# RF Wireless World

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## m-sequence Generator in MATLAB | 5G NR m-sequence

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 dPSS(n) and it is determined by NID(2). The m-sequence can be generated using following equation.
dPSS(n) = 1 - 2*x(m),
Where,
x(i+7) = {x(i+4) + x(i)}mod2
m = (n + 43*NID(2)) mod 127
0<=n<127 , NIDcell = 3*NID(1) + NID(2)
NID(1) ∈ {0, 1, ...,335}
NID(2) ∈ {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. Refer LTE PSS and SSS >> and Zadoff-chu sequence basics >> for more information.
➤5G NR PSS is defined in TS 38.211 where as LTE PSS is defined in TS 36.211 document.
➤dPSS(n) = 1 - 2*x(m),
➤du(n) = e-j*[π*u*n*(n+1)/63], n = 0, 1, .....30
➤du(n) = e-j*[π*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.

### 5G NR Control channels | 5G NR Traffic Channels | 5G NR Reference Signals and sequences

This 5G tutorial also covers following sub topics on the 5G technology:
5G basic tutorial
5G Frequency Bands
5G millimeter wave tutorial
5G mm wave frame
5G millimeter wave channel sounding
Difference between 4G and 5G
5G testing and test equipments
5G network architecture
5G NR Physical layer
5G NR MAC layer
5G NR RLC layer
5G NR PDCP layer