In Orthogonal Frequency Division Multiplexing (OFDM) based cognitive radio systems, power optimization algorithms have been evaluated to maximize the achievable data rates of the Secondary User (SU). However, unrealistic assumptions are made in the existing work, i.e. a Gaussian input distribution and traditional interference model that assumes frequency division multiplexing modulated Primary User (PU) with perfect synchronization between the PU and the SU. In this paper, we first derive a practical interference model by assuming OFDM modulated PU with imperfect synchronization. Based on the new interference model, the power optimization problem is proposed for the Finite Symbol Alphabet (FSA) input distribution (i.e., M-QAM), as used in practical systems. The proposed scheme is shown to save transmit power and to achieve higher data rates compared to the Gaussian optimized power allocation and the uniform power loading schemes. Furthermore, a theoretical framework is established in this paper to estimate the power saving by evaluating optimal power allocation for the Gaussian and the FSA input. Our theoretical analysis is verified by simulations and proved to be accurate. It provides guidance for the system design and gives deeper insights into the choice of parameters affecting power saving and rate improvement.
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