Finite Impulse Response Coefficients Research Articles

Adaptive Channel Equalization Using Seagull Optimization with Various Initialization Strategies

In a digital communication channel, the transmitted signal may be dispersive causing the information to not be transmitted as same. Due to the distortion, the communication channel is affected known as Inter-Symbol Interference (ISI). To reducing the ISI effect, adaptive channel equalization plays an important role in digital communication. In the proposed method, the Finite Impulse Response (FIR) channel ISI effect is reduced by the proposed optimization algorithm. The FIR channel weight or coefficients are optimized by the proposed Seagull Optimization Algorithm (SOA) with different initialization strategies. Normally, SOA has random initialization of population but to improve the process of adaptive channel equalization, Random Number Generation (RNG), Opposition based learning (OBL) and Quasi-Opposition based learning (QBL) methods are utilized for initialization. The objective function of the equalization process is minimization error values where the error value is estimated based on the desired signal and channel output signal. The experiment is carried out on the MATLAB platform. The proposed method's effectiveness is shown to compare the various initialization methods of RNG, OBL and QBL with SOA. Based on different SNRs, the error value is computed and shows the convergence results.

Efficient and Accurate Frequency-Invariant Beam Pattern Synthesis Utilizing Iterative Spatiotemporal Fourier Transform

An iterative spatiotemporal Fourier transform (STFT) method is presented to efficiently design finite-impulse-response (FIR) filter coefficients for generating a desired frequency-invariant (FI) beam pattern of an antenna array. In this method, by introducing the concepts of normalized temporal angular frequency and spatial angular frequency, the broadband pattern is treated as a spatiotemporal spectral distribution. The relationship between the FIR coefficient distribution and the spatiotemporal spectral distribution can be built as an STFT, and consequently the 2-D fast Fourier transform (2D-FFT) and inverse 2D-FFT (2D-IFFT) can be utilized to efficiently accomplish the transformation between the FIR coefficient distribution and the spatiotemporal spectral distribution. Thus, the proposed synthesis method starts from an initial spatiotemporal spectral distribution and then adopt an iterative modification-and-transformation strategy to successively update the obtained spatiotemporal spectral distribution and the corresponding FIR coefficients. Two kinds of pattern modification techniques including the mainlobe FI modification and broadband sidelobe control are adopted in each iteration. Several examples for synthesizing different FI patterns are conducted. Synthesis results show that the proposed method can obtain much better FI pattern performance in terms of both mainlobe FI property and sidelobe control than the original FT method whilst costing less CPU time than the convex optimization method especially for the case of large FI arrays.

Joint Polarization Tracking and Equalization in Real-Time Coherent Optical Receiver

We experimentally demonstrate a real-time polarization tracking and equalization method based on the state of polarization detection from the adaptive finite impulse response (FIR) filter coefficients in a polarization division multiplexed (PDM) coherent optical communication system. By calculating the variation of the polarization within a time interval, the polarization rotation speed can be evaluated. In a field-programmable gate array (FPGA), a feedback structure for polarization rotation speed detection and FIR coefficients update can be built up. In this feedback structure, the update coefficient of the filter will be adjusted to an optimal value with the change of detection result. The experimental results show that the establishment of this feedback structure improves the polarization tracking ability in the real-time coherent optical receiver.

A nonparametric Bayesian model for system identification based on a super‐Gaussian distribution

AbstractIn the acoustic signal processing applications of finite impulse response (FIR) system identification, it is important to develop the identification method that is robust to super‐Gaussian noises. Moreover, the identification method that estimates the FIR coefficients and the order of the unknown system is required, because the order of the unknown system is unavailable in advance. Therefore, in this paper, we propose a nonparametric Bayesian (NPB) model for FIR system identification using a super‐Gaussian likelihood and the beta‐Bernoulli process. In the proposed NPB model, we employ the hyperbolic secant distribution for the likelihood function. Then, we derive the inference algorithm to simultaneously estimate the FIR coefficients and the order of the unknown system. Our inference algorithm based on a hybrid inference approach combining the majorization‐minimization (MM) algorithm and the Gibbs sampler. The simulation results suggest that the proposed method outperforms the conventional identification algorithms in a super‐Gaussian noise environment.

Distributive FIR-Based Chromatic Dispersion Equalization for Coherent Receivers

We propose a novel and efficient multiplierless finite-impulse response (FIR)-based filter architecture for chromatic dispersion equalization (CDE) in coherent optical communication systems. After quantizing the FIR coefficients, we take advantage of the high multiplicity of their real and imaginary parts, employing the distributive property of multiplication over addition to sharply reduce the number of multiplication operations, obtaining the distributive FIR-CDE (D-FIR-CDE). Furthermore, the implementation of multiplication operations with shifts and additions allows us to obtain a multiplierless D-FIR-CDE (MD-FIR-CDE). The proposed equalizers are experimentally validated in a 100G polarization-multiplexed (PM)-QPSK long-haul optical link and compared against benchmark FIR-CDE and frequency-domain (FD)-CDE implementations. We demonstrate computational resources savings of over 99% in number of multiplication operations and 40% in number of additions, relatively to the FIR-CDE implementation. In addition, the D-FIR-CDE is also shown to compare favorably relatively to the most widely used FD-CDE, achieving significant gains both in terms of required chip area and latency: more than 99% and 30% fewer multipliers and additions, respectively, and a latency reduction of over 90%. We have also experimentally demonstrated that the performance penalty imposed by the coefficient quantization tends to decrease with increasing propagation length, rendering it as an attractive solution for efficient and high-performance chromatic dispersion compensation in long-haul optical fiber links.

FIR system identification based on a nonparametric Bayesian model using the Indian buffet process

In this paper, we propose a nonparametric Bayesian model combined with the Indian buffet process (IBP) for a finite impulse response (FIR) system. We develop an FIR system identification method that can simultaneously estimate the number of FIR taps and coefficients. In the proposed model, each FIR tap consists of a coefficient and a gain, and the gain is a binary value. An infinite-dimensional binary vector is composed of binary values, and we assume that this binary vector is generated by the IBP. To identify the FIR system, we specify the likelihood function and prior distributions of the parameters and derive their posterior distributions. We can simultaneously estimate the number of FIR taps and coefficients by sampling from posterior distributions using the Gibbs sampler. Our simulations demonstrate that although the number of FIR taps is unknown, the identification performance of the proposed method in a high signal-to-noise ratio environment is similar to or better than that of the conventional least square solution.

Single Minimum Nonlinearity Wiener System Identification by Weighted Principal Component Analysis

Wiener system identification with a finite impulse response (FIR) model is investigated in this paper, focusing on the challenging case of non Gaussian input distribution and non monotonic nonlinearity. The proposed method assumes that the static nonlinear function of the Wiener system has a single minimum (or maximum), but does not assume any parametrization of the nonlinear function. Based on a modified principal component analysis (PCA), referred to as weighted PCA, the FIR coefficients of the Wiener system are estimated without estimating the nonlinear function of the Wiener system. The numerical computation cost is essentially equivalent to those of two standard PCA. Numerical examples in harsh practical conditions, with data generated by Wiener systems involving a discontinuous nonlinear function or an infinite impulse response, are presented to illustrate the robustness and effectiveness of the proposed method.

High-Acceleration Precision Point-to-Point Motion Control With Look-Ahead Properties

This paper investigates the effects of two control algorithms on high-performance point-to-point motions. The emphasis here is to overcome challenges in precision positioning of high-acceleration tables in the presence of significant external disturbances and exited vibration: an A-type of iterative learning control (ILC) (A-ILC) algorithm for repetitive motions and a look-ahead finite impulse response (FIR) filter plus sliding-mode control (SMC) for nonrepetitive motions. The model-free convergence condition and the fastest converging parameter equation for A-ILC are given in the frequency domain. Then, the FIR coefficients are decided through the ILC results and modified to eliminate the friction effect. Experimental studies demonstrate that both the algorithms perform well and the FIR-SMC algorithm is robust in various experimental scenarios which include high acceleration (of 73.7 m/s2 or about 7.5 g), model parameters, and disturbance deviations from the position, velocity, and acceleration at which the ILC (and, hence, FIR) is trained.

Adaptive FIR Neural Model for Centroid Learning in Self-Organizing Maps

In this paper, a training method for the formation of topology preserving maps is introduced. The proposed approach presents a sequential formulation of the self-organizing map (SOM), which is based on a new model of the neuron, or processing unit. Each neuron acts as a finite impulse response (FIR) system, and the coefficients of the filters are adaptively estimated during the sequential learning process, in order to minimize a distortion measure of the map. The proposed FIR-SOM model deals with static distributions and it computes an ordered set of centroids. Additionally, the FIR-SOM estimates the learning dynamic of each prototype using an adaptive FIR model. A noteworthy result is that the optimized coefficients of the FIR processes tend to represent a moving average filter, regardless of the underlying input distribution. The convergence of the resulting model is analyzed numerically and shows good properties with respect to the classic SOM and other unsupervised neural models. Finally, the optimal FIR coefficients are shown to be useful for visualizing the cluster densities.

MIMO feed-forward design in wafer scanners using a gradient approximation-based algorithm

An experimental demonstration is given of a data-based multi-input multi-output (MIMO) feed-forward control design applied to the motion systems of a wafer scanner. Atop a nominal single-input single-output (SISO) feed-forward controller, a MIMO controller is designed having a finite impulse response (FIR) filter structure. The coefficients in this structure are obtained from a gradient approximation-based algorithm. The aid of the FIR filter structure is mostly through its efficient (and limited) set of perturbed-parameter experiments needed to obtain the FIR coefficients. The effectiveness of the optimized feed-forward design in achieving improved servo tracking performances is demonstrated on a high-speed and nano-accurate MIMO wafer stage of an industrial wafer scanner.

Optimized dynamic decoupling in active vibration isolation

To improve performances of a multi-input multi-output (MIMO) active vibration isolation system, the possibilities of dynamic decoupling are studied. This to avoid spill-over of disturbances from one controlled direction toward another via cross-coupling. The decoupling structure consists of two parts. For course decoupling a set of low-pass filters is selected and tuned about the coupled suspension-mode resonances. For fine decoupling a finite impulse response (FIR) decoupling structure is added for machine-specific tunings. The FIR coefficients are obtained by data-based optimization in which perturbed-parameter experiments are conducted to obtain the required gradients. The optimization maps the single-input single-output (SISO) low-pass filter structure onto a MIMO dynamic decoupling. Its effect is demonstrated on a 6-DOF professional isolation system both in time- and frequency-domain.

Dealing with Collinearity in Finite Impulse Response Models Using Bayesian Shrinkage

Finite impulse response (FIR) models are widely used in the chemical industry due to their simplicity and easily defined model structures. However, they usually require a large number of coefficients to capture the process dynamics. This large number of coefficients introduces collinearity or redundancy in the models, which usually increases the uncertainty of their estimation. This paper presents a Bayesian approach, called empirical Bayesian FIR (EBFIR) modeling, to deal with this collinearity problem. Unlike ridge regression (RR), which shrinks the FIR model parameters toward zero in order to reduce their variations, EBFIR makes better use of the data by estimating a prior density function for the FIR coefficients, which is then used within a Bayesian framework to shrink the FIR coefficients in a more rigorous fashion. The developed Bayesian approach is computationally inexpensive, as a closed form solution of the Bayesian estimate of the FIR coefficients is derived. The EBFIR approach is also more general than some of the existing methods, such as ordinary least squares regression (OLS) and RR, which are shown to be special cases of EBFIR. Finally, the developed EBFIR approach has been shown to outperform some of the commonly used existing FIR estimation methods over a wide range of noise levels.

A narrowband IIR digital filter with low sensitivity and roundoff noise

An efficient infinite-impulse response (IIR) structure is produced via spectral transformation of an appropriate finite-impulse response (FIR) prototype design. The filter specifications are prewarped to a halfband design by an allpass relationship to produce the efficient FIR prototype. The allpass coefficient is chosen to be exactly realizable with a small number of multiplier bits. Hence, the only coefficient quantization required is for the original FIR coefficients, which are relatively insensitive. The roundoff noise for fixed-point implementations is also quite low compared with conventional IIR designs. Scaling for overflow can be avoided completely, or, to save multipliers, a simple scale factor can be employed.

Adaptive digital correction of analog errors in MASH ADCs. I. Off-line and blind on-line calibration

Cascaded delta-sigma (MASH) modulators for higher order oversampled analog-to-digital conversion rely on precise matching of contributions from different quantizers to cancel lower order quantization noise from intermediate delta-sigma stages. This first part of the paper studies the effect of analog imperfections in the implementation, such as finite gain of the amplifiers and capacitor ratio mismatch, and presents algorithms and architectures for digital correction of such analog imperfections, as well as gain and spectral distortion in the signal transfer function. Digital correction is implemented by linear finite-impulse response (FIR) filters, of which the coefficients are determined through adaptive off line or on-line calibration. Of particular interest is an on-line "blind" calibration technique, that uses no reference and operates directly on the digital output during conversion, with the only requirement on the unknown input signal that its spectrum be bandlimited. Behavioral simulations on dual-quantization oversampled converters demonstrate near-perfect adaptive correction and significant improvements in signal-to-quantization-noise performance over the uncalibrated case, using as few as 5 FIR coefficients. An alternative on line adaptation technique using test signal injection and experimental results from silicon are presented in the second part, in a companion paper.