# OFDM system with cyclic prefix

I have:

• Bit rate $$R_b = 25.6 [Mbit/s]$$
• Sampling frequency at the input of the receiver: $$f_p = 8 [MHz]$$
• Protective spacing between successive OFDM symbols: $$τ = 16 [µs]$$
• The combined length of the OFDM symbol and the prefix: $$T_s = 80 [µs]$$

1. The number of signal samples per cyclic prefix

So here is the problem because I don't know how can I calculate this number of samples. I can calculate the number of data bits by this formula:

$$R_b = B/T$$ where T is the total transmission time ($$80 [µs]$$).

But I want samples, so maybe I should use the time of the cyclic prefix that is $$16 [µs]$$, but what next?

2. The size of the constellation (number of points) on a given sub-channel (assumption: in each sub-channel the same constellation and all sub-channels transmit data)

So I know this equation:

$$T_s = N*T_p$$

$$T_p = 0.000000125$$

But N here equals 640, so 640 = $$2^k$$, isn't there something wrong?

3. Size N of FFT / IFFT transformation

Isn't this that 640 I have counted above?

4. Provide the effective value of data transmission speed $$R_b$$ if 64 subchannels in each OFDM symbol are used for transmitting pilots

I don't know how to do this one

5. The number of information bits transmitted in each single OFDM symbol

Should I use this formula (thanks MarcusMuller!)?:

$$\frac{\log_2{N} k}{\frac{l_\text{FFT}}{f_\text{sample}}}$$

But there is another problem with k (because of 640 = $$2^k$$)...

Any suggestions? I will be grateful for any help!