Recently, cognitive wireless local area network over fiber (CWLANoF) is proposed as an improved architecture of the legacy infrastructure-based IEEE 802.11 WLAN Extended Service Sets (ESSs). This newly architecture combines radio over fiber (RoF) and cognitive radio technologies together in order to achieve centralized radio resource management and equal spectrum access through cooperative spectrum sensing. But in this architecture, so many sampling data makes the cognitive access point (CAP) to bear heavy stresses of data processing. To solve this problem, this paper introduces compressed sensing (CS) theory into CWLANoF and proposes an algorithm in order to improve the collecting process of sensing data. To implement this algorithm, the variance of each recover sensing sequence of remote access unit (RAU) is estimated using the wavelet transform, and the optimum weighting factor to each sensing sequence is obtained accordingly. In addition, this paper chooses a novel sampling matrix, structurally random matrix (SRM), in order to implement fast and efficient compressed sensing. Besides, this paper analyses the influences of number of non-zero components to recover success ratio, CPU time, SNR (signal-tonoise ratio) and MSE (mean square error). The simulation results show that CS model satisfy the architecture of CWLANoF's requirements well.