# Performance analysis of sequential carrier- and code-tracking receivers in the context of high-precision space-borne metrology systems

## TL;DR

This paper evaluates the performance of sequential carrier- and code-tracking receivers for high-precision space-based gravitational wave detection, highlighting the impact of modulation schemes and loop interactions on phase noise and ranging accuracy.

## Contribution

It introduces an analytical model for phase noise influenced by chip modulation and compares modulation schemes, demonstrating the advantages of binary offset carrier modulation for pico-meter phase noise levels.

## Key findings

- Binary offset carrier modulation outperforms BPSK for pico-meter phase noise.
- Delay-locked loop analysis reveals pulse shape distortion and ranging bias.
- Numerical simulations show sub-meter ranging accuracy despite modulation challenges.

## Abstract

Future space observatories achieve detection of gravitational waves by interferometric measurements of a carrier phase, allowing to determine relative distance changes, in combination with an absolute distance measurement based on the transmission of pseudo-random noise chip sequences. In addition, usage of direct-sequence spread spectrum modulation enables data transmission. Hereafter, we report on the findings of a novel performance evaluation of planned receiver architectures, performing phase and distance readout sequentially, addressing the interplay between both measurements. An analytical model is presented identifying the power spectral density of the chip modulation at frequencies within the measurement bandwidth as the main driver for phase noise. This model, verified by numerical simulations, excludes binary phase-shift keying modulations for missions requiring pico-meter noise levels at the phase readout, while binary offset carrier modulation, where most of the power has been shifted outside the measurement bandwidth, exhibits superior phase measurement performance. Ranging analyses of the delay-locked loop reveal strong distortion of the pulse shape due to the preceding phase tracking introducing ranging bias variations. Numerical simulations show that these variations, however, which originate from data transitions, are compensated by the delay tracking loop, enabling sub-meter ranging accuracy, irrespective of the modulation type.