# Spread spectrum bandwidth

Can someone explain how it derived the bandwidth for spread spectrum on following link http://www.ausairpower.net/OSR-0597.html (paragraph 9)?

## 2 Answers

The first equation is simply the well known relationship for channel capacity derived by Claude Shannon. The second equation is an approximation for cases when the SNR is much less than 1. It relies on another approximation: ln(1+x)=x when x is much less than one. The factor 1.44 is equal to 1/ln(2) which is needed because the Shannnon equation uses log2 rather than ln.

• But how he derived the required bandwidth of 208 kHz? – Quirik Oct 8 '16 at 12:45

From my FM telemetry days in the 70's I learned that the noise improvement factor from carrier/noise (CNR) demodulated to signal to noise ratio (SNR) was due to the modulation index, m = carrier BW/signal BW and the SNR improvement factor was something like 20log (m) above the noise threshold.

So I expect in digital spread spectrum the CNR to SNR improvement is something like 20 log (208kHz/3kHz)=36.8dB above the carrier CNR.

I don't know the precise formula on SNR improvement, which includes coding rules and correction improvement factors, but this gives you an idea of how it is calculated.

• The SNR in Shannon capacity formula is expressed in decibels? What about when SNR is negative number? – Quirik Oct 8 '16 at 16:40