Digital predistorter design using B-Spline neural network and inverse of De Boor algorithm

This contribution introduces a new digital predistorter to compensate serious distortions caused by memory high power amplifiers (HPAs) which exhibit output saturation characteristics. The proposed design is based on direct learning using a data-driven B-spline Wiener system modeling approach. The nonlinear HPA with memory is first identified based on the B-spline neural network model using the Gauss-Newton algorithm, which incorporates the efficient De Boor algorithm with both B-spline curve and first derivative recursions. The estimated Wiener HPA model is then used to design the Hammerstein predistorter. In particular, the inverse of the amplitude distortion of the HPA's static nonlinearity can be calculated effectively using the Newton-Raphson formula based on the inverse of De Boor algorithm. A major advantage of this approach is that both the Wiener HPA identification and the Hammerstein predistorter inverse can be achieved very efficiently and accurately. Simulation results obtained are presented to demonstrate the effectiveness of this novel digital predistorter design.

Single-carrier frequency domain equalisation for hammerstein communication systems using complex-valued neural networks

Single-carrier (SC) block transmission with frequency-domain equalisation (FDE) offers a viable transmission technology for combating the adverse effects of long dispersive channels encountered in high-rate broadband wireless communication systems. However, for high bandwidthefficiency and high power-efficiency systems, the channel can generally be modelled by the Hammerstein system that includes the nonlinear distortion effects of the high power amplifier (HPA) at transmitter. For such nonlinear Hammerstein channels, the standard SC-FDE scheme no longer works. This paper advocates a complex-valued (CV) B-spline neural network based nonlinear SC-FDE scheme for Hammerstein channels. Specifically, We model the nonlinear HPA, which represents the CV static nonlinearity of the Hammerstein channel, by a CV B-spline neural network, and we develop two efficient alternating least squares schemes for estimating the parameters of the Hammerstein channel, including both the channel impulse response coefficients and the parameters of the CV B-spline model. We also use another CV B-spline neural network to model the inversion of the nonlinear HPA, and the parameters of this inverting B-spline model can easily be estimated using the standard least squares algorithm based on the pseudo training data obtained as a natural byproduct of the Hammerstein channel identification. Equalisation of the SC Hammerstein channel can then be accomplished by the usual one-tap linear equalisation in frequency domain as well as the inverse B-spline neural network model obtained in time domain. Extensive simulation results are included to demonstrate the effectiveness of our nonlinear SC-FDE scheme for Hammerstein channels.

Nonlinear equalization of Hammerstein OFDM systems

A practical orthogonal frequency-division multiplexing (OFDM) system can generally be modelled by the Hammerstein system that includes the nonlinear distortion effects of the high power amplifier (HPA) at transmitter. In this contribution, we advocate a novel nonlinear equalization scheme for OFDM Hammerstein systems. We model the nonlinear HPA, which represents the static nonlinearity of the OFDM Hammerstein channel, by a B-spline neural network, and we develop a highly effective alternating least squares algorithm for estimating the parameters of the OFDM Hammerstein channel, including channel impulse response coefficients and the parameters of the B-spline model. Moreover, we also use another B-spline neural network to model the inversion of the HPA’s nonlinearity, and the parameters of this inverting B-spline model can easily be estimated using the standard least squares algorithm based on the pseudo training data obtained as a byproduct of the Hammerstein channel identification. Equalization of the OFDM Hammerstein channel can then be accomplished by the usual one-tap linear equalization as well as the inverse B-spline neural network model obtained. The effectiveness of our nonlinear equalization scheme for OFDM Hammerstein channels is demonstrated by simulation results.

B-spline neural network based single-carrier frequency domain equalisation for Hammerstein channels

A practical single-carrier (SC) block transmission with frequency domain equalisation (FDE) system can generally be modelled by the Hammerstein system that includes the nonlinear distortion effects of the high power amplifier (HPA) at transmitter. For such Hammerstein channels, the standard SC-FDE scheme no longer works. We propose a novel Bspline neural network based nonlinear SC-FDE scheme for Hammerstein channels. In particular, we model the nonlinear HPA, which represents the complex-valued static nonlinearity of the Hammerstein channel, by two real-valued B-spline neural networks, one for modelling the nonlinear amplitude response of the HPA and the other for the nonlinear phase response of the HPA. We then develop an efficient alternating least squares algorithm for estimating the parameters of the Hammerstein channel, including the channel impulse response coefficients and the parameters of the two B-spline models. Moreover, we also use another real-valued B-spline neural network to model the inversion of the HPA’s nonlinear amplitude response, and the parameters of this inverting B-spline model can be estimated using the standard least squares algorithm based on the pseudo training data obtained as a byproduct of the Hammerstein channel identification. Equalisation of the SC Hammerstein channel can then be accomplished by the usual one-tap linear equalisation in frequency domain as well as the inverse Bspline neural network model obtained in time domain. The effectiveness of our nonlinear SC-FDE scheme for Hammerstein channels is demonstrated in a simulation study.

On the power amplifier nonlinearity in MIMO transmit beamforming systems

In this paper, single-carrier multiple-input multiple-output (MIMO) transmit beamforming (TB) systems in the presence of high-power amplifier (HPA) nonlinearity are investigated. Specifically, due to the suboptimality of the conventional maximal ratio transmission/maximal ratio combining (MRT/MRC) under HPA nonlinearity, we propose the optimal TB scheme with the optimal beamforming weight vector and combining vector, for MIMO systems with nonlinear HPAs. Moreover, an alternative suboptimal but much simpler TB scheme, namely, quantized equal gain transmission (QEGT), is proposed. The latter profits from the property that the elements of the beamforming weight vector have the same constant modulus. The performance of the proposed optimal TB scheme and QEGT/MRC technique in the presence of the HPA nonlinearity is evaluated in terms of the average symbol error probability and mutual information with the Gaussian input, considering the transmission over uncorrelated quasi-static frequency-flat Rayleigh fading channels. Numerical results are provided and show the effects on the performance of several system parameters, namely, the HPA parameters, numbers of antennas, quadrature amplitude modulation modulation order, number of pilot symbols, and cardinality of the beamforming weight vector codebook for QEGT.

Optimal beamforming in MIMO systems with HPA nonlinearity

In this paper, multiple-input multiple-output (MIMO) transmit beamforming (TB) systems under the consideration of nonlinear high-power amplifiers (HPAs) are investigated. The optimal beamforming scheme, with the optimal beamforming weight vector and combining vector, is proposed for MIMO systems with HPA nonlinearity. The performance of the proposed MIMO beamforming scheme in the presence of HPA nonlinearity is evaluated in terms of average symbol error probability (SEP), outage probability and system capacity, considering transmission over uncorrelated quasi-static frequency-flat Rayleigh fading channels. Numerical results are provided and show the effects of several system parameters, namely, parameters of nonlinear HPA, numbers of transmit and receive antennas, and modulation order of phase-shift keying (PSK), on performance.

Impact of HPA nonlinearity on MIMO systems with quantized equal gain transmission

In this paper, we investigate the performance of multiple-input multiple-output (MIMO) transmit beamforming (TB) systems in the presence of nonlinear high-power amplifiers (HPAs). Due to the suboptimality of maximal ratio transmission/maximal ratio combining (MRT/MRC) under HPA nonlinearity, quantized equal gain transmission (QEGT) is suggested as a feasible TB scheme. The effect of HPA nonlinearity on the performance of MIMO QEGT/MRC is evaluated in terms of the average symbol error probability (SEP) and system capacity, considering transmission over uncorrelated quasi-static frequency-flat Rayleigh fading channels. Numerical results are provided and show the effects of several system parameters, such as the parameters of nonlinear HPA, cardinality of the beamforming weight vector codebook, and modulation order of quadrature amplitude modulation (QAM), on performance.

Comparing hybrid data assimilation methods on the Lorenz 1963 model with increasing nonlinearity

We systematically compare the performance of ETKF-4DVAR, 4DVAR-BEN and 4DENVAR with respect to two traditional methods (4DVAR and ETKF) and an ensemble transform Kalman smoother (ETKS) on the Lorenz 1963 model. We specifically investigated this performance with increasing nonlinearity and using a quasi-static variational assimilation algorithm as a comparison. Using the analysis root mean square error (RMSE) as a metric, these methods have been compared considering (1) assimilation window length and observation interval size and (2) ensemble size to investigate the influence of hybrid background error covariance matrices and nonlinearity on the performance of the methods. For short assimilation windows with close to linear dynamics, it has been shown that all hybrid methods show an improvement in RMSE compared to the traditional methods. For long assimilation window lengths in which nonlinear dynamics are substantial, the variational framework can have diffculties fnding the global minimum of the cost function, so we explore a quasi-static variational assimilation (QSVA) framework. Of the hybrid methods, it is seen that under certain parameters, hybrid methods which do not use a climatological background error covariance do not need QSVA to perform accurately. Generally, results show that the ETKS and hybrid methods that do not use a climatological background error covariance matrix with QSVA outperform all other methods due to the full flow dependency of the background error covariance matrix which also allows for the most nonlinearity.

The integration of figurative language and static depictions: an eye movement study of fictive motion

Do we view the world differently if it is described to us in figurative rather than literal terms? An answer to this question would reveal something about both the conceptual representation of figurative language and the scope of top-down influences oil scene perception. Previous work has shown that participants will look longer at a path region of a picture when it is described with a type of figurative language called fictive motion (The road goes through the desert) rather than without (The road is in the desert). The current experiment provided evidence that such fictive motion descriptions affect eye movements by evoking mental representations of motion. If participants heard contextual information that would hinder actual motion, it influenced how they viewed a picture when it was described with fictive motion. Inspection times and eye movements scanning along the path increased during fictive motion descriptions when the terrain was first described as difficult (The desert is hilly) as compared to easy (The desert is flat); there were no such effects for descriptions without fictive motion. It is argued that fictive motion evokes a mental simulation of motion that is immediately integrated with visual processing, and hence figurative language can have a distinct effect on perception. (c) 2005 Elsevier B.V. All rights reserved.