Random Access Channel

So what is RACH ?

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

I will describe it in frequency and time domain.
In Time Domain





Table 1

Preamble Format	TCP	TSEQ	Guard Period
0	3,168×Ts	24,576×Ts	2,976×Ts
1	21,024×Ts	24,576×Ts	15,840×Ts
2	6,240×Ts	2×24,576×Ts	6,048×Ts
3	21,024×Ts	2×24,576×Ts	21,984×Ts
4	448×Ts	4,096×Ts	288×Ts

Table 2

Preamble Format	Number of Subframes
0	1
1	2
2	2
3	3
4	1

From above table 1 we know that the Length of PRACH in time domain has a Cylic Prifix , T sequence , Guard Period.

where CP for ISI reduction.
 Nsecqence is Nzc-Point Zadoff chu sequence
Guard time allows for timing uncertainty due to the UE to eNodeB distance.

From above table 2 we know that the PRACH is spread over 1 or 2 or 3 subframes.

The preamble format Ue get to know from PRAHconfigindex in SIB2.

In Frequency Domain

PRACH has subcarrier spacing of 1.2Khz for FDD and 7.5Khz for TDD.

The PRACH is designed to fit in the same bandwidth as 6 RBs.

6RBs= 6 * 12 * 15 Khz = 1080 Khz

1080/1.25Khz = 864 subcarrier

It has a guard subcarrier upper and lower part which is 25 subcarrier means 25 * 1.25Khz = 30 (Aprox)

So our actual PRACH Subcarrier is 839.

The starting of RB for PRACH is know from PRACH Freq Offset.