We devise a cross-layer design (CLD) of carrier sensing multiple access with collision avoidance (CSMA/CA) at the medium access control (MAC) layer with spectrum sensing (SpSe) at the physical layer for cognitive radio networks (CRNs). The proposed CLD relies on a Markov chain model with a state pair containing both the SpSe and the CSMA/CA with exponential backoff from which we derive the transmission and collision probabilities. Due to the 2-dimensions of CSMA/CA model with exponential backoff, the resulted Markov chain is obtained with 3-dimensions. Simulation and numerical results are derived and illustrated highlighting the impact of SpSe in CSMA/CA with exponential backoff. The obtained results could be used as performance criteria to evaluate the performance of specific CRNs when they are deployed in a distributed coordination fashion that is prone to collisions.