Sasan H. Ardalan

An analysis of nonlinear behavior in delta - sigma modulators

This paper introduces a new method of analysis for deltasigma modulators based on modeling the nonlinear quantizer with a linearized gain, obtained by minimizing a mean-square-error criterion [7], followed by an additive noise source representing distortion components. In the paper, input signal amplitude dependencies of delta-sigma modulator stability and signal-to-noise ratio are analyzed. It is shown that due to the nonlinearity of the quantizer, the signal-to-noise ratio of the modulator may decrease as the input amplitude increases prior to saturation. Also, a stable third-order delta-sigma modulator may become unstable by increasing the input amplitude beyond a certain threshold. Both of these phenomena are explained by the nonlinear analysis of this paper. The analysis is carried out for both dc and sinusoidal excitations.

Fixed-point roundoff error analysis of the exponentially windowed RLS algorithm for time-varying systems

A fixed-point roundoff error analysis of the exponentially windowed RLS algorithm is presented. It is shown that a tradeoff exists in the choice of the forgetting factor λ. In order to reduce the sensitivity of the algorithm to additive noise, λ must be chosen close to one. On the other hand, the roundoff error increases as \lambda \rightarrow 1 . It is shown that the algorithm is stabilized with λ \lambda \rightarrow 1 . To derive the theoretical results, it is assumed that the input signal is a white Gaussian random process. Finally, simulations are presented which confirm the theoretical findings of the paper.

Table-based modeling of delta-sigma modulators using ZSIM

ZSIM, a nonlinear Z-domain simulator for sampled-data systems, is presented and verified. ZSIM integrates analytic tools, a difference equation simulator, a table-based nonlinear Z-domain simulator, and digital signal processing into a workstation environment to provide fast and accurate simulation of delta-sigma modulators. The use of table-based simulation allows simulation of circuit nonidealities including clock feedthrough and saturation. Benchmark comparisons of difference equation simulations and table-based simulations are presented for delta-sigma modulators suitable for use in voice-band coders. >

A soft decision-directed blind equalization algorithm applied to equalization of mobile communication channels

A new approach to decision-directed (DD) blind equalization is introduced based on a neural network classification technique. The new DD algorithm, the soft decision-directed equalization algorithm, is most effective for reconstructing binary phase shift keying and quadrature phase shift keying signals. The new DD blind equalizer can converge in closed eye situations. In the simulations, the performance of the soft DD algorithm was illustrated by applying it to a two-dimensional digital mobile communications system. A time-varying multipath fading channel model was used as the transmission medium. The performance of the soft DD blind equalization algorithm is compared to that of the standard DD algorithm, the maximum-level-error (MLE) algorithm, and the fast recursive least squares decision-feedback equalization (FRLS-DFE) algorithm. The simulation results demonstrate the improvement in performance achievable with the proposed soft DD equalization algorithm.<<ETX>>

Optimal signal processing of frequency-stepped CW radar data

An optimal signal processing algorithm is derived for estimating the time delay and amplitude of each scatterer reflection using a frequency-stepped CW system. The channel is assumed to be composed of abrupt changes in the reflection coefficient profile. The optimization technique is intended to maximize the target range resolution achievable from any set of frequency-stepped CW radar measurements made in such an environment. The algorithm is composed of an iterative two-step procedure. First, the amplitudes of the echoes are optimized by solving an overdetermined least squares set of equations. Then, a nonlinear objective function is scanned in an organized fashion to find its global minimum. The result is a set of echo strengths and time delay estimates. Although this paper addresses the specific problem of resolving the time delay between the first two echoes, the derivation is general in the number of echoes. Performance of the optimization approach is illustrated using measured data obtained from an HP-8510 network analyzer. It is demonstrated that the optimization approach offers a significant resolution enhancement over the standard processing approach that employs an IFFT. Degradation in the performance of the algorithm due to suboptimal model order selection and the effects of additive white Gaussian noise are addressed. >

A fast ARMA transversal RLS filter algorithm

A fast pole-zero (ARMA) transversal RLS (recursive least squares) algorithm is derived, using a geometric formulation and the concept of projection onto a vector subspace to derive a recursive solution. The algorithm estimates a parameter vector that contains both numerator and denominator coefficients of an unknown system transfer function, i.e. models an ARMA (pole-zero) process. The algorithm has a transversal filter structure, but is distinguished from previous multichannel transversal algorithms, wherein each input channel is constrained to have the same order; here the pole and zero orders can be independently and arbitrarily specified. The derivation of the algorithm uses permutation matrices similar to those in the ARMA fast Kalman algorithm, but achieves a significant reduction in computations when compared to that algorithm. It is shown that when the pole and zero orders of the ARMA process are correctly specified, the algorithm generates an extremely good estimate. Furthermore, if the poles and zeros are overspecified, it is shown that a spectral match is still achieved by mutual cancellation of superfluous poles and zeros. >

On the effect of input signal correlation on weight misadjustment in the RLS algorithm

New expressions are derived for the mean weight misadjustment in the recursive least squares (RLS) algorithm for first-order Markov channel estimation. The expressions derived are general in that they take into account the correlation in the input. It is shown that the additive system noise is amplified by a correlation amplification factor that is defined as a function of the input autocorrelation matrix eigenvalues. However, input correlation has almost no effect on the misadjustment due to time-varying system weights. These results are checked by simulations demonstrating excellent agreement with the theory. >

Detection of target distance in the presence of an interfering reflection using a frequency-stepped double side-band suppressed carrier microwave radar system

A technique for detecting the distance to a highly reflective target in the presence of an interfering reflection using a frequency-stepped double-sideband suppressed carrier (DSBSC) microwave-millimeter-wave radar system is analytically derived. The main result of the analysis shows that the measured group delays produced by the DSBSC system possess a periodicity inversely proportional to the difference between the time delays to the target and interferer, independent of the signal-to-interference ratio (SIR). Simulation results are presented in the context of electron plasma density range estimation using a block diagram communications CAD tool. A unique and accurate plasma model is introduced. A high-resolution spectral estimation technique, based on an autoregressive time series analysis is applied to the measured group delays, and it is shown that accurate target distance estimates may be obtained, independent of SIR. >

Optimization of transmitter and receiver filters for digital communication systems using mean field annealing

A technique for finding transmitter and receiver filters for a wide class of digital communication systems which minimize the bit-error rate (BER) is presented. The technique uses Monte Carlo simulation to estimate the BER and mean field annealing (MFA) to optimize the pulse shapes. Modeling of the link can be as complex as simulation will allow, while MFA is resistant to the statistical variation in the BER estimate from the simulation. Initially, the MFA technique was applied to a binary symmetric channel in a nonsimulation environment, and an approximate analysis of the behavior of MFA for this problem was performed. In a more complex example, MFA was coupled with Monte Carlo simulation techniques to find near-optimal transmit and receive filters for a satellite communications link, taking 6 CPU hours on a DECstation 3100. The BER of the link was found to be as much as three orders of magnitude lower when using the MFA-constructed optimal filters than when using filters from other comparison results. For this example, the pulse shapes obtained using MFA exhibit a low BER even as the parameter controlling the nonlinearity of the satellite-link model is varied over a wide range, thus showing the solution is robust. >

Sensitivity analysis of transversal RLS algorithms with correlated inputs

The effects of input signal correlation on the performance on finite-precision RLS (recursive-least-squares) algorithms we presented. It is shown that one way to analyze finite-precision effects is indirectly through the study of the sensitivity of the RLS algorithm to perturbations in the filter coefficients. The authors show that the mean deviation of the optimum error power grows linearly with time and is the same for both correlated and uncorrelated input samples. However, the variance of the deviation from the optimum increases with signal correlation. Upper and lower bounds are derived in terms of the ratio of the maximum eigenvalue of the sample autocorrelation matrix to the signal variance. (The deviation increases as the signal dynamic range increases.) Simulations are presented to verify the theory. A stable finite-precision RLS algorithm is derived by modeling roundoff errors and incorporating their effects into the algorithm.<<ETX>>