A memory polynomial based adaptive digital pre-distorter for optical communication transmitters

We developed ditherless auto bias control for optical IQ modulators with high baud rates and higher-order modulation formats. With 64 quadrature amplitude modulation formats at 65 Gbaud, a <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$Q$</tex>-factor of 7.8 dB was obtained.

Adaptive digital baseband predistortion is a highly effective and simple linearization technique which compensates for the nonlinear distortion of PAs. This paper presents an improved adaptive technique using discrete Newton's method efficiently applied to digital baseband lookup table (LUT) predisortion. We simplify and convert the hardship of adaptive updating LUT to the roots finding problem for a system of two element real equations on mathematics. And we deduce the improved adaptive iterative formula used for updating LUT based on discrete Newton's method. The iterative formula of the proposed method is in real number field, but secant method previously published is in complex number field. So the proposed method reduces the number of real multiplications and is implemented with ease by hardware. Furthermore, computer simulation results verify the LUT baseband predistortion using discrete Newton's method could rectify nonlinear distortion and improve system performance. Also, the simulation results reveal the proposed method reaches to the stable statement in fewer iteration times than secant method.

A new polynomial predistortion technique for linearizing nonlinear power amplifier is introduced. The proposed predistorter is based on direct learning, whereas most other techniques are based on the indirect learning architecture. The resulting structure of the proposed method is simpler than the existing ones. Computer simulation shows that the proposed method is robust to the initial conditions and attains comparable performance to other methods based on the indirect learning architecture under normal conditions.

This paper presents a fully adaptive digital pre-distortion using a multi-dimensional nonlinear model that is implemented in hardware without the use of any digital multipliers and operates at very wide instantaneous bandwidths (>1 GHz instantaneous bandwidth). This multi-dimensional compensator effectively mitigates linear and nonlinear distortion in RF power amplifiers by modeling the state of the device by tracking multiple functions of the input, which can include: the present input signal value; delayed values of the input (for memory effects); derivatives of the input (including higher order derivatives); integration of the input (including higher order integrals); signal statistics (e.g., mean, variance); current power level (RMS or peak); and polynomial functions of the input. The processing is implemented with memory instead of digital multipliers for low-power applications. It is calibrated using simple arithmetic operations that can be completed with low processing requirements and very quickly to track parameters that rapidly change over time, temperature, and power level such as in frequency-hopping systems. The approach has been demonstrated in realtime hardware providing 15–30 dB improvement in distortion.

Low power adaptive pre-distortion (APD) techniques are applied to nonlinear RF power amplifiers for mobile devices. An APD system is demonstrated which reduces spectral regrowth products by 10-20dB and increases modulation accuracy by 2-6X. The use of APD allows a reduction in 3G PA supply current by 2X and provides immunity to load mismatches as high as 8:1.

This paper presents adaptive phase-only memory digital pre-distortion (DPD) and gain/phase/delay imbalance correction techniques for outphasing power amplifiers (PAs). Least squares adaptation is used for the phase-only DPD and imbalance correction techniques. The performance of these techniques is verified by co-simulations and measurements of an outphasing PA implemented with two identical class-F PAs and a Chireix combiner. The Chireix combiner with compensating stubs added to achieve high efficiency introduces nonlinearity. The proposed adaptive phase-only memory DPD corrects for the nonlinearity due to the Chireix combiner. The proposed gain/phase/delay imbalance correction technique achieves total lower/upper adjacent channel power ratio (ACPR) improvements of 43.8/37.6 dB for 5-MHz and 46.2/38.3 dB for 10-MHz long-term-evolution signals in measurements. The fractional-sample delay imbalance correction reduces distortion at low input amplitudes and demonstrates on the order of a 10-dB ACPR improvement compared to full-sample delay imbalance correction.

Although fruitful studies have been conducted on carrier frequency offset (CFO) estimations in linear coherent optical fiber communication systems, there are few studies on CFO estimations and recoveries in the systems based on the nonlinear Fourier transform (NFT). Although the CFO is originated from the linear frequency domain, it definitely has effects on nonlinear spectra, including the shift of the nonlinear frequency and the phase rotations of the scattering data, which are similar to its effects on linear spectra. This work indicates that it is feasible to estimate frequency offset (FO) by capturing symbol variations in the nonlinear frequency domain (NFD) rather than in the linear frequency domain; the latter was usually exploited in the literature. Based on a thorough investigation of the FO induced behavior that appears in a nonlinear frequency division multiplexing (NFDM) system, we proposed a nonlinear frequency domain estimation method aided by training symbols (TS) using an angle search algorithm after NFT operations at the receiver. The discussions in this paper prove that the proposed method is generally applicable to the NFDM systems regardless of whether using single or multiple eigenvalues. A performance comparison between the NFD method and the conventional method in the linear frequency domain is performed with different modulation formats for both single and multiple eigenvalue NFDM transmission systems. The analysis results show that the proposed method holds the better stability and estimation accuracy in contrast with the linear domain estimation method. The TS overhead can also be deduced dramatically, which implies better transmission efficiency. Therefore, the NFD method is more powerful for eigenvalue NFDM transmission systems, especially for the scenarios where high order modulation formats and multiple eigenvalues are utilized.

In this paper, a method for improving feedback signal distortion over-compensation of a digital pre-distortion(DPD) system is presented. The method comprises the following steps: acquiring a distortion compensation characteristic parameter of an input signal in a forward channel of the digital pre-distortion system to form a forward channel distortion compensation lookup table(LUT), and compensating the input signal before digit-analog converter (DAC); acquiring an ideal compensation characteristic parameter of the input signal in a small closed loop without power amplification to form a feedback signal distortion compensation LUT for compensating in a feedback signal; and acquiring an ideal compensation characteristic parameter of the input signal in a big closed loop with power amplification to form a digital pre-distortion LUT dealing with power amplification non-linear distortion for compensating in the forward signal. Through the method, the over-compensation characteristic of the feedback signal can be further effectively counter balanced based on compensation to forward channel distortion to achieve the aim of improving the performance of the digital pre-distortion system.

High-symbol-rate coherentoptical transceivers suffer more from the critical responses of transceiver components at high frequency, especially when applying a higher order modulation format. We recently proposed a neural network (NN)-based digital pre-distortion (DPD) technique trained to mitigate the transceiver response of a 128 GBaud optical coherent transmission system. In this paper, we further detail this work and assess the NN-based DPD by training it using either a direct learning architecture (DLA) or an indirect learning architecture (ILA), and compare performance against a Volterra series-based ILA DPD and a linear DPD. Furthermore, we deliberately increase the transmitter nonlinearity and compare the performance of the three DPDs schemes. The proposed NN-based DPD trained using DLA performs the best among the three contenders. In comparison to a linear DPD, it provides more than 1 dB signal-to-noise ratio (SNR) gains at the output of a conventional coherent receiver DSP for uniform 64-quadrature amplitude modulation (QAM) and PCS-256-QAM signals. Finally, the NN-based DPD enables achieving a record 1.61 Tb/s net rate transmission on a single channel after 80 km of standard single mode fiber (SSMF).

An adaptive digital predistortion (PD) technique is proposed for linearization of power amplifiers (PAs) in multiple-input multiple-output (MIMO) transmitters. Instead of constructing a separate feedback path at each PA, we propose a PD technique based on a combined feedback, which adds all the PAs' outputs to form a single feedback. We develop an algorithm for finding the multiple PA characteristics jointly from the combined feedback. The PD parameters are calculated from the identified PA characteristics. Although the proposed method requires more computations for PA identification than the conventional method, its hardware implementation is much simpler and can overcome the crosstalk problem of a radio frequency (RF) selector, which is necessary for multiple feedback selection. The simulation results show that, despite its simple structure, the linearization performance of the proposed method is almost the same as the separate multiple feedback method.

Publication in the conference proceedings of EUSIPCO, Lausanne, Switzerland, 2008

This paper presents a parallel adaptive predistorter design technique for RF power amplifier linearization, based on the indirect learning architecture. The predistortion is accomplished by inverse modeling of the AM/AM response and modeling of the AM/PM response of a high power amplifier. In order to implement the predistortion adaptively, the coefficient vectors for the amplitude inverse and for the phase modeling are updated in parallel, from the amplitude response and phase response of the amplifier output, respectively. The performance of the proposed parallel adaptive predistortion linearizer (PAP-LZR) is illustrated by linearizing traveling wave tube (TWT) nonlinear amplitude and phase characteristics, suppression of intermodulation products, and adapting to a change in TWT parameters.

This paper considers the problem of predistortion of nonlinear systems which are described using IIR Hammerstein models by connecting two adaptive IIR Wiener systems. The first adaptive Wiener system is a training filter connected in parallel with the nonlinear system and its coefficients are estimated recursively using the Recursive Prediction Error Method (RPEM) algorithm. The second adaptive Wiener system is a predistorter connected tandemly with the nonlinear system and its coefficients are a copy from the training Wiener system. Simulation results show that the suggested RPEM algorithm effectively reduces spectral regrowth due to nonlinear distortion.

In-phase and quadrature (IQ) imbalances in optical transceiver, such as amplitude imbalance, phase imbalance, and IQ skew, can cause serious system performance degradation, especially when high order modulation formats are used. In this work, we present a method to isolate and separately monitor these various impairments from received signals by coherent digital signal processing (DSP). Receiver amplitude and phase imbalances could be compensated and monitored by Gram-Schmidt orthogonalization procedure (GSOP) and receiver skew could be compensated and monitored by a 4 x 4 or 4 x 2 multiple-input and multiple-output (MIMO) equalizer. Transmitter imperfections compensation and monitoring take place behind the residual frequency offset compensation and carrier phase recovery by a 4 x 4 MIMO equalizer based on minimal mean square error (MMSE) criterion. By these methods, we analyze and investigate the interaction of transceiver's impairments impact on each monitor numerically. After that, we conduct an experiment to verify the feasibility of the proposed method. All of these results show that each monitor could operate very robust even when multiple co-exist.

An efficient trellis-based phase noise mitigation algorithm is proposed to highly improve the performance of coherent transmission systems, especially in high order modulation formats. The proposed method targets the coherent optical systems where the performance is limited by various sources of phase noise including laser line-width, fiber non-linearity, and phase noise induced by phase-locked loop. Considering hardware limitations of ultra-high data rate processing in optical systems, a hardware-efficient parallelized and pipelined architecture is utilized. Experimental results in 200 Gb/s DP-16QAM co-propagated with 10-G channels demonstrate significant performance improvement over other existing methods.