Aerospace and Electronic Systems Magazine August 2017 - 47

Photo credit: NASA

fS being the sampling frequency, and ηb(nTS) is the noise component ([13], chapter 1).
Considering a real sampling front-end, the discrete baseband
signal from satellite u having a data and a pilot channel can be
expressed as

 s0p 


s1p 
,
c = s⊗p = 
  


 s N S −1p 

sbu (nTS ) = 2 Pbu, d d u (nTS − τ u )cdu (nTS − τ u )

where ⊗ denotes the Kronecker product. The length NP of the primary code depends on the signal and on the sampling frequency.
For example, the L5, E5a, and E5b pilot signals are binary phase
shift keying signals with a chipping rate of 10.23 MHz, therefore the usual minimum sampling frequency considered for these
signals is 20.46 MHz (twice the chipping rate, but this exact frequency is never used because of position accuracy problems [15]).
Since the length of the primary code is 1 ms, the minimum value
of NP is 20,460. The length NS of the secondary code is not related
to the receiver and depends only on the signal. For example, the
length of the secondary codes on the data and pilot channels is
respectively 10 and 20 chips for the L5 signal, 20 and 100 chips for
the E5a signal, and 4 and 100 chips for the E5b signal. Therefore,
the minimum value of N is 409,200 for the L5 pilot signal, and
2,046,000 for the E5a and E5b pilot signals.

cos(2π f bu nTS + ϕbu, d )
+ 2 P c (nTS − τ
u
b, p

u
p

u

) sin(2π f

(2)
u
b

nTS + ϕ

u
b, p

),

where Pbu, d and Pbu, p are the powers of the data and pilot channels, cdu
and c up are the pseudorandom codes of the data and pilot channels,
du is the data sequence, τu is an unknown delay, f bu is the baseband
frequency that includes the intermediate frequency, a global offset
caused by the local oscillator and the offset caused by the Doppler
effect, and ϕbu, d and ϕbu, p are the carrier phases of the data and pilot
channel [13], [14]. Note that this model is simplified, since it does
not take into account the Doppler effect on the code, or the local
oscillator effect on the sampling frequency for example (see [13],
chapter 1), but it is enough for our problem.
The pseudorandom codes cdu and c up are composed of a primary
code and of a secondary code (and potentially of a subcarrier, not
considered here but without impact on our discussion), and are also
called tiered codes. In these tiered codes, the primary code is repeated several times and each period is multiplied by a chip of the
secondary code. Since the primary and secondary codes are binary
codes taking +1 or -1 as value, the tiered code is also binary code
taking +1 or -1 as value. Using vector notation, denoting p the
primary code of length NP, and s the secondary code of length NS,
they can be defined as
 p0 
 s0 




p
s1 
1 
, s=
,
p=
  
  




 pN P −1 
 s N S −1 

(3)

where the subscript represents the sample for p and the chip for
s. The tiered code, denoted c, has thus a length N = NS NP and is
defined as
AUGUST 2017

(4)

PARALLEL CODE SEARCH ACQUISITION
The aim of the acquisition is to detect the visible GNSS satellites,
and to estimate their baseband frequency f bu and code delay τu, by
synchronizing local replicas with the incoming signal. The acquisition is thus a two-dimensional problem, for each satellite. There
are different methods to perform the acquisition, such as the serial search, which tests the different combinations for the carrier
frequency and code delay one by one [16]; the parallel frequency
search, which tests one code delay and several or all the carrier frequencies in parallel using an FFT [17], [18], [19]; the parallel code
search, which tests one carrier frequency and all the code delays
in parallel using an FFT-based correlation [20], [16], [13]; or there
are also methods that parallelize the search in the two dimensions
[21], [22], [23]. For a high sensitivity hardware receiver, the parallel code search seems the most suitable method because of its high
level of parallelization, its moderate memory requirements, and
because it can compensate the code Doppler whereas the parallel
frequency search and its derivatives cannot [13], [24].

IEEE A&E SYSTEMS MAGAZINE

47



Table of Contents for the Digital Edition of Aerospace and Electronic Systems Magazine August 2017

No label
Aerospace and Electronic Systems Magazine August 2017 - No label
Aerospace and Electronic Systems Magazine August 2017 - Cover2
Aerospace and Electronic Systems Magazine August 2017 - 1
Aerospace and Electronic Systems Magazine August 2017 - 2
Aerospace and Electronic Systems Magazine August 2017 - 3
Aerospace and Electronic Systems Magazine August 2017 - 4
Aerospace and Electronic Systems Magazine August 2017 - 5
Aerospace and Electronic Systems Magazine August 2017 - 6
Aerospace and Electronic Systems Magazine August 2017 - 7
Aerospace and Electronic Systems Magazine August 2017 - 8
Aerospace and Electronic Systems Magazine August 2017 - 9
Aerospace and Electronic Systems Magazine August 2017 - 10
Aerospace and Electronic Systems Magazine August 2017 - 11
Aerospace and Electronic Systems Magazine August 2017 - 12
Aerospace and Electronic Systems Magazine August 2017 - 13
Aerospace and Electronic Systems Magazine August 2017 - 14
Aerospace and Electronic Systems Magazine August 2017 - 15
Aerospace and Electronic Systems Magazine August 2017 - 16
Aerospace and Electronic Systems Magazine August 2017 - 17
Aerospace and Electronic Systems Magazine August 2017 - 18
Aerospace and Electronic Systems Magazine August 2017 - 19
Aerospace and Electronic Systems Magazine August 2017 - 20
Aerospace and Electronic Systems Magazine August 2017 - 21
Aerospace and Electronic Systems Magazine August 2017 - 22
Aerospace and Electronic Systems Magazine August 2017 - 23
Aerospace and Electronic Systems Magazine August 2017 - 24
Aerospace and Electronic Systems Magazine August 2017 - 25
Aerospace and Electronic Systems Magazine August 2017 - 26
Aerospace and Electronic Systems Magazine August 2017 - 27
Aerospace and Electronic Systems Magazine August 2017 - 28
Aerospace and Electronic Systems Magazine August 2017 - 29
Aerospace and Electronic Systems Magazine August 2017 - 30
Aerospace and Electronic Systems Magazine August 2017 - 31
Aerospace and Electronic Systems Magazine August 2017 - 32
Aerospace and Electronic Systems Magazine August 2017 - 33
Aerospace and Electronic Systems Magazine August 2017 - 34
Aerospace and Electronic Systems Magazine August 2017 - 35
Aerospace and Electronic Systems Magazine August 2017 - 36
Aerospace and Electronic Systems Magazine August 2017 - 37
Aerospace and Electronic Systems Magazine August 2017 - 38
Aerospace and Electronic Systems Magazine August 2017 - 39
Aerospace and Electronic Systems Magazine August 2017 - 40
Aerospace and Electronic Systems Magazine August 2017 - 41
Aerospace and Electronic Systems Magazine August 2017 - 42
Aerospace and Electronic Systems Magazine August 2017 - 43
Aerospace and Electronic Systems Magazine August 2017 - 44
Aerospace and Electronic Systems Magazine August 2017 - 45
Aerospace and Electronic Systems Magazine August 2017 - 46
Aerospace and Electronic Systems Magazine August 2017 - 47
Aerospace and Electronic Systems Magazine August 2017 - 48
Aerospace and Electronic Systems Magazine August 2017 - 49
Aerospace and Electronic Systems Magazine August 2017 - 50
Aerospace and Electronic Systems Magazine August 2017 - 51
Aerospace and Electronic Systems Magazine August 2017 - 52
Aerospace and Electronic Systems Magazine August 2017 - 53
Aerospace and Electronic Systems Magazine August 2017 - 54
Aerospace and Electronic Systems Magazine August 2017 - 55
Aerospace and Electronic Systems Magazine August 2017 - 56
Aerospace and Electronic Systems Magazine August 2017 - 57
Aerospace and Electronic Systems Magazine August 2017 - 58
Aerospace and Electronic Systems Magazine August 2017 - 59
Aerospace and Electronic Systems Magazine August 2017 - 60
Aerospace and Electronic Systems Magazine August 2017 - 61
Aerospace and Electronic Systems Magazine August 2017 - 62
Aerospace and Electronic Systems Magazine August 2017 - 63
Aerospace and Electronic Systems Magazine August 2017 - 64
Aerospace and Electronic Systems Magazine August 2017 - 65
Aerospace and Electronic Systems Magazine August 2017 - 66
Aerospace and Electronic Systems Magazine August 2017 - 67
Aerospace and Electronic Systems Magazine August 2017 - 68
Aerospace and Electronic Systems Magazine August 2017 - 69
Aerospace and Electronic Systems Magazine August 2017 - 70
Aerospace and Electronic Systems Magazine August 2017 - 71
Aerospace and Electronic Systems Magazine August 2017 - 72
Aerospace and Electronic Systems Magazine August 2017 - 73
Aerospace and Electronic Systems Magazine August 2017 - 74
Aerospace and Electronic Systems Magazine August 2017 - 75
Aerospace and Electronic Systems Magazine August 2017 - 76
Aerospace and Electronic Systems Magazine August 2017 - 77
Aerospace and Electronic Systems Magazine August 2017 - 78
Aerospace and Electronic Systems Magazine August 2017 - 79
Aerospace and Electronic Systems Magazine August 2017 - 80
Aerospace and Electronic Systems Magazine August 2017 - Cover3
Aerospace and Electronic Systems Magazine August 2017 - Cover4
http://www.brightcopy.net/allen/aesm/34-2s
http://www.brightcopy.net/allen/aesm/34-2
http://www.brightcopy.net/allen/aesm/34-1
http://www.brightcopy.net/allen/aesm/33-12
http://www.brightcopy.net/allen/aesm/33-11
http://www.brightcopy.net/allen/aesm/33-10
http://www.brightcopy.net/allen/aesm/33-09
http://www.brightcopy.net/allen/aesm/33-8
http://www.brightcopy.net/allen/aesm/33-7
http://www.brightcopy.net/allen/aesm/33-5
http://www.brightcopy.net/allen/aesm/33-4
http://www.brightcopy.net/allen/aesm/33-3
http://www.brightcopy.net/allen/aesm/33-2
http://www.brightcopy.net/allen/aesm/33-1
http://www.brightcopy.net/allen/aesm/32-10
http://www.brightcopy.net/allen/aesm/32-12
http://www.brightcopy.net/allen/aesm/32-9
http://www.brightcopy.net/allen/aesm/32-11
http://www.brightcopy.net/allen/aesm/32-8
http://www.brightcopy.net/allen/aesm/32-7s
http://www.brightcopy.net/allen/aesm/32-7
http://www.brightcopy.net/allen/aesm/32-6
http://www.brightcopy.net/allen/aesm/32-5
http://www.brightcopy.net/allen/aesm/32-4
http://www.brightcopy.net/allen/aesm/32-3
http://www.brightcopy.net/allen/aesm/32-2
http://www.brightcopy.net/allen/aesm/32-1
http://www.brightcopy.net/allen/aesm/31-12
http://www.brightcopy.net/allen/aesm/31-11s
http://www.brightcopy.net/allen/aesm/31-11
http://www.brightcopy.net/allen/aesm/31-10
http://www.brightcopy.net/allen/aesm/31-9
http://www.brightcopy.net/allen/aesm/31-8
http://www.brightcopy.net/allen/aesm/31-7
https://www.nxtbookmedia.com