I. INTRODUCTION  
A. Problem Formulation and System Model  
  
III. BACKGROUND: NARROWBAND AND COOPERATIVE SPECTRUM SENSING  
A. Narrowband Sensing Techniques  
B. Cooperative Sensing  
  
IV. NYQUIST MULTIBAND SPECTRUM SENSING  
B. Parallel Multiband Detection at Nyquist Rates  
C. Comparing Nyquist Multiband Detection Methods  
  
V. COMPRESSIVE SUB-NYQUIST WIDEBAND SENSING  
A. Multicoset Sampling and Blind Spectrum Sensing  
B. Modulated Wideband Converter  
C. Multirate Asynchronous Sub-Nyquist Sampler  
D. Remarks on Compressed Sampling Detectors  
  
VI. ALIAS-FREE-BASED SUB-NYQUIST WIDEBAND SPECTRUM SENSING  
A. Alias-free Sampling Notion  
B. Randomised Sampling Schemes  
C. Reliable Alias-free Sampling Based Multiband Spectrum Sensing  
  
VII. COMPARISON BETWEEN SUB-NYQUIST SPECTRUM SENSING ALGORITHMS  
A. CS Versus Alias-free Sampling for Multiband Detection  
B. Numerical Examples  
  
VIII. CONCLUSIONS AND OPEN RESEARCH CHALLENGES