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The use of extra collecting horns in the focal plane of an antenna as a means of determining the Direction of Arrival (DOA) of the signal impinging on it, provided it is within the antenna beam, is considered. Our analysis yields a relatively simple algorithm to extract the DOA from the horns' outputs. An algorithm which, in effect, measures the thermal noise of the horns' signals and determines its effect on the uncertainty of the extracted DOA parameters is developed. Both algorithms were implemented in software and tested in simulated data. Based on these tests, it is concluded that this is a viable approach to the DOA determination. Though the results obtained are of general applicability, the particular motivation for the present work is their application to the pointing of a mechanically deformed antenna. It is anticipated that the pointing algorithm developed for a deformed antenna could be obtained as a small perturbation of the algorithm developed for an undeformed antenna. In this context, it should be pointed out that, with a deformed antenna, the array of horns and its associated circuitry constitute the main part of the deformation-compensation system. In this case, the pointing system proposed may be viewed as an additional task carried out by the deformation-compensation hardware.

Twenty-one radar images of the surface of Venus obtained between 1972 and 1982 have been compared to follow the motion of 28 distinct features. The delays and Doppler shifts of these features with respect to the subradar points on the various days were used in a nonlinear least-squares parameter estimation algorithm to refine the period and pole orientation of Venus. The period is found to be -243.022 + or - 0.003 days; the right ascension and declination of the pole are: alpha = 272.816 + or - 0.14 deg; beta = 67.218 + or - 0.05 deg (B1950). These standard error estimates attempt to include effects of systematic errors.

Weights for K-beam system computed K/6 times faster. In single-frequency adaptive-array communication system in whick K mobile users communicate with central station equipped with n-antenna array. Each K signal recoverable by taking specific weighted sum of n complex antenna voltages.

A decomposition of the adapted pattern generated by an adaptive array operating in an environment with one narrowband signal, K-1 narrowband jammers, and programmed to produce the maximum SNR is presented. The antenna voltage pattern is demonstrated to be a linear combination of K (or less) basis patterns, each from a sole source, and the kth basis pattern becomes the desired signal realized by the array. Isotropic array patterns result in retrodirective basis patterns, and the decomposition can be configured to obtain the retrodirective beams for all K.

The antenna pattern of a receiving adaptive array is investigated for the case of its operation in an environment of one desirable narrow-band signal and (K-1) narrow-band jammers. Results show that the adapted (voltage) antenna pattern of the array is a linear combination of k (or less) basis-patterns, each of which is a function of one source only. It is determined that these basis-patterns have a simple physical meaning in that the k-th basis-pattern is the pattern formed by the array when the transmission of source k is considered a desired signal and all other sources are turned off.

Attention is given to a narrow-band communication system consisting of a central station trying to receive signals simultaneously from K spatially distinct mobile users sharing the same frequencies. One example of such a system is a group of aircraft and ships transmitting messages to a communication satellite. A reasonable approach to such a multiple access system may be based on equipping the central station with an n-element antenna array where n is equal to or greater than K. The array employs K sets of n weights to segregate the signals received from the K users. The weights are determined by direct computation based on position information transmitted by the users. A description is presented of an improved technique which makes it possible to reduce significantly the number of required computer operations in comparison to currently known techniques.

A closed-form expression for the steady-state output signal-to-noise ratio (SNR) of an n-element adaptive array excited by one desired narrow-band signal and K - 1 narrow-band jammers is obtained. This is facilitated by representing each excitation by a complex n-dimensional vector - the excitation vector. It is shown that the important system parameters are functions of scalar products of pairs of these excitation vectors. In particular, the normalized output SNR of the array is shown to be the ratio of determinants whose elements involve these scaler products. Such determinants are also shown to be involved in the expressions for the optimal array weights.

A single frequency communication system is considered consisting of K possibly moving users distributed in space simultaneously communicating with a central station equipped with a computationally adapted array of n = or K antennas. Such a configuration could result if K spacecraft were to be simultaneously tracked by a single DSN complex consisting of an n antennas array. The array employs K sets of n weights to segregate the signals received from the K users. The weights are determined by direct computation based on known position information of the K users. Currently known techniques require (for n = K) about (4/3)K to the 4th power computer operations (multiply and add) to perform such computations. A technique that accomplishes this same goal in 8 K to the 3rd power operations, yielding a reduction by a factor K/6, was developed.

The steady-state behavior of an adaptive array is considered and the degradation of its output SNR in the presence of jammers is analyzed. It is shown that for given incident powers (of jammers and signal), there are geometric configurations of the sources exciting the array for which the SNR degradation is much more pronounced than for other configurations. This result is proved for the case where the thermal noise power of each array receiver is negligible compared to the total power intercepted by the array from each jammer. The result is general, being valid for an array of n arbitrary antennae in an arbitrary three-dimensional configuration. It is stated in terms of linear dependence relationships among the n-dimensional vectors that describe the effects of the sources on the array.

Two radar observations of a set of three relatively small features on the surface of Venus have facilitated a refined determination of the spin vector of Venus. The period is found to be 243.019 + or 0.014 days, while the obliquity is 177.22 + or - 0.18 deg. The effects of deviations from exact sphericity on the interpretation of the measurements are discussed at length and the question of resonance with earth is reexamined.

Two designs have been developed for cost-effective, fast transformation of data points in small batches (where N is equal to or less than 32). One design is applicable to N prime and one to all N.

A high-resolution study of the surface of Mercury with a 2.388 GHz radar reveals the existence of hills and valleys with heights (depths) of about 1 km. There is also evidence supporting the existence of craters with diameters of about 50 km and depths of about 700 m.

The main characteristics of the discrete Fourier transform (DFT) algorithm considered by Winograd (1976) is a significant reduction in the number of multiplications. Its primary disadvantage is a higher structural complexity. It is, therefore, difficult to translate the reduced number of multiplications into faster execution of the DFT by means of a software implementation of the algorithm. For this reason, a hardware implementation is considered in the current study, taking into account a design based on the algorithm prescription discussed by Zohar (1979). The hardware implementation of a FORTRAN subroutine is proposed, giving attention to a pipelining scheme in which 5 consecutive data batches are being operated on simultaneously, each batch undergoing one of 5 processing phases.

A detailed and complete description of Winograd's discrete Fourier transform algorithm (DFT) is presented omitting all proofs and derivations. The algorithm begins with the transfer of data from the input vector array to the working array where the actual transformation takes place, otherwise known as input scrambling and output unscrambling. The third array holds constraints required in the transformation stage that are evaluated in the precomputation stage. The algorithm is made up of several FORTRAN subroutines which are not to be confused with practical software algorithmic implementation since they are designed for clarity and not for speed.

The new DFT algorithm of S. Winograd is developed and presented in detail. This is an algorithm which uses about 1/5 of the number of multiplications used by the Cooley-Tukey algorithm and is applicable to any order which is a product of relatively prime factors from the following list: 2,3,4,5,7,8,9,16. The algorithm is presented in terms of a series of tableaus which are convenient, compact, graphical representations of the sequence of arithmetic operations in the corresponding parts of the algorithm. Using these in conjunction with included Tables makes it relatively easy to apply the algorithm and evaluate its performance.

Device, which converts directly from analog signal to its radix (-2) representation, is based on successive approximation approach.

Modification of conventional digital counting filter is designed to store all possible combinations of filter coefficients in random access memory. Filter includes analog-to-digital coverter, X shift register, memory, accumulator, and digital-to-analog converter.

High-speed variation of counting digital filter implements count in a way which allows shortest permissible spacing between samples of input signal to be small fraction of time it takes to compute output sample.

Hybrid device, which is modification of counting digital filter, obtains high speed through lower precision mainly effected by substituting analog device for digital counter.

Filter has array of line segments of various lengths which may be switched into circulating line by machine operator. Design is useful in cases where filter speed is not critical; by sacrificing speed, filter can be made at lower cost.

Overall design of filter combines radix converter with ADC in single functional unit that directly converts analog input to its negative binary representation. Four basic elements of filter are fixed register, shift register, counter, and accumulator.

The digital filtering algorithm of W. D. Little, which employs a large RAM to obtain high speed, is implemented in a simple hardware configuration. The nonrecursive version of this filter is compared to the counting digital filter and found to be competitive for low-order filters up to order 7 (8 coefficients).

High precision moments for fourier coefficients of arbitrary functions

Matched filters for optimal high speed detection of binary signals

Negative radix conversion results applied to logical design of serial converter

Trench algorithm for Toeplitz matrix inversion, presenting proof for nonHermitian matrices case

Venus map, discussing two dimensional technique using radar range and Doppler shift for study of surface

Several embodiments of a counting digital filter of the non-recursive type are disclosed. In each embodiment two registers, at least one of which is a shift register, are included. The shift register received j sub x-bit data input words bit by bit. The kth data word is represented by the integer.

Analysis of the bit-level operations involved in the convolutions realizing recursive digital filters leads to hardware designs of such filters based on the operation of counting. Various designs realizing both the canonic and 'direct' forms are presented with particular emphasis on low-cost low-speed high-flexibility machines.

Analysis of the bit-level operations involved in the convolution realizing a nonrecursive digital filter leads to hardware designs of digital filters based on the operation of counting. Two distinct designs are outlined: the first one is capable of very high speed but is rather expensive; the second is quite slow but has the advantages of low cost and high flexibility. The basic designs considered utilize fixed-point representation for the data and filter coefficients. Variants allowing floating-point representation of the coefficients are also described.