GPS Receiver Testing

From the airplane pilot operating guiding a Boeing 747, to the everyday consumer using a GPS navigation system in his car, to the hobbyist searching for buried treasure in the forest, GPS technology is quickly becoming integrated into a wide variety of applications. As innovation drives GPS receivers to even better performance, techniques used to characterize performance are becoming increasingly sophisticated as well. Today, the power of software enables you to create GPS waveforms that accurately emulate the real word signal. In addition, advances in instrument bus technology enable record and playback of live GPS signals with PXI instrumentation.

Introduction

As GPS technology becomes more commonplace on the commercial market, many design goals are aimed at improving characteristics such as: 1) lower power consumption, 2) tracking of weak satellites, 3) faster acquisitions times, and 4) more accurate position fixes.  In this application note, you will learn how to make a variety of GPS receiver measurements including: sensitivity, noise figure, position accuracy, time to first fix (TTFF), and position deviation.  Our goal is to provide engineers with a thorough understanding of GPS measurement techniques.  For engineers who are new to GPS receiver measurements, this paper will provide a comprehensive overview of common measurements.  For engineers who are already experienced at performing GPS measurements, this paper can be used as a resource to introduce new instrumentation technology.  This application note is structured according to the following sections:

1.      Basics of GPS Technology
2.      GPS Measurement Systems
3.      Overview of Common Measurements
   1. 1. Sensitivity
      2. Time to First Fix (TTFF)
      3. Position Accuracy and Repeatability
      4. Tracking Accuracy and Repeatability

For each section, we will provide several practical tips and techniques.  More importantly, you can compare your results to typical results that we have observed from GPS receivers.  By correlating your results with both ours and theoretical measurements, you can be sure that your measurement data is valid.

 

Introduction to the GPS Navigation System

The Global Positioning System (GPS) is a space-based radio navigation system managed by the U.S. Air Force.  While GPS was originally developed as a military positioning system, it has significant benefits for civilian use as well.  In fact, it is likely that many of you already use GPS receivers in your car, boat, or even cell phone.  The GPS navigation system consists of 24 satellites which transmit multiple message signals in the L1 and L2 frequency bands.  In the L1 band, at 1.57542 GHz, each satellite generates a 1.023 Mchips BPSK (binary phase shift keying) spread spectrum signal.  The spreading sequence uses pseudorandom (PN) sequence called the C/A (coarse acquisition) code.  Although the spreading sequence is 1.023 Mchips, the actual message data rate is 50 Hz [1].  At the system’s original deployment, GPS receivers were able to achieve a typical accuracy of greater than 30 to 20 meters.  This level of accuracy was due to an intentional random timing error added by the US military for security reasons.  However, on May 2^nd, 2000, the error source (call selective availability) was removed.  Today, receivers are able to achieve better than 5 meters of maximum error, with typical errors as low as 1 to 2 meters. 

In both the L1 and L2 (1.2276 GHz), GPS satellites also generate an additional signal known as the ‘P code.’  This signal is a 10.23 Mbps BPSK modulated signal which also uses a PN sequence as spreading code as well.  The ‘P’ codes are transmitted are used by the military for even greater position precision.  In the L1 band, they are transmitted 90 degrees out of phase with the C/A codes to ensure that both can be detected at the same carrier [2].  P codes in the L1 band have a signal power of -163 dBW and a power of -166 dBW in the L2 band.  By contrast, the broadcast power for C/A codes in the L1 band is a minimum of -160 dBW on the earth’s surface.

 

GPS Navigation Message

For C/A codes, the navigation message consists of 25 frames of data, and each frame contains 1500 bits [2].  In addition, each frame is divided into five 300-bit sub-frames.  With a receiver acquiring C/A codes, it takes exactly 6 seconds to acquire one sub-frame and thirty seconds to acquire one frame.  Note that the thirty seconds required to acquire an entire frame actually has profound implications on some of the measurements we will discuss later one.  In fact, the time to first fix measurement (TTFF), is usually greater than thirty seconds because this is the minimum needed for the receiver to acquire an entire frame.

In order to achieve a position fix, most receivers must have updated almanac and ephemeris information.  This information is actually contained in the message data transmitted by the satellites, and each sub-frame contains a unique set of information.  Generally, we can describe the sub-frames as having the following data [2][7]:

Sub-frame 1: Contains clock correction, accuracy, and health information of satellite

Sub-frame 2-3: Contains the precise orbital parameters use to compute the exact location of each satellite

Sub-frames 4-5: Contains coarse satellite orbital data, clock correction, and health information.

Almanac and ephemeris information is critical for the receiver to obtain a position fix.  At a high level GPS receivers return position through a simple triangulation algorithm, once the distance to each satellite (pseudorange) is known.  In fact, combination of pseudorange and satellite location information enables the receiver to accurately identify its own position. 

Using either the C/A or P codes, receivers are able to achieve a 3D position fix by tracking up to four satellites.  While the process of tracking a satellite is quite complex, the basic idea is that the receiver can estimate its position by determining the distance to each tracked satellite.  Because signals propagate at the speed of light (c), or 299,792,458 m/s, a receiver can calculate the distance from the satellite, called the ‘pseudorange,’ by the following equation:

Equation 1. Psedorange as a function of time interval [1][4]

The actual process of achieving position fixes information occurs by the receiver decoding the message data sent from each satellite.  With each satellite broadcasting their unique position, the receiver is able to use the pseudorange difference between each satellite to determine its exact location [8].  Using triangulation, a receiver requires three satellites to achieve a 2D position fix, and four satellites to achieve a 3D position fix.

Setting up a GPS Measurement System

The primary product required to test a GPS receiver is an RF vector signal generator that is capable of simulating GPS signals.  In this application note, you will learn how to use the NI PXI-5671 and NI PXIe-5672 RF vector signal generators for precisely this purpose.  This product can be combined with the NI GPS toolkit to generate from 1 to 12 simultaneous GPS satellites. 

The design of a complete GPS measurement system also involves a number of different accessories as well to guarantee the best performance.  For example, external fixed attenuators can be used to improve power accuracy and noise floor performance.  In addition, a DC blocker might be required for some receivers, depending on whether the receiver supplies a DC bias to its direct input port.  The complete system for a GPS signal generation is shown in the figure below:

[+] Enlarge Image

Figure 1. Block diagram of GPS generation system

You can observe in figure 1 that up to 60 dB of external RF attenuation (padding) is often used when testing GPS receivers.  Fixed attenuators provide the measurement system with at least two benefits.  First, they ensure that the noise floor of the test stimulus is well below the thermal noise floor (-174 dBm/Hz).  Second, they can actually be used to improve the power accuracy: because signal level can be calibrated with a high-precision RF power meter.  While only 20 dB of attenuation is required to meet the noise floor goal, you can achieve best power accuracy and noise floor performance when using 60 to 70 dB of attenuation.  While RF power calibration is discussed in a later section, a table illustrating the affect of attenuation on noise floor performance is illustrated in figure 2.

Figure 2. Comparison of instrument power required for various attenuation

As we observe in figure 2, attenuation can be used to attenuate noise, but not below the thermal noise floor of -174 dBm/Hz. 

 

RF Vector Signal Generator

When choosing an RF vector signal generator, note that both the NI PXI-5671 and NI PXIe-5672 RF vector signal generators are supported by the NI GPS toolkit for LabVIEW.  While devices are capable of generating GPS signals, the NI PXIe-5672 vector signal generator is preferred because of the high-speed PCI Express data bus and available on-the-fly IF equalization.  Both instruments stream GPS waveforms, sampled at 1.5 MS/s (IQ) from disk at a total data rate of 6 MB/s.  While this data rate can easily be sustained on a PXI controller hard drive, an external drive is recommended for additional storage capacity.  A typical PXI system with the NI PXIe-5672 is pictured in the figure below:

Figure 3. PXI system with NI PXIe 5672 VSG and NI PXI-5661 VSA

The GPS toolkit is capable of creating waveforms that are up to 12.5 minutes (25 frames) in length, which is the duration of an entire navigation message.  Sampled at 6 MB/s, the maximum file size is approximately 7.5 GB.  Because the waveform size, all waveforms can be stored on one of several different hard disk options.  Various hard waveform storage sources include:

• • Hard disk on PXI Controller (120 GB hard drive upgrade is recommended)
  • External RAID volumes such as the HDD 8263 and HDD 8264
  • External USB 2.0 hard disk (tested with Western Digital Passport Hard Drive)

Each of the hard drive configurations listed above are capable of supporting more than 20 MB/s of continuous data streaming.  Thus, any of these options will enable both simulation and record and playback of GPS signals.  As you will learn in a later section, a combination of simulated and recorded GPS waveforms can be used for comprehensive characterization of GPS receiver performance.

Creating Simulated GPS Signals

Because a GPS receiver uses satellite message data to obtain almanac and ephemeris information, this information is required for simulation of GPS signals as well.  Almanac and Ephemeris information is supplied as a text file, and provides information about satellite location, altitude, health, and orbit patterns.  In addition, the waveform creation process also allows you to select custom parameters such as time of week (TOW), location (longitude-latitude-altitude), and simulated receiver velocity.  Based on this information, the toolkit automatically selects up to 12 satellites, calculates all Doppler shift and pseudorange information information, and produces the resulting baseband waveform.  For getting started, sample almanac and ephemeris files are included in the toolkit installer.  In addition, they can be downloaded directly from the following sites:

• • Almanac information (The Navigation Center of Excellence) http://navcen.uscg.gov/gps/almanacs.htm
  • Ephemeris information (NASA Goddard Space Flight Center) http://cddis.gsfc.nasa.gov/gnss_datasum.html#brdc

Using custom almanac and ephemeris files, you can create GPS signals from specific dates and times, dating back several years.  Note that when selecting these files, it is important to chose files that correspond to the same date.  In general, almanac and ephemeris information is updated daily, and files from the same day should be used when choosing a specific date and time.  Note that ephemeris files are often downloaded in a compressed *.Z format.  Thus, you must extract the file using a unzip utility before using it with the GPS toolkit. 

While most GPS simulation use cases can be covered using the toolkit in “automatic mode,” where Doppler and pseudorange information is programmatically calculated, it can also be used in manual mode as well.  In manual mode, however the user can specify each satellite’s information independently.  Figure 4 (below) shows the available input parameters for both modes of operation.

¹LLA (longitude, latitude, altitude)

Figure 4. Default values for automatic and manual GPS toolkit mode

Note the GPS time of week is automatically coerced by the toolkit to a range of possible values specified by the ephemeris file.  Thus if a value is chosen that is out of range of the given ephemeris file, the toolkit will automatically the next-closest possible value and report a warning to the user.  An example program, “niGPS Write Waveform To File,” can be used to create GPS baseband waveforms (automatic mode) and the front panel is shown in the figure below.

Figure 5. GPS test waveforms can be created with a simple example program.

Note that the specific measurements chosen will determine the type of GPS test file that you will create.  For example, when measuring receiver sensitivity, a single satellite simulation should be used.  On the other hand, measurements that require a position fix (such as TTFF and position accuracy) will require you to use a GPS signal which simulates multiple satellites.  Because of this need, the toolkit ships with example programs for both single satellite and multiple satellite simulations.

Recording GPS Signals off the Air

One unique but increasingly common method of creating GPS waveforms is by recording them off of the air.  In this scenario, signals are recorded with a vector signal analyzer (such as the NI PXI 5661) and the recorded data is generated with a vector signal generator (such as the NI PXIe-5672).  Because recording GPS signals enables you to capture real-world signal impairments, signal playback allows you to observe how the receiver will perform in its deployment environment.

GPS signals can be recorded off of the air in a fairly straightforward manner.  In an RF recording system, appropriate antennas and amplifiers are combined with PXI vector signal analyzer and hard disk to capture up to several hours of continuous data.  For example, a 2 TB RAID (redundant array of inexpensive disks) is capable of recording up to 25 hours of GPS waveform.  While the specific technologies that enable streaming are not discussed here, greater detail and example code can be found at: http://www.ni.com/streaming/rf.  In the following sections, you will learn how to configure an appropriate RF front end for a RF record and playback system.

Each type of wireless communications signal has different requirements on bandwidth, center frequency, and required gain.  For the case of GPS, the essential requirement is to record 2.046 MHz of RF bandwidth at a center frequency of 1.57542 GHz.  Based on the bandwidth requirements, the sample rate must be at least 2.5 MS/s (1.25 x 2 MHz).  Note: the 1.25 multiplier is based on the filter roll-off of the PXI-5661 DDC (digital downconverter) at the decimation stage.

In the tests described below, a sample rate of 5 MS/s (20 MB/s) was used to ensure the entire bandwidth was captured.  Because data rates of 20 MB/s or more can be achieved with standard PXI controller hard drives, it is actually not necessary to use an external RAID volume to stream GPS signals to disk.  However, we recommend use of an external hard disk for two reasons.  First, it allows you to increase overall storage capacity and record multiple waveforms.  Second, use of external hard disks does not introduce undue stress on the hard drive of the PXI controller.  In the tests described below, a USB 2.0 external hard disk was used.  This drive, a 320 GB Western Digital Passport, operates at a disk speed of 5400 RPM.  In our testing, typical read and write speeds were on the order of 25 to 28 MB/s.  Thus, it can be used both for simulated (6 MB/s) and recorded (20 MB/s) GPS waveform data streaming.

The trickiest aspect of recording GPS signals is selection and configuration of the appropriate antenna and LNA (low noise amplifier).  You will observe that with a typical passive patch antenna, the typical peak power in the L1 GPS band will range from -120 to -110 dBm (we observed power at -116 dBm).  Because power level of GPS signals is so small, significant amplification is required to ensure that the vector signal analyzer can capture the full dynamic range of the satellite signals.  While there are several ways to apply the appropriate level of gain to the signal, we have found that that the best results can be achieved when using an active GPS antenna in conjunction with the NI PXI-5690 pre-amplifier.  With two cascaded LNA’s each providing 30 dB of gain, the total gain applied will be 60 dB (30 + 30).  Thus, the resulting peak power observed by the vector signal analyzer is increased from -116 dBm to -56 dBm.  An example system using this configuration is illustrated in the figure below:

Figure 6. GPS receivers implement cascaded LNAs.

Note that one essential requirement of the recording system is the active GPS antenna.  An active GPS antenna combines a patch antenna and an LNA into a single package.  These antennas typically require a DC bias voltage of 2.5V to 5V and can be easily purchased as an off the shelf product for about $20 USD.  For simplicity, use one with an SMA connector.  As we will observe in following section, the noise figure of the first LNA in an RF front end is crucial to ensure that the recording instrumentation adds as little noise as possible to the off-the-air signal.  Also note that the vector signal analyzer shown in figure 6 is a simplified diagram.  The actual PXI-5661 is a three-stage super-heterodyne vector signal analyzer and is slightly more complex than the illustration.

With 60 dB applied to the off-the-air signal, you should observe the peak power in the L1 at about -60 to -50 dBm.  If you configure the VSA in swept spectrum mode to analyze the entire spectrum, you will also notice power in bands outside the L1 band (FM and cellular) at power levels that are actually higher than the GPS signal.  However, the peak power of out-of-band signals will not typically exceed -20 dBm, and will be filtered by one of the VSA’s several bandpass filters.  One of the easiest ways to verify that that the RF front end of the recording device is sufficient is by opening the RFSA demo panel example program.  Using this program, you can visualize the RF spectrum at the L1 GPS band.  A typical view of the spectrum is shown in figure 7.  Note that this spectrum screenshot was taken outdoors at the GPS center frequency.  An active GPS antenna and PXI-5690 pre-amplifier was used to apply a combined total of 60 dB of gain.

Center Frequency: 1.57542 GHz

Span: 4 MHz

RBW: 10 Hz

Averaging: RMS, 20 Averages

Figure 7. GPS is only visible in the spectrum with a narrow RBW

Using an RF record and playback LabVIEW example program discussed earlier, configure the reference level to -50 dBm, the center frequency to 1.57542 GHz, and the IQ sample rate to 5 MS/s.  A front panel of a configured example is shown in the figure below:

Figure 8. Front panel of RF record and playback example.

The maximum recording duration of a GPS signal is dependent on the sample rate and the maximum storage capacity.  Using a 2 TB raid volume (the largest addressable disk size in Windows XP), signals can be recorded at 5 MS/s for up to 25 hours.

Configuring the RF Front End

With cascaded LNA’s providing 60 dB of gain, you will significantly increase the power at the front end of the vector signal analyzer.  From our measurement, 60 dB of gain was enough to increase the peak power from -116 dBm to -56 dBm.  It should also be noted that with 60 dB of gain applied (and a 1.5 dB noise figure), the noise power of the signal will be –112 dBm/Hz (-174 + Gain + F).  Thus, the maximum obtainable SNR of the signal, 56.5 dB (-56 dBm +112.5 dBm), is actually less than the dynamic range of the instrument.  Thus, we can be sure that with 80 dB of dynamic range, our VSA will be able to record the maximum possible SNR without introducing noise the off-the-air signal. 

When recording any signal off the air, it is a good practice to set the reference level at least 5 dB above the typical peak power to account for any signal strength anomalies.  While this reduces the effective dynamic range of the VSA in some cases, GPS signals are unaffected by this technique.  Because the maximum theoretical SNR of a GPS signal at the antenna input is 58 dB (-116 + 174), we gain no advantage by recording more than 58 dB of dynamic range at the VSA.  Thus, we can essentially “throw away” 10 dB or more of our instrument’s dynamic range without affecting the quality of the recorded signal (at this bandwidth, the PXI-5661 will have a dynamic range of better than 75 dB).

With the reference level appropriately set, it is important to properly configure the RF front end of the recording device.  As previously mentioned, best RF recording results can be achieved when using an active GPS antenna.  While the active antenna uses a built-in LNA to provide up to 30 dB of gain with a low noise figure, it must also be supplied with a DC bias.  Several biasing methods are described below.

 

Method 1: Active Antenna Powered by GPS Receiver

The first method to power an active antenna is with a DC bias ‘T.’  Using this component, a DC signal (3.3 V in our case) is applied to the DC port of the bias ‘T,’ which applies the appropriate DC offset to the active antenna.  Note that the precise DC voltage that should be applied will depend in the DC power requirements of the active antenna.  A diagram illustrating the connections is shown in the figure below.

Figure 9.  A DC bias ‘T’ can be used to power an active GPS antenna

Observe in figure 9 that a PXI-4110 programmable DC power supply can be used to supply the DC bias signal.  While many off-the shelf power supplies (including many less expensive ones) could have been used for this application, we used the PXI-4110 was simply as a matter of convenience.  Also, while a generic off-the-shelf bias tee that is operational up to 1.58 GHz can be used, the one used in this experiment was purchased from www.minicircuits.com.

 

Method 2: Active GPS Antenna Powered by Receiver

A second method that can be used to power the active GPS antenna is with the receiver itself.  Most off-the-shelf GPS receivers use a single port to power an active GPS antenna, and this port is already biased with an appropriate DC signal.  Combining an active GPS receiver a splitter and DC blocker, we can power an active LNA and simply record the signal observed by the GPS receiver.  A diagram of the appropriate connections is shown below:

Figure 10. A DC blocker allows us record and analyze the GPS signal

 

As we observe in figure 10, DC bias from the GPS receiver is used to power the LNA.  Note that method 2 is particularly useful for drive tests, because you can observe the receiver’s characteristics such as velocity and dilution of precision while the recording is being performed.

Cascaded Noise Figure Calculations

To calculate the total noise that will be added to the recorded GPS signal, you can simply determine the noise figure for the entire RF front end.  As a matter of principle, the noise figure of the entire system will always be dominated by the first amplifier in the system.  Noise figure can be thought of as the ratio of SNR_in to SNR_out (see: Noise Figure for measurement techniques) through any RF component or system.  When recording GPS signals, it is necessary to determine the noise figure of the entire RF front end.

When performing a cascaded noise figure calculation, you will actually first convert each noise figure and gain to its linear equivalent, which is called the ‘noise factor.’  When calculating the noise figure for a system with cascaded RF components, you can first determine the system noise factor and then convert to noise figure.  Thus, system noise figure must be calculated using the following equation:

Equation 2. Noise figure calculation for cascaded RF amplifiers [3]

Note that both noise factor (nf) and gain (g) are shown in lowercase, as they are linear and not logarithmic relationships.  Thus, we will also introduce the conversion from linear to logarithmic gain and noise figure (and vice versa) in the equations below:

Equations 3 through 6. Conversions between linear and logarithmic gain and noise figure [3]

An active GPS antenna using a built-in LNA (Low Noise Amplifier) will typically provide 30 dB of gain while introducing a noise figure that is typically on the order of 1.5 dB.  The second stage in the recording instrumentation, the NI PXI-5690 provides 30 dB of additional gain as well.  Though its noise figure is higher (5 dB), the second amplifier actually introduces very little noise into the system.  As an academic exercise, you can use equation 2 to calculate the noise factor for the entire RF front end of the recording instrumentation.  Gain and noise figure values are expressed in the figure below:

Figure 11. Noise figure and factors of the first two components of the RF front end.

 According to the calculations above, we can determine the overall noise factor for the receiver:

Equation 7. Cascaded noise figure for an RF recording system

Converting noise factor into a noise figure (in dB), we apply equation 3 to yield the following results:

Equation 8.  Noise figure of the first LNA dominates the noise figure of the receiver

As equation 8 illustrated, the noise figure of the first LNA (1.5 dB) dominates the noise figure of the entire measurement system.  Thus, with the VSA configured such that the noise floor of the instrument is less than that of the input stimulus, your recording will only introduce 1.507 dB of noise to the off-the-air signal.

Talking to the GPS Receiver

While many receivers may use proprietary software that enables the user to visualize information such as longitude and latitude, a more standardized approach is required for automated measurements.  Fortunately, a wide variety of receivers can be configured to talk to a PXI controller through a protocol known as NMEA-183.  In this case, the receiver will continuously send commands through either a serial or USB cable.  In NI LabVIEW, all commands can be parsed to return satellite and position fix information.  The NMEA-183 protocol supports six basic commands, and each provides unique information.  These commands are described in the table below:

Figure 12. Overview of basic NMEA-183 commands

For practical testing purposes, the GGA, GSA, and GSV commands are the most useful.  More specifically, information from the GSA command can be used to determine whether the receiver as achieved a position fix and is used in TTFF (time to first fix) measurements.  When performing sensitivity measurements, we will actually use the GSV command to return C/N (carrier-to-noise) ratios for each satellite that is being tracked.

While we will not describe the MNEA-183 protocol in great depth here, note that all command information can be found at various websites such as: http://www.gpsinformation.org/dale/nmea.htm#RMC.  In LabVIEW, these commands can be parsed using the NI-VISA driver.

 

Figure 13. LabVIEW example using NMEA-183 protocol

 

 GPS Measurement Techniques

While a wide variety of measurements can be use to characterize the performance of a GPS receiver, several common measurements apply to all GPS receivers.  In this section, you will learn the theory and practice of performing measurements such as: sensitivity, time to first fix (TTFF), position accuracy/repeatability, and position tracking uncertainty.  It should be noted that there are many different methods that can be used to validate position accuracy and perform functional test of receiver tracking ability.  While we will describe several basic methods, our described methods are by no means the complete set.

 Introduction to Sensitivity Measurements

Sensitivity is one of the most important measurements of a GPS receiver’s capability.  In fact, for many commercial-grade GPS receivers, it is often the only RF measurement performed in production test of the final product.  At a high level, the sensitivity measurement defines the lowest satellite power level at which a receiver is still able to track and achieve a position fix on satellites overhead.  As one might expect, GPS receivers are required to apply significant gain through several cascaded LNAs to amplify the signal to the appropriate power level.  Unfortunately, while an LNA will increase signal power, it also will degrade SNR.  Thus, as the RF power levels of a GPS signal decrease, SNR decreases and eventually the receiver will no longer be able to track the satellite. 

Many GPS receivers actually specify two sensitivity values, acquisition sensitivity and signal tracking sensitivity [9].  As the names suggest, acquisition sensitivity represents the lowest power level at which a receiver will be able to achieve a position fix.  By contrast, signal tracking sensitivity is the lowest power level at which a receiver will be able to track an individual satellite.

Fundamentally, we can define sensitivity as the lowest power level at which any wireless receiver will produce a desired minimum bit error rate (BER).  Because BER is can be well correlated with carrier-to-noise (C/N) ratio, sensitivity is often measured by validating measuring the C/N ratio reported by the receiver a known input power level. 

Note that the C/N ratios for each satellite are directly reported by the GPS receiver chipset.  This value can be calculated through a number of mechanisms, and some receivers actually approximate it by calculating a BER of the message date.  Modern GPS receivers will typically report a peak C/N in the range of 54 to 56 dB-Hz when stimulated with a high-power test stimulus.  The C/N limit is fitting because even with a clear view of the sky, a GPS receiver is likely to report C/N values ranging from 30 to 50 dB-Hz.  For typical GPS receivers, the minimum C/N ratio required to achieve a position fix (acquisition sensitivity) ranges on the order of 28 to 32 dB-Hz.  Thus, for a particular receiver, sensitivity can be defined as the minimum power level required for the receiver to produce the minimum position fix C/N ratio. 

In theory, sensitivity can be measured with either a single-satellite or multi-satellite test stimulus.  In practice, this measurement is performed most commonly with single-satellite test, because RF power can be more easily and more reliably determined.  By definition, sensitivity is the lowest power level at which a receiver returns a desired minimum C/N (carrier-to-noise) ratio.  As we will examine in our subsequent discussion, a receiver’s sensitivity is highly dependent on the noise figure of the RF front end.  Mathematically, we can relate sensitivity to the noise figure of the receiver according to the following equation:

Equation 9. Sensitivity as a function of C/N and noise figure.

In equation 9, we observe that sensitivity can be expressed as a function of both C/N ratio and noise figure.  As an example, if our minimum C/N required for position tracking is 32 dB-Hz, a receiver with a noise figure of 2 dB would have a sensitivity of -140 dBm (-174 + 32 + 2).  However, when testing the baseband transceiver alone, the first LNA is often bypassed.  A typical receiver is illustrated in the figure below

Figure 14. GPS receivers often cascaded several LNA’s [6]

As we observe in Figure 14, a typical GPS receiver will actually cascade several LNA’s to provide sufficient gain to the GPS signal.  As we examined in our earlier discussion, the first LNA will dominate the noise figure for the entire system.  In Figure 14, we will assume that LNA₁ has a gain of 30 dB and a NF of 1.5 dB.  In addition, we will assume that the entire RF front end has a gain of 40 dB and a NF of 5 dB.  Note that because the noise power after LNA₂ will exceed thermal noise of -174 dBm/Hz, the bandpass filter will attenuate both signal and noise.  As a result, it will have little affect on SNR.  Finally, we will assume that the GPS chipset produces a gain of 40 dB with a noise figure of 5 dB.  For the entire system we can calculate the noise figure of the entire system to be:

Figure 15. Gain and NF in both linear and logarithmic form

 According to the calculations above, we can determine the overall noise factor for the receiver:

Equations 10 and 11.  Noise figure of the first LNA dominates the noise figure of the receiver.

From equation 10 and 11, we determine that our GPS receiver with an active antenna connected has a noise figure of approximately 1.5 dB.  Note that we essentially ignored the third term in the cascaded noise figure equation.  Because this value is so small, we can essentially eliminate the term. 

In some cases, a GPS receiver will use an active antenna with a buit-in LNA.  Thus, the test point will bypass the first LNA of the receiver.  In this case, the noise figure is dominated by the second LNA, which often has a greater noise figure than that of the first.  If we remove LNA₁, we can calculate the noise figure from LNA2 looking into the receiver with the following equation:

Equations 12 and 13.  Noise figure of a receiver with first LNA removed

As equations 12 and 13 illustrates, removing the LNA with the best noise figure significantly affects the noise figure for the entire receiver.  Note, that while this exercise in calculating the noise figure for a “typical” GPS receiver is purely theoretical, it is nonetheless important.  Because the receiver’s reported C/N ratio is highly dependent on the noise figure of the system, knowing the system’s noise figure can help us set appropriate C/N test limits.

Single-Satellite Sensitivity Measurement

Now that we understand the basic theory of the sensitivity measurement, the following section will walk us through the process of performing an actual measurement.  In a typical test system, a simulated L1 single-satellite carrier is fed into the RF port of the DUT through a direct connection.  To report the C/N ratio, we will establish that our receiver is configured to communicate via the NMEA-183 protocol.  In LabVIEW, we will simply read the maximum reported satellite C/N from parsing the three GSV commands.

According to the GPS specification documents, the power of a single L1 satellite should be no less than -130 dBm at the Earth’s surface [7].  However, consumer demands to use GPS receivers indoors or in urban environments have pushed the typical test limits much lower.  In fact, many GPS receivers report position tracking sensitivity down to -142 dBm and signal tracking down to -160 dBm.  Most GPS receivers can maintain lock of a signal 6dB below the typical operating point very quickly, so we will use an average RF power level of -136dBm for our test stimulus. 

For best power accuracy and noise floor performance, we recommend use of external attenuation at the output of the RF vector signal generator.  In most scenarios, 40 dB – 60 dB of external attenuation is sufficient to enable us to operate the generator in a more linear region (power ≥ -80 dBm).  Because the fix attenuation of each pad contains some uncertainty, we must first calibrate our system to determine the exact power of the test stimulus.

In this calibration phase, we are able to account for: 1) signal peak-to-average ratio, part-to-part variation of attenuators, and insertion loss of any cabling used.  To calibrate the system, disconnect cabling from the DUT and re-connect the exact same cable to an RF vector signal analyzer such as the PXI-5661.

Part A: Single-Satellite Calibration

When performing sensitivity measurements, RF power level accuracy is one of the most important characteristics of the signal generator.  Because receivers will report C/N to with 0 digits of precision (i.e. 34 dB-Hz), sensitivity measurements in production test are made within ± 0.5 dB of power accuracy.  Thus, it is important to ensure that our instrumentation will have equal or better performance.  Because general purpose RF instrumentation is specified for operation across a broad range of power levels, frequency ranges, and temperature conditions, it is often possible to achieve measurement repeatability that is much better than the specified instrument performance by performing a basic system calibration.  In the following section, we will provide insight into two methods that can be used to guarantee the best RF power accuracy.

Method 1: Single Passive RF Attenuator:

Although use of external attenuation is required to ensure the best noise density for GPS signal generation, only 20 dB of attenuation is actually require to ensure that the noise density is below the -174 dBm/Hz.  When using a 20 dB fixed pad, we simply program our instrument to an RF power level that is 20 dB above the desired level.  To hit our target of -136 dBm, the instrument is programmed to -115 dBm (assuming 1 dB cable insertion loss) and the 20 dB attenuator is connected directly to the output of the generator.  The resulting RF power will be -136 dBm, but with added uncertainty.  Assuming our 20 dB fixed pad has an uncertainty of ± 0.25 dB, and the RF generator has an uncertainty of ± 1.0 dB at -116 dBm, the overall uncertainty will be ± 1.25 dB.  Thus, while method 1 is the simplest and does not require calibration, the use of multiple components in the system without calibration introduces substantial uncertainty.  Note that one of the greatest contributors to instrument uncertainty is VSWR, or voltage standing wave ratio.  With a passive attenuator connected directly to the output of the instrument, the standing wave reflected back to instrument is actually attenuated as well. With one of the greatest contributors to power uncertainty reduced, overall power accuracy will be improved. 

Note that a high-end VNA can also be used to measure the exact passive attenuator as well.  Using this measurement device, you can determine the exact attenuation applied by the pad to within ± 0.1 dB of uncertainty.

 

Method 2: Multiple Passive Attenuators with Calibration

A second method for calibrating RF power is to use a high-precision RF power meter (measurements better than ± 0.2 dB accuracy down to -70 dBm) in conjunction with a series of fixed attenuators.  Because we will be operating the RF generator at a fixed frequency and over a relatively small power range, we can effectively calibrate any error introduced by the generator.  In addition, because passive attenuators will operate with linear behavior at a fixed frequency, we can also calibrate their uncertainty as well.  With method 2, the key to ensuring the best performance is to configure a generation system with as little uncertainty as possible.  With a high precision power meter with better than 80 dB of dynamic range (often a dual-head instrument), we are able to ensure the best measurement uncertainty.

Using a high-precision power meter, you calibrate the system with three measurements, one for the RF power of the vector signal generator, and two measurements to calibrate the attenuators.  To achieve the best uncertainty, you should configure a system such that the least number of measurements are necessary.  For a resulting RF power level of -136 dBm, you can program the RF instrument to a power level of -65 dBm and use 70 dB of fixed attenuation (assuming 1 dB insertion loss).  To determine the exact RF power level that should be programmed, you can calibrate the exact attenuation achieved through fixed padding.  The calibration process is as follows:

1)     Program the VSG to a power level of +15 dBm

To do this, open measurement and automation explorer and use the test panels.  Using the test panel, generate a 1.58 GHz continuous wave (CW) signal at +15 dBm.

2)     Measure RF power with precision power meter

Using the precision RF power meter, observe that the power is +14.78 dBm (or similar), which is within the instrument’s power accuracy specifications.

3)     Attach 70 dB fixed attenuators (30 dB + 20 dB + 20 dB) and any cabling

4)     Measure RF power with precision power meter

With the power meter configured to the maximum number of averages (512), measure the RF power level.  Our reading was -56.63 dBm.

5)     Calculate total RF loss

By subtracting -56.63 dBm from +14.78 dBm, you can determine that the combination of attenuators and cabling will introduce 71.41 dB of power loss.  Note that many attenuators are often specified to have an uncertainty of up to ± 1.0 dB.  Thus, the measured attenuation can vary by as much as ± 3.0 dB.  Thus, it is important to calibrate a series of attenuators to ensure that the exact attenuation is known with less uncertainty.

Based on the calibration routine for the attenuators and cabling, you can next determine the RF power level required to achieve -136 dBM.  With 71.41 dB of attenuation introduced, you will need to program the RF vector signal generator to a power level of -58.59 dBm.  To verify that the programmed power is as expected, following the steps listed below.

 6)     Attach the precision power meter directly to the RF vector signal generator

All attenuators and cabling are removed for this step.

 7)     Program the RF generator to value necessary for a final power of -136 dBm.

The programmed value should be -58.59 dBm, which is -136 dBm + 71.41 dB.

8)     Measure the resulting power with a power meter.

Note that the measured RF power can vary in accordance to the power accuracy of our instrument.  While -58.59 was measured, actual results will vary slightly from one instrument to the next, as per the uncertainty of the instrument. 

9)     Adjust the generator power until the power meter reads -58.59 dBm

Although the RF generator will operate within the tolerance of the specification, this value is repeatable and can be calibrated by adjusting the RF power until the appropriate value is measured.

Using the method described above, we are able to determine the resulting RF power with only three RF power measurements.  Thus, assuming our measurement device has an uncertainty of ± 0.2 dB, we can be certain that the power uncertainty at – 136 dBm will be ± 0.6 dBm  (3 x 0.2).

Part B: Sensitivity Measurement

Now that power of our RF measurement system has been calibrated, we can simply measure sensitivity by programming our RF generator to the power level at which we expect the receiver to return the minimum C/N.  While the exact RF power used to measure sensitivity will vary from one receiver to the next, the ratio of receiver of C/N to RF power is perfectly linear.  In our test, we can assume that required C/N ratio is 28 dB-Hz to achieve a position fix.  As from equation 12, you can derive a relationship between the C/N ratio of the receiver and its noise figure.

Equation 14. C/N as a function of noise figure and satellite power

Assuming a constant satellite power, we can observe the the carrier-to-noise ratio reported by the receiver is merely a function of the noise figure of the receiver.  Various achievable C/N ratios are illustrated in the figure below.

Figure 16. C/N as a function of noise figure

Generally, the GPS decoding chipset on a receiver determines the minimum C/N ratio required to achieve a position fix.  However, it is the noise figure of the entire receiver that determines the C/N ratio that can be achieved at a given power level.  Thus, when measuring sensitivity, it is important to know the minimum C/N ratio required to achieve a position fix.

To measure sensitivity you actually have several options.  As we observed in the table above, RF power is directly correlated with sensitivity.  Thus, you can either measure the receiver’s C/N ratio at the given sensitivity power level, or we can derive sensitivity based on RF power at a different power level.

To illustrate this point, observe the relationship between RF signal power and a GPS receiver’s C/N ratio for various power levels.  Note that the measurements shown below were made by applying a stimulus that bypassed the first LNA, and that the overall receiver’s noise figure is approximately 8 dB.  Results are shown in figure 17, below.

 

Figure 17. Receiver C/N as a function of RF power.

As figure 17 illustrates, the example measurements suggest a completely linear relationship between RF power and C/N ratio.  The one exception occurs when a high input power is used to stimulate the C/N ratio, in which case the receiver reports is maximum possible C/N value.  However, these results are as expected, since the chipset used for the experiment does not report C/N values greater than 54 dB-Hz in any conditions.

Based on the linear relationship between RF power and sensitivity reported in figure 7, production test of a GPS receiver can be done by stimulating the receiver at a variety of power levels.  If the receiver will report a C/N value of 28 dB-Hz at -142 dBm, it will also report a C/N value of 34 dB-Hz at -136 dBm.  In scenarios where measurement speed is important, a higher C/N value can be used, and the sensitivity information can be extrapolated from the result.

Determining Noise Figure

It should be noted that based on equations 13 and 14, you can also determine the noise figure of the receiver or chipset based on the reported carrier-to-noise ratio.  This is shown in equation 15, below.

Equation 15. Receiver noise figure as a function of power and C/N ratio.

As we observe from figure 17, the noise figure of a receiver is directly proportional to the RF power level and carrier-to-noise ratio.  From this relationship, we can simply measure the chipset’s noise figure by correlating the RF power level with the C/N.  Note that in this measurement, you will increment the generator’s power in 0.1 dB increments.  Because the NMEA-183 protocol reports satellite C/N to the nearest decimal digit, estimating noise figure beyond 1 digit of precision will require us to investigate the C/N rounding of the receiver.  Example results are shown in figure 18, below.

Figure 18. Correlation of DUT power and receiver C/N.

As figure 18 illustrates, RF power levels between -136.6 dBm and  -135.7 dBm all yield the same C/N ratio of 30 dB-Hz.  Based on the rounding principles involved when reporting NMEA-183 data, it is safe to assume that a power level of -136.1 dBm produces a C/N ratio of 30.0 dB-Hz.  Using equation 14, the chipset’s noise figure is therefore -174.0 dBm + -136.1 dBm + 30.0 dB-Hz = 7.9 dB.  Note that this calculation is dependent on two uncertainty factors, the power uncertainty of the vector signal generator, and the C/N uncertainty reported by the receiver.

 

Multi-Satellite GPS Receiver Measurements

While sensitivity measurements require a single-satellite stimulus, many other receiver measurements require a test stimulus which simulates multiple satellites.  More specifically, measurements such as time to first fix (TTFF), position accuracy, and dilution of precision all require the receiver to obtain a position fix.  Because a receiver requires at least four satellites to obtain a 3D position fix, each of these measurements will take longer than the sensitivity measurements.  As a result, many position fix measurements are performed in validation and verification, and not in production test. 

In this section you will learn two methods to provide the receiver with a multi-satellite signal.  In the discussion of GPS simulation, you will learn how to perform TTFF and position accuracy measurements.  In the discussion on RF record and playback, you will learn techniques to validate receiver performance over a broad range of environmental conditions.

 

Measuring Time to First Fix (TTFF) and Position Accuracy 

Time to first fix (TTFF) and position accuracy measurements are most important in the design validation stage of a GPS receiver.  If you can picture many consumer GPS applications, the time that it takes for the receiver to return its actual location can significantly affect the receiver’s usability.  In addition, the accuracy with which a receiver returns its reported location is also important as well.

In order for a receiver to obtain a position fix, it must download the almanac and ephemeris information from the satellite through a navigation message.  Because it takes thirty seconds for a receiver to download an entire GPS frame, a “cold start” TTFF condition can take anywhere from thirty to sixty seconds. In fact, many receivers specify several TTFF conditions.  The most common are:

Cold Start: The receiver must download almanac ephemeris information to achieve a position fix.  Because at least one GPS frame must be downloaded from each of the satellites, most modern receivers will achieve a position fix from a cold start condition in 30 to 60 seconds.

Warm Start: The receiver has some almanac information that is less than one week old, but does not have any ephemeris information.  Typically, the receiver will know the time to within 20 seconds and the position to within 100 kilometers [2].  Most modern GPS receivers will achieve a position fix from a warm condition in less than 60 seconds, but can sometimes achieve a position fix in much less time.

Hot Start: A hot start occurs when a receiver has up-to-date almanac and ephemeris information.  In this scenario, the receiver only needs to obtain timing information from each satellite to return its position fix location.  Most modern GPS receivers will return a position fix from a hot start condition within anywhere from 0.5 to 20 seconds.

In most cases, TTFF and position accuracy are specified at a specific power level.  It is worth noting that it is valuable to verify the accuracy of both of these specifications under a variety of circumstances.  Because GPS satellites will circle the earth every 12 hours, the range of available satellites will vary substantially even throughout the course of one day to ensure that our receiver returns the appropriate result under a broad range of conditions.

In the following section, we will explain how to perform both TTFF and position accuracy measurements using two sources of data, including: 1) live data where the receiver is set-up in its deployment environment with an antenna, 2) recorded data where a receiver is tested with an RF signal that was recorded off of the air, and 3) simulated data where an RF generator is used to simulate the exact time-of-week when live data was recorded.  By testing a receiver with three different sources of data, we can verify that our measurements from each source are both repeatable and correlated with other data sources.

 

Measurement Setup

For best results, you should choose a recording location where satellites are be least obstructed from surrounding buildings.  In our case, the top floor of a six story parking deck provided sufficient view of the sky, and access to as many satellites as possible.  Note that TTFF measurement can be performed using various start modes of the GPS chipset.  As an example, the SIRFstarIII chipset allows you to reset the receiver for factory, cold, warm, or hot start modes.  The measurements shown below are the result of tests performed using this receiver.

In order to measure horizontal position accuracy, we must determine the error based on the reported latitude and longitude coordinates.  Because these figures are reported in degrees, we can convert to meters with the following approximation:

Equation 16. Calculating GPS position error

Note from the equation above that 111,325 meters (111.325 km) is equivalent to one degree (of 360) rotation around the earth.  This figure is based on a calculation of the earth’s circumference being 360 x 111.325 km = 40.077 km.

 

Off-The-Air GPS

Measuring a receiver’s TTFF in an off-the-air scenario, where the receiver is directly connected to an antenna was the least precise.  However, this measurement is nonetheless important, because it allows us to calibrate the automated measurements made from recorded and simulated GPS signals.  The SIRFstar III chipset can be programmed into a mode which places the receiver into a cold start scenario, and all measurements were made using the TTFF values reported by the receiver.  Note that the GPS receiver used had a specified cold start TTFF time of 32.6 seconds.  In our measurements, we achieved the following results:

Figure 19. TTFF and maximum C/N for off-the-air GPS signals

Based on the initial off-the-air results, we can observe that our GPS receiver is capable of achieving TTFF of 33.2 with a standard devation of 3.0 seconds.  These measurements are within reasonable tolerance of the chipset’s TTFF specification.  More importantly, however, we can compare this measurement with results achieved through both simulated and recorded GPS data.

Based on the equation for linear deviation above, we can calculate the linear standard deviation of each measurement from the mean position.

 

Figure 20. Reported LLA for off-the-air GPS signals

Note that in order to correlate off-the-air GPS signals with simulated and playback signals, it is important to correlate the power of the off-the-air signal.  When making TTFF and position accuracy measurements, the exact RF power level will not substantially affect the result.  Thus, it is sufficient to generally correlate RF power by matching the C/N ratio of off-the-air, simulated, and recorded GPS signals.

 Recorded GPS Signals

While TTFF and position deviation can be measured with live signals, these measurements are often non-repeatable, as satellites are constantly orbiting the earth.  One technique for obtaining repeatable TTFF and position accuracy measurements is with recorded GPS signals.  Thus, in this section, we will discuss how to correlate live GPS signals with recorded GPS signals.

Recorded GPS signals can be re-generated using an RF vector signal generator.  Upon playback, the easiest way to calibrate the RF power level power is by matching the live C/N ratio with the recorded C/N ratio.  When observing off-the-air signals, we notice that the peak C/N of between 47 and 49 dB-Hz for all live signals. 

At a playback power level that results in the same C/N ratio as the live signal, we can be certain that the reported TTFF and position accuracy will be well correlated with that of the live signal.  In figure 21, below, we report TTFF results for four different trials, at time-of-week (TOW) values that are similar with the live off-the-air signal.

Figure 21. Reported TTFF for off-the-air GPS signals

In addition to measuring time to first fix, we can also measure the latitude, longitude, and altitude reported by the GPS receiver.  Results are shown in the figure below.

Figure 22. Reported LLA for off-the-air GPS signals

It should be noted from the results in figures 21 and 22 that we are able to achieve reasonably repeatable TTFF and LLA (latitude, longitude, altitude) results using recorded GPS signals.  However, it is also worth noting that the error and standard deviation for each of these measurements is slightly larger than for the off-the-air measurements.  However, while the absolute accuracy is larger, the repeatability is better than with off-the-air measurements.

Simulated GPS Signals

A final source of GPS test signals for time-to-first-fix and position accuracy measurements is simulated multi-satellite GPS signals.  With the NI GPS toolkit for LabVIEW, we are able to simulate up to 12 satellites at user-defined time-of-week, week number, and receiver location.  With this method of GPS signal simulation, the primary benefit is that it results in a GPS signal with the best possible signal to noise ratio.  In fact, unlike live and recorded GPS signals, it is possible to create repeatable signals where the noise power is extremely small.  To illustrate this, the frequency domain of a simulated multi-satellite signal is illustrated in figure 23. 

VSA Settings

Center: 1.57542 GHZz

Span: 4 MHz

RBW: 100 Hz

Averaging: RMS, 20 Average

 

Figure 23.  Power-in-band measurement of simulated multi-satellite GPS signal

When testing a receiver with simulated multi-satellite waveform, we can again estimated the required RF power by coorelating the receiver’s reported C/N ratio. 

Once the RF power level is properly correlated, we can proceed to measure TTFF.  When measuring TTFF, first start the RF vector signal generator.  After five seconds, manually place the receiver into “cold” start mode.  Once the receiver obtains a position fix, it will report the TTFF information.  Results for the simulated GPS signal are reported are shown in the figure below:

Figure 24.  TTFF values for four unique simulations

Note from figure 24 that all simulations were chosen with the same LLA (latitudes, longitude, and altitude). 

In addition, to measuring TTFF, we can also calculate LLA accuracy and repeatability by creating simulations at various time-of-weeks.  Note that it is crucial to test accuracy at various time-of-weeks, because the available satellites will change substantially even over the course of several hours (shown in figure 24).  The resulting latitude, longitude, and altitude information is show in figure 25, below.

Figure 25. Horizontal accuracy for various TOW simulations

In figure 25, note that horizontal error in meters can be calculated absolutely based on the simulated position.  As shown in figure 20, error is determined from the following equation:

Equation 17. Position error for simulated GPS signals

For the receiver used in our experiments, the maximum horizontal position error 5.2 meters and the average horizontal position error is 1.5 meters.  Thus, the results from figure 18 illustrate that our receiver is well within the specified limits.

As we have mentioned earlier, accuracy that a receiver is likely to attain is highly dependent upon the available satellites that it has to lock to.  Thus, while a receiver’s accuracy is likely to vary substantially over the course of several hours (when satellites change), the repeatability from one run to the next is generally quite small.  To verify that this is the case with our GPS receiver, we can perform multiple trials of a particular simulated GPS waveform.  This is done primarily to verify that the RF instrumentation does not addition uncertainty to the simulated GPS signal.  As we observe in figure 26 (below), our example GPS receiver reports highly repeatable measurements when the same binary file is used over and over again.

Figure 26. Error is highly repeatable for each trial of the same waveform

As we can observe from figure 20 is that one of the greatest benefits of using simulated GPS signals is that they enable us to achieve repeatable position results.  This is highly important in the design validation stage of our development, because it enables us to determine if the reported position does not vary from one design iteration to the next.

Measuring Dynamic Position Accuracy 

A final method of GPS receiver testing is measuring the receiver’s tracking ability to maintain a position fix at a wide range of power levels and velocities.  Historically, one common approach to this type of testing (often merely a functional test) is with a combination of drive testing and multi-path fading emulation.  In a drive test, a prototype receiver is simply driven through a route that is known for introducing significant signal impairments.  While the drive test is a simple way to apply natural impairments to GPS satellite signals, these measurements are often non-repeatable.  In fact, the combination of factors such as: movement in GPS satellites, changes in weather conditions, and even time of year can affect a receiver’s performance.

Thus, one increasingly common method to validate receiver performance in a scenario with significant signal impairments is by recording the GPS signal on a drive test.  For more details on how to configure a GPS recording system, see the earlier section.  Note that with a drive test scenario, there are several PXI chassis options.  The simplest option is to use a DC chassis and power it off the car battery.  A second option is to use the standard AC chassis, with an inverter used to power the chassis of the car’s power supply.  Between these two options, the DC chassis will consume less power, but it will also be more difficult to power back in the lab.  With the results shown below, a standard AC chassis was used, and it was powered off a system consisting of an extra car battery plus a DC to AC inverter.

Once we have completed our recording of a GPS signal, we can test the receiver over and over again with the same set of test data.  In the experiments described below, we tracked the receiver’s latitude, longitude, and velocity over time.  Data was read from the receiver using a serial port and reading NMEA-183 commands at a rate of once per second.  In the measurements shown below, we simply report receiver characteristics such as position and satellite carrier-to-noise ratios.  Note that these measurements can also be performed while analyzing other information as well.  While horizontal dilution of precision (HDOP) was not measured in the results below, this characteristics also provides significant information about a receiver’s position fix accuracy.

For best results, the command interface of the receiver and the RF generation should be tightly synchronized.  With the results shown below, the RF vector signal generator was synchronized with the GPS module by using the data line of the COM port (pin 2) as a start trigger.  Using this synchronization method, the vector signal generator and GPS receiver will be synchronized to within one clock cycle of the arbitrary waveform generator (100 MS/s).  Thus, the maximum skew should be 10 µS.  It should be noted that since we will be reporting latitude and longitude of the receiver, the inaccuracy induced by synchronization error will be 10µs x Max Velocity (m/s), or 0.15 mm. 

Using the configuration described above, we are able to report the receiver’s latitude and longitude over time.  The results are illustrated in the figures below:

Figures 27 and 28. Receiver latitude and longitude over the course of a 4 minute span.

As the data from figures 27 and 28 illustrates, use of a recorded drive test signal reports static and position and velocity information.  In addition, we can observe that this information is relatively repeatable from one trial to the next – evidenced by the difficulty in graphically observing each individual trace.  In fact, it is repeatability for the receiver that we are most interested in.  Because repeatability information will provide us with an estimate of how a GPS receiver’s accuracy changes over time, we also compute the standard deviation between each sample in the waveforms above.  In figure 29 (below), we graph standard deviation of position (relative to mean position) between each synchronized sample over time.

Figure 29. Standard deviation of both latitude and latitude over time.

When observing the horizontal standard deviation, it is interesting to note that the standard deviation appears to rapidly increase at time = 120 seconds.  To investigate this phenomenon further, we also plot the total horizontal standard deviation against the receiver’s velocity (m/s) and a proxy for C/N ratio.  Our assumption is that satellite C/N ratio will only affect the receiver in the condition that there is no high-power satellite.  Thus, we graph a proxy for C/N by averaging the C/N ratios for the four highest satellites reported by the receiver.  The results are shown in figure 30 (below).

Figure 30. Correlation of position accuracy and C/N ratio.

As we observe in figure 30, the peak horizontal error (in standard deviation) occurring at time = 120 seconds is directly correlated with satellite C/N ratios, and not correlated with receiver velocity.  At this sample, the standard deviation is nearly 2 meters, while it is less than 1 meter throughout most other times.  Concurrently, we see the top 4 C/N average drop from nearly 45 dB-Hz to 41 dB-Hz.

The exercise above not only illustrates the affect of C/N ratio on position accuracy, but also illustrates the types of analysis that can be conducted using recorded GPS data.  For the experiment above, the drive recording of the GPS signal was actually conducted in Huizhou, China (a city north of Shenzhen).  However, the actual receiver was tested at a later date in Austin Texas.

Conclusion

As we have seen from the techniques described above, there are a variety of methods for testing GPS receivers.  While basics measurements such as sensitivity are almost always used in production test, measurement techniques can be used to validate a receiver’s performance.  While these testing techniques are varied, note that each that each method of testing can be performed within a single PXI system.  In fact, GPS receivers can be tested with both simulated and recorded baseband waveforms.  With a combined approach, engineers are able to perform comprehensive of multiple aspects of GPS receiver functionality: from sensitivity to tracking repeatability.

References

[1] Pratt, Bostonian, and Allnutt. Satellite Communications

[2] Navstar GPS User Equipment Introduction, September 1996

[3] Gu, Quzheng, RF System Design of Transceivers for Wireless Communications, Springer, 2005. Fundamentals

[4] Ward, Phillp W., Betz, John W., and Hegarty, Christopher J.  Chapter 5: Satellite Signal Acquisition, Tracking and Data Demodulation, excerpt from: Understanding GPS: Principles and Applications by Elliot D. Kaplan, Artech House, 2005.

[5] Global Positioning System: Theory and Applications, Edited by Bradford W. Parkingson and James J. Spilker

[6] Braasch, Michael S. and Van Dierendonck, A. J.  GPS Receiver Architectures and Measurements, Proceedings of the IEEE, 1999.

[7] Global Positioning System Standard Positioning Service Signal Specification, 1995.

[8] Global Positioning System Standard Positioning Service Signal Specification.  Annex A, Standard Positing Service Performance Specification, 1995.

[9] Goldberg, Hans-Joachim. Atmel Whitepaper: Measuring GPS Sensitivity, 2007.

Additional Resources

• NI GPS Toolkit for LabVIEW
• RF Stream to Disk Example Set
• www.ni.com/rf

 

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