We investigate the bandwidth allocation and power control schemes in orthogonal frequency division multiplexing (OFDM) based multi-hop cognitive radio networks

and the color-sensitive graph coloring (CSGC) model is viewed as an efficient solution to the spectrum assignment problem. We extend the model by taking into account the power control strategy to avoid interference among secondary users and adapt dynamic topology. We formulate the optimization problem encompassing the channel allocation

power control with the interference constrained below a tolerable limit. The optimization objective with two different optimization strategies focuses on the routes rather than the links as in traditional approaches. A heuristic solution to this nondeterministic polynomial (NP)-hard problem is presented

which performs iterative channel allocation according to the lowest transmission power that guarantees the link connection and makes channel reuse as much as possible

and then the transmission power of each link is maximized to improve the channel capacity by gradually adding power level from the lowest transmission power until all co-channel links cannot satisfy the interference constraints. Numerical results show that our proposed strategies outperform the existing spectrum assignment algorithms in the performance of both the total network bandwidth and minimum route bandwidth of all routes

meanwhile

saving the transmission power.