Notation, Acronyms, and Conventions

2 Notation, Acronyms, and Conventions

Table 1Update * defines some acronyms used in this article. Since it is always clear from context, I use the same symbol for theoretical statistical quantities (e.g., underlying spectra) and estimates derived from finite data sets (e.g., sample spectra). All power spectra are two-sided.

Table 1: Some acronyms and notation used in this paper.

Symbol	Meaning
acf	autocorrelation function
AMC	Advanced Media Calibration system (see Section 4.3)
DOY	day-of-year, i.e., January 20 = DOY 020
DSN	Deep Space Network, the NASA/JPL spacecraft communications and tracking network with antennas at complexes in Australia, Spain, and the United States
DSS	Deep Space Station (identifier for specific antennas in the DSN, e.g., “DSS 25”)
f	Fourier frequency
FTS	Frequency and Timing System, the reference for two-way Doppler tracking
Ka-band	a deep space communications frequency $≃$ 32 GHz (for Cassini, “Ka1” is the downlink referenced to the X-band uplink; “Ka2” is the downlink referenced to the Ka-band uplink)
KaT	Cassini’s “Ka-band Translator” which accepts an uplink Ka-band signal and phase-coherently translates it to a downlink Ka-band signal for retransmission to earth
LISA	Laser Interferometer Space Antenna, a future low-frequency GW observatory [24 *]
one-way	Doppler tracking where the downlink is referenced to an oscillator on the spacecraft
pdf	probability density function [88 *]
S-band	a deep space communications frequency $≃$ 2.3 GHz
scintillation	phase fluctuation due to wave propagation in a random medium [106 , 79 , 40 , 99 , 71 *]
SEP angle	sun-earth-probe angle, the apparent solar elongation angle of the spacecraft
S_x(f)	power spectrum of x(t), i.e., Fourier transform of $⟨x (t)x (t + τ)⟩$ [73 , 89 ]
T	duration of an observation
T₂	two-way light time between earth and spacecraft
three-way	Doppler tracking where the received downlink is coherently referenced to an uplink signal from another station
two-way	Doppler tracking where the downlink is coherently referenced to the uplink signal
X-band	a deep space communications frequency $≃$ 8.4 GHz
x $∗$ y	convolution of time series x(t) and y(t) [34 ]
y(t)	generic time series of fractional frequency, $Δ ν∕ν0$ [23 *] ( $y2(t)$ : time series of two-way Doppler fractional frequency) ( $y3(t)$ : time series of three-way Doppler fractional frequency)
$ν$	radio frequency
$σy(τ)$	Allan deviation, fractional frequency stability at integration time $τ$ [23 *]
$𝜃$	angle between GW propagation direction and earth-spacecraft vector; $μ$ = cos( $𝜃$ )

	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