I'm looking for a formula to calculate the bit error rate of a wifi communication 802.11a/b/g according to the distance between transmitter and receiver.
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There is no one-line "formula", if that is what you are looking for. Traditionally, BER is captured at link-level, meaning it considers the effect of:
- Modulation (BPSK, QPSK, etc.)
- Channel coding rate
- Multipath fading and channel conditions (eg. AWGN, Rayleigh fading, etc.)
However, once you talk about distance between TX-RX, we are talking about propagation effects, shadowing, which are part of system-level simulations.
Moereover, your question is ambiguous: you simply state 802.11a/b/g without mentioning whether you are talking of OFDM or DSSS, what channel bandwidth, etc.
Depending on the scenario, there are lots of IEEE papers, ex: BER simulation for WLAN networks in realistic environment
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$\begingroup$ Ok I agree with you. I didn't give any information about. I made a mistake. Now I will be more specific. Let's suppose that the propagation come in free space and suppose that the modulation used is BPSK and we have a channel that introdues AWGN $\endgroup$– MazzySep 25, 2012 at 15:16
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$\begingroup$ BER for BPSK in AWGN is given in almost every elementary textbook on digital communications, or look here, $BER = \frac12 erfc(\sqrt{\frac{E_b}{N_o}})$. What this doesn't say is the effect of OFDM and channel coding in the least. The best way is to perform simulations and get an empirical BER vs SNR curve. Then may be you can use curve-fitting and deduce a formula, if your really want one. $\endgroup$– SatishSep 25, 2012 at 15:25
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$\begingroup$ But in that formula there is no presence of distances. How can I introduce it? $\endgroup$– MazzySep 25, 2012 at 15:45
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1$\begingroup$ Yup, that's what I said: there is no direct formula to relate distance to BER. BER is almost always plotted as a function of SNR ($E_b/N_0$) for a given MCS (modulation and coding scheme). If you want to consider TX-RX distance, you must also consider path loss, lognormal shadowing, Doppler effect, and such large-scale parameters. BER is for "lower-level" details, but parameters like RSSI, cell throughput, etc. are used to observe the effect of TX-RX distance. $\endgroup$– SatishSep 25, 2012 at 16:04
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$\begingroup$ mmm I'm not totally agree with you. according to relation you gave me I can found that the Energy per bit of the receiver is equal to $\frac{E_{b}^{tx}}{{\gamma}}$ where ${\gamma}$ is the attenuation in free space that it is equal to $(\frac{4{\pi}d}{{\lambda}})^2$ where $d$ is the distance between transmitter and receiver and ${\lambda}=\frac{v}{f}$ $\endgroup$– MazzySep 25, 2012 at 16:14