# Does the data rate of ofdm depends on number of subcarriers

I am trying to investigate the performance of OFDM system practically, I am using sampling rate $$1 GSps$$ giving bandwidth $$B = 0.5 GHz$$. What I find is when setting the number of subcarriers $$N = 64$$ or $$N = 128$$; the performance is OK. However, when increasing it into $$N = 1024$$; the performance becomes worse. Why does that happen? Is that related into the achieved data rate as it increases when increasing the number of subcarriers?

According to my understanding, the subcarriers spacing $$\Delta f = \frac{B}{N}$$ so increasing the number of subcarriers $$B$$ will decrease the subcarrier spacing at the expense of performance. Is that analysis correct or there are other reasons? What's the effect of reducing the subcarrier spacing on the performance ?

• "Gbps" is a bitrate, not a sampling rate. If you mean a sampling rate of 1 GHz, or 1 billion samples per second, 1 GSps, then that gives you a bandwidth of 1 GHz, considering that OFDM is a complex baseband technique. So, that part of your question raises a lot of questions! Aug 4 at 10:11
• Sorry for the typo error, yes, it's 1 GSps. 2- Sampling at 1 GSps will give a bandwidth of 1 GHz ?! Normally, The bandwidth is half of the sampling frequency; A bandwidth of 1000 Hertz means that the sampling frequency is set to 2000 samples/second. How did you calculate it to be 1 GHz ? Aug 4 at 10:43
• no, that's only the case for real-valued sampling. But as said, OFDM is a complex baseband technique, and you get 1 GHz unambiguous bandwidth (from -500 to +500 MHz) for 1GSps. Note that this is really the basics of complex baseband, which are fundamental to OFDM! Aug 4 at 10:48
• @MarcusMüller Yes, that's right that we will have (-500 to +500), but having sampling frequency of 1 GHz will produce maximum bandwidth of 0.5 GHz according to the basic concept of Nyquist criteria, is it right? . What is the relationship with the nature of baseband signal? Aug 4 at 11:35
• @MarcusMüller Could you please explain that point of sampling rate is same of bandwidth, which means that sampling at 1 GHz gives also bandwidth of 1 GHz. Is there any reference for your explanation? Aug 4 at 13:52

According to my understanding, the subcarriers spacing Δf=B/N so increasing the number of subcarriers B will decrease the subcarrier spacing and hence increase the achieved data rate at the expense of performance. Is that analysis correct or there are other reasons?

No, it's not correct (by itself without a lot of assumptions that you'd need to do, which usually aren't true!)

The DFT, no matter the length, just divides the overall bands in orthogonal subbands. If your noise was white before, that means the average SNR is totally regardless of number of subcarriers.

If we don't ignore the guard interval: On the contrary, given that your channel's impulse response is independent of what OFDM system you build, the guard interval/cyclic prefix has constant length. Since with more subcarriers, you get more samples per OFDM symbol, and hence longer symbols, that means with more subcarriers, you spend a smaller percentage of your transmit time and energy on cyclic prefix/guard interval, and your amortized symbol rate grows.

So, it's not clear why you're seeing what your seeing. Things that might happen:

• Your frequency synchronization is not perfect. Then, a fixed amount of frequency offset will lead to more inter-carrier interference. But: the more subcarriers you have, the longer your synchronization symbol can be, and typically, your frequency estimator variance drops by the same amount. If you have more subcarriers, adjust your frequency synchronization accordingly! This is inherent with techniques like Schmidl&Cox, as these use full OFDM symbols for estimation, and hence get more energy with longer OFDM symbols, but not for all possible frequency estimation methods.
• Your timing synchronization is not perfect. The phase of the same subcarrier in consecutive OFDM symbols rotates. Of course, that means that the longer the OFDM symbol, the more it rotates. But: for the same amount of data, you'd need proportionally more OFDM symbols with shorter symbols (=fewer subcarriers), so that's again a case of "amortized" identical error. What might be happening is that you do a per-subcarrier phase recovery (this is not usual in practical OFDM system, but who knows what kind of synchronization you have!) and the PLLs on each subcarrier need to be adjusted to the length of the symbols, and you forgot to do that.
• Your channel is time-variant, so that with longer symbols, your pilots just don't occur often enough. But more subcarriers also allow you to put in proportionally more pilots without losing rate. So, that would be a design mistake in increasing symbol duration without adjusting pilot insertion
• I didn't get what is not correct in my phrase!!, Increasing the number of subcarriers will surely decrease the subcarriers spacing and hence the symbol duration will be decreased, right? Let's assume that all synchronization tasks are ideal and done correctly, is there relationship between the number of subcarriers and data rate? Aug 4 at 10:41
• no, not right. It will be increased. Aug 4 at 10:48
• is there relationship between the number of subcarriers and data rate? That's what the first three paragraphs of my answer explain. Aug 4 at 10:49
• Sorry, what will be increased? 2- let's ignore the guard interval. Normally, when having available bandwidth $B$, so when increasing the number of subcarriers; the subcarrier spacing will be decreased. Aug 4 at 11:01
• yes, but the symbol duration increases. Remember what the whole deal about using the DFT for OFDM is! Aug 4 at 11:17