## Random Access Channel

The Random Access Channel (RACH) is an uplink transmission used by the UE to initiate synchronization with the eNodeB.

### RACH Coding

The relationship between RACH, a transport channel, and PRACH, a physical channel, as described by [2], is shown in the following table.

Transport Channel (TrCH)Physical Channel
RACHPRACH

However, there are not actually any coding processes that take place to encode the RACH transport channel onto the input of the PRACH. Also, there is no logical channel which maps into the input of the RACH transport channel; the RACH originates in the MAC layer. The RACH effectively consists of a number of parameters within the MAC layer which ultimately control how and when the PRACH physical channel is generated.

### The PRACH

The PRACH transmission (the PRACH preamble) is an OFDM-based signal, but it is generated using a different structure from other uplink transmission; most notably it uses narrower subcarrier spacing and therefore is not orthogonal to the PUSCH, PUCCH and SRS, therefore those channels will suffer from some interference from the PRACH. However, the subcarrier spacing used by the PRACH is an integer submultiple of the spacing used for the other channels and therefore the PUSCH, PUCCH and SRS do not interfere on the PRACH.

#### PRACH preamble time structure

The PRACH preamble consists of a cyclic prefix, useful part of the sequence and then a guard period which is simply an unused portion of time up to the end of the last subframe occupied by the PRACH.

This guard period allows for timing uncertainty due to the UE to eNodeB distance.

Therefore the size of the guard period determines the cell radius, as any propagation delay exceeding the guard time would cause the random access preamble to overlap the following subframe at the eNodeB receiver.

The use of an OFDM transmission with cyclic prefix allows for an efficient frequency domain based receiver in the eNodeB to perform PRACH detection.

#### PRACH formats

There are five PRACH preamble formats which have different lengths for the cyclic prefix, useful part of the symbol, and guard period.

Preamble FormatTCPTSEQGuard Period
03,168×Ts24,576×Ts2,976×Ts
121,024×Ts24,576×Ts15,840×Ts
26,240×Ts2×24,576×Ts6,048×Ts
321,024×Ts2×24,576×Ts21,984×Ts
4448×Ts4,096×Ts288×Ts

Note that Preamble Format 4 is only applicable for TDD in special subframes (subframe 1 or 6) and with Special Subframe Configuration that results in UpPTS with 2 symbols duration i.e. the Preamble Format 4 PRACH sits in UpPTS. Formats 2 and 3 have two repetitions of the nominal PRACH sequence which provides more total transmit energy and therefore allows for detection at lower SNRs. Also, Format 1 versus 0 and Format 3 versus 2 have a longer guard period, allowing for a larger cell size. The downside is that when the cyclic prefix time, sequence time and guard period are totaled up, some of the formats require multiple subframes for transmission.

Preamble FormatNumber of Subframes
01
12
22
33
41

The penalty for using multiple subframes is a reduction in the capacity for normal uplink transmission.

#### PRACH Preamble Frequency Structure

As already mentioned, the PRACH uses a narrower subcarrier spacing that normal uplink transmission, specifically 1250 Hz for formats 0–3 and 7500 Hz for format 4. The ratio of the normal uplink subcarrier spacing to PRACH subcarrier spacing, K, is K=12 for formats 0–3 and K=2 for format 4.

The PRACH is designed to fit in the same bandwidth as 6 RBs of normal uplink transmission. For example, 72 subcarriers at 15,000 Hz spacing is 1.08 MHz. This makes it easy to schedule gaps in normal uplink transmission to allow for PRACH opportunities.

Therefore, there are 72×K subcarriers for the PRACH, specifically 864 for formats 0–3 and 144 for format 4. As will be explained in the following subsection, the PRACH transmission for formats 0–3 uses 839 active subcarriers, and for format 4 uses 139 active subcarriers; the number of active subcarriers is denoted NZC.

As with normal uplink SC-FDMA transmission there is a half subcarrier (7500 Hz) shift, which for the PRACH is a K/2 subcarrier shift. A further subcarrier offset, φ (7 for formats 0–3 and 2 for format 4), centers the PRACH transmission within the 1.08 MHz bandwidth.

Preamble Formatφ+K/2NZC72KNZCφK/2
0–31383912
431392

#### PRACH Subcarrier Content

The actual PRACH transmission is an OFDM-based reconstruction of a Zadoff-Chu sequence in the time domain. The OFDM modulator is used to position the Zadoff-Chu sequence in the frequency domain (i.e. to place the 6RBs of PRACH transmission in the 6 consecutive RBs starting from some particular physical resource block, denoted ${n}_{PRB}^{RA}$ in the standard). If the output of the OFDM modulator in the time domain is to be a Zadoff-Chu sequence, the input to the OFDM modulator must be a Zadoff-Chu sequence in the frequency domain. Therefore, the active subcarriers, which total NZC in number, are set to the values of an NZC-point DFT of an NZC-sample Zadoff-Chu sequence.

### PRACH Conformance Tests

Conformance tests for the PRACH, as defined in section 8.4 of [1], test the false alarm rate and detection rate of the PRACH in various environments. For a demonstration of how to perform the PRACH false alarm rate test specified in section 8.4.1, see PRACH False Alarm Probability Conformance Test. For a demonstration of how to perform the PRACH detection rate test specified in section 8.4.2, see PRACH Detection Conformance Test.

## References

[1] 3GPP TS 36.104. “Evolved Universal Terrestrial Radio Access (E-UTRA); Base Station (BS) Radio Transmission and Reception.” 3rd Generation Partnership Project; Technical Specification Group Radio Access Network. URL: https://www.3gpp.org.

[2] 3GPP TS 36.212. “Evolved Universal Terrestrial Radio Access (E-UTRA); Multiplexing and channel coding.” 3rd Generation Partnership Project; Technical Specification Group Radio Access Network. URL: https://www.3gpp.org.