Sequential good channel search for multi-channel cognitive radio

In this paper, we consider how to quickly search for a free channel with large channel gain in a multi-channel cognitive radio (CR) system. In the problem considered, the CR pair sequentially inspect unoccupied channels. When the CR pair inspect a particular channel, sequential estimation is used. After each step of the sequential estimation, the CR pair need to make the following decisions: 1) whether to accept the channel currently under inspection as a good channel and terminate the search process; and 2) if the CR pair decide to continue the search process, the pair need to decide whether to stay in the same channel to take more sample for more accurate channel estimation or switch to another channel in hoping for finding a better channel. We show that the optimal decision rules that minimize a properly chosen cost function have a simple structure. In particular, both the termination and switching rule are of threshold type. Numerical results are provided to support the optimal solution.