High-accuracy wideband signal transmission is essential for 5G and Beyond wireless communication systems. Memory nonlinearity in transmitters is a serious issue for the goal, because it deteriorates the quality of signal and lowers the system performance. This paper studies a post-reception nonlinear compensation (PRC) schemes consisting of frequency domain equalizers (FDEs) and a blind nonlinear compensator (BNLC). A frequency-domain memory nonlinearity modeling approach is employed, and several PRC configurations with FDEs and BNLC are evaluated through computer simulations. It is concluded that the proposed PRC schemes can effectively compensate memory nonlinearity in wideband transmitters via frequency-selective propagation channel. By implementing the PRC in a base station, uplink performance will be enhanced without any additional cost and power consumption in user terminals.

Broadband amplifiers have been used in modern wireless communication systems. However, the accompanying disadvantage is that there is more nonlinear interference in the available operating frequency band. In addition to the in-band intermodulation distortion which affecting adjacent frequency bands the most important is harmonic distortion. In this letter we present a robust and low complex digital harmonic canceling model called cross-disturbing harmonic (CDH) model for broadband power amplifiers (PAs). The approach introducing cross terms is used to enhance the robustness of the model, thereby significantly increase the stability of the system. The CDH model still has excellent performance when actively reducing the number of coefficients. Comparisons are conducted between the CDH model and the other state-of-the-art model called memory polynomial harmonic (MPM) model. Experimental results show that the CDH model can achieve comparable performance as the MPM model but with much fewer (43%) coefficients.

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.

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.

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.

For the modeling of power amplifiers (PAs) using sub-Nyquist-rate sampling (sub-sampling), a quadratic down-converting architecture with a parallel-cascade method is suggested. Its performance was analyzed regarding the sampling rate below the input Nyquist rate. As a result, the model from the sub-sampling below the input Nyquist rate characterized long-term memory effects whereas the memoryless model could not. The measurement results from RF PAs with the mWiMAX signal verified the modeling performance of this architecture. Also, for the modeling of memoryless PAs, it was shown that this sub-sampled model is still effective regardless of the sampling rate.

This paper discusses an efficient discrete model for nonlinear RF power amplifier (PA) with long-term memory effects and analyzes its error. The procedure of converting RF signals and systems into a discrete domain is explained for a discrete baseband memory polynomial model. Unlike a previous simple memory polynomial model, the proposed discrete model has two different sampling frequencies: one for nonlinear system with long-term memory effects and one for input signal. A method to choose an optimal sampling frequency for the system and a discrete memory depth is proposed to minimize the sensitivity of the system for perturbation of the measured data. A two-dimensional sensitivity function which is a product of relative residual and matrix condition number is defined for least square problem of the proposed model. Examples with a wideband WiBro 3FA signal and a WCDMA 4FA signal for nonlinear transmitters are presented to describe the overall procedure and effectiveness of the proposed scheme.

This paper presents a digital predistorter with a wideband memory effect compensator for a Doherty power amplifier (PA). A simple memory-predistortion model, which consists of a look-up-table (LUT) and an adaptive filter equalizing memory effects, and a new memory effect estimation algorithm using a direct-learning architecture are proposed. The proposed estimation algorithm has an advantage that a transfer function of a feedback circuit does not affect the learning process. The predistorter is implemented in a field programmable gate array (FPGA) and a digital signal processor (DSP). The transmitter has achieved distortion level of -50.8 dBr at signal bandwidth away from the carrier, and PA module efficiency of 24% with output power of 43 dBm at 2595 MHz under a 20 MHz-bandwidth orthogonal frequency division multiplexing (OFDM) signal using laterally diffused metal oxide semiconductor (LDMOS) FETs.

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.

Orthogonal frequency division multiplexing (OFDM) signals have high peak-to-average power ratio (PAPR) and cause large nonlinear distortions in power amplifiers (PAs). Memory effects in PAs also become no longer ignorable for the wide bandwidth of OFDM signals. Digital baseband predistorter is a highly efficient technique to compensate the nonlinear distortions. But it usually has many parameters and takes long time to converge. This paper presents a novel predistorter design using a set of orthogonal polynomials to increase the convergence speed and the compensation quality. Because OFDM signals are approximately complex Gaussian distributed, the complex Hermite polynomials which have a closed-form expression can be used as a set of orthogonal polynomials for OFDM signals. A differential envelope model is adopted in the predistorter design to compensate nonlinear PAs with memory effects. This model is superior to other predistorter models in parameter number to calculate. We inspect the proposed predistorter performance by using an OFDM signal referred to the IEEE 802.11a WLAN standard. Simulation results show that the proposed predistorter is efficient in compensating memory PAs. It is also demonstrated that the proposal acquires a faster convergence speed and a better compensation effect than conventional predistorters.

An inter-modulation distortion (IMD) compensation method for thermal memory effect using a multistage RC-ladder circuit has been proposed. The IMD caused by the thermal memory effect on an InGaP/GaAs HBT amplifier was compensated for by inserting a multistage RC-ladder circuit in the base bias circuit of the amplifier. Since heat flux owing to self-heating in the transistor can be approximated with a multistage thermal RC-ladder circuit, the canceling of IMD by an additional electrical memory effect generated from the RC-ladder circuit is predicted. The memory effects cause asymmetrical characteristics between upper and lower IMD. The IMD caused by the memory effects is expressed as a vector sum of each origin. By adjusting an electrical reactance characteristic for sub-harmonics affected by the thermal memory effect in the amplifier circuit, the asymmetric characteristic is symmetrized. The parameters of the RC-ladder circuit were estimated so that the adjusted electrical reactance characteristic is reproduced in simulation. A fabricated InGaP/GaAs HBT amplifier with the thermal memory effect compensation circuit exhibited a symmetrized and suppressed IMD characteristics.

Nonlinear distortions in power amplifiers (PAs) generate spectral regrowth at the output, which causes interference to adjacent channels and errors in digitally modulated signals. This paper presents a novel method to evaluate adjacent channel leakage power ratio (ACPR) and error vector magnitude (EVM) from the amplitude-to-amplitude (AM/AM) and amplitude-to-phase (AM/PM) characteristics. The transmitted signal is considered to be complex Gaussian distributed in orthogonal frequency-division multiplexing (OFDM) systems. We use the Mehler formula to derive closed-form expressions of the PAs output power spectral density (PSD), ACPR and EVM for memoryless PA and memory PA respectively. We inspect the derived relationships using an OFDM signal in the IEEE 802.11a WLAN standard. Simulation results show that the proposed method is appropriate to predict the ACPR and EVM values of the nonlinear PA output in OFDM systems, when the AM/AM and AM/PM characteristics are known.

This paper presents analysis and identification method of Wiener-Hammerstein system to characterize a nonlinear RF transmitter in fundamental frequency zone. A two-tone signal is used to analyze and identify a Wiener-Hammerstein model. A RF signal is converted to baseband-equivalent complex signal, and Wiener-Hammerstein model is considered to have a baseband equivalent complex polynomial and linear filters. For a two-tone input signal, closed form descriptions of the output signal in the time domain and frequency domain are developed using a newly suggested nonlinearly modulated two-tone phasors (NMTP). The relationship between frequency terms of input and output signals in RF transmitters are represented with linear matrix-vector equation based on NMTP analysis. An advantage of the proposed method is its simplicity using closed form analysis and linear approximation. In addition, we can model a wideband system with relatively narrowband measurements by sweeping two-tone signal. The prediction of spectral regrowth and the predistortion performance for WiBro 1FA signal demonstrate the validity of the proposed approach in identifying the nonlinear RF transmitters.

Distortion characteristics caused by the thermal memory effect in power amplifiers were accurately predicted using a multi-stage thermal RC-ladder network derived by simplifying the heat diffusion equation. Assuming a steep gradient of heat diffusion near an intrinsic transistor region in a semiconductor substrate, the steady state temperature, as well as the transient thermal response at the transistor region, was estimated. The thermal resistances and thermal capacitances were adjusted to fit a temperature distribution characteristic and a step response characteristic of temperature in the substrate. These thermal characteristics were calculated by thermal FDTD simulation. For an InGaP/GaAs HBT, a step response characteristic for a square-wave voltage signal input was simulated using a large-signal model of the HBT connecting the multi-stage thermal RC-ladder network. The result was verified experimentally. Additionally, for an RF-amplifier using the HBT, the 3rd-order intermodulation distortion caused by the thermal memory effect was simulated and this result was also verified experimentally. From these verifications, a multi-stage thermal RC-ladder network can be used to accurately design super linear microwave power amplifiers and linearizers.

This paper describes a high power GaN-FET amplifier which is developed for wideband code division multiple access (W-CDMA) base stations. We design a bias network which is symmetrically arranged to the RF line (two way bias network) in order to reduce impedance at a baseband frequency of the multi-carrier W-CDMA signal. As a result, the amplifier with the two way bias network successfully suppressed memory effects. Therefore, the application of a DPD technique to the GaN-FET amplifier with the two way bias network demonstrates almost 20 dB linearity improvement in IM3 and considerable improvement in higher order IMD, resulting in low IMD of less than -50 dBc at the highest ever reported W-CDMA average output power of 76 W.

In this paper, we propose a transmitter structure in digital QAM systems where pre-compensator compensates for nonlinearity with "memory effects" at the output amplifier. The nonlinearity is modeled as a linear time-invariant filter cascaded by memoryless nonlinearity (Wiener model), whereas the pre-compensator comprises an FIR-type adaptive filter that follows a memoryless predistorter based on a series expansion with orthogonal polynomials for digital QAM data. The predistorter and the adaptive filter of the pre-compensator are stochastically and directly adapted using the error signal. The theoretically optimum parameters of the predistorter are approximately solved whence the steady-state mean square compensation error is calculated. Simulations show that the proposed pre-compensator can be adapted to achieve a sufficiently small compensation error, restoring the original QAM constellation through linearization and equalization of the nonlinearity with memory effects.

Memory type polymer dispersed liquid crystal (PDLC) can be applied to a thermal addressing display device cell. Making use of its easy fabrication of large area display using flexible film substrate, the PDLC film can be used as reusable paper for direct-view mode display. In this study, memory type PDLC cells are prepared with an aluminum reflector deposited onto one side of the substrate and the reflection property in the PDLC cell with the reflector is clarified and compared to that without the reflector in the off-, on- and memory-states. The increase of contrast ratio and the decrease of driving voltage can be concurrently realized by decreasing the cell thickness by attaching the reflector. In addition, the reflected light in the off-state is bright and colorless due to the reflector, as compared with the weak, bluish reflected light in the cell without the reflector. Reflected light in the on-state and the memory-state are tinged with blue.

The transient behavior in the fractal admittance acting as a non-integer-rank differential/integral operator, Y(s) ∝ sa with -1a1 and a0, is examined from the point of view of memory effects by employing the distributed-relaxation-time model. The internal state of the diode is found to be represented by the current spectrum i(λ, t) with respect to the carrier relaxation rate λ, leading to a general formulation of the long-time-tail memory behavior characteristic of the operator. One-to-one corrsepondence is found among the input voltage in the past ν(-t), the short-circuit current isc(t) and the initial current spectrum i(λ, 0) within the framework of the Laplace-type integral transformation and its inverse, assuring that each response retains in principle the entire information on the corresponding input, such as the functional form, the magnitude, the onset time, and so forth. The current and voltage responses are exemplified for various single-pulse voltage inputs. The responses to the pulse-train inputs corresponding to different ASCII codes are found to be properly discriminated between one another, showing the potentials of the present memory effects.