This paper describes a time-domain expression based on the physical model of power amplifiers where electric memory effect is considered to be caused by even-order nonlinearity and bias impedance. It is demonstrated that the time-domain expression is consistent with the general memory polynomial reported by D.R. Morgan et al. To confirm validity of the physical model, a simple method is proposed to measure amplitude and phase of IMD by two tone test: the phase is extracted from measured small signal S-parameters of the amplifier under test. The method is applied to a GaN FET amplifier under condition that memory effect is enhanced by applying inductive cable for DC supply. Frequency dependent IMD is fitted by a parallel connection of L, C, and R: it has been confirmed that the frequency dependence of IMD is given by the bias impedance at even order harmonics of envelope frequency. The frequency dependence assures the validity of the physical model as well as the time-domain expression.

This paper describes a method to design a predistorter (PD) for a GaN-FET power amplifier (PA) by using nonlinear parameters extracted from measured IMD which has asymmetrical peaks peculiar to a memory effect with a second-order lag. While, computationally efficient equations have been reported by C. Rey et al. for the memory effect with a first-order lag. Their equations are extended to be applicable to the memory effect with the second-order lag. The extension provides a recursive algorithm for cancellation signals of the PD each of which updating is made by using signals in only two sampling points. The algorithm is equivalent to a memory depth of two in computational efficiency. The required times for multiplications and additions are counted for the updating of all the cancellation signals and it is confirmed that the algorithm reduces computational intensity lower than half of a memory polynomial in recent papers. A computer simulation has clarified that the PD improves the adjacent channel leakage power ratio (ACLR) of OFDM signals with several hundred subcarriers corresponding to 4G mobile radio communications. It has been confirmed that a fifth-order PD is effective up to a higher power level close to 1 dB compression. The improvement of error vector magnitude (EVM) by the PD is also simulated for OFDM signals of which the subcarrier channels are modulated by 16 QAM.

In recent years, digital predistortion linearizers have been used in power amplifiers for mobile communications because they are simpler and provide higher power efficiency than conventional feedforward systems. However, in systems that cover a wider frequency band, it is impossible to disregard the frequency characteristics of their various parameters since the degradation that can result causes a decline in output power efficiency which is the most important property of a power amplifier. To date, no detailed studies have been carried out on predistortion compensation systems. Thus, we focused our research on these systems and in this paper we report the simulation and experimental results we obtained for clarifying these effects. In our experiments, we used a W-CDMA power amplifier to determine how much the distortion compensation effect is degraded by the frequency characteristics of analog RF circuits. The results of experiments to determine the relationship between the ACLR (Adjacent Channel Leakage power Ratio) and power efficiency are also reported.

To reduce laborious tasks of the phase determination, our previous paper has proposed a method to derive phase reference for two-tone intermodulation distortion (IMD) measurement of a power amplifier (PA) by using small-signal S-parameters. Since the method is applicable to low output power level, this paper proposes an iterative process to extend the applicable power level up to 1-dB compression. The iterative process is based on extraction of linear response: the principle of the extraction is described theoretically by using an accurate model of the PA with memory effect. Measurement of two-tone IMD is made for a GaN FET PA. Validity of the iteration is confirmed as convergence of the extracted linear response to that given by the product of S21 and input signal. Measured results also show validity of the physical model of the memory effect provided by Vuolevi et al. because beat frequency dependences of IMD's are accurately fitted by bias impedances at even order harmonics of envelope frequency. The PA is characterized by using measured results and the third and fifth order inverses of the PA are designed. Improvement of IMD is theoretically confirmed by using the inverses as predistorters.

This paper describes the details of the iteration process used to determine the transfer functions of linear time-invariant (LTI) circuits causing the memory effect of power amplifier (PA). An outline of the method is reported in our work presented at ICCS2012. The accuracy of the method is improved by using cross-correlation spectra at three signal levels, and its validity is confirmed by a computer simulation. The method can be applied to online updating of PAs operating in mobile communication systems. The updating is realized separately from the fast varying nonlinear coefficients. The possibility of updating with a short interval is indirectly shown for the nonlinear coefficients using a procedure similar to that of memoryless PAs. For PAs characterized by the method, this paper also describes the inverses that cancel the nonlinear distortion with minimum complexity. The validity of the inverse is confirmed by a computer simulation on the power spectrum of the PA for orthogonal frequency-division multiplexing (OFDM) signals with 500 subcarriers. The simulated spectra show that the fifth order or higher inverses are effective in keeping adjacent channel leakage power ratio (ACLR) lower than -60dB at the practical signal level. Improvements in the error vector magnitude (EVM) due to the inverse were also confirmed by reductions of gain and phase variations under varying envelope conditions.