IEEE Geoscience and Remote Sensing Magazine - December 2014 - 13

The LC2 sequence has the same chip rate of the C/A signal, but it is composed of two PRN codes of different length.
On one side the moderate length code (CM) is 10230 chips
long, repeats every 20 ms, and it is modulated with navigation data. On the other side, the long code (CL) has 767250
chips, repeats every 1.5 s, and has no data modulation. Each
code is generated at 511.5 MHz and then multiplexed on a
chip-by-chip basis to obtain the composite signal at a rate of
1.023 chips/s. A detailed description can be found in [66].
Navigation information such as ephemeris, almanacs,
or corrections and constellation health are conveyed by the
50 Hz bi-phase code D ^ t h . All the bit/chip transitions in
the C/A, P, and D codes are synchronous, since they are all
driven by the same clock. These various signals are broadcast at L-band, thus suffering low atmospheric and rain
attenuations. The carrier frequencies are all multiples of
10.23 MHz: fL1 = 154 $ 10.23 MHz = 1575.42 MHz; fL2 =
120 $ 10.23 MHz =1227.60 MHz; and fL5 =115 $ 10.23 MHz
= 1176.45 MHz.
The frequency spacing between L1 and L2 allows estimation of the ionospheric delay as:
f 22
Dt 1 = 2 2 $ d ^Dt h,
f1 - f2

R BOC s (am, m) ^x h = K t c ^x h ) / k =-a +1 ^a - k h 62 $ d ^x - 2k h
a -1

- d ^x - 2k - 1 h - d ^t - 2k + 1h@,

(5)

where Dt 1 is the time delay at the frequency L1 due to the
ionosphere, f1 and f2 are the L1 and L2 frequencies and
d ^Dt h is the measured time difference between frequencies
f1 and f2 .
The minimum received power for the L1 P signal is on
the order of -133 dBm for a 0 dBic right-hand circularly polarized (RHCP) antenna. At L1 the C/A signal is 3 dB higher
than the P signal. At L2 the P code is transmitted 3 dB below the L1 P signal. The SNR for the direct signal ranges between 39 dBHz and 52 dBHz, depending on the geometry,
the actual transmitted power, and the instrumental and
propagation losses [67]. Within the GPS satellite antenna
field of view (FOV), the different signal attenuation due to
different propagation losses and atmospheric absorption is
compensated with the pattern itself of the transmitting antenna. More specifically, the edge of the Earth is 14° off the
antenna boresight, and therefore the pattern maximum is
located at this angle.
The transmitted signal is RHCP, and so it is immune to
the ionospheric Faraday rotation and the receiving antenna
does not have to be pointing to the transmitting satellite to
avoid polarization mismatch.
The new L5 signal designed for Safety of Life (SoL) applications is broadcast in a radio band reserved exclusively
for aviation safety services. It features higher power, larger
bandwidth, and an advanced signal design including two
in-phase and quadrature multiplexed signals: a navigation
data channel and a data-free channel to allow more robust
carrier phase tracking. It began in 2010 with GPS Block IIF.
As of June 25, 2014, six GPS satellites are broadcasting this
signal, and it will be available for all 24 GPS satellites by
2021 [68].
december 2014

Other satellite navigation systems such as Galileo share
the same frequency bands, as illustrated by Fig. 6 (see also
[69]). The PRN sequences are not necessarily generated using shift registers, but instead using look-up tables. Also,
advanced modulation techniques (Binary Offset Carrier
Signals or BOC) are used to increase the achievable accuracy with the same bandwidth [70]. The BOC modulation
is the result of multiplying the PRN code with a sub-carrier
which is equal to the sign of a sine or a cosine waveform,
yielding so-called sine-phased or cosine-phased BOC signals, respectively, as shown in [71]. The BOC signal is commonly referred to as BOC ^m, n h where fs = m $ 1.023MHz
MHz and fc = n $ 1.023MHz, and unless indicated in
a different way, when talking about BOC signals, it will
always be understood as the sine-phased variant. For the
sine-phased BOC signals (i.e. L1M, E1B and E1C), the autocorrelation function (ACF) can be expressed as an addition
of triangles [72]:

ieee Geoscience and remote sensing magazine

(6)

where a = n/m is the symbol ratio and t c = x c /a For the
cosine-phased BOC signals (i.e. E1A), the ACF is given by:
R BOCc (am, m) ^x h = K t c ^x h ) / k =-a +1 ^a - k h66d ^x - 2kh
a -1

+ d ^x - 2k - 1 h + d ^x - 2k + 1h
- 4d ^x - 2k - 1/2 h - 4d ^x - 2k + 1\2 h@ . (7)

Finally, the ACF for the E5 signal can be closely approximated using the general expression of a CDBOC
modulation:
R 1 ^x h = K TB ^x h
12

N 1 -1 N 2 -1 N 1 -1 N 2 -1

)

/ / / /

i =0

k = 0 i1 = 0 k1 = 0

^-1 hi +i 1 +k +k 1

$ d ^x - ^i - i 1h TB 1 - ^k - k 1 h TB 12 h,

R 2 ^x h = K TB (x) )

(8)

12

/ lN=0-1 / mN =-01 / lN =-01 / mN -=10 / Np =0-1 / Np =-01 ^-1hl +l +m +m
3

4

3

1

4

1

res

res

1

d ^x - ^l - l 1h TB 3 - ^m - m 1 h TB 34 - ^p - p 1h TB 12 h,
R AltBOC(a N21 , a) ^x h = R 1 ^x h + R 2 ^x h,

1

1

$

(9)

(10)

where TB i = x c /N i, TB ij = x c /N i N j, and N res = N 1 N 2 /N 3 N 4 .
Fig. 7 shows the ACF's absolute value for infinite bandwidth signals. As an example, Fig. 7a is the composition of
three functions: a triangle of base [-1, +1] C/A code chips
(corresponding to the L1 C/A signal), another triangle of
base [-0.1, +0.1] C/A code chips (corresponding to the P
code), and two side peaks (corresponding to the M code, if
available, depending on the satellite).
Table 1 shows the main signal characteristics for the GPS
L1 and L5 and for the Galileo E1 and E5 bands. The carrier
13



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