Hi,

I have been investigating RACH preamble planning and the properties of Root Zadoff-Chu sequences as used in 3GPP.

From Wikipedia, Zadoff-Chu sequences have the following properties:

• The auto correlation of a Zadoff–Chu sequence with a cyclically shifted version of itself is zero, i.e., it is non-zero only at one instant which corresponds to the cyclic shift.
• The cross-correlation between two prime length Zadoff–Chu sequences, i.e. different values of u = u1, u = u2 is constant 1/√NZC, provided that u1- u2 is relatively prime to NZC

However:

• NZC is chosen to be the prime number 839 in preamble formats 0-3
• The physical root sequence number u is between 1 to 838

Since any u1- u2 from the allowed u set are always relatively prime to NZC= 839, I can understand that the cross correlation between any u1, u2 , always equals to 1/√NZC given u1 is not equal to u2 and they are both chosen from 1 - 838.

in 3GPP, 36.211 Table 5.7.2-4 the standard further defined a logical root sequence number. in particular, it also partitioned different groups ( rows), which every group has a different amount of root sequence numbers.

The intent behind this mapping (logical to physical) is not understood to me. Working with only the physical root sequence numbers seems to be sufficient for RACH planning given the properties above.

My questions are:

• Why is this table needed?
• Why is the logical to pyhsical mapping done this way?
• Why is it partitioned to different rows?

Thanks in advance,

Guy