In this paper, we investigated the overfitting characteristics of nonlinear equalizers based on an artificial neural network (ANN) and the Volterra series transfer function (VSTF), which were designed to compensate for optical nonlinear waveform distortion in optical fiber communication systems. Linear waveform distortion caused by, e.g., chromatic dispersion (CD) is commonly compensated by linear equalizers using digital signal processing (DSP) in digital coherent receivers. However, mitigation of nonlinear waveform distortion is considered to be one of the next important issues. An ANN-based nonlinear equalizer is one possible candidate for solving this problem. However, the risk of overfitting of ANNs is one obstacle in using the technology in practical applications. We evaluated and compared the overfitting of ANN- and conventional VSTF-based nonlinear equalizers used to compensate for optical nonlinear distortion. The equalizers were trained on repeated random bit sequences (RRBSs), while varying the length of the bit sequences. When the number of hidden-layer units of the ANN was as large as 100 or 1000, the overfitting characteristics were comparable to those of the VSTF. However, when the number of hidden-layer units was 10, which is usually enough to compensate for optical nonlinear distortion, the overfitting was weaker than that of the VSTF. Furthermore, we confirmed that even commonly used finite impulse response (FIR) filters showed overfitting to the RRBS when the length of the RRBS was equal to or shorter than the length of the tapped delay line of the filters. Conversely, when the RRBS used for the training was sufficiently longer than the tapped delay line, the overfitting could be suppressed, even when using an ANN-based nonlinear equalizer with 10 hidden-layer units.

At present, the application of different types of memristors in electronics is being deeply studied. Given the nonlinearity characterizing memristors, a circuit with memristors cannot be treated by classical circuit analysis. In this paper, memristor is equivalent to a nonlinear dynamic system composed of linear dynamic system and nonlinear static system by Volterra series. The nonlinear transfer function of memristor is derived. In the complex frequency domain, the n-order complex frequency response of memristor is established by multiple Laplace transform, and the response of MLC parallel circuit is taken as an example to verify. Theoretical analysis shows that the complex frequency domain analysis method of memristor transforms the problem of solving nonlinear circuit in time domain into n times complex frequency domain analysis of linear circuit, which provides an idea for nonlinear dynamic system analysis.

In the recently developed Flexible Wireless System (FWS), the same platform needs to deal with different wireless systems. This increases nonlinear distortion in its wideband power amplifier (PA) because the PA needs to concurrently amplify multi-band signals. By taking higher harmonics as well as inter- and cross-modulation distortion into consideration, we have developed a method to analytically evaluate the adjacent channel leakage power ratio (ACPR) and error vector magnitude (EVM) on the basis of the PA's nonlinear characteristics. We devise a novel method for modeling the PA amplifying dual-band signals. The method makes it possible to model it merely by performing a one-tone test, making use of the Volterra series expansion and the general Wiener model. We then use the Mehler formula to derive the closed-form expressions of the PA's output power spectral density (PSD), ACPR, and EVM. The derivations are based on the assumption that the transmitted signals are complex Gaussian distributed in orthogonal frequency division multiplexing (OFDM) transmission systems. We validate the method by comparing measurement and simulation results and confirm it can appropriately predict the ACPR and EVM performance of the nonlinear PA output with OFDM inputs. In short, the method enables correct modeling of a wideband PA that amplifies dual-band signals merely by conducting a one-tone test.

The multiple-input multiple-output (MIMO) performance of the modulated scattering antenna array (MSAA) is analyzed numerically for the first time in indoor environment based on an approach to hybridization of the Volterra series method and method of moments (MoM) in this letter. Mutual coupling effect between the Modulated scattering element (MSE) and the normal antenna element is also considered in this analysis. It is found that MIMO performance of the MSAA is improved with reducing the array spacing of the MSAA in 4 different indoor receiving areas. At the same time, the simulated results of the MSAA are compared with those of the dipole antenna array at the same condition.

In this paper, we investigate a coded solution to compensate for the nonlinear distortion of TDMA satellite waveforms. Based on a Volterra-type channel model and the turbo principle, we present a turbo-like system that includes a simple rate-1 encoder at the transmit side in addition to a conventional channel encoder; the receive side iteratively equalizes the nonlinear channel effect and decodes the received symbols. Some other design alternatives are also explored and computer simulated performance is presented. Numerical results show that significant improvement over conventional approaches can be achieved by the proposed turbo system.

A new method of cancellation of IM3 using current feedback has been proposed for a multi-stage RFIC amplifier. In order to cancel the IM3 present in an output signal of the amplifier, the IIP3 level and IM3 phase of the amplifier are adjusted by means of feedback circuit techniques, so that the target specification is satisfied. By estimating the IIP3 level and IM3 phase variations for two states in situations with and without feedback possessing linear factors, the parameters of a feedback circuit can be calculated. To confirm the validity of the method, we have investigated two approaches; one including an analytical approach to designing a two-stage feedback amplifier, achieving an IIP3 level improvement of 14.8 dB. The other method involves the fabrication of single-stage amplifiers with and without feedback, operating at 850 MHz, both of which were designed as an integrated circuit using a 0.18 µm SiGe BiCMOS process. The fabricated IC's were tested using a load-pull measurement system, and a good agreement between the estimated and measured IIP3 level and IM3 phase variations has been achieved. Further studies show that the error in these variations, as estimated by the method, has been found to be less than 1.5 dB and 15 degrees, respectively, when the load admittance at 1701 MHz was greater than 1/50 S.

Distortion analysis of nonlinear circuits is very important for designing analog integrated circuits and communication systems. In this letter, we propose an efficient frequency-domain approach for calculating frequency response curves, which is based on HB (harmonic balance) method combining with ABMs (Analog Behavior Models) of Spice. Firstly, nonlinear devices such as bipolar transistors and MOSFETs are transformed into the HB device modules executing the Fourier transformations. Using these modules, the determining equation of the HB method is formed by the equivalent sine-cosine circuit in the schematic form or net-list. It consists of the coupled resistive circuits, so that it can be efficiently solved by the DC analysis of Spice. In our algorithm, we need not to derive any troublesome circuit equations, and any kinds of the transformations.

A simple method has been proposed for the measurement of the output power and phase characteristics of the 3rd-order inter-modulation distortion (IM3) components appearing in multistage power amplifiers. By adopting a unique definition of the phase for the IM3 components that is independent of the delay time caused by transmission lines and other instrument devices, it is possible to measure the phase, merely by using a vector signal analyzer. It is demonstrated that an accurate estimation of the IM3 characteristics of two-stage cascaded power amplifiers for cellular radio handheld terminals can be made by using the IM3 characteristics of the 1st and 2nd-stage amplifiers as measured by the proposed method. The results indicate that it is possible to reduce the dissipation power by 18% at 28 dBm RF output power with respect to conventional measurement methods. Further studies show that the error in the resultant vector of the estimated IM3 is less than 1 dB, when the asymmetry characteristics of the IM3 sidebands in the 2nd-stage amplifier are less than 7.3%.

In this paper a second order Volterra series model of an operational amplifier (opamp) circuit is presented. Such a model is suitable to the investigation of the rectification and demodulation effects of radio frequency (RF) interference superimposed on the nominal input signals and on the power supply voltage of an opamp. On the basis of the new model, some design criteria to improve the immunity of opamps to RF interference are proposed. Model predictions are verified by comparison with experimental test results.

A nonlinear Volterra-series analysis of multiple ion-implanted GaAs FETs is given that relates carrier profile parameters of ion-implantation to nonlinear rf characteristics of a FET. Expressions for nonlinear coefficients of transconductance are derived from drain current-voltage characteristics of a multiple ion-implanted FET. Nonlinear transfer functions (NLTFs) are then obtained using Volterra series approach. Using these NLTFs third-order intermodulation distortion and power gain are explicitly given. A good agreement has been found between the calculation and the measurement for a medium power GaAs FET with a total gate width of 800 µm operated at 10-dB back off, verifying the usefulness of the present analysis.

For finite Volterra series systems, this paper investigates the stability of the exact model matching (EMM) control we have already presented. First, in order to analyze the stability of the EMM system, we present modified small gain theorems depending on the magnitude of the external input (s) in the cases of one input and two inputs. Next, with the help of the theorem for feedback systems with two inputs, we clarify the condition under which the control system is stable for the reference input magnitude within a certain range, and is also robust for small disturbances. The modified small gain theorems are effective for the stability analysis of the nonlinear feedback control systems which do not have affine finite gain.

Optical Feedering between Base Stations and Control Station is an effective technique for future microcellular mobile communication systems. The use of Laser Diode (LD) in such a system leads to the generation of intermodulation products, which consequently affect a system performance and ultimately restrain the maximum number of users that the system can serve. The problem becomes further intensified in case of CDMA system which is a candidate for future cellular mobile and personal communication systems. In this paper LD's Nonlinearity compensation technique for Direct Sequence spread spectrum CDMA signals in optical communication system is presented. This technique involves the implementation of a nonlinear block herein after called Post Nonlinearity Recovery Block (PNRB). This block is designed to exhibit the characteristics inverse to those of LD. The block is designed theoretically by deriving the complete expressions for Transfer functions. Some useful results of theoretical investigation of a proposed scheme have been presented, which form the basis for the experimental test system. The work is novel because, (i) Compensation analysis has been carried out for DS-CDMA signals for the first time, and (ii) Compensation has been proposed on the control station instead of base station, which is different from the conventional techniques and offers several additional advantages. Performance of the system with and without PNRB is evaluated by Intermodulation Distortion (IMD) and SNR Analysis. The results show that LDs' nonlinearity distortion level can be compensated to a remarkable extent.

A novel total harmonic distortion (THD) measuring technique is proposed. A modified Volterra series using harmonics in place of powers of the sinusoidal input is used to identify the nonlinear models of the source and the device under test (DUT). The least-mean square (LMS) adaptive algorithm is applied for identification. While maintaining comparable speed and accuracy this technique provides a more flexible test procedure than conventional methods, in terms of the frequency resolution, the number of samples, and the sampling rate. It outperforms conventional methods when there is a bin energy leakage, which occurs in a non-coherent system. In addition, it is real-time computing while other conventional methods post process blocks of data. Simulation results collaborate the analytical results.