The detection of moving targets by passive radio temperature measurements is studied. A radio image is reconstructed by linear spatial filtering of simultaneous measured brightness samples, obtained by multiple regularly spaced antenna beams. With fixed spatial filters, the receiver integration time must be short enough to freeze motion, thus limiting the signal-to-noise ratio obtained in the reconstruction image. It is shown that in the one-dimensional case a time-varying matched spatial filter yields the same signal-to-noise ratio in the reconstructed image as would be obtained from a stationary target with a fixed matched filter.>

Abstract We present counting formulas for the number of different ways to grow a given rooted tree, over a specified number of intervals. We call these growth plans, or simply plans. This problem arises, for example, in analog toll‐connect networks in which it is desired to introduce digital technology to serve increasing circuit requirements, in the cheapest way. Each circuit in such a network extends from a particular node called the toll center to one of the other nodes. The toll center corresponds to the root, and the portion of the network containing digital equipment corresponds to the rooted subtree whose growth we study. Even for networks of modest size and few growth intervals, the number of plans is too large to permit finding the cheapest by an exhaustive search. We observe that plans differing only in their growth pattern in the neighborhood of some particular node have cost differences that depend principally on their local growth patterns. It is therefore often possible to eliminate at a single stroke a large class of plans having a specified local growth plan at a particular node. By repetition, the number of remaining plans that must have their individual total costs computed can often be reduced to a number sufficiently small for an exhaustive search. We describe two types of local growth behavior appropriate for eliminating classes of plans in this network problem, and give corresponding counting formulas for the number of tree growth plans under these restrictions. A generalized counting formula with arbitrary local restrictions at each node is presented; this general formula contains the prior results as special cases. Finally, an example illustrates the great reduction in number of plans that can sometimes be obtained.

The author seeks the maximum number of users possible for multiuser, spread-spectrum radio systems, as the signal set is varied, under the following ideal conditions: 1) no fading; 2) synchronous system; 3) orthogonal signal set for each user; 4) matched-filter individual receivers; 5) no additive noise. Welch (1974) has given an upper bound on the number of vectors (or equivalently signals)wpossible in ad-dimensional space, given the maximum cross-correlation magnitudeCmaxbetween any vector pair. However, the error rate for the systems under study may depend on a suitably defined root-mean-square cross correlationCrms, rather than on the maximum cross correlationCmaxof a vector set. Welch's results are extended tod-dimensional vector sets of sizewdivided into alphabets of sizeA, the vectors of each alphabet being strictly orthogonal, and the maximum size of such a vector set is given as function ofCrms. It is demonstrated that as Welch's limit is approached, all cross correlations must approachCmax, and given precise limits on the way in which this must occur. Similarly, close to the present bounds (in terms ofCrms) all rms cross correlations must be close toCrms. Particular examples are given of signal sets close to the present bounds.

An ELF (extremely low frequency) communication system has been proposed for communication from land to submerged submarines. We present an analytical study of conceptual feasibility of such a system and discuss some of its properties. We find no fundamental technical reason why such a system is infeasible. The present work yields the general structure of the receiver, and estimates for the important parameters of such a system. Nonlinear processing ahead of the FSK (frequency-shift keying) receiver in the submarine appears essential. Such processing greatly reduces the effects of atmospheric noise due to nearby lightning storms, and hence, makes reliable operation possible at much smaller transmitter power.