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

m-sequence Generator in MATLAB

• Mathworks database has following m-sequence generation program with m-files.
• Download version 1.0.0.0 developed by Giedrius Buracas from following link using login details after subscribing with mathworks.