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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?

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    $\begingroup$ 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. $\endgroup$
    – AlexTP
    Aug 8, 2023 at 7:53
  • $\begingroup$ 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. $\endgroup$ Aug 8, 2023 at 11:54
  • $\begingroup$ @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? $\endgroup$
    – wanderer
    Aug 8, 2023 at 19:26
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    $\begingroup$ @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. $\endgroup$
    – AlexTP
    Aug 8, 2023 at 21:17

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