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I have data on the number of devices in a wired network and the data rates on links among these devices. I also know the positions of these devices from which I can compute the distances between the devices.
The idea is that if I were replace the wired network with wireless infrastructure, how much bandwidth am I looking for. Would let's say 200MHz be sufficient for such a case.
Assuming that the BER is very good, how should I go about in calculating the total bandwidth in such a network.
There are many variables involved, but you may proceed as follows. Assume the bit rate in a link is $R_b$. First of all, you choose a constellation; let's say you go with 16-QAM, which transmits four bits per symbol. Now you have a symbol rate $$R_1=R_b/4.$$ Next, you choose an encoder that gives you the BER you need. This encoder will have a certain code rate $R_c$. After encoding, you now have a symbol rate $$R_2=\frac{R_1}{R_c}.$$ Next, you need to take into account the overhead: you need framing and training data. Let's say the overhead is $x\%$. Then your final symbol rate is $$R_3=(1+x)R_2.$$ Now you can calculate the bandwidth you need: $$B=\gamma R_3,$$ where $\gamma$ is an "excess bandwidth" over the theoretical $B=R_3$. The excess bandwidth is typically between 1 and 2.
In summary: the symbol rate is given by the data rate, the constellation, the encoder, and the overhead. The bandwidth is determined by the symbol rate and the excess bandwidht factor.
Note that each of these variables affects the others. For example, if you choose QPSK instead of 16-QAM, you'll have better BER, but $R_1$ will be larger. However, now you need an encoder with smaller rate, so $R_2$ will be smaller. And so on. So, you need to find a combination of variables that you can implement within your constraints and that gives you the BER and data rate you need.
I am still a bit unclear but I am happy to adjust the response if more data becomes available.
Assuming that what you have now resembles a weight matrix $W$, where the weights are the transmission rates of each link, then, the total bandwidth is simply the sum of all entries of $W$.
This doesn't say much about the network.
If, instead, you were to calculate a suitable average of $W$, then that would tell you the average bandwidth between any two nodes. A better approximation to that would be an all-to-all "shortest" path calculation which would take $W$ into account.
This is a bit more informative about the network's "bandwidth" between its nodes.
Finally, you could calculate the network's throughput. This metric can take into account what is actually sent through the network and might be a more accurate, given the circumstances.
You also mention "distance". In this case, you might have to derive an average "weight" for each link for a given distance / conditions to study the bandwidth/rate/throughput behaviour at different configurations.
Hope this helps.
EDIT: It has subsequently come to my attention through this question that the phrase "...the weights are the transmission rates of each link, then, the total bandwidth is simply the sum of all entries of $W$." contains an error when it practically equates bandwidth with transmission rate. This is not correct even for something as simple as BPSK. The "differences" are due to the Baud Rate and encoding schemes employed.
