Spreading Code Optimization for Low-Earth Orbit Satellites via Mixed-Integer Convex Programming

TL;DR

This paper introduces a novel two-stage block coordinate descent method utilizing mixed-integer convex programming to optimize spreading codes for low-earth orbit satellite navigation, improving correlation properties with shorter codes.

Contribution

It presents a new optimization approach combining BCD and MICP to design spreading codes with zero autocorrelation sidelobes, applicable to arbitrary code sizes and lengths.

Findings

Effective for codes of length 127 and 257

Optimizes correlation properties while enforcing ACZ

Applicable to arbitrary code sizes

Abstract

Optimizing the correlation properties of spreading codes is critical for minimizing inter-channel interference in satellite navigation systems. By improving the codes' correlation sidelobes, we can enhance navigation performance while minimizing the required spreading code lengths. In the case of low earth orbit (LEO) satellite navigation, shorter code lengths (on the order of a hundred) are preferred due to their ability to achieve fast signal acquisition. Additionally, the relatively high signal-to-noise ratio (SNR) in LEO systems reduces the need for longer spreading codes to mitigate inter-channel interference. In this work, we propose a two-stage block coordinate descent (BCD) method which optimizes the codes' correlation properties while enforcing the autocorrelation sidelobe zero (ACZ) property. In each iteration of the BCD method, we solve a mixed-integer convex program (MICP) over a block of 25 binary variables. Our method is applicable to spreading code families of arbitrary sizes and lengths, and we demonstrate its effectiveness for a problem with 66 length-127 codes and a problem with 130 length-257 codes.