In LTE, the Physical RA Channel (PRACH) is used for initial network access, but the PRACH does not carry any user data, which is exclusively sent on the Physical Uplink Shared Channel (PUSCH). Instead, the LTE PRACH is used to achieve uplink time synchronization for a UE which either has not yet acquired, or has lost, its uplink synchronization. The RA preamble sent on the PRACH has the structure shown in FIG. 4, where it is seen to comprise a cyclic prefix followed by a preamble sequence derived from a Zadoff-Chu root sequence. In the time domain, the PRACH may span between one to three subframes for FDD LTE. Any unused portion of the last PRACH subframe is utilized as a guard period. In the frequency domain, the PRACH spans six resource blocks (1.08 MHz).

Several methods have been proposed for how to detect the PRACH preambles, see e.g., [S. Sesia. I. Toufik. M Baker “LTE, The UMTS Long Term Evolution, From Theory to Practice”, Second Edition, John Wiley & Sons Ltd., 2011]. Here both a full frequency domain and a hybrid time-frequency approach are presented. In a full frequency approach, the received signal is processed with a Fast Fourier Transform (FFT) corresponding to the length of the preamble. Hence, an FFT of length 24,576 is thus required for each antenna. Dedicated hardware is commonly used for this PRACH FFT. After this large FFT, the PRACH bandwidth is extracted, which is a subset of the output from this large FFT. A power delay profile is calculated by a frequency matched filter followed by an Inverse Discrete Fourier Transform (IDFT) and absolute square.

In the hybrid time-frequency approach, a low-pass filter is first used in the time domain in order to extract the PRACH bandwidth. This lowpass filter is followed by an FFT of a size much smaller than 24,576. One such low-pass filter has to be applied to each antenna signal.