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"Low-Frequency Gravitational Wave Searches
Using Spacecraft Doppler Tracking"

J. W. Armstrong

	Abstract
1	Introduction
2	Notation, Acronyms, and Conventions
3	Gravitational Wave Signal Response
4	Apparatus and Principal Noise Sources
	4.1	Frequency standard noise
	4.2	Plasma scintillation noise
	4.3	Tropospheric scintillation noise
	4.4	Antenna mechanical noise
	4.5	Ground electronics noise
	4.6	Spacecraft transponder noise
	4.7	Thermal noise in the ground and spacecraft receivers
	4.8	Spacecraft unmodeled motion
	4.9	Numerical noise in orbit removal
	4.10	Aggregate spectrum
	4.11	Summary of noise levels and transfer functions
5	Signal Processing
	5.1	Noise spectrum estimation
	5.2	Sinusoidal and quasiperiodic waves
	5.3	Bursts
	5.4	Stochastic background
	5.5	Classification of data intervals based on transfer functions
	5.6	Frequency-time representations
	5.7	Qualifying/disqualifying candidates
	5.8	Other comments
6	Detector Performance
	6.1	Observations to date
	6.2	Near-future observations
	6.3	Sensitivity to periodic and quasi-periodic waves
	6.4	Burst waves
	6.5	Sensitivity to a stochastic background
7	Improving Doppler Tracking Sensitivity
8	The LISA Low-Frequency Detector
9	Concluding Comments
	Acknowledgements
	References
	Footnotes
	Updates
	Figures
	Tables

9 Concluding Comments

This paper discussed the principles of operation and status of spacecraft Doppler tracking, the current-generation GW detector technology in the $∼$ 10^–6 to 10^–1 Hz band. Doppler tracking differs from all other currently-operating detectors in that the size of the apparatus (earth-spacecraft distance) is large compared with the GW wavelength. As a consequence times-of-flight of GWs and radio waves through the apparatus are important, resulting in a three-pulse signal response and various two-pulse noise responses. The different signal and noise transfer functions suggest data analysis approaches for various waveforms; some of these approaches were outlined here. The sensitivity of current-generation Doppler observations was discussed as well as what would be required to improve this sensitivity by another order of magnitude (to $∼$ 10^–17 for sinusoidal waves). Further large sensitivity improvements in the low-frequency band will require dedicated multi-spacecraft arrays in space. Until such a dedicated mission flys, spacecraft tracking will provide the best observational capability in the low-frequency GW band.