Sub-Nyquist Cyclostationary Detection for Cognitive Radio

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 paper, 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, which 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. In particular, we show that the cyclic spectrum can be reconstructed from samples obtained at $4/5$ of the Nyquist rate, without any sparsity constraints on the signal. 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.