# Sampling rate in Wifi 802.11 -> 20 MHz enough with a BW of 20 MHz?

In a Wifi 802.11n context, I'm looking to find the sampling rate to perform some processing on the signal and I've something I cannot understand : in the book Next Generation Wireless LAN's: 802.11n and 802.11ac, I would like to know the meaning of this sentence :

In 802.11a, the fundamental sampling rate is 20 MHz, with a 64-point FFT/IFFT. The Fourier transform symbol period, T, is 3.2 μs in duration and F is 312.5 kHz.

Why is the sampling rate « 20 MHz » ? The bandwitch of the Wifi 802.11 is 20 MHz so my first idea would be to double this value to validate the Nyquist-Shannon criterion. In addition, the guard interval is not included ?

The radio-frequency signal of 802.11n can have a bandwidth of 20 MHz or 40 MHz. But even if it is 20 MHz, it can be sampled at 20 MSa/s if an I/Q demodulator is used: at the receiver the radio-frequency signal is downconverted to the baseband. The I/Q demodulator has two lowpass output signals (Inhphase/Quadrature or real/imaginary part) with bandwidth 10 MHz each. Two samplers with 20 MSa/s each are then sufficient to fulfill the sampling criterion.

There are other receiver architectures where the received signal is first downconverted to an intermediate frequency (for example 10 MHz) and is then sampled at a higher rate (for example 40 MSa/s). In this case only one sampler is necessary.

The guard interval has only a negligible influence on the signal bandwidth. It is not included in the "Fourier transform period $T$", because it is only added after the transform. The symbol duration after the transmitter IFFT is therefore $$T = N/f_\mathrm s = 64/(20\,\text{MHz}) = 3.2\,\mathrm{\mu s}$$

• OK I understand but why the GI is negligible ? For example, the GI of 1/4 will result of an addition of (3.2µs/4) = 0.8µs so a total symbol time of 4 µs (vs 3.2µs). The duration to send a symbol will increase, which should result in a decrease in bandwidth... – kbu Aug 28 '14 at 7:55

The guard interval (or more precisely the cyclic prefix) does not change the bandwidth of the signal in the frequency domain because the guard interval is removed before taking the FFT of the signal.

One way in which the signal is oversampled in the time domain is by zero-padding subcarriers in the frequency domain. e.g. 802.11n 20 MHz uses 64 subcarriers - 48 subcarriers are data, 4 are pilots, 11 are zero-padded on either side of the spectrum, and 1 is the null DC subcarrier.