Tracking the Frequency Translation of a Sum of Orthogonal Sinusoids

The maximum likelihood approach is used to derive a method for estimating and tracking the frequency translation of a signal consisting of a sum of orthogonal sinusoids corrupted by additive white noise. The likelihood function is reduced to an equivalent statistic expressed in terms of the squared magnitude of the finite Fourier transform of the received signal. A function that generates an error signal for a frequency translation tracking loop is derived, and a method of generating the error signal using the discrete Fourier transform (DFT) of the received signal weighted by a linear ramp is suggested. Two noise-free examples are presented.     

Carrier Tracking by Smoothing Filter Improves Symbol SNR

The potential benefit of using a smoothing filter to estimate a carrier phase over use of phase-locked loops (PLL) is determined. Numerical results are presented for the performance of three possible configurations of an all-digital coherent demodulation receiver. These are residual carrier PLL, sideband-aided residual carrier PLL, and finally sideband aided with Kalman smoother. The average symbol SNR after losses due to carrier phase estimation is computed for different total power SNRs, symbol rates, and symbol SNRs. It is found that smoothing is most beneficial for low symbol SNRs and low symbol rates. Smoothing gains up to 0.7 dB over sideband-aided residual carrier PLL, and the combined benefit of smoothing and sideband aiding relative to residual carrier loop is often in excess of 1 dB.     

Composite Bound on Arrival Time Estimation Errors

Time of arrival (TOA) estimation of narrowband signals is a problem of considerable practical interest in radar and sonar applications. A new technique is presented to analyze the mean square error (MSE) performance of TOA estimation schemes, based on recently developed lower bound. We obtain a complete characterization of the MSE as a function of the signal and noise parameters. The results are given in a simple closed-form analytical expression.     

Design of the HEAO Main Bus Shunt Regulator

The High Energy Astronomy Observatory (HEAO) main bus regulator contains a redundant error amplifier (REA) and a 12-section sequenced shunt transconductance amplifier (STA) in which not more than three and not less than one shunt section are in an active control mode regardless of a failure in any one of the twelve sections. The part of the work concerned with the shaping of the frequency response of the REA and STA minor feedback loops and of the teolator major feedback loop is described. Emphasis is on the application of a general design technique embodying a "design-analyze-measure iteration loop," in which a first-cut design and analysis is corrected ard improved after experimental observation of discrepancies and deficiencies. In particular, an incipient high-frequency oscillation was thereby reliably eliminated. It is demonstrated that analysis techniques involving a minimum of algebra can provide full quantitative information on an efficient and reliable system design.     

Limiting Performance of Generalized Sign Test Detector

The limiting performance of the generalized sign test detector as the number M of target returns becomes infinite has been derived by Hansen and Olsen [1]. Simple expressions are derived herein for the limiting performance for finite M as K, the number of noise samples in the reference set, becomes infinite. Curves are presented which indicate how this limiting performance is approached as K is increased for both constant target returns and fluctuating target returns.     

Cross Correlation of Orthogonally Polarized Backscatter Components

The backscattering of an elliptically polarized plane wave from two kinds of complex radar objects is considered from the standpoint of coherency theory, and the antenna polarizations that give rise to maximum correlated and uncorrelated orthogonally polarized components in the receiving channels are discussed. The resulting observations may find application in radar systems which use the correlation between the received orthogonally polarized components for detecting targets in natural and man-made interference.     

Properties of Staggered PRF Radar Spectral Components

Expressions for moving target indicator (MTI) improvement factor limitation due to pulse repetition frequency (PRF) staggering and loss of target detectability for various values of Doppler frequency in the passband are presented. It is also shown that the product of variance of stagger periods and clutter variance is an important parameter determining the performance of a staggered PRF MTI radar.     

UVCS Observations and Modeling of Streamers

We present results derived from the analysis of an equatorial streamer structure as observed by the UVCS instrument aboard SOHO. From observations of the H I Lyα and Lyβ lines we infer the density and temperature of the plasma. We develop a preliminary axisymmetric, magnetostatic model of the corona which includes the effects of gas pressure gradients on the magnetic structure. We infer a coronal plasma β > 1 in the closed field regions and near the cusp of the streamer. We add to the model a parallel velocity field assuming mass flux conservation along magnetic flux tubes. We then compute the Lyα emissivity and the line-of-sight integrals to obtain images of Lyα intensity, taking into account projection effects and Doppler dimming. The images we obtain from this preliminary model are in good general agreement with the UVCS observations, both qualitatively and quantitatively. This revised version was published online in June 2006 with corrections to the Cover Date.     

Principles of Invariance in Radiative Transfer

We have reviewed the principle of invariance, its applications and its usefulness for obtaining the radiation field in semi-infinite and finite atmospheres. Various laws of scattering in dispersive media and the consequent radiation field are studied. The H-functions and X- and Y-functions in semi-infinite and finite media respectively are derived in a few cases. The Discrete Space Theory (DST) which is a general form of the Principle of Invariance is described. The method of addition of layers with general properties, is shown to describe all the properties of multiple scattering. A few examples of the application of DST such as polarization, line formation in expanding stellar atmospheres, etc., and a numerical analysis of DST are presented. Other developments in the theory of radiative transfer are briefly described. This revised version was published online in June 2006 with corrections to the Cover Date.     

Streamer Evaporation

Streamer evaporation is the consequence of heating in ideal MHD models because plasma is weakly contained by the magnetic field. Heating causes inflation, opening of field lines, and release of solar wind. It was discovered in simulations and, due to the absence of loss mechanisms, the ultimate end point is the complete evaporation of the streamer. Of course streamers do not behave in this way because of losses by thermal conduction and radiation. Heating is also expected to depend on ambient conditions. We use a global MHD model with thermal conduction to examine the effect of changing the heating scale height. We also extend an analytic model of streamers developed by Pneuman (1968) to show that steady streamers are unable to contain plasma for temperatures near the cusp greater than ∼ 2 × 10⁶ K. This revised version was published online in June 2006 with corrections to the Cover Date.