GNSS TimeReceiver

Project GNSS Reradiator
GNSS reradiator to receive GPS, Galileo L1/E1 indoors
Status	In progress
Contact	cmpxchg
Last Update	2020-04-10

What is a GNSS / GPS ReRadiator ?
An Indoor GNSS Re-Radiator uses an indoor, in-room antenna, to transmit a low-power GNSS signal that is a copy of a GNSS signal picked up on the roof. The signal is intended only for devices present in the room. In addition to this, it can be used to directly feed a GNSS- or GPS Time Receiver placed indoors. For the latter, no re-radiating antenna is needed, but a similar installation is needed to get the GNSS signal intact indoors.

Application of GNSS ReRadiators
One application of GNSS ReRadiators are fire- and ambulance services, vehicles parked inside a garage, without a direct view of the sky. The ReRadiator will wirelessly, via the same frequency, keep the cars/devices supplied with current GNSS RF data. This way, the latest orbit and clockinformation will be available right when they leave the garage. Leaving the garage might cause a slight change in level of the signal, and phase will also change slightly, small enough to be picked up effortlessly by the signal correlators in the GNSS receiver. Acquisition of a signal on a fast moving vehicle in a city might fail, and will take at least 30 seconds if not provided with recent GPS RF data and synchronised clocks.

Why are 4 satellites needed to calculate an accurate GNSS position ?
Intuition would lead to the belief that 3 spheres should already provide a unique, earth-height, intersection.
In practice, 4 satellites are used, and 5 in some RTK applications.
The PVT (position, velcity and time) calculation involves pseudo-ranges to four satellites, each can have a different path, refracted slightly through the atmosphere. This bent path creates an error that is dependent on weather and elevation, that can be reduced to a 'total electron count' number. The error would be too big, it is not the about 7 to 12 meter accurate position that is expected by GPS/GNSS users.
Also, the local clock offset must be determined, which is calculated through the use of the fourth satellite in the equation.

What GPS/Galileo/GNSS updates can I receive with an indoor replica of the GNSS signals ?
The updates to the satellite orbits and clock drifts are continously transmitted by each GPS or Galileo satellite.

GPS 'broadcast ephemeris' data is valid for 4 hours and is updated every 2 hours, and contains exact information on the orbit and position within that orbit. It also contains a clock offset relative the the GPS master clock maintained at a central location on ground.
The 'Broadcast ephermeris' part of the signal is unique to each satellite and is broadcast in 3 of the 5 frames transmitted every 30 seconds. This three times 6 second period aligned to each half-minute is the reason that almost all GPS receivers have a cold-start of a little over 30 seconds (signal acquisition and receiver turn-on time alignment might be variable)
GPS Almanac data is also transmitted by each GPS satellite, over a period of 12.5 minutes, using the other 2 of the 5 6-seconds frame every 30 seconds. GPS Almanac is a map with coarse information of all (other) GPS satellites that might not yet be visible on the sky but could be tried to be acquired, for example to replace one that just went out of view.
There is no dependency on internet for either GPS Broadcast Ephemeris data or GPS Almanac data. All data comes from the same source, the satellite, and is synchronized up to the nanosecond level. A receiver can obtain syncrhonisation with this clock by integrating over many 20 msec periods. The same periods result in a 50 bps per-satellite datastream.
Receivers do not have clocks that are compact, good and low-power enough to maintain precision over many hours, so they have to start searching in the noise (a few milliseconds to seconds on modern receivers), and then pull in the most recent Broadcast Ephermeris. Some receivers allow prediction of orbits using precomputed/extrapolated data, 'quickgpsfix' - but this data needs to be confirmed when the real data comes in after 30 seconds.

Can one navigate indoor using only GNSS signals?
Navigation and timing receivers, receiving a re-radiated GNSS signal, can acquire a position indoor, but will calculate an position that approximates the location of the rooftop antenna.
It is not possible to calculate one's position within the room, only the range to 'the' or 'one of' the GNSS ReRadiators can potentially be calculated. For this, information on the delay of the antenna, amplifiers, cables and filters is needed, which is not, or not directly, part of the re-broadcasted, analog RF signal.

What happens in the GNSS receiver with a 'ReRadiator' signal source instead of direct-sky, own antenna, is an apparent pseudo-range 'bias' of all (typically 4) satellites that end up in the positon/velocity/time solution (PVT).
If this 'common bias' in pseudo-range is assumed zero, it will result in a calculated position that is 'deeper' than the roof antenna, and offset opposite to the side where the highest-elevation satelites are present at that moment. Having a position below earth should not be a big problem, it will resolve to an above-earth position on a map. Height will be much less accurate compared to lattitude/longtitude with GNSS signals anyway.
Almost all receivers will default to the highest elevation satellites that are received, since they have the least amount of range-errors introduced by the atmosphere, and such radio-path are generally free of obstacles and reflections. In addition, reflections via a flat surface will invert the polarity of the circulairy polarized signal, causing losses in well-designed polarized GNSS receive antenna's

How strong are ReRadiated GNSS signals?
If the power level is kept close to the specified -128 dBm outdoor level (GPS), it will not escape the room.

GPS is specified at -128 dBm receive level on earth, WiFi receivers minimum level is about -98 dBm, about 30 dB difference, which is a factor of 1000 in power. Wifi uses 2400-2480 MHz and ca 11 MHz wide, GPS is 1575.42 MHz and 2 MHz wide. This is a very low level, it is below the thermal noise level for that bandwidth, and is impossible to see on a spectrum analyser. Nevertheless it can be detected, by correlation.

The GPS satellites output each ca 27 watts towards earth on the L1 frequency (1575.42 MHz, ca 2 MHz wide). The temperature of the antenna is very low. After this the signal travels ca 22000 km, and arrives at a GPS receiver antenna in ca 70 milliseconds. These L1 are the only signals that a retransmitter should transmit.

There is a significant amount of gain needed, many tens of decibels, and this has to be gain with a very low noise-figure, i.e, as few random, uncorrelated noise added by the signal chain. The source of the ReRadiator is a point-source receiver, hopefully with a well-defined phase center of the signals arriving from the various directions. This accumulates only a few square millimeters to many square centimeters of the radio signal, hopefully picking up only sky-sourced radio signals.

This tiny GNSS signal needs to be spread out, still in spectrum-analyser-unobservable noise form, over the room via the re-radating antenna. No more than 20 or 30 dB per gain stage is possible. After each stage, filtering is needed to prevent out-of-band signals being amplified, that will be picked up in some amount (-20 dB or more) by the antenna.

Out-of-band unwanted signals, for example, a nearby GSM modem outputting up to 2 watts in the range of 700-900 MHz, will be much stronger than the GPS signal.
Computers, DRAM memory busses or monitor cables can also leak high-frequency information (EMI), whose (mostly odd) harmonics (1x, 3x, 5x, 7x the source frequency) can end up in the GNSS band of 1575.42 MHz, which is ca 2 MHz wide, and a few MHz wider if filters have to be taken into account

Unwanted strong signals could, worst-case, saturate the input stage, applying signals that go toward the voltage rail in the first or one of the following amplifier stages. Next to that, lower level interference can also distort due to unavoidable non-linearities in the RF amplifier, which creates mixing products within the band of the GNSS receiver, These cause leakage of additional, unwanted, noise in the amplifier output.
It can also trigger automatic gain control adjustment in the receiver, trying to keep the apparent noise within bounds. Such noise reduces the chance that a zero-crossing resulting into a digital bit going to the correlator, will not be detected, and correlation or carrier-to-noise ratio will decrease, or tracking of the satelite will be (temporarly) lost.

Why is an 'active antenna' needed ?
The 'noise figure' of the first amplification stage is the most important, since that noise will dominate the noise-figure of the complete chain. Friis formula for noise. The first amplification stage will always be right behind the antenna itself, before any cable or other element with non-perfect impedance matching and attenuation.
The only thing in front of the first gain stage, or in between two stages, is a filter to supress out-of-band signals. For this, often SAW filters are used, Surface Acoustic Wave filters. These tiny electro-mechanical devices provide enough attenuation outside the designed frequency, while providing amble insertion loss in the pass-band. They are mechanically stable and provide reproducible results.

How is an 'active antenna' powered ?
An 'active antenna' will not radiate signals back via the antenna to the environment. 'Active' means it will amplify the signal before transmitting it down a cable to the receiver. The power needed for this is relatively small for a wired installation, a tens of milliAmps, but needs to be provided by the upstream device/receiver. The active antenna has a circuit to pull the DC signal from the cable, and will transmit an RF signal, around 1575.42 MHz, upstream to the indoor receiver and powersupply. The upstream-device needs to provide a DC bias to it's input.

This is similar to how Satelite receiver LNB's are powered. An inductor will provide a DC signal of 3.3 to 5 volts to the center conductor of the coaxial cable. A series capacitor is placed after the bias to allow the RF signal to be fed to a receiver's gain stage or filter.
To be inserted: Schematic of DC bias

GPS patch antenna's with a magnetic base are cheap and almost always have one or two gain stages and filters built-in

GPS orbits
GPS satellites orbit the earth in a little less than 12 hours, the aim is half a sidereal day. Galileo satellites use a higher orbit and orbit in around 10 hours. Towards the poles one will find more GPS satellites near the equator. Glonass has better coverage of the poles, but a lower chance of direct-overhead satellites near the equator, All GPS satellites transmit on several L-band frequencies, but the L1 signal on 1574.42 MHz is used by 99% of all receivers.

GPS and Galileo signal: CDMA in BSPK and BOC form
The L1 (1575.42 MHz, equals E1 in Galileo parlance) signals of the 24 GPS satellites are transmitted by using a BPSK stream of chips, at 1023000 chips per second, or about 1 msec per sequence-cycle of 1023 chips. This is called CDMA, Code Division Multiple Access, which can take many shapes, even a north-american phone standard is named after this modulation principle.

CDMA means a repeating bit-pattern, or better, 'chip' pattern, where the sign of all the 'chips' in the sequence are inverted once in a while, in order to modulate the payload data, or bits. The chip rate is very high, 1023000 chips per second, the bitrate really low, 50 (gps) or 250 bits per second (galileo)

The GPS signal can be produced with an LFSR, one or two Linear Feedback Shift Registers that produce, together with a few XOR gates feedback network, a repeating bitpattern of 2^n-1 length, or 1023 bits - ('chips' in CDMA parlance). In GPS this is the XOR of two shorter LFSRs (Gold codes).

A receiver works by generating the known LFSR/CDMA/chips signal with exactly the right frequency and phase, and performs a correlation with the received noise, over the period of up to 20 milliseconds.
After the search or 'acquisition phase', which can take a few seconds depending on processing power, the signal can be tracked using this simpler setup.

GNSS Signal Acquisition

Acquisition can be done using two methods, DFT/FFT and convolution in the frequency domain, or the simpler, all digital, an exhaustive search with correlation of a tens of msec, going over a search range of about 35 kHz (expected doppler range and owm frequency offset), with a resolution of about 0.5 Hz, and a code-offset space, with a resolution of about half a chip of code-offsets, thus 1023 * 2 = 2046 chips, a table of 70x2046, almost 144'000 tries. The integration period and number of correlators applied in parallel can drastically reduce this time. This is the reason old (90's era) receivers took very long to calculate a position.

Once acquired, the found correlation peak can tracked by three correlators for each satellite the receiver wants to track. Three correlators on subsequent half-chips are used, early, precise and late (E,P,L). The height of correlation between the three is used to feedback a loop that tracks the phase and frequency-drift (Doppler) of the locally generated signal.

Every 20 msec, the correlation peak can also invert - the inverted LFSR signal is transmitted to indicate a 0-bit or 1-bit of the 50 bps GPS signal, or the 250 bps Galileo signal

How is Galileo different from GPS?
The european Galileo satellite constellation is using a similar concept as GPS, Russia's Glonass and China's Beidou. GPS and Glonass were the first signals, Galileo and Beidou came later.
Russia is using their own frequency and need a different RF frontend, downconverter stage and antenna with sensitivity in the 1600 MHz band.
Galileo and GPS, and also Beidou use exactly the same frequency, 1575.42 MHz ca 2 to 4 MHz wide. Galileo uses 2046 chips instead of 1023 chips per symbol, so only a little more bandwidth is needed to receive both GPS and Galileo with the same RF frontend.

Is it legal to transmit GNSS indoor ?
In the Netherlands, one is required to report and per April 2017 also acquire a license (vergunning) for a GNSS reradiation installation to Agentschap Telecom. This to help track down nearby interference to other nearby GPS/GNSS users.
Since the reRadiated GNSS signal is still very weak, it will generally not escape via windows or walls to the outside, and it will not become an 'oscillator'.
The rooftop receive antenna should pick up signals from satellites from all directions, except the ones reflected from the ground or via other buildings or own windows.
Compared to building a complete-to-time/to-position receiver, building a GNSS ReRadiator or roof-based 'GNSS receptor' is a lot simpler, only 'basic' RF knowledge is needed.
There are many cheap modules available that accept a cable-based GPS/GNSS signal, and output a simple lat/lon position, and height. Some also provide long-term accurate time, in addition to reasonable short-term accurate time (GPS-DO, disciplined oscillator). Some allow external clock inputs, or have a reference clock output, from 32 kHz timer-based signals to full 1, 5 or 10 MHz outputs.

Where can I read more technical info on GPS and Galileo?
With both GPS and Galileo, a position and time can be gathered, without have to relay this information via a third-party radio network, like the internet, 2G/3G/4G etc.
Next to the official US-provided NavStar documentation, explanation of the system is documented in the following books and information sources:

2007 - Kai Borre - A software Defined GPS and Galileo Receiver
2009 - Frank van Diggelen - A-GPS
2007 - Blog of Michele Bavaro on development on various GNSS / GPS / Galileo / Beidou / Glonass receivers
2017 - Article displaying gratitude after the disappearce of Kai Borre summer 2017
2014 - Navipedia Website maintained by ESA on almost all operating GNSS systems by ESA (Galileo) and others
2017 - Agentschap Telecom aanvraag GNSS repeater per 1 April 2017 (tegenwoordig 'enkel hulpdiensten' - geen kantoor, hangars, geen checks?)