sen to provide an integer number of samples at the system sampling rate. The cyclic prefix can be inserted before the up-sampling and time-domain frequency shift, in order to minimize the intermediate storage requirements. Assuming sampling rate of 30.72 MHz and considering that the random-access preamble spans 0.8 ms, it can be concluded that the number of samples in time is equal to 24576. Furthermore, if the PRACH subcarrier spacing is assumed to be 1.25 kHz and the subcarrier spacing for PUSCH and PUCCH is 15 kHz, in order to maintain the same sampling rate, a 12 X 2048 point DFT operation would be needed for the PRACH signal generation at the transmitter side, if the entire processing is done in the frequency domain. An alternative approach is to use time-domain signal generation and extraction which involves up- sampling and filtering operations at the transmitter. The drawback of time-domain imple- mentation is that the up-sampling from 1.08 MHz to the system sampling-rate of 30.72 MHz is difficult to implement. The implementation of the PRACH signal at the gNB receiver can take a frequency-domain or a hybrid time/frequency-domain approach. As illustrated in Fig. 4.84 as an example, the common parts to both approaches are the cyclic prefix removal, which always occurs at the Chapter 4 Sampling rate R Sampling rate fs To RF NR -point Subcarrier Repeat Cyclic prefix circuitry sequence Insertion mapping Preamble length T (N A samples) (SizeN PRACH transmitter architecture 1 Sampling rate fIFFT Sampling rate fs To RF Repeat Cyclic prefix Time- circuitry insertion sequence domain (Size NRA) sampling Phase shift PRACH transmitter architecture 2 Frequency domain method NDFT-point Subcarrier Concatenated periodic correlations of demapping all cyclically-shifted Versions of the Root ZC sequence Sampling rate f Sampling rate R Cyclic prefix Signature detection Received signal removal (Size NDFT +NCP) Time- domain NFFT-point Subcarrier Complex frequency demapping conjugation shift Signature0 Signature3 Signature1 Sig