Geometric aspects of long-term noncoherent integration

Long-term integration is defined as integration, perhaps interrupted, over time periods long enough for targets to move through volumes in space resolvable by the radar. Because the motion of the target is unknown prior to detection, long-term integration must be performed along multiple paths representing plausible target paths. The geometry of such a set of integration paths affects detection performance in several ways. The simplest implementation of long-term integration, using constant radial velocity paths, is investigated. The effects of path geometry on detection is quantified and optimized for a target whose motion is nearly radial but otherwise unknown     

A noise insensitive solution to an ambiguity problem in spectralestimation

The instantaneous frequency measurement (IFM) receiver is capable of measuring the center frequency of single frequency pulses over a wide range (bandwidth) of center frequencies. Because of various constraints, the frequency resolution requirement results in long correlator delay times that reduce the single correlator bandwidth. A large bandwidth can be achieved only if two or more correlators are used. The problem of estimating frequency is then reduced to the simultaneous congruence problem of number theory. A design procedure is presented for solving the congruence problem for a given amount of noise protection, a stated frequency resolution, a minimum bandwidth, and a fixed level of precision (bits) in the IFM receiver     

Signal-to-Noise Ratio of Arbitrary Power-Series Nonlinear Amplifier

A general analysis of the effect of an arbitrary power-series nonlinear amplifier followed by a coherent mixing device on signal-to-noise ratio (SNR) is performed. An expression is derived for the improvement factor which is defined as the logarithm of the ratio of the output SNR to the input SNR. This expression is applicable to the coherent amplitude detector and phase locked loop as well as noncoherent amplifier by appropriate selections of the detection angle. Moreover, the improvement factor can be obtained for noise with an arbitrary amplitude distribution. To demonstrate the applicability of this analysis, the improvement factors of the nonlinear amplifiers such as a power-law amplifier and a power-series amplifier with positive and negative discriminations are numerically calculated for the cases where the input noise amplitude distributions are Rician and triangular.     

Plasma transport across the heliopause

Existing heliopause models are critically rediscussed under the new aspect of possible plasma mixing between the solar wind and the ambient ionized component of the local interstellar medium (LISM). Based on current kinetic plasma theories, effective diffusion rates across the heliopause are evaluated for several models with turbulence caused by electrostatic or electromagnetic interactions that could be envisaged in this context. Some specific cases that may lead to high diffusion rates are investigated, especially in regard to their LISM magnetic field dependence.For weak fields (less than 10^–7 G), macroscopic hydrodynamic instabilities, such as of Rayleigh-Taylor or Kelvin-Helmholtz-types, can be excited. The resulting plasma mixing rates at the heliopause may amount to 20–30% of the impinging mass flow.Recently, an unconventional new approach to the problem for the case of tangential magnetic fields at the heliopause was published in which a continuous change of the plasma properties within an extended boundary layer is described by a complete set of two-fluid plasma equations including a hybrid MHD-formulation of wave-particle interaction effects. If a neutral sheet is assumed to exist within the boundary layer, the magnetic field direction is proven to be constant for a plane-parallel geometry. Considering the electric fields and currents in the layer, an interesting relationship between the field-reconnection probability and the electric conductivity can be derived, permitting a quantitative determination of either of these quantities.An actual value for the electrical conductivity is derived here on the basis of electron distribution functions given by a superposition of Maxwellians with different temperatures. Using two-stream instability theory and retaining only the most unstable modes, an exact solution for the density, velocity, and magnetic and electric fields can be obtained. The electrical conductivity is then shown to be six orders of magnitude lower than calculated by conventional formulas. Interestingly, this leads to an acceptable value of 0.1 for the reconnection coefficient.By analogy with the case of planetary magnetopauses, it is shown here for LISM magnetic fields of the order of 10^–6 G or larger that field reconnection processes may also play an important role for the plasma mixing at the heliopause. The resulting plasma mixing rate is estimated to amount to an average value of 10% of the incident mass flow. It is suggested here that the dependence of the cosmic-ray penetration into the heliosphere on the distribution of reconnecting areas at the heliopause may provide a means of deriving the strength and orientation of the LISM field.A series of observational implications for the expected plasma mixing at the heliopause is discussed in the last part of the paper. In particular, consequences are discussed for the generation of radio noise at the heliopause, for the penetration of LISM neutrals into the heliosphere, for the propagation of cosmic rays towards the inner part of the solar system and for convective electric field mergings into the heliosphere during the course of the solar cycle, depending on the solar cycle variations. With concern to a recent detection of electrostatic plasma waves by plasma receivers on Voyagers 1 and 2, we come to an interesting alternate explanation: the heliopause, rather than the heliospheric shock front, could be responsible for the generation of these waves.     

The extra-galactic background light: A modern version of Olbers' paradox

A non-technical discussion is given of the energy density E of the extra-galactic background light. The fact that E is small means that the space between galaxies is dark, which is a modern version of a classical problem in astronomy known as Olbers' paradox. It is seen that the order of magnitude of E is fixed by the order of magnitude of the lifetime of the galaxies, as pointed out by Harrison; but that the expansion of the Universe can affect E by a smaller factor, typically about 2. These comments should help to end persistent confusion about the effects of the lifetime of the galaxies and the expansion of the Universe on the darkness of the night sky. It is hoped that Olbers' so-called paradox can now rest in peace.     

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.     

Small Aperture Angle Measurement for Active Echo Location Systems

The problem of bearing estimation for active systems is examined from the point of view of the generalized wideband ambiguity function (GAF). The maximum likelihood (ML) estimator is derived and its local and global properties are discussed. A structure is proposed which searches the three-dimensional ambiguity surface in two stages first, in range-Doppler, and then, in bearing with the goal of reducing search complexity when utilizing highly resolvent waveforms. Comparisons are made between the ML estimators and structures utilizing phase information which generate closed form estimators. The beneficial results of full bandwidth utilization are discussed in terms of both local and global properties of the GAF.     

Modeling Random Gyro Drift Rate by Data Dependent Systems

A new modeling procedure is presented in which a mathematical model for random gyro drift rate is obtained directly from the original observations without requiring any theoretical conjectures or preprocessing of the data. The adequate model so obtained confirms the presence of a random walk component causing the "steady state" drift and a stochastic component of the nature of correlated noise. It also provides a quantitative measure of the relative contribution of each component, useful in determining the quality of the gyro in guidance over extended periods.     

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.