m-sequence Generator in MATLAB

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 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)}mod2

m = (n + 43*N_ID⁽²⁾) mod 127

0<=n<127 , N_ID^cell = 3*N_ID⁽¹⁾ + N_ID⁽²⁾

N_ID⁽¹⁾ ∈ {0, 1, ...,335}

N_ID⁽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.
➤d_PSS^{(n) = 1 - 2*x(m),

➤d_u⁽ⁿ⁾ = e^{-j*[π*u*n*(n+1)/63]}, n = 0, 1, .....30

➤d_u⁽ⁿ⁾ = e^{-j*[π*u*(n+1)*(n+2)/63]}, n = 31, 32, .....61}