How Many Users Can a Satellite Network Support?

[noobish]

Homework Statement

Freq band uplink: 13 - 14 GHz
downlink: 10 - 11 GHz
transponder bandwidth: 5 transponder x 54 MHz
channel using linear polarization
EIRP = 59 dBW
G/T = 13.5 (max) dB/K
QPSK modulation

Homework Equations

If each user is offered data rate of 256 kbps, with bit error rate of 10^(-5), and access the network at probability of 0.2

Determine the number of users that can be supported and the Earth station antenna diameter.

The Attempt at a Solution

I spent some time to think about it, but I'm quite clueless..
I would appreciate if some clue is given, what should I first find?

 

[KataKoniK]

First, you need to calculate the bandwidth required for each user. This can be done by using the Shannon-Hartley theorem, which states that the maximum data rate (R) for a channel with bandwidth (B) and signal-to-noise ratio (SNR) is given by R = B*log2(1+SNR). In this case, the SNR can be calculated using the EIRP and G/T values.

Next, you can calculate the number of users that can be supported by dividing the transponder bandwidth by the bandwidth per user. This will give you the maximum number of users that can access the network simultaneously.

To calculate the Earth station antenna diameter, you can use the Friis transmission equation, which relates the power received (Pr) to the transmitted power (Pt), the distance between the transmitter and receiver (d), the frequency (f), and the antenna gains (Gt and Gr). You can rearrange this equation to solve for the antenna diameter (D) as D = (c/(4*pi*f))*sqrt((Pt*Gt*Gr)/(Pr)). Here, c is the speed of light.

Using this equation, you can calculate the required antenna diameter for the given frequency band, EIRP, and G/T values. This diameter would need to be large enough to transmit and receive signals from the maximum distance between the Earth station and the users.

Overall, the number of users that can be supported and the Earth station antenna diameter will depend on the specific values used for the calculations. You may need to make some assumptions or estimations in order to solve the problem.