Signal Processing - September 2017 - 54

[4]-[6]. Each Doppler search trial involves several computations, proportionate to the number of digital samples
in the signal observation interval, resulting in substantial
consumption of computing and power resources, right at
the beginning of the position fix process in the receiver.
A number of processing techniques have been proposed to
reduce the computational complexity of a Doppler search
in signal acquisition.

GPS L2C signal

Accumulated
Energy

GPS L2C is an emerging modern GNSS signal with an intensive Doppler search requirement due to a longer code period.
We considered the GPS L2C signal as an appropriate choice
for discussion on the subject topic, but the discussions remain
valid to other GNSS signals as well. The GPS L2C signal,
currently broadcast by 19 satellites, is the first modernized
civilian GPS signal to become available. The new signal could
generate US$5.8 billion by 2030 [7], [8]. When compared to
the legacy L1 course/acquisition (C/A) signal, L2C alone delivers enhanced reliability and greater operating range, including
indoor environments, due to its longer ranging codes, a pilot
channel, and a forward error correction coding [9]-[12]. Also,
when combined with L1 C/A, L2C enables ionospheric correction, allowing dual-frequency civilian GPS users to enjoy
military accuracy levels without the complex semicodeless
tracking of an L2 precision (encrypted) [P(Y)] signal. Transmitted on the GPS L2 carrier of 1227.6 MHz, the L2C code
consists of two components, the civil moderate (CM) code and
civil long (CL) code, multiplexed together on a chip-by-chip
basis, as illustrated in Figure 2. The CM code repeats every 20 ms
and modulates the navigation message data civilian navigation
(CNAV), whereas the data-free CL code has a period of 1.5 s.
The codes are synchronized such that each CL period contains
exactly 75 CM code epochs. The chip rate of individual code
components is 0.5115 Megachips per second (Mcps) while the
composite L2C code runs at 1.023 Mcps [12].
A number of processing techniques have been proposed
to reduce the computational complexity of a Doppler search
in L2C signal acquisition. In [13]-[15], double-block zeropadding is applied on each 1-ms segment of the received signal. This reduces the computational complexity in the delay
dimension by computing several shorter FFTs as compared
to a straight full-length FFT while, at the same time, decreasing the Doppler search computations by performing circular

shifting of FFT results instead of repeating the code correlation step for each Doppler trial. In [16], the number of test
hypothesis for a Doppler search are reduced by performing
subperiod correlations in the time domain, and a differential
semicoherent combining technique is applied to compensate
for a residual carrier while minimizing the signal-to-noise ratio
loss by exploiting the statistical independence of noise across
individual result samples. In [17], hypercodes were introduced
for efficient L2C signal acquisition, where adjacent subperiod
segments of CL code, considered to have quasi-orthogonal
characteristics, are overlaid to construct a hypercode. In a
recent technique called chipwise (CW) correlation [18], the
baseband L2C signal is averaged over each code chip period,
i.e., approximately 0.97752 ns , so that a 20 ms signal segment
is compressed to contain only 20,460 samples. The technique
is further extended as double-CW correlation [19] to perform
the averaging operation over every two chips, further reducing
the correlation processing complexity at the cost of, on average, an extra loss of 1.3 dB in the acquisition sensitivity.
All of the techniques described previously, however, perform
the Doppler search at the original full sampling rate, determined
by the radio-frequency front end of the receiver, which must
remain above the Nyquist limit of the direct sequence spread
spectrum-modulated GNSS signal.
For detailed discussion, we present a new low-rate processing approach for a Doppler search in GNSS signal acquisition.
The presented approach is an application of a low-rate processing
technique for GNSS signal tracking, recently developed by the
authors of [20]-[22].
In this technique, the Doppler search is carried out with
averaged signals, downshifted to sampling rates lower than
chip-rates of the ranging-code of the GNSS signal without
compromising the acquisition performance yet significantly
reducing the computational load. By conducting experiments
on real GPS L2C satellite signals, we demonstrate that, for the
standard ±5 kHz GPS Doppler range, by averaging the received
L2C signal over 0.01 ms intervals, the required Doppler search
is accomplished at a processing rate of only 100,000 samples/s
(sps) without losing the acquisition sensitivity.

The low-rate Doppler search system
The system for a Doppler search at a low processing rate is
illustrated in Figure 3. The system consists of two signal processing stages distinguished by their processing rates.

TCL= 1.5 s
T = 20 ms
CM + CL2

CM + CL1

1
0.5
0

Dopple
r Offse
t

de
Co

y
la
De

Doppler offsets experienced by a GNSS satellite signal. High energy levels
establish the presence of the signal.

1.023 Mc/s

20,460 Chips
CM Chips

FIGURE 1. A signal search grid constituted by potential code delays and carrier

CL Chips

FIGURE 2. One complete period of the GPS L2C code.

IEEE SIGNAL PROCESSING MAGAZINE

September 2017

CM + CL75

Table of Contents for the Digital Edition of Signal Processing - September 2017