5G NR Gold Sequence Generation in MATLAB

This page provides information on the 5G NR Gold sequence, including a MATLAB simulation of the gold sequence generator and its use in 5G NR technology.

Introduction

In 5G NR wireless systems, three main types of sequences are used: Zadoff-Chu sequences, Gold sequences, and m-sequences. Gold sequences are used in CP-OFDM, Zadoff-Chu sequences are used in DFT-s-OFDM (specifically for SSS), and m-sequences are used in PSS.

Gold Sequence Use in 5G NR

• It is a BPSK modulated sequence with a length of 127.
• It is used for the NR SSS (Secondary Synchronization Signal).
• It helps to resolve time/frequency offset ambiguity problems that were encountered with Zadoff-Chu sequences in previous LTE technology.
• SSS is a component of the 5G NR SS (Synchronization Signal) along with PSS.
• The combination of SS and PBCH (Physical Broadcast Channel) is referred to as SSB (SS Block) in NR.
• DMRS (Demodulation Reference Signal) sequences for CP-OFDM Physical layer are QPSK based on Gold sequences.
• Generic pseudo-random sequences are defined by a length-31 Gold sequence.

It is specified in TS 38.211 as follows:

The output sequence $c(n)$ of length $M_{PN}$, where $n = 0, 1, ..., M_{PN} - 1$, is defined as:

$c(n) = (x_1(n + N_c) + x_2(n + N_c)) \mod 2$

$x_1(n + 31) = (x_1(n + 3) + x_1(n)) \mod 2$

$x_2(n + 31) = (x_2(n + 3) + x_2(n + 2) + x_2(n + 1) + x_2(n)) \mod 2$

where $N_c = 1600$ and the first m-sequence $x_1(n)$ is initialized with:

$x_1(0) = 1$, $x_1(n) = 0$, $n = 1, 2, ..., 30$.

The initialization of the second m-sequence, $x_2(n)$, is denoted by $C_{init}$, and its values depend on the specific application of the sequence.

Gold Sequence Generator in MATLAB

• MathWorks offers a Gold sequence generation program with m-files.
• You can download version 1.0.0.0 developed by Sanjeet Kumar from [MathWorks](Link needed, requires login). You’ll need to log in after subscribing to MathWorks.
• This m-file generates Gold Sequences of length 31 by taking the modulo-2 sum of two m-sequence generators.