In this thesis, a reduced-rank multistage Wiener filter based CFAR detector is applied for spectrum sensing in cognitive radio. Spectrum sensing is an essential component in cognitive radio. In order to enhance the performance of primary user signal detection under the multipath fading environments, a multiple antenna technique is employed at the secondary user. In addition, the general sidelode canceller (GSC) is utilized prior to the detection to suppress the effect of interference and noise. And then the AMF CFAR test is utilized for the secondary user. For the purpose of reduction of computational complexity and reliable performance, reduced-rank processing is a well-known technique under the condition of finite sample support in short sensing time. The numerical results show that the reduced-rank multistage Wiener filter based AMF CFAR detector outperforms the full rank filter-based detector in a finite number of samples.