detection for Cognitive Radio

“…The structure of R a x (f ), for a given a ∈]0, fs] andf ∈ [0, fs − a] was analyzed in [26]. It was found that the non zero entries of R a…”

“…It follows that R a x (f ) is 2K-sparse with additional structure. A detailed analysis can be found in [26].…”

“…The resulting (6N − 4) × 1 vector composed of these selected elements, denoted by r a x (f ), is 2K-sparse and its support presents additional structure. The case a = 0 corresponds to noisy recovery and a noise component needs to be added to (16); see [26].…”

“…In each iteration, we add an internal loop that, for a selected element originally from the diagonals of R a x (f ), checks for a corresponding non-zero element from the anti-diagonals, and vice versa. The structured OMP method is formally presented in [26].…”