of late, many researchers have been interested in sparse representation of signals and its applications such as Compressive Sensing in Cognitive Radio (CR) networks as a way of overcoming the issue of limited bandwidth. Compressive sensing based wideband spectrum sensing is a novel approach in cognitive radio systems. Also in these systems, using spatial-frequency opportunistic reuse is emerged interestingly by constructing and deploying spatial-frequency Power Spectral Density (PSD) maps. Since the CR sensors are distributed in the region of support, the sensed PSD by each sensor should be transmitted to a master node (base-station) in order to construct the PSD maps in space and frequency domains. When the number of sensors is large, this data transmission which is required for construction of PSD map can be challenging. In this paper, in order to transmit the CR sensors' data to the master node, the compressive sensing based scheme is used. Therefore, the measurements are sampled in a lower sampling rate than of the Nyquist rate. By using the proposed method, an acceptable PSD map for cognitive radio purposes can be achieved by only 30% of full data transmission. Also, simulation results show the robustness of the proposed method against the channel variations in comparison with classical methods. Different solution schemes such as Basis Pursuit, Lasso, Lars and Orthogonal Matching Pursuit are used and the quality performance of them is evaluated by several simulation results over a Rician channel with respect to several different compression and Signal to Noise Ratios. It is also illustrated that the performance of Basis Pursuit and Lasso methods outperform the other compression methods particularly in higher compression rates.