In this paper we consider an SS/TDMA system with M uplink beams, N downlink beams, and K, 1 \leq K \leq \min (M, N) transponders. An optimal time slot assignment algorithm for any M, N, K, and any traffic matrix is presented, where optimality means achieving the minimal possible total duration for the given traffic matrix. The number of switching matrices generated by the algorithm is bounded above by N^{2} - N + 1 for K = M = N and MN + K + 1 otherwise. Extensive simulation results on randomly generated matrices are carried out, showing that the average number of switching matrices generated is substantially lower than the bounds.

An Optimum Time Slot Assignment Algorithm for an SS/TDMA System with Variable Number of Transponders

The variance and spectrum of amplitude scintillations due to scattering in both turbulent clear air and rain, are investigated. Included are the important aspect of antenna aperture smoothing with special emphasis on earth-space paths and the equations derived are applicable to system design and remote sensing. A detailed comparison with published experimental results is carried out and the agreement found is good. Two approaches are described in detail: 1) the point receiver classical wave scattering results are modified to include aperture effects, 2) a scalar scattering cross-section approach is combined with the radar equation and the results derived are similar to those of 1). In addition, approach 2) includes the case of rain. Among the results found it is shown that because the scintillation intensity depends on the ratio between the antenna diameter and the diameter of the Fresnel zone in the turbulent region, low elevation paths counteract the tendency to smoothing by large earth station antennas and the scintillations observed remain large. Also pure scattering induced rain scintillations, even in the millimeter region, are in general reduced to an almost negligible level due to aperture smoothing even though for a theoretical point receiver they would be very intense. The time variability of rain attenuation and its polarization dependence as a source of apparent scintillations are also discussed.

Scattering induced microwave scintillations from clear air and rain on earth space paths and the influence of antenna aperture

An increasing number of commercial applications are being promoted for future Ka-band satellite communication systems. Many of these systems will involve low-margin very small aperture terminals (VSATs). These systems are subject to important atmospheric propagation degradations that affect the quality of transmission and the link availability. The objective of this paper is to characterize the Ka-band channel and evaluate the performance degradation in VSATs resulting from atmospheric propagation, impairments. In particular microwave propagation through a turbulent atmosphere is discussed, and the statistical characterization and modeling of tropospheric scintillation is reviewed. Moreover, the paper extends the method proposed by Filip and Vilar (1990) for the long-term characterization and modeling of the combined effect of rain impairments and scintillation. Specifically, the increase in noise temperature during rain events is added to the Filip-Vilar model. This leads to a five-parameter global fading distribution that is used to predict typical Ka-band satellite link outage time, the mathematical formalism is illustrated by applying the method to the selected case of the Advanced Communications Technology Satellite (ACTS)-Georgia Tech experimental downlink. Numerical results confirm that both rain impairments and scintillation are important factors in the design of Ka-band VSAT systems.

Channel characterization and modeling for Ka-band very small aperture terminals

Extensive experimental results are presented on the statistics of tropospheric amplitude scintillations on an X -band satellite down-link obtained using the orbital test satellite beacon transmissions. The experimentally found distribution is shown to depart significantly from the expected log-normal distribution, and this is explained in terms of a Gaussian process with a time variable standard deviation from which a universal model is derived. It has been found that on average no less than about 100 h of data are required before the probability density and cumulative probability distribution functions approach stationarity. The statistics of the scintillation intensity are also presented, and a log-normal distribution of intensity is shown to be in good agreement with observations from other experimental sites. Link budget implications are outlined together with a simple strategy for the investigation of the scintillation process at any ground station.

Experimental and theoretical statistics of microwave amplitude scintillations on satellite down-links

Single scattering properties of ice crystals are described at microwave frequencies using discrete dipole approximations and Rayleigh scattering techniques. For a given shape, the average bulk densities of ice crystals can be estimated using the ratio of the copolarized radar signal in a linear (horizontal, vertical) polarization basis. Reflectivity depends on the ice content (g/spl times/m/sup -3/), and also on both size distribution parameters and average bulk density of the scatterers. Differential propagation phase is primarily a function of shape, ice water content, and is independent of size distribution parameters. Thus, by using a combination of polarimetric radar measurements, average ice content, bulk density, and shape of distributed scatterers call be inferred. These techniques become quite complex in the case of a winter storm where scatterers can exist with varying shape and bulk densities. Polarimetric radar properties of such complex distributed scatterers are modeled. Physical variations in the relation among ice water content, reflectivity, and differential propagation phase are considered with respect to change in the shape of size distribution, bulk density,,and average shape of the scatterers. Also, simultaneous polarimetric radar observations and in situ aircraft measurements are shown to demonstrate practical applicability of the techniques. >

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Polarimetric radar studies of atmospheric ice particles

The amplitudes of satellite signals sometimes scintillate ± several decibels when heavy cumulus clouds pass through the radio path on hot summer days. These scintillations have been measured on a 19-GHz and 28-GHz earth-space path using 7-m and 0.6-m antennas at Crawford Hill, New Jersey. Scintillation intensity at 28 GHz is 1.2 times that at 19 GHz, consistent with the ƒ7/12 frequency dependence produced by a thin turbulent layer. The scintillation process is polarization-independent and has a low-pass power spectrum with a cutoff frequency of about 0.3 Hz. Rain attenuation often accompanies the more intense scintillation. The mean duration of scintillation-produced fades is short (about 1.3 s for fades greater than 1 dB), but over 1000 fades of over 1 dB at 28 GHz were observed in two summer months. Because of their weak frequency dependence these short but frequent events could produce repeated outages on 4- and 6-GHz earth-space links having low attenuation margins.

Observations of cloud‐produced amplitude scintillation on 19‐ and 28‐GHz earth‐space paths

Strong depolarization (sometimes > −20 dB) at 19 and 12 GHz occurring with low signal attenuation (often <1 dB) and associated with summer thunderstorms was described earlier. This paper describes winter observations at 19 and 28 GHz of what appears to be the same phenomenon. The depolarization is a few dB stronger at 28 GHz but is highly correlated between the two frequencies. The winter depolarization events appear when ground temperatures are near or below freezing and clouds are along the path. These events are caused by differential phase shift through ice crystals in the clouds.

Depolarization of 19 and 28 GHz earth‐space signals by ice particles

This paper describes the receiving electronics built at the Bell Laboratories Crawford Hill facility at Holmdel, New Jersey to use the 19-and 28-GHz beacons on the COMSTAR satellites for propagation measurements. The receiving system accurately determines attenuation, differential phase, depolarization, bandwidth limitations and angular scatter of these signals produced by rain. This highly reliable system operates continuously and unattended; it automatically reacquires the beacon signals after dropout due to severe attenuation or momentary power outage. Correlations among strong and weak signal components are used to permit detection of weak cross-polarized signals during severe fading. Receiver noise bandwidths as low as 1.6 Hz are used. A high degree of phase stability is achieved in all circuits and components.

COMSTAR experiment: The 19- and 28-GHz receiving electronics for the crawford hill COMSTAR beacon propagation experiment

One year of propagation data were obtained for a 19-GHz earth-satellite path terminating at Crawford Hill, New Jersey. These data were analyzed to determine the depolarizing and attenuating properties of liquid (rain) and solid (ice) hydrometeors along the path. The observed projections of the symmetry axes of ice and rain hydrometeors were found, generally, to lie near the horizontal and vertical planes. Ice deviates from this orientation more than rain; ice occasionally is found at any possible orientation. The observed differential attenuation and differential phase for a given copolarized signal attenuation were lower than those seen on terrestrial paths. Present terrestrial rain models do not adequately describe these results. Maximum depolarization was observed to occur for linear incident polarizations near 45°. This maximum depolarization is sufficient to significantly affect the performance of dual-polarization satellite communications systems. Depolarization close to the minimum attainable for instantaneously optimized linear incident polarizations was observed most of the time for fixed vertical and horizontal polarizations. These minimum depolarization levels were low enough to have little effect on most dual-polarization systems.

H. W. Arnold

Papers

Observations of cloud‐produced amplitude scintillation on 19‐ and 28‐GHz earth‐space paths

Depolarization of 19 and 28 GHz earth‐space signals by ice particles

COMSTAR experiment: The 19- and 28-GHz receiving electronics for the crawford hill COMSTAR beacon propagation experiment

Properties of attenuating and depolarizing atmospheric hydrometeors measured on a 19-GHz earth-space radio path

Differential attenuation and depolarization measurements from a 19 GHz Comstar satellite beacon propagation experiment