Spectrum scarcity is an important challenge faced by high-speed wireless communications. Meanwhile, caused by current spectrum assignment policy, a large portion of spectrum is underutilized. Motivated by this, cognitive radio (CR) has emerged as one of the most promising candidate solutions to improve spectrum utilization, by allowing secondary users (SUs) to opportunistically access the temporarily unused spectrum, without introducing harmful interference to primary users. Moreover, opening of TV white space (TVWS) gives us the con dence to enable CR for TVWS spectrum. A crucial requirement in CR networks (CRNs) is wideband spectrum sensing, in which SUs should detect spectral opportunities across a wide frequency range. However, wideband spectrum sensing could lead to una ordably high sampling rates at energy-constrained SUs. Compressive sensing (CS) was developed to overcome this issue, which enables sub-Nyquist sampling by exploiting sparse property. As the spectrum utilization is low, spectral signals exhibit a natural sparsity in frequency domain, which motivates the promising application of CS in wideband CRNs. This thesis proposes several e ective algorithms for invoking CS in wideband CRNs. Speci cally, a robust compressive spectrum sensing algorithm is proposed for reducing computational complexity of signal recovery. Additionally, a low-complexity algorithm is designed, in which original signals are recovered with fewer measurements, as geolocation database is invoked to provide prior information. Moreover, security enhancement issue of CRNs is addressed by proposing a malicious user detection algorithm, in which data corrupted by malicious users are removed during the process of matrix completion (MC). One key spotlight feature of this thesis is that both real-world signals and simulated signals over TVWS are invoked for evaluating network performance. Besides invoking CS and MC to reduce energy consumption, each SU is supposed to harvest energy from radio frequency. The proposed algorithm is capable of o ering higher throughput by performing signal recovery at a remote fusion center.

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