Power allocation for joint interweave and underlay cognitive radio systems with arbitrary input distributions

In the literature, the Gaussian input is assumed in power optimization algorithms. However, this assumption is unrealistic, whereas practical systems use Finite Symbol Alphabet (FSA) input, (e.g., M-QAM). In this paper, we consider the optimal power for joint interweave and underlay CR systems given FSA inputs. We formulated our problem as convex optimization and solved it through general convex optimization tools. We observed that the total SU transmit power is always less than the power budget and remains in interference limited region only over the considered distance range. Therefore, we re-derive optimal power with interference constraint only in order to reduce the complexity of the algorithm by solving it analytically. Numerical results reveal that, for the considered distance range, the transmit power saving and the rate gain with the proposed algorithm is in the range 16-92% and 7-34%, respectively, depending on the modulation scheme (i.e., BPSK, QPSK and 16-QAM) used.