Computational Precision Requirements for Optimal Weights in Adaptive Processing

The required accuracy for computing the estimated optimum weights of an adaptive processor has been analyzed by investigating the effects of errors in computing the inverse matrix. It is shown that the required precision depends upon the matrix. An equation for the general case is derived. Several special cases are considered in detail. It is shown that the case of a single interference source requires the highest precision. The least stressing case is identifi'ed and compared to the worst case. The requirements for a "typical" case are also considered. A comparison of the requirements for the covariance matrix estimation technique and for adaptive weight implementation using gradient descent techniques is given. It is shown that there is a dichotomy in that cases that do not stress one technique tend to stress the other.     

The strong stability of most natural motions

Problems of Hamiltonian Mechanics can generally be simplified by some Von Zeipel transformations which reduce the influence of short period parameters and lead to very slowly variable functions: the “quasi-integrals”; however these transformations are implicit and then difficult to use.An explicit construction of the quasi-integrals is presented here and is used to integrate the motion of an artificial satellite perturbed by the zonal harmonics of the Earth gravitational potential; the quasi-integrals are also used to obtain informations on the stability of natural satellites, i.e. lower bounds on the duration of escape or capture.     

Baseband Modeling and Distortion Equalization of the DeLange FM Oscillator by Functional Methods

Exact and approximate baseband models of the DeLange frequency-modulated oscillator are derived. Exact and approximate baseband distortion equalizers, that may be used to predistort the modulation voltage so that the distortion in the output phase of the oscillator is removed, are also given.     

Effects of Modulation Nonlinearity on the Range Response of FM Radars

The effect of modulation nonlinearity on the range response of FM radars with harmonic processing and ?triangle? modulation is derived. The nonlinearity may be desirable or undesirable; that is, the sidelobe level of the range response may be decreased or increased depending on the shape and amount of nonlinearity. The results of this paper may be used to predict the actual range laws of existing ?linear? FM radars; or, alternately, to specify the desired amount of modulation nonlinearity for new FM radars so that superior sidelobe suppression can be realized.     

The Circular Synthetic Radar

A new type of synthetic radar, the circular synthetic radar, uses a simple interferometer whose elements are mounted at the ends of a horizontal boom rotating about a vertical mast. Pulses are radiated alternately ?in-phase? and in ?phase-quadrature.? The returning echoes are also detected incoherently, both ?in-phase? and in ?phase-quadrature.? The four distinct outputs are fed into an on-line computer which, after a Fourier analysis, synthesizes a mapping function of the azimuthal distribution of targets.     

Recursive Computation of the Generalized Q Function

A recursive method of computing values of the generalized Q function is described. The Q function is also interpreted in terms of noncentral chi-square distributed random variables, and in terms of the difference between Poisson random variables.     

Further Results on Multipath Angle Error Reduction Using Multiple-Target Methods

The two-target technique proposed by the author in an earlier paper [1] for reducing radar multipath angle tracking errors has been simulated on a digital computer assuming an actual closed-loop system. When tracking with noise, the technique provides angle error performance which compares quite favorably with the expected performance given in [1] Furthermore, the large bias errors usually encountered in normal monopulse systems at low elevation angles are removed. Results of typical tracks are given, both for the method of [1], and for a modified version of the method which applies primarily to shipboard radar systems. Some results on loss of lock are also presented.     

A UHF True Logarithmic IF Amplifier

A UHF ?true logarithmic IF? which yields a carrier output proportional in amplitude to the logarithm of the carrier input has been constructed. Although this ?true? form has been known for a number of years, it appears to have been neglected in development. Good performance has been obtained over a 60-dB input signal range with rise and fall times of 2 ns per 20 dB. A high-level, detected dc coupled output without the use of any dc amplifier is obtained. Coherent signal processing of the output carrier is possible, and other important advantages to this type of logarithmic IF are described.