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In this paper we study the problem of identifying active subcarriers in anOFDM signal from compressive measurements sampled at sub-Nyquist rate. Theproblem is of importance in Cognitive Radio systems when secondary users (SUs)are looking for available spectrum opportunities to communicate over them whilesensing at Nyquist rate sampling can be costly or even impractical in case ofvery wide bandwidth. We first study the effect of timing offset and derive thenecessary and sufficient conditions for signal recovery in the oracle-assistedcase when the true active sub-carriers are assumed known. Then we propose anOrthogonal Matching Pursuit (OMP)-based joint sparse recovery method foridentifying active subcarriers when the timing offset is known. Finally weextend the problem to the case of unknown timing offset and develop a jointdictionary learning and sparse approximation algorithm, where in the dictionarylearning phase the timing offset is estimated and in the sparse approximationphase active subcarriers are identified. The obtained results demonstrate thatactive subcarrier identification can be carried out reliably, by using thedeveloped framework.

Compressive Identification of Active OFDM Subcarriers in Presence of Timing Offset