4.1 Dipole antenna
The horizontal polarization is the key requirement for the antenna design. Among the typical antenna types, the loop antenna is horizontally polarized for all the azimuths and thus serves as a favorable option. However, the internal loop/wire inductance makes the loop antenna difficult to be matched [14]. To simplify the antenna fabrication, a customized wire antenna was designed and built, which is given in Figure 7. The simulated radiation pattern of this antenna, which is shown in Figure 8, approximates a theoretical half wavelength dipole antenna and it can be matched easily by adjusting the bending angles of the four wire legs [16]. For simplicity, it will be referred as dipole antenna in the later paragraphs. The half wavelength dipole antenna is well modeled in antenna theory; thus, the important characteristics related to the snow sensing are listed below.
4.1.1 Radiation pattern
The radiation pattern of the half wavelength dipole antenna is as follows:
(14)
where θ is the zenith angle and ϕ is the azimuth angle in spherical coordinate frame. If the radiation pattern is irrelevant to ϕ, this antenna is referred as an omnidirectional antenna. Please note that there are two nulls at θ = 0° and θ = 180° and also the maximum radiation intensity locates at θ = 90°.
4.1.2 Vector effective length
The vector effective length of the half wavelength dipole antenna is given by
(15)
Where is the unit vector in the direction of zenith angle in spherical coordinate frame. For a receiving antenna, the open circuit voltage Voc stimulated by the incident electric field can be calculated by
(16)
Note that both and are vectors and only if they are in the same direction will Voc reach its maximum value. The polarization efficiency p
e
which is given by
(17)
is used to describe this polarization mismatch between the incident electric field and the receiving antenna.From (15), this dipole antenna will be vertically polarized if it is placed upright. The simulated gain pattern in Figure 8 verifies the validity of the half wavelength dipole model. The simulation shows that the gain in the phi direction (corresponding to the horizontal polarization gain if the antenna is placed upright) is negligible compared to the gain in theta direction (corresponding to the vertical polarization gain if the antenna is placed upright). If this dipole antenna is placed upright, the vertical component of the L2C signal will be received exclusively and the horizontal component will be rejected, which is against to our intension.
However, if this antenna is tipped, it will be horizontally polarized at the direction θ = 90° (here, θ is the zenith angle of the antenna), which is the desired polarization for the desired antenna. Please note that since the radiation pattern is omnidirectional, the phase response for the direct and reflected horizontally polarized waves are also constant, and thus ϕ
a
is zero.
This dipole antenna is made up of a hardline coax cable, stripped of its outside copper layer to expose the inner pin and soldered four copper wire legs on it. The length of the inner pin and the legs is 5.5 cm and the bending angle is 45°. A network analyzer was used to tune the design, locating the null of |S11| (S11 is the complex reflection coefficient of one-port network) at the L2 frequency by adjusting the length of pin and the bending angles of the four legs.
4.2 Software-defined receiver
4.2.1 Front end - universal software radio peripheral
A universal software radio peripheral (USRP) N210 platform from Ettus Research Inc. (Santa Clara, CA, USA) is shown in Figure 9. This device served as the raw intermediate frequency (IF) data collection platform from which the software defined GPS L2C receiver was developed.
The USRP has the following features that make it a powerful RF/IF data collection tool.
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Wide frequency range from 0.8 to 2.35 GHz, which covers all the GPS frequencies (L1, 1,575.42 MHz; L2, 1,227.6 MHz; L5, 1,176.45 MHz).
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Sampling rates is up to 50 Msps and wide RF bandwidth (25 MHz), which enables low-loss sampling for any GPS signal.
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14-bit ADCs/DACs enable high dynamic range and quantization resolution.
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The USRP has a 1 Gb Ethernet interface which enables data transfer at any sampling rate and bit level.
As the L2C signal is of interest, the center frequency and sampling rate are set to 1,227.5 MHz (giving an IF of 100 KHz) and 2 Msps, respectively.
4.2.2 Signal processing
A SDR has been developed to process the raw IF data collected by the USRP to provide maximum flexibility into the receiver processing. It is an extension of the open source L1 Matlab receiver documented in [17]. L2C is the new civil code signal transmitted at L2 frequency (1,227.6 MHz) with the same chipping rate as the L1 C/A code. This new civil signal is available on only a subset of the current GPS constellation (on the current/future Block IIR-M, Block IIF and Block III satellites). At the time of the experiment, there were nine GPS satellites (PRN 1, 5, 7, 12, 15, 17, 25, 29, and 31) that broadcast this new signal. The L2C signal has the following advantages for snow sensing compared to L1 C/A code, which is demonstrated in [6].
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L2C has superior code cross correlation (40 dB compared to CA's 24 dB) and continuous wave interference rejection.
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L2C has a pilot (data-free) channel for extended integration time.
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Improved data structure for enhanced data demodulation offers a 5-dB improvement compared to the L1 C/A.
In a typical SDR, the delay lock loop (DLL) and phase lock loop (PLL) are used to track the code phase and the carrier phase of the received signal. However, the dipole antenna has no suppression of the reflected signal so the combined SNR could be very low when the direct signal and the reflected signal are of opposite phases. The traditional tracking loop may lose lock when the reflected signal degrades the direct signal. An open loop (OL) tracking is an alternative to the traditional tracking loop that can provide additional sensitivity. The OL tracking does not use feedback loops but rather performs repetitive acquisitions at a particular time interval. The OL tracking provides a more robust tracking approach than the traditional closed loop tracking and avoids the need for tracking thresholds and reacquisition algorithms. An advantage of this USRP/SDR implementation is that SNR estimates are available at a much higher update rate than the geodetic GPS receivers (which typically operate at 1 Hz) and the high-rate SNR can be averaged to obtain lower noise measurement.