Accurate analysis of spectral regrowth of nonlinear power ampliﬁer driven by cyclostationary modulated signals Mahdi Majidi • Abbas Mohammadi • Abdolali Abdipour Received: 30 July 2012 / Accepted: 16 November 2012 / Published online: 12 December 2012 Ó Springer Science+Business Media New York 2012 Abstract In this paper we present an exact analytical expression to calculate the spectral regrowth at the output of a nonlinear power ampliﬁer (PA) using the higher order cumulants and Poisson summation formula. This PA is driven by the ﬁltered digitally modulated signals. To improve the accuracy of the calculations, the cyclosation- arity of the input signal is considered. Moreover, closed- form expressions for the 1-dB compression and saturation points are extracted as a function of the PA model parameters, higher order statistics of the input signal, and the transfer function of the pulse shaping ﬁlter. In addition, an analytical expression for the adjacent channel power (ACP) and a closed-form expression of the ACP ratio are derived. This is followed by investigation of the effect of the PA nonlinearity on the performance of receiver. Sim- ulation studies are carried out to verify the accuracy of the derived expressions. Excellent agreement between the analytical and simulation results is achieved. Keywords Power ampliﬁer nonlinearity  Power spectral density  Adjacent channel interference  Average transmit and receive power  Saturation and 1-dB compression points 1 Introduction A power ampliﬁer (PA) is a vital part of any wireless transmitter where it ampliﬁes the electric radio signal before it can be transmitted through the antenna [1]. The nonlinear behavior of PA could cause to AM/AM (ampli- tude to amplitude) and AM/PM (amplitude to phase) dis- tortion [2]. Circuit linearity and power efﬁciency are two conﬂicting requirements in PA such that the efﬁciency is maximum at the saturation point of the PA, where non- linear effects are the most severe [3]. In addition, because signiﬁcant part of power consumption in communication systems are due to PAs, accurate analysis of their charac- teristics are needed for energy efﬁcient or green commu- nications [4]. Because of the nonlinear behavior of the PA, increasing the transmitter power causes the expansion of the band- width which is called spectral regrowth [5]. The resulting power spectral density (PSD) should comply with the spectral masks imposed by the regulatory bodies [1]. In addition, the adjacent channel power (ACP) must be lim- ited. For example, in cognitive radio networks the inter- ference level at the active primary receiver shouldn’t exceed a certain level which is called interference tem- perature [6]. Adjacent channel power ratio (ACPR), another metric of spectral regrowth which is the ACP divided by the power in the desired channel [7], can be obtained from the PSD. Therefore, having an accurate expression of the PA output PSD is necessary. Moreover, it can help us select a suitable pulse shape and the corre- sponding roll-off factor. Even if the use of linearization is inevitable, the accurate analytical PSD could be useful for identifying the adequate amount of linearization and selection or even designing a suitable method of lineari- zation. Analytical solutions can guide us to ﬁnd the optimal operating conditions of the PA. If the input of the PA can be assumed as a stationary complex Gaussian random process, the PSD of the PA output has been derived in [7–9] for different PA models. M. Majidi  A. Mohammadi (&)  A. Abdipour Microwave/mm-Wave and Wireless Communications Research Lab, Electrical Engineering Department, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran e-mail: abm125@aut.ac.ir 123 Analog Integr Circ Sig Process (2013) 74:425–437 DOI 10.1007/s10470-012-9986-5