# number of subcarriers for an OFDM system

For an OFDM system, it is necessary to know the number of subcarriers. For example for the subcarrier $k^e$, we must have: $B_k <B_c$ with $B_c$ the channel coherence bandwith. And $B_k=\frac{1} {NT+I}$ with $I$ is the guard interval, $T$ is the symbol time and $N$ the number of subcarriers.

Here is my questions:

1. For example, for $N=3$, we have $B_k<B_c$. Is the number of subcarriers small? Because I always see, N = 64, 1024, ...
2. Is there a minimum number of subcarriers?
• 0. what is $B_k$ and how do you come up with this derivation? 1. yes, N=3 is smaller than 64 and than 1024, but maybe it is already enough ... 2. the minimum number is 1 and this is what called monotone OFDM is recent industrial specs. – AlexTP Jul 13 '18 at 9:16

Now, 3 is indeed a choice that is very small. I wouldn't build an OFDM system with 3 subcarrieres, simply because the smallest cyclic prefix that you can build is then $\frac 13$ of the symbol length – and chances are, you need more than one $\frac1{B_{subcarrier}}$ as guard interval to "capture" the whole channel impulse response.