Optimal sequential channel estimation for multi-channel cognitive radio

In this paper, we consider how to quickly obtain accurate channel gain estimates for multi-channel cognitive radio systems. A sequential setup, in which the cognitive users estimate available channels one by one, is considered. In addition, the channel estimation for each channel is also sequential. In particular, cognitive users will determine whether to finish the estimation process of the current channel and switch to next channel for estimation based on the training symbols received so far. To balance the tradeoff between the estimation error and time spent on the channel estimation, we aim to design a switch function and an estimator that minimize a linear combination of these two factors. We obtain the optimal solution for the general case. Numerical results are provided to show the substantial gain of our solution over that of uniformly allocating training time to each channel.