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Note that adding (11.28) to (11.27) gives equation (11.18). It is necessary to start with initial values (guesses) for U(i) and (i). The two-dimensional Newton-Raphson method computes the following equations simultaneously:

(9.6)

Dual polarization frequency reuse on a given satellite is performed by implementing the same frequency band in two different transponders which serve the same coverage area, but with two orthogonal polarizations The two polarizations may be linear (eg horizontal and vertical) or circular (right hand circular polarization: RHCP and left hand circular polarization: LHCP) On the satellite, there can be two different antennas, one for each polarization or a common antenna can be used In the latter case, the (transmit or receive) antenna is connected to the transponder through a microwave coupler with two orthogonally polarized ports, called an ortho-mode transducer (OMT) On the earth stations, there is always a common antenna equipped with a transmit/receive OMT Typical values of the discrimination between the two polarizations are between 30 and 35 dB.

When we calculated total portfolio level returns in Part I, we adjusted the total fund market value by the external cash ows, i.e. contributions and withdrawals, before calculating returns. When we calculated security and segment level returns, we adjusted the market value by the purchases and sales of the security itself. In this section we look at how the two types of transactions come together via cash balances enabling the calculation of returns for the complete portfolio. We start with an example using a newly established portfolio. EXHIBIT 15.15

10:2-6

Dual polarization frequency reuse techniques, which employ either circular or linear polarized transmissions, can be impaired by the propagation path through the Earth's atmosphere, resulting in interference between the two orthogonal polarized transmissions This phenomenon, referred to as depolarization or cross-polarization, is induced by two sources: Faraday effect, which is caused by the Earth's magnetic field in the ionosphere, and precipitation, primarily rain or ice crystals Faraday effect causes a time-varying and frequency-dependent polarization rotation (not depolarization) in the orientation of the polarization plane Peak values of Faraday rotation can be as high as 9 at 4 GHz and 4 at 6 GHz If Faraday rotation is significant at the frequency of operation, a method of providing differential rotation of the planes of polarization must be provided at the earth station antenna.

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This is because the direction of rotation, as seen in the direction of propagation, is opposite for transmit relative to receive Faraday rotation has a negligible effect on circular polarization and, in many cases for frequencies above 10 GHz, for linear polarization as well Rain-induced depolarization is caused by non-spherical rain drops, which produce a different attenuation and phase shift between orthogonal linear components of the signal which degrades the discrimination between either linearly or circularly polarized signals Although differential phase shift is the primary cause of depolarization, differential attenuation also becomes important above 10 GHz Propagation models have been developed to predict depolarization impairments due to rain and other meteorological factors In regions with very high rainfall rates (such as Central America and tropical zones), dual polarization frequency reuse operation could be subject to implementation problems For more details, see Annex 1 ( 3).

The application of dual polarization frequency reuse places additional requirements on the satellite and earth station antennas: a) As explained above, each part of the antenna must transmit (or receive) only RF fields according to its own polarization (eg LHCP) and must be isolated from the other polarization (eg RHCP): this requirement is called polarization discrimination (or polarization isolation) If polarization discrimination is not sufficient (eg less than 24 to 28 dB depending on other possible interference noise sources and including imperfect satellite and earth station antennas and also propagation medium effects), a signal at the same frequency will appear from the.