How do I calculate the maximum data rate between a wireless transmitter and receiver?

Question

I am trying to model a wireless communication network with a receiver (Rx) and a transmitter (Tx). If Tx and Rx have known maximum data rates in bps, how do I calculate how the maximum data rates degrade as distance between the two is increased? Or is this an incorrect assumption on my part, and the max rates instead remain constant?

For my model I do know the signal-to-noise ratio at any given time. What I am really interested in is a specific equation that I can plug any relevant values into.

Answer 1

Tigger is correct. The theoretical maximum bit rate can be calculated by solving for R from Eb/No = SW/NR where Eb is the energy per bit, No is the noise power per bit, S is the signal strength, W is the bandwidth, N is the noise power spectral density, and R is the bit rate. In practice, as Tigger also notes, it's a lot more complicated! For example, in a noisy or low signal environment, you might use error detecting/error correcting encoding (i.e. Viterbi or Reed/Solomon) to get a lower bit error rate, but you would then transmit more bits (the encoding bits) than you would for unencoded -- thus a lower effective bit rate. Entire books are devoted to this subject. Sklar's is one of the best, see first reference.

To simplistically answer your question, power received is related to the gain of the receiving antenna, the power transmitted, the gain of the transmitting antenna, the distance, the wavelength, and the gain of the receiving antenna. See equation 5.13 in second reference.

Pr = (PtGt/4piR^2)(lamda^2/4pi)Gr

In your example, all are constant except R^2. So received power decreases by the square of the distance. Since bit error rate is determined by Eb/No, insist that Eb/No, in the first equation, be held constant. Thus, your bit rate also decreases by the square of the distance.

Answer 2

If all other parts of the link stay the same, the carrier power-to-noise power ratio (C/N) will degrade in sympathy with the square of the ratio of the distances. This will cause the bit energy-to-noise power density ratio (Eb/N0) to decrease and thus the bit error rate to increase. This assumes the data rate is also fixed as well as the modulation and forward error correction.

So if you want to maintain a certain bit error rate, you will need to keep the C/N from degrading. One way to do this is to decrease the data rate and thus the bandwidth of the signal. Since the noise power (the N in the C/N) is dependent on the bandwidth the C/N can be maintained and so will the bit error rate.

I haven't gone through the algebra, but I'm thinking the relation would look something like:

(d2/d1)^2 varies as (R1/R2)

where d is the distance and R is the data rate.

I am assuming the modulation and forward error correction are still fixed.

If you do some algebra with the basic link equations, I do believe that is where you will end up.

Send me an email if you want to discuss further.

Answer 3

The maximum data rates of the TX and RX depend on the bandwidth of the circuits, and simplistically it might seem that the least of these will settle the issue.

But for communication between them the max data rate is affected by the noise in the system, and this will depend on the noise of the propagation medium, the noise figure of the RX, the power level of the TX, the transmission loss, and the maximum tolerable error rate.

Satisfactory data transmission can be achieved with higher noise at a lower bitrate because of the statistical nature of the noise, and the time-domain averaging of signals which occurs in the RX.

Sorry I cannot be more specific. I think you will need to consult a good textbook to get the full answer

Answer 4

Theoretically, the data rates do not depend on distance. However, in practical designs they do. As the S/N ratio decreases, the wireless systems switch to more sophisticated coding techniques that require more bandwidth per data rate (or, conversely, since the bandwidth is fixed, less data rate per bandwidth). Thus, with an IEEE 802.11g system, the optimal data rate is 54 Mbps, but as the S/N increases with distance from the access point, the data rate is ratcheted down to 22, then 11, and finally 5.4 Mbps.

Answer 5

Data Rate Formula