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A novel multiuser dynamic radio resource allocation scheme for spectral efficiency optimization in a cognitive ultra wideband radio system is presented in this paper. A new expression of computing the interference power to the primary users over the UWB multipath channel is derived in this work based on the Fenton-Wilkinson method. The subcarriers of the UWB system are grouped into subcarrier blocks according to the system coherence bandwidth. Then, a series of M-ary quadrature amplitude modulation zones are generated over each UWB subcarrier block according to the channel gain of each block and the bit error rate threshold of the system. The transmitted power and bits are optimally distributed among the UWB subcarrier blocks for the use of those zones with a maximum modulation level on each subcarrier block. The performance of the radio resource allocation schemes is analyzed over different UWB channel models. The results show that the spectral efficiency of the system is significantly improved by an optimal resource allocation technique.