# How the increasing of sampling frequency in OFDM didn't cause increase on the required channel bandwidth

In OFDM, how the increasing of sampling frequency didn't cause increase on the required channel bandwidth (fs>>BW), as i know sampling frequency means number of samples per second, if this number of samples increased by logic the the needed bandwidth increase.

• So, you believe that if you have a sine wave, its frequency depends on your sampling rate? – MBaz May 17 '17 at 22:44
• No, but the increasing of number of samples isn't mean more data to be transmitted, and so on more bandwidth . – user24907 May 18 '17 at 7:40
• If no sine wave changes, then the spectrum of your signal does not change, thus the bandwidth does not change, no matter how expensive the DAC and clock frequency. They are independent (as long an Nyquist is satisfied). – hotpaw2 May 18 '17 at 14:05
• Thanks alot @hotpaw2 , another question please , in OFDM , if the sampling frequency increased, null subcarriers will be added, isn't each one of these null subcarriers has its own bandwidth (regardless its contain), and so on the required bandwidth increase? – user24907 May 18 '17 at 14:35
• @AlexTP You might have nailed it. If we start with the discrete-time OFDM symbol s[n], and increase the sampling rate (defined by the time interval between successive samples of s[n], then the OFDM symbol becomes "shorter" and therefore its bandwidth will increase. – MBaz May 18 '17 at 14:57

You can say the null subcarriers have their own bandwidth if you define an alphabet including "zeros" and use null carriers to transmit these "zeros". As the comment of MBaz,

If we start with the discrete-time OFDM symbol s[n], and increase the sampling rate (defined by the time interval between successive samples of s[n]), then the OFDM symbol becomes "shorter" and therefore its bandwidth will increase.

But it is not the case. The OFDM symbol $T_u = N_{dft} T_s = 1/\Delta f$.

In this bandwidth interpretation, I think the term "virtual subcarrier" is more appropriate.

What you send over by electromagetic wave is data in $N$ active subcarriers $< N_{dft}$, or the frequency positions of null/virtual subcarriers can be used for other systems; because when you revert back the time domain signal to the frequency domain, what you need is the frequency positions of these active subcarriers.

It is easier to think OFDM as FDM. In this case you have $N$ narrowbands of bandwidth $B_{nb}$ and a sample rate $F_s > N B_{nb}$ is required for practical implementations, such as easily-realizable anti-aliasing filters. OFDM is simply one implementation of this system by using $\Delta f = B_{nb}$ and $F_s = N_{dft} \Delta f = N_{dft} B_{nb} > N B_{nb}$.

• Thanks alot @Alex TP, your words " the frequency positions of null/virtual subcarriers can be used for other systems" means that these subcarriers have its own frequency position. For example if i have 600 active subcarriers, 424 null subcarriers and these 424 null subcarriers are centerened at the middle, that mean the first active data subcarrier will be centered at (424/2*Δf). If that what happens, that means the bandwidth increased to be equal sampling frequency. correct for me please. – user24907 May 20 '17 at 18:19
• @user24907 the subcarrier positions should be like this image i.stack.imgur.com/CxTXu.png – AlexTP May 20 '17 at 21:59
• null subcarriers centered at middle is a delusion of DFT implementation. If you use Matlab/Octave, you should use fftshift function. – AlexTP May 20 '17 at 22:00
• TP Could you please give more explaination or any link to understand it? – user24907 May 21 '17 at 17:23
• @user24907 for fftshift ? fr.mathworks.com/help/matlab/ref/fftshift.html – AlexTP May 21 '17 at 18:15