In general one does not measure point processes, but rather measures an integral of the process over a specific interval. In this note we have investigated how the covariance of a specific class of processes is altered by a finite measurement.

A continuing interest exists in the Department of Defense to stress technology wherever it may result in the improvement of a military system. One important area where this is currently occurring is in laser communications. Specifically, an extensive effort is underway to exploit the "Blue/Green" transmission window in the ocean and develop a strategic laser communication system operating between an orbiting satellite and a submerged submarine. In this paper we discuss some of the operational motivations for such a system together with a generic system design.

A multiple scattering model is used and extended to characterize the channel between underwater and airborne (satellite) terminals at optical frequencies. The effects of the air/sea interface are also included with approximate solutions accurate for elevation angles above 45°. The results are presented in terms of a radiance function which is related to the transform of the spatial covariance function (mutual coherence function). The primary losses are shown to be a result of the water absorption coeffecient and not the extinction coefficient. The scattering losses can be isolated from the absorption losses and for certain cases, where the receiver is imbedded in the scattering medium, can be completely recovered. New components may be required to achieve this performance. The effects of ocean roughness are shown to have a minimal effect upon the subsurface reception while causing possible beam steering of subsurface transmission. Although substantial losses are experienced, duplex operation can be achieved at modest data rates.

In reducing the data from a recent series of high altitude balloon to aircraft measurements atLband, some qualitative results were reported concerning the negative correlation between the vertical and horizontal polarizations. Some of these data are presented in strip chart form to display this effect. In addition, a plot of the sum of the squares of the two polarizations is also presented to indicate the level of the received power and the possible benefits of power combining. Finally, the joint envelope density is examined in the 1imit of deep fading and the power fades are compared with those for independent combining.

In this paper we formulate the general problem of determining the photoelectron "counting" distribution resulting from an electromagnetic field impinging on a quantum detector. Although the detector model used was derived quantum mechanically, our treatment is wholly classical and includes all results known to date. This combination is commonly referred to as the semiclassical approach. The emphasis, however, lies in directing the problem towards optical communication. The electromagnetic field is assumed to be the sum of a deterministic signal and a zero-mean narrow-band Gaussian random process, and is expanded in a Karhunen-Loève series of orthogonal functions. Several examples are given. It is shown that all the results obtainable can be written explicitly in terms of the noise covariance function. Particular attention is given to the case of a signal plus white Gaussian noise, both of which are band-limited to\pm BHz. Since the result is a fundamental one, to add some physical insight, we show four methods by which it can be obtained. Various limiting forms of this distribution are derived, including the necessary conditions for those commonly accepted. The likelihood functional is established and is shown to be the product of Laguerre polynomials. For the problem of continuous estimation, the Fisher information kernel is derived and an important limiting form is obtained. The maximum a posteriori (MAP) and maximum-likelihood (ML) estimation equations are also derived. In the latter case the results are also functions of Laguerre polynomials.

In many applications a Poisson shot noise (PSN) process is said to statistically "represent" its intensity process. In this paper an investigation is made of the relationship between a PSN process and its intensity, when the latter is a sample function of a continuous stochastic process. The difference of the moments and the mean-square difference between the two processes are examined. The continuity assumption on the intensity permits the development of a sequence of moment relationships in which the effect of the PSN parameters can be seen. The results simplify and afford some degree of physical interpretation when the component functions of the PSN are "rectangular," or when the intensity process does not vary appreciably over their time width. An integral equation is derived that defines the component function that minimizes the mean-square difference between the two processes. It is shown that a "degenerate" form of component function induces complete statistical equality of the two processes. The problem has application to optical communication systems using photodetectors.