Network access node and a client device for generating and using randoms access sequences

An apparatus, comprising:

• at least one processor;
• a memory coupled to the at least one processor, wherein the memory stores a program to be executed by the at least one processor, and wherein the program comprises instructions which, when executed by the at least one processor, instruct the at least one processor to perform operations comprising:
• receiving a control message from a network access node, wherein the control message indicates a cyclical shift value NCS and a third order coefficient value a3 of a subset of sequences (k);
• determining a cubic polynomial phase sequence (si) belonging to the subset of sequences (k) based on the cyclical shift value NCS and the third order coefficient value a3;
• transmitting the determined cubic polynomial phase sequence (si) as a random access preamble to the network access node.

A method, comprising:

• generating a subset of sequences (k) belonging to a set of sequences (), wherein:
• the subset of sequences (k) comprises a plurality of cubic phase polynomial sequences (si, sj) of length L with a third order coefficient value a3;
• an auto-correlation for a sequence (si) in the generated subset of sequences with a cyclically shifted version of itself (s′i) is less than or equal to √{square root over (L)} when the cyclically shifted version (s′i) is cyclically shifted less than a cyclical shift value NCS;
• a cross-correlation between a first sequence (si) and a second sequence (sj) in the generated subset of sequences (k) is less than or equal to √{square root over (L)};
• and
• a cross-correlation between the first sequence (si) and the second sequence (sj) in the generated subset of sequences (k) is less than or equal to √{square root over (L)} when one of the first sequence (si) and the second sequence (sj) is cyclically shifted less than the cyclical shift value NCS;
• and
• transmitting a control message to a client device, wherein the control message indicates the cyclical shift value NCS and the third order coefficient value a3.