Frequency Response Computation and Error Analyses

Aim To derive the error formulae for the algorithm of frequency response computation. Methods This algorithm was introduced theoretically, the error sources of the algorithm were analyzed and the formulae of the main error were derived. Results The repeatability and stability of the processing results of the algorithm are better than those measured by 1250 Frequency Analysor. Conclusion The error formulae derived are theoretically right and practically valid.

Performance Analysis for Orthogonal Time Frequency Space Modulation Systems with Generalized Waveform

Orthogonal time-frequency space(OTFS),which exhibits beneficial advantages in high-mobility scenarios,has been considered as a promising technology in future wireless communication systems.In this paper,a universal model for OTFS systems with generalized waveform has been developed.Furthermore,the average bit error probability(ABEP)upper bounds of the optimal maximum likelihood(ML)detector are first derived for OTFS systems with generalized waveforms.Specifically,for OTFS systems with the ideal waveform,we elicit the ABEP bound by recombining the transmitted signal and the received signal.For OTFS systems with practical waveforms,a universal ABEP upper bound expression is derived using moment-generating function(MGF),which is further extended to MIMO-OTFS systems.Numerical results validate that our theoretical ABEP upper bounds are concur with the simulation performance achieved by ML detectors.

Some of Advances on the Error Analysis in the Frequency Domain for a Digital Simulation Model

This paper surveys a number of recent advances in the error analysis in the frequency domain for a digital simulation model. It is emphasized to discuss the errors in characteristic roots and transfer funcnon of the digital simulation model, the frequency domain errors of the data transfers between thesimulation submodels, and some compensation methods for the errors. Some of the questions to be answered are also presented.

Error Analysis in Frequency Domain for Linear Multipass Algorithms

Error analysis methods in frequency domain are developed in this paper for determining the characteristic root and transfer function errors when the linear multipass algorithms are used to solve linear differential equations. The relation between the local truncation error in time domain and the error in frequency domain is established, which is the basis for developing the error estimation methods. The error estimation methods for the digital simulation model constructed by using the Runge-Kutta algorithms and the linear multistep predictor-corrector algorithms are also given.

Goal-oriented error estimation applied to direct solution of steady-state analysis with frequency-domain finite element method

Based on the concept of the constitutive relation error along with the residuals of both the origin and the dual problems, a goal-oriented error estimation method with extended degrees of freedom is developed. It leads to the high quality locM error bounds in the problem of the direct-solution steady-state dynamic analysis with a frequency-domain finite element, which involves the enrichments with plural variable basis functions. The solution of the steady-state dynamic procedure calculates the harmonic response directly in terms of the physical degrees of freedom in the model, which uses the mass, damping, and stiffness matrices of the system. A three-dimensional finite element example is carried out to illustrate the computational procedures.

Impacts of space-time-frequency synchronization errors onwide-band target echo characteristics of bistatic/multistatic radar

Bistatic/multistatic radar has great potential advantages over its monostatic counterpart. However, the separation of a transmitter and a receiver leads to difficulties in locating the target position accurately and guaranteeing space-timefrequency synchronization of the transmitter and the receiver.The error model of space-time-frequency synchronization in a motion platform of bistatic/multistatic radar is studied. The relationship between the space synchronization error and the transmitter platform position, receiver platform position, moving state, and beam pointing error, is analyzed. The effect of space synchronization error on target echo power is studied. The target scattering characteristics are restructured by many separate scattering centers of the target in high frequency regions. Based on the scattering centers model of the radar target, this radar target echo model and the simulation method are discussed. The algorithm of bistatic/multistatic radar target echo accurately reflects the scattering characteristics of the radar target, pulse modulation speciality of radar transmitting signals, and spacetime-frequency synchronization error characteristics between the transmitter station and the receiver station. The simulation of bistatic radar is completed in computer, and the results of the simulation validate the feasibility of the method.

Specification and Measurement of Mid-Frequency Wavefront Errors

Mid-frequency wavefront errors can be of the most importance for some optical components, but they're not explicitly covered by corresponding international standards such as ISO 10110. The testing methods for the errors also have a lot of aspects to be improved. This paper gives an overview of the specifications especially of PSD. NIF, developed by America, and XMM, developed by Europe, have both discovered some new testing methods.

Specifications and control of spatial frequency errors of components in two-beam laser static holographic exposure for pulse compression grating fabrication

The large-aperture pulse compression grating(PCG) is a critical component in generating an ultra-high-intensity, ultra-short-pulse laser;however, the size of the PCG manufactured by transmission holographic exposure is limited to large-scale high-quality materials. The reflective method is a potential way for solving the size limitation, but there is still no successful precedent due to the lack of scientific specifications and advanced processing technology of exposure mirrors. In this paper, an analytical model is developed to clarify the specifications of components, and advanced processing technology is adopted to control the spatial frequency errors. Hereafter, we have successfully fabricated a multilayer dielectric grating of 200 mm × 150 mm by using an off-axis reflective exposure system with Φ300 mm. This demonstration proves that PCGs can be manufactured by using the reflection holographic exposure method and shows the potential for manufacturing the meter-level gratings used in 100 petawatt class high-power lasers.

Joint frequency offset tracking and PAPR reduction algorithm in OFDM systems

This paper presents an algorithm that aims to reduce the peak-to-average power ratio（PAPR） of orthogonal frequency division multiplexing（OFDM） communication systems while maintaining frequency tracking.The algorithm achieves PAPR reduction by applying the complex conjugates of the data symbol obtained from the frequency domain to cancel the phase of the data symbol.A likelihood estimator is used to obtain the sub-carrier phase error due to the residual carrier frequency offset（RCFO） using the same complex conjugates as a pilot signal.Furthermore,a joint time and frequency domain multicarrier phase locked loop（MPLL） is developed to compensate additional frequency offset.Simulation results show that this algorithm is capable of reducing PAPR without impacting the frequency tracking performance.

Grating lobes suppression method for stepped frequency GB-SAR system

A grating lobes suppression method for chirp-subpulse stepped frequency（CSSF） signals is proposed, which is applied to deformation monitoring using the ground based synthetic aperture radar（GB-SAR） system. This method is based on accurate estimation and correction of the phase and amplitude error along two dimensions（range and azimuth）, i.e., the error estimation inside the subpulse（in-subpulse error） and across the stepped frequency subpulses（cross-subpulse error） of transmitted CSSF signals. Validated both with simulated data and experimental data recorded in the deformation monitoring campaign, it can be seen that the method as well as the relative conclusions can be fully and effectively applied to most of the stepped frequency systems.

Estimation of DOA and Doppler Frequency on Nonideal UCA

The problem of estimating direction of arrivals (DOA) and Doppler frequency for many sources is considered in the presence of general array errors (such as amplitude and phase error of sensors, setting position error of sensors). Adopting direct array manifold in a uniform circular array (UCA), the estimation of Doppler frequency can be obtained by DOA matrix. Based on analyzing the statistic characters of general array errors, the estimation of DOA can be obtained by Weight Total Least Squares. Numerical results illustrate that the estimator is robust to general array errors and show the capabilities of the estimator.

Design and Analysis of Spatial Modulation Based Orthogonal Time Frequency Space System

In this paper,we design a spatial modulation based orthogonal time frequency space(SMOTFS)system to achieve improved transmission reliability and meet the high transmission rate and highspeed demands of future mobile communications,which fully utilizes the characteristics of spatial modulation(SM)and orthogonal time frequency space(OTFS)transmission.The detailed system design and signal processing of the SM-OTFS system have been presented.The closed-form expressions of the average symbol error rate(ASER)and average bit error rate(ABER)of the SM-OTFS system have been derived over the delay-Doppler channel with the help of the union bounding technique and moment-generating function(MGF).Meanwhile,the system complexity has been evaluated.Numerical results verify the correctness of the theoretical ASER and ABER analysis of the SM-OTFS system in the high signal-to-noise ratio(SNR)regions and also show that the SM-OTFS system outperforms the traditional SM based orthogonal frequency division multiplexing(SM-OFDM)system with limited complexity increase under mobile conditions,especially in high mobility scenarios.

MOTION COMPENSATION FOR WIDE BEAM SAR BASED ON FREQUENCY DIVISION

Aperture-dependent motion compensation is important for wide beam Synthetic Aperture Radar(SAR) data processing.This paper studies a wide beam motion compensation algorithm based on frequency division.It takes blocks along azimuth dimension in frequency domain and applies an-gle-variant motion compensation in time domain.With this frequency division based motion com-pensation approach,the effects of aperture-dependent residual phase errors are corrected precisely.The rationale and procedure of this algorithm are introduced in detail.Point targets and images of a P-band airborne SAR with motion errors are simulated to validate this algorithm.Compared with the wide beam motion compensation algorithms based on time division,the proposed algorithm has better performance,especially in terms of high-frequency motion errors.

CARRIER FREQUENCY OFFSET ESTIMATION FOR INTERLEAVED OFDMA UPLINK BASED ON SUBSPACE PROCESSING

This paper investigates Carrier Frequency Offset (CFO) estimation in the uplink of the Orthogonal Frequency-Division Multiple Access (OFDMA) systems with the interleaved subcarrier assignment. CFOs between the transmitters and the uplink receiver will destroy orthogonality among different subcarriers, hence resulting in inter-carrier interference and multiuser interference. A two-stage frequency offset estimation algorithm based on subspace processing is proposed. The main advantage of the proposed method is that it can obtain the CFOs of all users simultaneously using only one OFDMA block. Compared with the previously known methods, it not only has a relatively low implementation complexity but is also suitable for random subchannel assignment.

Unsupervised FIR adaptive filtering and its frequency domain analysis

An unsupervised minimum mean square error FIR adaptive filtering （UAF） algorithm is proposed to estimate the system＇ s input signal. The algorithm only uses the system＇ s output signal and noise variance without requiring knowledge of a reference signal. The frequency analysis shows that the UAF is a multi-spot bandpass filter with passing frequency determined by the system＇ s input signal. Namely, the UAF chooses the expected frequency and extremely restricts the unwanted fre- quency signal by using weight-updating scheme in time domain. However, the UAF presents the Gibbs phenomenon since the ideal filter is infinitely long which is unrealizable. The simulation and experimental results show that the UAF could effectively reduce the amplitude of the noise and im- prove the signal to noise ratio.

The Effect and Compensation of Phase Noise on Orthogonal Frequency Division Multiplexing (OFDM) System

Orthogonal Frequency Division Multiplexing (OFDM) is characterized by its high data rate. However, the modulation method used in the system is subject to the influence of phase noise due to the need of time synchronization. In this paper, an algorithm based on MMSE (minimum mean square error) is developed to compensate the influence of both the common phase error (CPE) and inter carrier interference (ICI), which are two aspects of phase noise, under common Gaussian white noise. The result of noise cancellation is presented in signal-to-noise ratio (SNR) and symbol error rate (SER). Like digital signal in general, SNR can reduce SER with or without phase noise compensation. The compensation of phase noise significantly reduces the SER of the decoded signal. However, the bandwidth of phase noise still determines the signal accuracy. Under high bandwidth of phase noise, increasing SNR will only slightly increase SER, which is not efficient.

Carrier frequency offset estimation for a generalized OFDMA uplink

A residual carrier frequency offset （CFO） estimation scheme is proposed for the uplink of orthogonal frequency division multiple access （OFDMA） systems. Multiple access interference caused by CFOs in the uplink is investigated, as it severely affects the performance of a classical maximum likelihood （ML） frequency estimator. By the use of the estimated CFOs of the active users, the linear maximum mean square error （LMMSE） equalization is performed before the ML frequency estimator for the interference cancellation, which can help to sufficiently improve the estimation accuracy for the residual CFO of the incoming user. Analysis and simulations show that the modified ML estimator provides a tradeoff between estimation accuracy and computational complexity caused by the LMMSE interference cancellation, and the proposed method allows OFDMA systems flexibly allocating subcarriers to users.

THE THEORETICAL BER PERFORMANCE ANALYSIS OF A COOPERATIVE DIVERSITY SCHEME IN FREQUENCY SELECTIVE FADING CHANNEL

A novel cooperative diversity scheme based on Distributed Space-Time Block Coding and Multi-Carrier Code Division Multiple Access (DSTBC-MC-CDMA) is proposed which works well in frequency selective fading channels with multiple single-antenna users. And an analytical error model is established to describe the symbol decoding errors between interusers, based on which a close form expression for theoretical Bit Error Rate (BER) performance of the scheme is derived to analyze the influence of the interuser decoding errors on the BER performance of the scheme. Then simulation is complimented to verify the analytic result above, which also shows that the BER performance of DSTBC-MC-CDMA outgoes that of non-cooperative MC-CDMA with considerable gains. Further- more, the simulations coincide with the theoretical results well.

BER Performance of Frequency Domain Differential Demodulation OFDM in Flat Fading Channel

A closed form expression for the bit error rate (BER) performance of frequency domaindifferential demodulation(FDDD) for orthogonal frequency division multiplexing system in flat fadingchannel is derived.The performance is evaluated by computer simulation and compared with the timedomain differential demodulation(TDDD).The results indicate that the performance of FDDD is betterthan that of TDDD,and the lower band of BER in the former is lower than that of the latter.

Integral Performance Criteria Based Analysis of Load Frequency Control in Bilateral Based Market

Performance index based analysis is made to examine and highlight the effective application of Particle Swarm Optimization (PSO) to optimize the Proportional Integral gains for Load Frequency Control (LFC) in a restructured power system that operates under Bilateral based policy scheme. Various Integral Performance Criteria measures are taken as fitness function in PSO and are compared using overshoot, settling time and frequency and tie-line power deviation following a step load perturbation (SLP). The motivation for using different fitness technique in PSO is to show the behavior of the controller for a wide range of system parameters and load changes. Error based analysis with parametric uncertainties and load changes are tested on a two-area restructured power system. The results of the proposed PSO based controller show the better performance compared to the classical Ziegler-Nichols (Z-N) tuned PI and Fuzzy Rule based PI controller.