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I n t r d u c t i o nThe system considered i n t h i s p a p e r i s a twoway comunication link using ground based transmitter-receiver pairs and a passive reflective s a t e l l i t e , This configuration allms comunications at reasonable pmer levels over distances well beyond the normal l i n e of s i g h t range of high frequency equipment.Maximum power i s d e l i v e r e d by each transmitter (Tx) whenever it i s i n operation, so the signal pmer delivered t 3 the receiver (Rx) i s maximum when the distance travelled by the signal i s minimum, o r when t h e s a t e l l i t e i s most nearly over the geometric center of the two ground s t a t i o n s . Minimum p m e r i s r e c e i v e d when the s a t e l l i t e i s j u s t above the horizon from one o r both of the ground s t a t i o n s . A typical received pmer vs. time curve i s as shown i n Fig. 1, where T denotes the time interval over which the s a t e l l i t e i s i n l i n e of s i g h t view f r m both stat i o n s . It i s not unusual for the received pmer t o vary as much as 1OOO:l during a transmission i n t e r v a l , which may vary f r m s e v e r a l minutes t o twenty minutes o r so, depending upon several factors including the distance between ground s t at i o n s , s a t e l l i t e h e i g h t , and hm nearly the satell i t e passes directly overhead. The system under consideration uses a wideband form of frequency modulation (FN) , and a phase locked loop (PLL) Rx i s used t o t r a c k t h e Doppler frequency s h i f t s caused by s a t e l l i t e motion, follow the instantaneous phase mdulation of the carrier signal, and provide the desired demdulated output signal. This type of Rx performs well as long as the signal t o noise pmer r a t i o , denoted by S/N, i s above the threshold level required t o maintain a phase locked condition. Since the noise pmer is apprsimately uniformly distributed in the frequency range about the received signal, N i s d i r e c t l y r e l a t e d t o the Rx BW. Thus, when S i s small, performance above Rx threshold requires narrm Rx BW. The Ibc BW may be increased as the satellite passes overhead and S increases, but m u s t be reduced as the s a t e l l i t e approaches the opposite horizon and S decreases again. The maximum information rate of the communication system i s d i r e c t l y r e l a t e d t o the Rx BW, s o i t i s desirable t o use maximum instantaneous Rx BW as the performance c r i t e r i o n i n developing an adaptive cmunication link. The remainder of t h i s paper i s devoted to a discussion of the general characteristics of an adaptive control system designed to maximize the information transmission capability of the cmmunication link introduced in the previous paragraphs per satellite pass. Only a minimum of detail regarding the comunication system i s provided, and emphasis i s placed throughout upon the adaptive controller, although an effort i s made to indicate the general operating characteri s t i c s of the ?Ix and Rx, p a r t i c u l a r l y t h e l a t t e r . It w ...

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We describe a new algorithm designed to quickly and robustly solve general linear problems of the form Ax = b. We describe both serial and parallel versions of the algorithm, which can be considered a prioritized version of an Alternating Multiplicative Schwarz procedure. We also adopt a general view of alternating Multiplicative Schwarz procedures which motivates their use on arbitrary problems (even which may not have arisen from problems that are naturally decomposable) by demonstrating that, even in a serial context, algorithms should use many, many partitions to accelerate convergence; having such an over-partitioned system also allows easy parallelization of the algorithm, and scales extremely well. We present extensive empirical evidence which demonstrates that our algorithm, with a companion subsolver, can often improve performance by several orders of magnitude over the subsolver by itself and over other algorithms.

The harmonic analysis of binary approximations to trigonometric reference functions employed in digital signal processing functions is described. An analytic representation of the decomposition of sine or cosine functions into elementary rational binary functions is suggested which permits a direct solution to the problem of calculating the harmonics of the error of approximation. For applications, such as ROM based frequency -synthesizers, angle-encoders, and discrete Fourier transformations, the approach illustrated provides a convenient method of relating the precision of functional implementation of microelectronically integrated functions to the harmonic content of the functional error.