digital communications - General questions regarding OFDM modulation

In Orthogonal frequency division multiplexing (OFDM), data symbols are modulated using an N pt-IFFT operation to produce ONE output OFDM

Assume we have total of $N$ QAM symbols which are input to the IDFT operation.

1) Is the output time domain samples $X_k$ also of length $N$ in length?

2) If ONE data QAM symbol has symbol duration $T$, is ONE OFDM symbol of symbol duration $T$ or is one SAMPLE of the OFDM symbol of duration $T$?

Thanks looking forward for your answers

Update

One example of OFDM modulator is the one used in LTE, in particular the subcarrier bandwidth is 15 KHz, and the OFDM symbol (and not one sample of the OFDM symbol) is 1/15k = 66.67 $\mu $ sec which is equal to the transmission time of one symbol (for example 1 QAM) over one subarrier. If my understanding is correct than the answer provided below is wrong. Can somoeone please double check?

Thanks

Answer

Assume we have total of N QAM symbols which are input to the IDFT operation.

1) Is the output time domain samples Xk also of length N in length?

No. Remember IFFT is a radix-2 operation. The output of the IFFT is next nearest power of two to the number of QAM symbols. For example for 6 Resource block configuration (1.4 MHz) there are 72 subcarriers. The number of IFFT bins and hence the no. of IFFT output samples for this configuration is 128 with 128-72 is zero padded samples. 66.6 μ sec is useful symbol duration corresponding to the IFFT output. We also have to add the cyclic prefix to this useful symbol to produce the final OFDM symbol as shown in the following figure [1]

2) If ONE data QAM symbol has symbol duration T, is ONE OFDM symbol of symbol duration T or is one SAMPLE of the OFDM symbol of duration T?

One QAM symbol duration is 1/BW where BW is the transmission bandwidth.