m-sequence Generator in MATLAB for 5G NR

This page covers 5G NR m-sequence. It mentions simulation of m-sequence generator in MATLAB and use of m-sequence in 5G NR technology.

Introduction

There are three sequences used in 5G NR wireless system viz. Zadoff chu sequence, gold sequence and m-sequence. Gold sequence is used in CP-OFDM, Zadoff-chu sequence is used in DFT-s-OFDM (for SSS) and m-sequence is used in PSS.

m-sequence use in 5G NR

It is a BPSK modulated sequence with length of 127.
It is used for NR PSS (Primary Synchronization Signal).
It is used to fix time/frequency offset ambiguity problem encountered in zadoff-chu sequence used in the previous LTE technology.
PSS is part of 5G NR SS along with SSS.
The combination of SS and PBCH is referred to as SSB in NR.
Two m-sequences are used to generate gold sequence for 5G NR.
It is used in PSS sequence generation as defined in TS 38.211.

It is represented by $d_{PSS}(n)$ and it is determined by $N_{ID}^{(2)}$ .

The m-sequence can be generated using following equation.

$d_{PSS}(n) = 1 - 2*x(m)$ , Where,

$x(i+7) = \{x(i+4) + x(i)\} \mod 2$

$m = (n + 43*N_{ID}^{(2)}) \mod 127$

$0<=n<127$ , $N_{ID}^{cell} = 3*N_{ID}^{(1)} + N_{ID}^{(2)}$

$N_{ID}^{(1)} \in \{0, 1, ...,335\}$

$N_{ID}^{(2)} \in \{0, 1, 2\}$

The difference between NR PSS and LTE PSS is as follows.

NR PSS uses m-sequence where as LTE PSS uses zadoff-chu sequence.
LTS PSS is mapped on 72 subcarriers where as NR PSS is mapped on 127 active subcarriers.
5G NR PSS is defined in TS 38.211 where as LTE PSS is defined in TS 36.211 document.
$d_{PSS}(n) = 1 - 2*x(m)$ ,
$d_u(n) = e^{-j*[\pi*u*n*(n+1)/63]}$ , n = 0, 1, …30
$d_u(n) = e^{-j*[\pi*u*(n+1)*(n+2)/63]}$ , n = 31, 32, …61