OFDM design considerations for choosing the number of subarriers $N$

I was trying to think of all possible constraints or factors that needs to be taken into consideration while designing an OFDM-based wireless communication system (For example, LTE, 5G technologies etc).

Assume the bandwidth is $$B$$. The coherence bandwidth and the coherence time of the channel are $$B_c$$ and $$T_c$$ respectively. Let $$T_s =1/B$$ denote the symbol time. How do you decide on the number of subcarriers $$N$$?

I have the following thoughts:

1. $$N$$ should be a power of 2 for FFT based implementation.
2. $$NT_s < T_c$$ for the channel to be coherent over total OFDM symbol duration.
3. $$NTs >> NT_{cp}$$ otherwise it is inefficient in terms the information rate where $$T_{cp}$$ is the duration of CP.
4. $$NTs >> NT_{cp}>T_d$$ for avoiding ISI where $$T_d$$ is the delay spread.
5. $$N$$ should not be too large as it increase decoding delay.
6. $$N$$ too large can lead to very high PAPR which is an issue as well.

Please let me know your thoughts about the above w.r. t their correctness. Are there any other similar constraints on the design of $$N$$ for an OFDM system?

• 1 is not necessarily a hard constraint, N can be the product of small prime numbers. For 2-4, read this question. For 5, do not mix N and delay for OFDM as we have both time and frequency dimensions. No comment for 6. Aug 8, 2023 at 7:53
• yeah power-of-two is really not strictly necessary, especially since you often want constant-zero guard carriers at the band edges, anyway, you get quite a lot of flexibility here. Aug 8, 2023 at 11:54
• @AlexTP Could you clarify your concern about point 5. I meant as N increases $NT_s$ increases. Thus, you have to wait that long to start doing your FFT processing at receiver. So, it leads to an increase in decoding delay. Am I right? Aug 8, 2023 at 19:26
• @wanderer you are right, if $T_s$ (hence bandwidth $B=1/T_s$) is fixed and increasing the number of subcarrier $N$ means reducing subcarrier spacing $\Delta f = B/N$. However, OFDM systems are often designed from fixed $\Delta f$ (mostly for synchronization issues), and therefore increasing $N$ is equivalent to increasing $B$ but the OFDM symbol duration $1/\Delta f$ is intact. This is true at least for 5G and LTE, the systems you have mentioned. Aug 8, 2023 at 21:17