DETAILED DESCRIPTION Broadcast satellites are typically characterized by a relatively small number of up-link transmission source nodes and a large number of down-link destination nodes.
For the up-link, of course, the number of ground stations equipped with transmit capability may be quite large, but only a small subset actually transmit at any given time.
The total up-link data rate, as measured by the sum of the rates for each source, is typically much smaller than the down-link rate as measured by the sum of the rates for each destination.
Because of the disparity between the up- and down-link rates, it is convenient to treat the two separately.
In regard to the down-link, each down-link message is a multiple of some basic minimum message unit and these message units can be numbered, for example, from 1 to M.
When used for television broadcasting, for example, each message unit might be a television channel.
When applying the present invention to broadcasting in the United States, for example, the United States is divided into N spot beam footprints which completely span the region occupied by the receiving sites or terminals.
Stated differently, each point in the United States is within the 3 dB contour of some spot beam.
The aperture of the satellite antenna determines both the beamwidth and the number N of spot beam footprints required.
As a result thereof, an M.
times.
N receive matrix R can be constructed: ##EQU1## where element r.
sub.
i,j =1 if message unit i is to be received by a ground station within the jth spot beam footprint and is zero otherwise.
From matrix (1), the minimum required down-link power is determined as follows.
Since all message units are of the same bit rate, each message unit requires, for example, P watts of power to be received in some given spot beam footprint.
Clearly, P varies inversely with the spot beam antenna gain.
Therefore, the total required down-link power P.
sub.
D is the product of P and the number of message destinations in matrix (1), i.
e.
, ##EQU2## Having determined the minimum required down-link power, it is to be noted that within this constraint, matrix (1) can be modified upon demand
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