Expressions for the Autocorrelation Function and Power Spectral Density of BOC Modulation Based on Convolution Operation

Jiangang Ma,Yikang Yang,Jisheng Li,Hengnian Li

doi:10.1155/2020/2063563

Abstract

We present universal expressions for the autocorrelation functions (ACFs) of the Binary Offset Carrier (BOC), Multiplexed BOC (MBOC), and Alternative BOC (AltBOC) modulations based on convolution operations. We also derive the expressions for the power spectrum densities (PSDs) of these modulations using the Fourier transform of their ACFs. The results obtained in this contribution are useful for Global Navigation Satellite System (GNSS) signal simulation, performance evaluation, and high-performance acquisition and tracking algorithm design. The derivation methods of the expressions for the ACFs are common and can be used to derive expressions for the ACFs of other BOC-based modulations.

Highlights

We present universal expressions for the autocorrelation functions (ACFs) of the Binary Offset Carrier (BOC), Multiplexed BOC (MBOC), and Alternative BOC (AltBOC) modulations based on convolution operations
Considering a BOC signal as the product of a pseudorandom noise (PRN) spreading code modulated data with a square-wave subcarrier, we assume that the PRN spreading code is random, infinite, aperiodic, identically distributed, and independent, and the signal bandwidth is infinite
Where fs denotes the subcarrier frequency and sign(·) is the sign function. e BOC signal is typically denoted by BOC(fs, fc), fc which equals to 1/Tc is the PRN spreading code chip rate. e designation BOC(α, β) with reference frequency fref which equals to 1.023 MHz is used as the abbreviation of BOC(fs, fc), the subcarrier frequency fs α × fref, and the PRN spreading code rate fc β × fref

Summary

Introduction

E expressions for the ACFs of BOCsin(pn,n), BOCcos(pn,n), MBOC(6, 1, 1/11), and constant and nonconstant envelope AltBOC(15, 10) are presented in [8, 16,17,18]. We present universal expressions for the ACFs of the BOC, MBOC, and AltBOC modulations based on convolution operations. E signal model of AltBOC can be expressed as sAltBOC 􏽘 􏼐cDL + jcPL 􏼑pA∗ltBOC t − kTc􏼁

Results

Conclusion