Bounds on the overhead of spectrum sensing in cognitive radio

We study a cognitive radio network in which a secondary user must sense the medium and share this information with a fusion center prior to data transmission. The objective of this work is to derive bounds on the overhead required to convey such information. We formulate a rate-distortion framework to capture this effect and compute upper and lower bounds on the rate-distortion function. We also derive in closed form the optimal value of the sampling period at the secondary user as a function of the primary user traffic. Numerical results demonstrate the accuracy of this optimal value and also captures the tradeoff between the rate and the resulting distortion.