Linearization of power amplifiers has become an important issue, with the advent of linear modulation methods in mobile communication. The predistortion is the most commonly used technique for linearizing an amplifier in order to improve the linearity degree of amplifiers and reduce the out-of-band emission of the transmitter. An adaptive predistorter for linearizing a power amplifier in a mobile transmitter is studied utilizing a complex spectral convolution. Analytical and simulation results show that a complex convolution method which requires no additional local oscillator or phase reference can be used to measure the out-of-band power and utilized the scalar quantity to update the predistorter's coefficients, in order to minimize the out-of-band power.