IEEE - Aerospace and Electronic Systems - September 2019 - 54

Regenerative Ranging for JPL Software-Deﬁned Radios
Table 5.

The ratio Eb =N0 is

Periods and Rn Values for CCSDS T4B Code

Eb =N0 ¼

n

n

Rn

1

2

0.9387

2

7

0.0613

3

11

0.0613

4

15

0.0613

5

19

0.0613

6

23

0.0613

The CCSDS T4B range code is a logical combination
of component PN codes [7]. There is a set of numbers Rn
that is a characteristic of this range code and that affects
measurement performance. These values, technically
called normalized cross-correlation factors with no lag,
are calculated as [7]
Rn ¼

M
1 X
CT 4B ðmÞCn ðmÞ;
M m¼1

1

n

6

where CT 4B ðmÞ ¼ Æ1 is the sequence, length M, of the
T4B range code and Cn ðmÞ ¼ Æ1 is the sequence of
the nth component PN code. The range clock consists of
alternating þ1 and À1. The values Rn are listed in Table 5,
along with the period n of each component PN code.

PD
N0 Á Rb

where Rb is the telemetry bit rate. The carrier-loop SNR
rC is
rC ¼

PC
N0 Á BC

where BC is the noise-equivalent bandwidth of the carrier
loop.

ACKNOWLEDGMENTS
This work was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract
with the National Aeronautics and Space Administration.
The authors would like to thank the following from JPL for
their contributions in the regenerative ranging development in
Iris transponder: H. Xie and J. Hamkins provided the MATLAB codes for regenerative ranging associated with time synchronization; K. Botteon provided the Iris firmware for signal
processing test points; M. Shihabi, M. Pugh, C. Volk, B. Burgett, M. Chase, S. Holmes, L. McNally, A. Yarlagadda, D.
Bell, L. Epp, S. Dolinar, J. Lazio, and S. Townes.

REFERENCES
[1] A. Klesh et al., "INSPIRE: Interplanetary nanospacecraft
pathfinder in relevant environment," in Proc. AIAA SPACE

CALCULATION OF PERFORMANCE

Conf. Expo., San Diego, CA, USA, 2013, pp. 1-6.

The range error s R due to noise can be calculated from
PR =N0 . The square of s R is [9]
s 2R

c2
¼
2
2
32p Á fRC Á R1 2 Á T Á PR =N0

[2] C. B. Duncan et al., "Iris transponder-Communications
and navigation for deep space," in Proc. Small Satellite
Conf., Logan, UT, USA, 2014, pp. 1-10.
[3] A. Klesh et al., "MarCO: Early operations of the first
CubeSats to Mars," in Proc. Small Satellite Conf., Logan,
UT, USA, 2018, pp. 1-6.

where c is the speed of electromagnetic waves in vacuum, fRC is the range-clock frequency, and T is the
integration time of the range measurement. Pacq is calculated as [9]

[4] M. Pugh et al., "The Universal Space Transponder: A next
generation software defined radio," in Proc. IEEE Aerosp.
Conf., Big Sky, MT, USA, Mar. 2017, pp. 1-14,
doi: 10.1109/AERO.2017.7943866.
[5] R. J. DeBolt, D. J. Duven, C. B. Haskins, C. C. DeBoy, and

Pacq ¼

6
Y

T. W. LeFevere, "A regenerative pseudonoise range tracking system for the New Horizons spacecraft," presented at
the 61st Annu. Meeting Institute Navigation, Cambridge,

Pn

n¼2

where the probability Pn of acquiring the nth code component (2 n 6) is
1
Z

1
Pn ¼ pﬃﬃﬃ
p À1


0
pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ1n À1
1
þ
erf
x
þ
R
T Á PR =N0
n
2
A
eÀx @
dx
2

MA, USA, Jun. 2005.
[6] L. Iess, S. Asmar, and P. Tortora, "MORE: An advanced
tracking experiment for the exploration of Mercury with
the mission BepiColombo," Acta Astronaut., vol. 65,
pp. 666-675, 2009.
[7] Consultative

where erfðÁÞ is the error function.
54

Committee

for

Space

Data

Systems,

"Pseudo-noise (PN) ranging systems," CCSDS 414.1-B-2,
Feb. 2014.

IEEE A&E SYSTEMS MAGAZINE

SEPTEMBER 2019
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