Signal Processing - September 2017 - 61

Table 1. Channel parameters of some GNSS signals that belong to (1a)-(1c).
A P /A D

D (t )

PP (t )

PD (t )

S P (t )

S D (t )

SC P (t )

SC D (t )

GPS L1 C/A

-

R b = 50

-

L c = 1023
R c = 1.023

-

-

-

-

(1a)

GPS L2C

CM and CL
codes are
chip-by-chip
multiplexed

R s = 50

L c = 767, 250
R c = 0.5115

L c = 10230
R c = 0.5115

-

-

-

-

(1c)

GPS L5

1

R s = 50

L c = 10230
R c = 10.23

L c = 10230
R c = 10.23

L c = 20
R c = 0.001

L c = 10
R c = 0.001

-

-

(1b)

Galileo E1 OS

1

R s = 250

L c = 4092
R c = 1.023

L c = 4092
R c = 10.23

-
L c = 25
R c = 250 Hz

CBOC(−)

CBOC(+)

(1c)

Galileo E5a

1

R s = 50

L c = 10230
R c = 10.23

L c = 10230
R c = 10.23

L c = 100
R c = 0.001

L c = 20
R c = 0.001

-

-

(1b)

Glonass L1 C/A

-

R s = 50

-

L c 511
R c = 0.511

-

-

-

-

(1a)

Note that CBOC(!) = 10/11 sinBOC ^ 1, 1 h ! 1/11 sinBOC ^1, 1 h, where sinBOC(1,1)= sign[sin(2 rR c t )].

L1 C/A and Glonass L1 C/A signals and (1b) can be used for
GPS L5, Galileo E5a, and Galileo E5b signals, where pilot and
data channels are modulated by quadrature phase-shift keying
(QPSK); and (1c) is for GPS L1C, GPS L2C, Galileo E1 OS
(open service), and (maybe) BeiDou B1, where signals are separated by the spreading code or by time-division multiplexing.
Note that the BeiDou B1 modulation scheme is not fixed yet at
the time of writing this article, but it is found in [5] that one of
the most probable options for BeiDou B1 is a combination of
a BPSK-modulated data channel and a quadrature-multiplexed
BOC (QMBOC)-modulated pilot channel, where, in QMBOC,
the pilot channel has most (88%) of its power in the same phase
and the rest in the quadrature phase to the data channel. Therefore, an acquisition function may process the BeiDou B1 signal
as an in-phase signal in (1c) to reduce the receiver complexity.
Note also that Galileo E5 alternate BOC (AltBOC) modulation cannot be expressed using (1b); however, the lower and
upper mainlobes of Galileo E5 AltBOC can be represented by
two QPSK-modulated signals in (1b), respectively. The channel
parameters of some of the GNSS signals belonging to (1a), (1b),
and (1c) are summarized in Table 1 [5], where the unspecified
units of R b, R s (encoded symbol rate), L c, and R c are bits/s,
symbols/s, chips, and megahertz (MHz), respectively.
The acquisition functions for the GNSS signals in (1b) and
(1c) are discussed in the section "Channel Combining Techniques for New GNSS Signals." In this section, we use the GPS
L1 C/A signal (1a) to introduce the fundamentals of GNSS
acquisition and let T p , T1, and T20 represent the primary code
period in seconds, 1 ms, and 20 ms, respectively. To detect the
prompt code phase x and Doppler frequency fD of an incoming GNSS signal, an acquisition function performs a correlation at the time instant h between the incoming signal y ^ t h
and a receiver replica x ^ t h for the lth code phase and mth
Doppler-frequency hypothesis (in a complex form)
x ^t; l, mh = P ^t - l∆ xh e j2r^ fI + m∆ f ht

(2)

to generate a correlation output for the lth code phase and mth
Doppler-frequency hypothesis as
R 6h, l, m@ =

/ y6n + h@x6n; l, m@,

N co - 1

(3)

n=0

where N co is the number of samples received during the coherent correlation interval Tco for a sampling frequency fs (i.e.,
N co = fs Tco ) and R 6h, l, m@ = R I 6h, l, m@ + jR Q 6h, l, m@ . In
general, the acquisition function employs a (postcorrelation)
integration function G ($), as shown in Figure 1, that combines
the pilot and data channel components and integrates consecutive correlation outputs to further increase the acquisition
sensitivity. The integration techniques for G ($) are introduced
using the GPS L1 C/A signal as an example, and the channelcombining techniques are introduced in the section "Channel
Combining Techniques for New GNSS Signals."

Coherent integration technique
When the coherent correlation interval Tco is much smaller
than Tb as in the conventional GPS L1 C/A signal receivers
that use Tco = T1 = 1 ms, the data D ^ t h can be assumed constant during an integration. Therefore, the resulting consecutive coherent correlation outputs can be coherently added for
N i (1 # N i 1 20) times to build a coherently integrated detection variable Z = Z co, as in Table 2. Note that N i is called the
accumulation length, and that Z co is equivalent to the detection variable for a coherent correlation with a long coherent
correlation interval N i Tco . In general, this technique amplifies the signal peak amplitude (i.e., Z co | H 1 ) by N i times.
However, when N i & 1, there can be bit transition(s) during the
overall interval N i Tco, which often causes a significant degradation of the signal peak power, Z co | H 1 .

Noncoherent integration technique
To avoid the bit transition problem in the long coherent integration, an acquisition function may choose Tco much smaller than

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