Noise properties of pulse-width modulated power converters:open-loop effects

The pulse-width modulation (PWM) process in DC-DC and DC-AC power converters introduces characteristic nonlinear behavior. When PWM is performed in the presence of noise, specific effects are seen on the duty ratio and consequently on the output of the converter. Small-signal concepts do not model nonlinear noise issues. Here, the probability density function of the duty ratio and its implications are obtained analytically, given external noise that follows a Gaussian distribution. The results are verified with Monte Carlo simulation and confirmed by experiments. For a DC-DC converter, noise is shown to introduce a DC shift at the output. The degree of nonlinear effect on a converter depends on the noise derivative level. For an inverter, noise can produce significant DC offset at the output. Closed-form expressions from the analysis can be used to evaluate noise sensitivity of a design     

Phase noise in LC oscillators

Analytical methods for the phase-noise analysis of LC-tuned oscillators are presented. The fundamental assumption used in the theoretical model is that an oscillator acts as a large-signal LC-tuned amplifier for purposes of noise analysis. This approach allows us to derive closed-form expressions for the close-to-carrier spectral density of the output noise, and to estimate the phase-noise performance of an oscillator from circuit parameters using hand analysis. The emphasis is on an engineering approach intended to facilitate rapid estimation of oscillator phase noise. Theoretical predictions are compared with results of circuit simulations using a nonlinear phase-noise simulator. The analytical results are in good agreement with simulations for weakly nonlinear oscillators. Complete nonlinear simulations are necessary to accurately predict phase noise in oscillators operating in a strongly nonlinear regime. To confirm the validity of the nonlinear phase-noise models implemented in the simulator, simulation results are compared with measurements of phase noise in a practical Colpitts oscillator, where we find good agreement between simulations and measurements     

An analytic approach for CDMA output of feedforward power amplifier

In this paper, a novel method is introduced to predict the Code-Division Multiple-Access (CDMA) output spectrum of an RF power amplifier linearized with feedforward technique based on transfer function. In this method, an RF power amplifier is modeled mathematically by nonlinear complex envelope transfer function based on AM-AM and AM-PM distortion diagrams. Using this model, analytic expressions of CDMA output spectrum of power amplifier is calculated. Having mathematical model of RF power amplifier leads to derive analytic expressions for InterModulation (IM) products in feedforward amplifier. Based on these expressions, IM products are related to nonlinear complex envelope transfer function of feedforward amplifier. Then, CDMA output spectrum of feedforward linearization technique is predicted. The loops imbalances in feedforward technique are considered in analysis. Finally, the results of derived expressions in MATLAB software are compared with ADS simulations results and good agreements were achieved. Employing this method gives insight for feedforward analysis and loops imbalances effects in feedforward amplifier for CDMA applications.     

Analytical performance evaluation of the OFDM systems in the presence of jointly fifth order nonlinearity and phase noise

This paper presents an exact theoretical analysis of the performance degradation in an orthogonal frequency division multiplexing (OFDM) system when the signal including phase noise is passed through a nonlinear circuit such as high power amplifier (HPA). This circuit is modeled as a fifth order memory-less nonlinear polynomial model (5th order MLNPM). The nonlinear model is derived from important electrical parameters such as gain, 1-dB compression and 3rd order intercept point. Theoretical analysis shows that the detected data symbol at the receiver consists of attenuated version of the original transmitted data symbol, common phase error (CPE), inter-sub-carrier interference (ICI), third and fifth order intermodulation (IM) components. The analytical expressions for intermodulation noise term are derived using combinatorial methods. By use of the derived expressions, a closed-form output signal to noise ratio (SNR), degradation factor (DF) and probability of error can be evaluated theoretically. For verifying the accuracy of our analysis, comparisons between the theoretical and simulated results with electrical parameter of an actual and applicable HPA are presented. The comparisons show that bit error rate (BER) of analytical results is closely match with simulation results for OFDM system using M-QAM modulation.     

Nonlinear Evolution of Gaussian ASE Noise in ZMNL Fiber

This paper investigates the evolution of kurtosis of the input Gaussian amplified spontaneous emission (ASE) noise in a nonlinear fiber with negligible dispersion. The nonlinear Schrodinger equation (NLSE) describing propagation in optical fibers is simplified such that the fiber represents a zero memory nonlinear (ZMNL) system, and this approximation allows the development of analytical formulas for the statistical moments of the output noise. It is possible to calculate moments of all integer orders and the explicit expressions for the first four moments are given. The investigations show that the ASE noise does not preserve its Gaussian character when Kerr nonlinearity is significant. This observation proves that the common assumption of the Gaussian output ASE is not necessarily valid. Numerical simulations are provided to support the derivation. Kurtosis deviating significantly from the value typical for Gaussian noise is also an indicator that BER calculation in the coherent systems based on the assumption that ASE is Gaussian is likely to be inaccurate.     

Analysis and Optimization of Noise in Bipolar RF Harmonic Mixers

A noise analysis of bipolar harmonic mixers (BHM) used for direct-conversion receivers is presented in this paper. Analytical and simulated results for the transfer function of the mixer are presented. Simple analytical expressions describing noise contribution from all sources are derived. Estimation of flicker noise quite agrees with harmonic-balance simulation results. Based on the derived expressions, total time average noise power spectral density (PSD) at the output is compared with simulation results. For the recommended regions of operation, error is less than 20%. The overall BHM noise figure (NF) is calculated and optimized based on a simple extracted formula. Errors introduced by analysis remain within a 1.5-dB margin with respect to simulation results. The validity of analysis for high frequencies is justified. The effect of flicker noise coefficient on the overall mixer NF is compared for different available processes.     

Analytic behavior of the LMS adaptive line enhancer for sinusoidscorrupted by multiplicative and additive noise

The least mean squares adaptive line enhancer (LMS ALE) has been widely used for the enhancement of coherent sinusoids in additive wideband noise. This paper studies the behavior of the LMS ALE when applied to the enhancement of sinusoids that have been corrupted by both colored multiplicative and white additive noise. The multiplicative noise decorrelates the sinusoid, spreads its power spectrum, and acts as an additional corrupting noise. Closed-form expressions are derived for the optimum (Wiener filter) ALE output SNR as a function of the residual coherent sine wave power, the noncoherent sine wave power spectrum, and the background additive white noise. When the coherent to noncoherent sine wave power ratio is sufficiently small, it is shown that a nonlinear (e.g., square law) transformation of the ALE input results in a larger optimum ALE output SNR     

Improvements to the standard theory for photoreceiver noise

The standard theory for photoreceiver noise unrealistically defines the system transfer function solely in terms of the input and output pulse shapes, based on the assumption that equalization is provided at the receiver output. Most photoreceivers reported in the literature, however, are only front ends and do not include equalizers, making direct application of the conventional noise expressions inappropriate. Even if equalization is provided, a signal-dependent definition of the transfer function will be accurate only under certain limited conditions. Furthermore, it is unrealistic to assume a given pulse shape at the input. In this paper we consider the effect of incorporating a more realistic transfer function into the conventional noise theory. We choose the transimpedance amplifier for our analysis due to its widespread popularity; however, our approach is general and can he applied to a broad class of photoreceivers. Since our transfer function is based on a physical circuit, our results can be used to estimate photoreceiver noise performance without making any assumptions on the input or output pulse shapes     

Stochastic analysis of the LMS algorithm with a saturationnonlinearity following the adaptive filter output

This paper presents a statistical analysis of the least mean square (LMS) algorithm with a zero-memory scaled error function nonlinearity following the adaptive filter output. This structure models saturation effects in active noise and active vibration control systems when the acoustic transducers are driven by large amplitude signals. The problem is first defined as a nonlinear signal estimation problem and the mean-square error (MSE) performance surface is studied. Analytical expressions are obtained for the optimum weight vector and the minimum achievable MSE as functions of the saturation. These results are useful for adaptive algorithm design and evaluation. The LMS algorithm behavior with saturation is analyzed for Gaussian inputs and slow adaptation. Deterministic nonlinear recursions are obtained for the time-varying mean weight and MSE behavior. Simplified results are derived for white inputs and small step sizes. Monte Carlo simulations display excellent agreement with the theoretical predictions, even for relatively large step sizes. The new analytical results accurately predict the effect of saturation on the LMS adaptive filter behavior     

比较阈值电路中噪声对信号传输作用的研究

本文研究了光电探测系统的比较阈值电路中的噪声对信号传输的影响。从理论上计算了该系统的输出自相关函数、功率谱密度和信噪比；分析了比较阈值电路中的随机共振现象；说明对非线性系统可以用噪声来增强信号的传输能力。     

Theory of CCD transfer noise from a circuit model

The transfer function and noise of a CCD can be accounted for by a simple block model of the elementary cell. From the analysis of ann-cell device, the noise properties of the output signal are derived in both the frequency and the time domain. The approach requires no approximations to calculate the power spectral density and amplitude variance so that the validity of asymptotic expressions can be evaluated. The model lends itself easily to include noise sources other than the transfer noise.     

Analysis and comparison of several simple impulsive noise mitigation schemes for OFDM receivers

In this paper, we analyze and compare the performance of OFDM receivers with blanking, clipping and combined blanking-clipping nonlinear preprocessors in the presence of impulsive noise. Closed-form analytical expressions for the signal-to-noise ratio at the output of three types of nonlinearity are derived. Simulation results are provided that show good agreement with theory.     

Spectral analysis of quantization noise in a single-loopsigma-delta modulator with DC input

An exact discrete-time analysis of the moments and spectra of the quantization noise of a discrete-time single-loop sigma-delta modulator with a DC input is presented. An exact difference equation for the discrete-time nonlinear system is used to evaluate the first- and second-order moments and power spectrum of the binary quantizer noise and the binary quantizer output for a single-loop sigma-delta encoder with a DC input. It is shown that the sample mean and power of the binary quantization noise are consistent with the common uniform distribution assumption, but that the autocorrelation and power spectrum are not consistent with the white noise assumption. The results are used to evaluate the overall sample average mean squared quantization error as a function of the decimation filter used     

The Effect of a Bandpass Nonlinearity on Signal Detectability

When an angle-modulated signal plus noise constitute the input to a bandpass device exhibiting a nonlinear input-output power characteristic and AM to PM conversion, the noise component of the output has altered first- and second-order statistics. A method of evaluating the two-dimensional first-order statistics of this noise is presented. The effect on signal detectability of a nonlinearity inserted between two channel noise sources is studied; expressions for the mean square received phase error and probability of error (for coherent digital phase modulation) are derived. The hard limiting satellite channel, with Gaussian noise on the up and down links, is examined in detail, and it is demonstrated that the limiter can significantly affect signal detectability.     

Error rate and outage of dual‐hop DF relay system with selection combining over Rice fading

Performance of dual‐hop decode‐and‐forward relay system with selection‐combining receiver is analyzed over Rice fading channels. The following closed‐form expressions of performance metrics are derived: moment generating function for selection‐combining receiver output signal‐to‐noise ratio, exact average bit error rate of noncoherent modulations, approximate average symbol error rate for coherent modulations, and outage probability. We also obtain simple asymptotic expressions for moment generating function, exact average bit error rate, average symbol error rate, and outage probability, which are useful to characterize the diversity order and the coding gain. The optimal power allocation analysis suggests that the optimal power allocation factor is independent of total signal‐to‐noise ratio and source‐to‐destination link fading parameters. The accuracy of the obtained analytical expressions are supported by computer simulation results.     

Roundoff noise in multirate digital filters

The roundoff noise problem for multirate digital filters is difficult because rate changing inside the filter makes both scaling and roundoff noise calculation complicated. With a new multirate filter analysis technique, the transfer function between any two points inside a multirate filter can be easily found, thus, simplifies the scaling and noise calculation. This paper finds theL _P scaling and derives the roundoff noise expressions for fixed point implementations of the multistage decimator, interpolator, and multirate narrow-band low-pass filter. It is shown that the noise source at a low sampling rate stage is more important than that at a higher sampling rate stage. Methods to reduce output roundoff noise are discussed.This research was supported by NSF grant ECS 81-00453.     

Analysis of microwave MESFET power amplifiers for digital wireless communications systems

The analysis of microwave MESFET power amplifiers (PAs) for digital wireless communications by using the hybrid Volterra-series method is presented in this paper. Compared with the traditional approach in the pure frequency-domain operation, the hybrid method has the advantage of fast computation for the continuous spectral signals with the same accuracy. The major modification is the equivalent baseband formulations in the time domain for the digital modulation signal, and the frequency-domain treatment with the nonlinear system via Volterra-series expansion. The MESFET two-dimensional current model is utilized and detailed current expressions are given to account for the gate-drain cross-term effects, while the nonlinear capacitors are also considered to describe the MESFET nonlinear characteristics completely. Circuit-level simulation yields the output modulation signal parameters with the measured data confirmation. System performance degradations due to nonlinear distortions of the MESFET PA are also performed for the communication link with the additive white Gaussian noise channel model. These results would be very useful in PA designs for digital wireless communications systems.     

Theoretical analysis and performance of OFDM signals in nonlinearAWGN channels

Orthogonal frequency-division multiplexing (OFDM) baseband signals may be modeled by complex Gaussian processes with Rayleigh envelope distribution and uniform phase distribution, if the number of carriers is sufficiently large. The output correlation function of instantaneous nonlinear amplifiers and the signal-to-distortion ratio can be derived and expressed in an easy way. As a consequence, the output spectrum and the bit-error rate (BER) performance of OFDM systems in nonlinear additive white Gaussian noise channels are predictable both for uncompensated amplitude modulation/amplitude modulation (AM/AM) and amplitude modulation/pulse modulation (AM/PM) distortions and for ideal predistortion. The aim of this work is to obtain the analytical expressions for the output correlation function of a nonlinear device and for the BER performance. The results in closed-form solutions are derived for AM/AM and AM/PM curves approximated by Bessel series expansion and for the ideal predistortion case     

Symbol error rate performance of nonlinear OFDM receiver with peak value threshold over frequency selective fading channel

Nonlinear blanking and clipping methods are widely used in Orthogonal Frequency Division Multiplexing (OFDM) receiver to mitigate impulse interference. To quantitatively analyze the reliability performance of nonlinear OFDM receivers with pulse blanking and clipping based on peak value threshold, the symbol error rate (SER) performance of nonlinear OFDM receiver over frequency selective Rayleigh and Ricean fading channels is presented. Firstly, the analytical expressions of instantaneous output signal-to-interference and noise ratio (SINR) for nonlinear OFDM receivers with regular method, peak value blanking and peak value clipping are derived. Then, the SER performance of nonlinear OFDM receiver over frequency selective Rayleigh and Ricean fading channels is given based on the SINR expressions. Finally, simulation results are demonstrated to show good agreement with theoretical results. It has been observed that the peak value blanking method has achieved the best SER performance, and the inter-carrier interference based on the peak value blanking and peak value clipping will lead to error floor.