Effect of GPS III weighted voting on P(Y) receiver processing performance

2 WEIGHTED VOTING

GPS III satellites transmit multiple biphase signals and components on the L1 carrier: C/A, P(Y), and M signals, as well as two components of the L1C signal. The P(Y) signal and the pilot and data components of the L1C signal (respectively denoted L1C_P and L1C_D) are combined on the in-phase quadrature of the carrier using weighted voting. Weighted voting combines the three biphase constituents into a single constant-envelope biphase signal, enabling the constituents to be received at different useful power levels. Weighted voting employs time multiplexing of the majority vote of P(Y), L1C_P, and L1C_D interlaced with pure values of the two constituents to be received at a higher power than the third, as described in Spilker and Orr (1998). Setting the average time fraction of the majority vote and of the two pure constituents establishes the relative received powers of the three constituents.

Majority voting of three uncorrelated baseband biphase unit-power constituent signals or components, when the useful received power from each is to be the same, can be expressed as a logical operation on binary representations of the signal values. For this work, however, it is more convenient to describe majority voting by the algebraic expression:

1

where 𝜇xyz(t) is the result from majority voting; the constituent signals x(t), y(t), and z(t) are mutually uncorrelated each taking on values ±1. It is readily shown that the useful received power for each constituent is 25% of the total power, so 25% of the power in Equation (1) is not useful to these receivers. Also, the magnitude-squared of 𝜇_xyz(t) is unity, showing that it has a constant envelope.

When the constituent signals have autocorrelation functions (ACF) R_x(τ), R_y(τ), and R_z(τ), respectively, then the majority vote waveform has stationarized ACF:

2

(Since each signal is cyclostationary, the stationarized statistics are used where appropriate.) Note that, since the signals are cyclostationary, R_xyz(τ) is not, in general, equal to R_x(τ)R_y(τ)R_z(τ).

The power spectral density (PSD) of the majority vote waveform shown in Equation (1) is the Fourier transform of Equation (2):

3

For the following, let x(t) represent the L1C_P component, y(t) represent the P(Y) signal, and z(t) represent the L1C_D component. For this case, x(t)y(t)z(t) is approximately a BPSK-R(10) waveform, so

4

where Φ_L1Cp(f), Φ_P(𝑌)(f), and Φ_L1Cd(f) are, respectively, the unit-power PSDs of L1Cp, P(Y), and L1C_D and Φ_BPSK-R(10)(f) is the unit-power PSD of a signal with BPSK-R(10) spreading modulation, all assuming ideal long spreading codes.

For weighted voting, let the fraction of time that only x(t) is transmitted be denoted φ_x, the fraction of time that only y(t) is transmitted be denoted φ_y, and the fraction of time that the majority vote is transmitted is φ_z = 1−φ_x − φ_y. In the aggregate waveform, the desired ratio of useful average power for x(t) relative to z(t) is P_x/P_z ≥ 1, and the desired ratio of useful average power for y(t) relative to z(t) is P_y/P_z ≥ 1. Then,

5

Observe that . Since Equation (5) is linear in the square roots of the useful power ratios, their solution is

6

The fraction of majority voted waveform is then

7

From the U.S. National Coordination Office for Space-Based Positioning Navigation and Timing (2018a, 2018b), the minimum specified received powers are P_P(Y) = −161.5 dBW, P_L1CD = −163.0 dBW, and P_L1CP = −158.25 dBW. Table 1 summarizes the received power fractions and ratios for infinite bandwidth. These values would change somewhat for broadcast signals after bandlimiting to ±15.345 MHz, since the different signals and components have different fractions of their power outside of that bandwidth.

Solving Equation (6) when P_x/P_z = 2.9849 and P_y/P_z = 1.4121 yields the solution φ_x = 0.2495, φ_y = 0.0646. From Equation (7), the fraction of majority voted waveform is then φ_z = 0.6859. For a unit-power aggregate waveform, the fraction of useful L1C_P power is (0.2495 + 0.5 × 0.6859)² = 0.3510, the fraction of useful P(Y) power is (0.0646 + 0.5 × 0.6859)² = 0.1661, and the fraction of useful L1C_D power is (0.5 × 0.6859)² = 0.1176, with 63.5% of the power being useful by one of the constituent’s receivers, or approximately 2.0 dB loss in useful signal power relative to linear combining, where all the power would be useful. Thus, if y(t) is to be received at a given power, the composite weighted vote waveform must be received at 1/0.1661 = 6.02 times the power, or 7.8 dB higher than the desired useful power for y(t). To provide the minimum specified received P(Y) signal power, the minimum received power of the weighted vote waveform is −161.5 dBW + 7.8 dB = −153.7 dBW.

An implementation of weighted voting signal generation is shown in Figure 1. First, the three signals are majority voted in accordance with Equation (1). Next, a sample of the majority vote signal and a sample of the P(Y) signal are passed into an interlacing switch, where the switch selection at each sample is based on the comparison of a uniform random number generator (RNG) value on [0, 1) and the fraction φ_y. The sample output from the first interlace switch is passed into the second interlace switch along with a sample of the L1C_P component. The output of the second interlacing switch is again determined by comparing the current RNG value against the probabilities φ_y and φ_x +φ_y, then selecting the appropriate sample. The resulting composite weighted waveform has the appropriate ratio of P(Y), L1C_P, and L1C_D to ensure the specified received power ratios between the signals.

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FIGURE 1

Generation of weighted voting signal

Suppose there is such a signal where pure x(t) is transmitted φ_x ≥ 0 of the time, pure y(t) is transmitted φ_y ≥ 0 of the time, and the majority vote of x(t), y(t), and z(t) is transmitted a fraction (1−φ_x −φ_y) ≤ 1 of the time. Let the interlacing occur fast enough that these fractions are approximately retained over any time segment of signal T processed by a receiver. Over that time, the interlaced waveform can be represented by the time multiplexing of three different segments:

8

For analysis purposes, the granularity of these segments does not matter if it is much finer than the integration time used by receivers but not so rapid as to significantly change the PSDs of the signals. The switching is synchronized to signal generation. In practice, the locations of pure and majority voted samples are randomized, as shown in Figure 1, to randomize any effects on spreading codes or other signal characteristics and to produce similar average fractions of each segment for different receiver processing time intervals.

Under the same assumptions used previously, the normalized PSD of the resulting weighted voting waveform is then

9

using the values of φ_x and φ_y derived previously for GPS III relative power levels. Transmitting the weighted voting waveform so that the useful received powers for each signal and component are at minimum specified levels requires the received power of the weighted voting waveform to be −153.7 dBW, with PSD

10

3 ANALYZING WEIGHTED VOTING EFFECTS ON RECEIVED CARRIER POWER TO NOISE DENSITY

The effect of weighted voting is compared to that of a baseline where the same signals are being transmitted by the satellite, but using linear combining rather than weighted voting. Even though linear combining is impractical, using it as a baseline isolates the effect of weighted voting without changing the intrasatellite interference caused by the other signals. For conservatism, the intrasatellite interference considered here does not include the C/A signal, since the C/A signal is in phase quadrature to the P(Y) signal and it assumed the P(Y) signal processing is phase-coherent. Assume the same received powers described earlier and an ICD-appropriate signal power for the M signal. The PSD of this intrasatellite interference with interference from linear combining is then

11

where Φ_M(f) is the unit-power PSD for the M signal. The PSDs for the L1C signal components are multiplied by two in Equation (11) to account for the fact that these two signal components always have the same carrier phase as P(Y), rather than being received at random relative carrier phase as is typical for interference.

Let P(Y) be received at power K C_P(𝑌), where C_P(𝑌) corresponds to the specified minimum power of −161.5 dBW, and K is a dimensionless multiplier that affects the received power from all of the signals from the satellite, due to a combination of receive antenna gain, propagation loss, and setting of transmitter power at the satellite. K can be greater than unity when the satellite is overhead and transmitting “hot” and maybe less than unity for satellites at low elevation, due to diminished receive antenna gain. Thus, Φ_{linear, intrasatellite}(f) is also scaled by K relative to the minimum specified received power levels.

When the received waveform consists only of the signals from the satellite of interest (neglecting C/A signal as discussed above and also neglecting intrasystem, intersystem, and external interference) and thermal noise having PSD of N₀, the effective C/N₀ due to the combination of noise and intrasatellite interference, if the satellite uses linear combining (ignoring processing losses), is

12

where it is assumed that the precorrelation bandwidth β_r being large enough to pass virtually all the desired signal’s power. The following numerical results use the standard value of N₀ corresponding to −201.5 dBW/Hz and β_r = 20.46 MHz, for which more than 96% of the transmit power (defined over 30.69 MHz) is within the precorrelation bandwidth.

In contrast, when weighted voting is employed, the PSD of the intrasatellite interference is <?TeX

13

The effective C/N₀ that accounts for weighted voting interference is then <?TeX

14

again neglecting intrasystem, intersystem, and external interference. The additional interference from interplexing degrades the C/N₀ compared to linear combining.

A second effect also is involved with the random implementation of weighted voting. Over sequential receiver integration times of length T, the amount of pure x(t) fluctuates around φ_xT, the amount of pure y(t) fluctuates around φ_yT, and the amount of y(t) in the majority voted section fluctuates around 0.5(1 − φ_x −φ_y)T.

A computer simulation was used to quantify the fluctuation of the correlation peak due to these random effects. A pure signal was used with no noise or interference. A uniform random number generator was run at a rate of 20.46 MHz with a correlation integration time of T selected. The logic described in Figure 1 was used to determine how many pure samples of x(t) and y(t) were generated over the correlation integration time. Random, independent, and identically distributed binary values of x(t), y(t), and z(t) were generated to produce the majority voted values, and the number of values matching y(t) and antipodal to y(t) were counted. Each realization of this simulation yielded a net number of correct values of y(t), which is proportional to the height of the correlation peak. The sample mean and sample standard deviation of this quantity were computed over many trials, and the correlator output SNR was defined as

15

The effective C/N₀ is calculated from the SNR by Betz (2015):

16

The simulation was run for 1,000 trials for correlation integration times of 1 msec and 10 msec, yielding estimated effective C/N₀ of 65.0 dB-Hz and 64.9 dB-Hz, respectively, so a value of 65.0 dB-Hz is used for the (C/N₀)_fluc.

The overall weighted voting C/N₀ is the combination of the weighted voting interference and the fluctuation

17

Ideally, but never achieved in practice, a single satellite would only be transmitting a P(Y)-signal, yielding a C/N₀ with no intrasatellite interference:

18

Intrasatellite interference causes the effective C/N₀ to diverge from the idealistic case with no interference. Linear combining involves the intrasatellite interference, while the weighted voting involves both the intrasatellite interference and the degradation from weighted voting. The additional degradation from weighted voting, compared to linear combining, is negligible below about 50dB-Hz.

4 COMPUTER SIMULATION OF WEIGHTED VOTING

The MATLAB (MATLAB is a registered trademark of MathWorks) simulation developed to crosscheck the analytical results is identical to that described in the companion paper (Betz & Cerruti, 2019). The only exception is that the L1 signal is generated using the weighted voting scheme shown in Figure 1 to combine P(Y), L1C_D, and L1C_P at the appropriate power. Each of P(Y), L1C_D, and L1C_P are generated from random chip sequences. The weighted voting signal is then added to a BOC (10,5) signal generated using random chips to represent the M signal with carrier phase that changes randomly every 1 ms relative to the phase of the P(Y) signal.

5 PREDICTED EFFECT OF WEIGHTED VOTING ON RECEIVER PROCESSING

Even if the transmitted P(Y) signal were ideally transmitted by linear combining with the other signals, interference and noise would degrade the reception of the P(Y)-signal. In an open-sky environment, this interference includes intrasatellite signals (the other signals transmitted by the same satellite), intrasystem interference (from signals transmitted by other GPS satellites in view), intersystem interference (from signals transmitted by satellites in other satnav constellations (Satellite-Based Augmentation Systems, Galileo, BeiDou Navigation System, Quasi-Zenith Satellite System)), and external interference (from non-satnav systems). This interference would tend to mask the effects of weighted voting. The results in this section consider only intersatellite interference, not intrasystem, intersystem, or external interference, and thus exaggerate the effects of weighted voting relative to real-world conditions.

First, consider a conventional receiver (with the ability to generate the full signal replica) of the L1 signal—such as a receiver using the P-code signal if it were being transmitted without encryption. Figure 2 shows (C/N₀)_{eff, no int.}, (C/N₀)_{eff, lin. interference}, and (C/N₀)_WV. The ideal case with no intrasatellite interference never happens in practice since the satellite is transmitting the other signals, but is shown as a reference. The case of linear combining is the benchmark, since it includes intrasatellite interference that is unavoidable due to transmission of the other signals. The case of weighted voting includes the intrasatellite interference as well as the additional degradation due to weighted voting. The results are virtually identical at smaller values of K, but diverge as K becomes larger. Since intrasatellite interference and weighted voting have imperceptible effect when K is 0 dB, the C/N₀ is very close to −161.5 dBW – (-201.5 dBW/Hz) = 40 dB-Hz. The analytical and simulation results are very close to each other.

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FIGURE 2

C/N₀ of the L1 P(Y) Signal shown for ideal signal in white noise, linear combining with intrasatellite interference, and weighted voting with intrasatellite interference; curves are analytical results, and Xs are simulation results

Figure 3 shows the degradation in L1 C/N₀ from weighted voting relative to linear combining with intrasatellite interference in both cases. This degradation is an imperceptible 0.1 dB or less at input C/N₀ values less than 45 dB-Hz and less than 1 dB at 55 dB-Hz, which is the highest practical level for P(Y) reception. The degradation is still less than 1 dB even at the highest practical input C/N₀ values, where tracking performance would not be noticeably affected by such a small degradation. Again, the simulation and analytical results match very closely.

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FIGURE 3

Degradation in L1 P(Y) Signal C/N₀ caused by weighted voting of the signals, relative to linear combining of the signals; curves are analytical results, and Xs are simulation results

The remaining results in this section show the effect on high-precision receiver processing for which performance models are provided in Betz and Cerruti (2019). These dual-channel codeless and semicodeless processing techniques have been applied to the GPS P(Y) signals on the L1 and L2 carrier frequencies for many years, enabling civil receivers to perform highly accurate dual-frequency carrier phase tracking without accessing a GPS civil signal on a second frequency. Different approaches have been developed and employed over the years:

• Single-channel codeless processing that exploits the signal’s cyclostationarity,

• Dual-channel codeless processing intended to exploit broadcast of identical signals on both carriers,

• Dual-channel semicodeless processing intended to also exploit signal construction involving the product of a higher rate known spreading waveform and an unknown spreading waveform at a known lower chip rate, producing a higher signal-to-noise ratio estimate of the unknown spreading waveform,

• Dual-channel soft-decision semicodeless processing intended also to exploit the known spreading modulation with unknown spreading code bits to produce a soft-decision estimate of the unknown spreading waveform.

These different approaches involve progressively more detailed hypotheses about the signal structure and more complex receiver processing while providing increasing performance.

As derived and confirmed using computer simulations in Betz and Cerruti (2019), the performance of dualchannel codeless and semicodeless processing considered in this paper is expressed using the same parametric form,

19

with approximate coefficients, all positive, listed in Table 2. Derivation of this expression is based on the assumption that identical signals are received at two different frequencies but with uncorrelated noise, and the signal is constructed as the product of BPSK-R spreading modulations with the known higher spreading code chip rate of f_c, which is 10.23 MHz for the P(Y) signal. Also, f_c/N is the one-sided filter bandwidth used in dual-channel semicodeless processing and the integrate-and-dump rate for soft-decision dual-channel semicodeless processing. We use N consistent with the assertion in Lorenz and Gourevitch (1995). The fraction of received signal power passed by front-end filtering is φ². In the table, , and Γ(20) = 2.23.

GPS III satellites are required to provide P(Y) on L1 and L2 both with a minimum received power of −161.5 dBW. Assume K is the same on both channels. If there were no interference, Equation (18) would apply, and that is approximately the case for the L2 channel, since L2C is in phase quadrature to P(Y), and interference from the M signal broadcast from that satellite is negligible (the effective N₀ from the M signal interference is more than 20 dB less than the thermal noise PSD). Consequently, for the baseline case with linear combining of the L1 signals causing intrasatellite interference, but no intrasystem, intersystem, or external interference,

20

When weighted voting is employed,

21

Substituting Equations (20) and (21) into Equation (19) and using the coefficients from Table 2 enables assessment of how much weighted voting degrades the C/N₀ from codeless or semicodeless processing.

Figure 4 shows the output C/N₀ from codeless and semicodeless processing with linear combining and weighted voting of the L1 signals. Simulation results for linear combining and weighted voting are virtually identical in many cases. As shown in Betz and Cerruti (2019), dual-channel soft-decision semicodeless processing outperforms dual-channel semicodeless processing, and both significantly outperform dual-channel codeless processing. Even in the conservative situation examined here (no intersystem, intrasystem, or external interference that would mask degradation from weighted voting), the degradation in output C/N₀ is only discernible for values of K greater than 10 dB and fractions of a dB for practical values of K.

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FIGURE 4

Output C/N₀ from codeless and semicodeless processing shown for both linear combining and weighted voting. Curves are analytical results, △’s are simulation results for linear combining, and ▽’s are simulation results for weighted voting

Figure 5 shows the difference between output C/N₀ with linear combining and with weighted voting. Even in the conservative situation examined here, the degradation is less than 1 dB overall practical input C/N₀ values.

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FIGURE 5

Analytical degradation in output C/N₀ from codeless and semicodeless processing due to weighted voting, compared to linear combining

At the high output C/N₀ values of interest, the variance (in radians-squared) of carrier tracking errors due to noise and interference for a Costas loop or coherent phase-locked loop (PLL) is approximately , where ρ_L is the loop SNR given by ρ_L = (C/N₀)_{c, s, d}/B_L, and B_L is the one-sided effective rectangular bandwidth of the carrier tracking loop in hertz. The root-mean squared (RMS) carrier tracking pseudorange error for L2 in centimeters is then given by

22

Comparing the use of Equation (20) with the use of Equation (21) in Equation (19) using Table 2 and a conservative value of 20 Hz for B_L yields the results in Figure 6. On the scale used, the results for weighted voting are in distinguishable from those for linear combining, indicating that weighted voting has no perceptible effect on carrier tracking accuracy.

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FIGURE 6

Analytically predicted carrier tracking errors due to noise, interference, and weighted voting for codeless and semicodeless processing

Figure 7 shows the differences in carrier tracking errors from Figure 6, using an expanded ordinate scale. RMS errors from weighted voting contributes are small fractions of a millimeter, demonstrating that weighted voting has negligible effect on carrier tracking performance for codeless or semicodeless processing.

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FIGURE 7

Analytically predicted carrier tracking error differences between weighted voting and linear combining

6 DIRECT ANALYSIS OF RECORDED WEIGHTED VOTE EVENT

In December 2017, Aerospace performed a focused study to evaluate the backward compatibility effects of weighted vote combining. The purpose of this effort was to perform a forward-looking, low-complexity analysis on the most impactful expected effects of weighted vote. To this end, GPS III Mission Data Unit (MDU) signals were recorded by an Averna recording system, and the resulting baseband IQ samples were directly analyzed in MATLAB (Utter, 2017).

The receivers most vulnerable to any change in signal combining are those using codeless or semicodeless carrier tracking of the GPS P(Y) code. Though the P(Y) code is encrypted to restrict access to authorized military users, civil users are nevertheless able to combine short coherent integration windows to allow carrier tracking of the P(Y) signal (Woo, 2000). This was necessary to allow dual-band ionospheric correction prior to the addition of modernized civil signals. However, the use of short integration windows raised concerns that such receivers could be more susceptible to statistical variation caused by weighted vote combining.

A phase-error detector (PED) is an integral component of the carrier tracking loop. Two figures of merit, derived from the “MAP-motivated” semicodeless PED circuit, were evaluated to allow conclusions to be drawn with detailed simulations of countless receiver designs. This PED is the most commonly used because it has been proven optimal for semicodeless receivers (Woo, 2000).

Weighted vote combining could have two possible impacts on this PED. The first is a change in the magnitude of the PED output, i.e., the expected value of that output for a given change in carrier phase, also known as the “S-curve.” A change to this curve could cause the overall tracking loop bandwidth to be different from the original design intent. For simplicity, we measure a single figure of merit, the gain, which is the small-signal slope of the S-curve near the origin. The gain is measured by introducing a small phase shift to the recorded baseband signal and measuring the change in mean PED output. Units for this figure of merit are PED output magnitude, normalized to the integrate-and-dump frequency, per radian of deflection, i.e., dB-(Hz/rad). Ideally, any new combining method should not change the gain at all from the historical norm; increases or decreases are equally undesirable.

The second possible change is in the noise statistics of the PED output. A change in the signal combining method can introduce short-term incidental correlations with the signal of interest, which can change the noise statistics at the PED output. For an input with constant phase, the noise power is simply the variance at the PED output, measured in radians-squared. An increase in noise at the PED output proportionally increases the carrier tracking noise with a scaling factor that depends on the loop bandwidth. To better measure such changes independently of possible changes to the gain, as noted above, the figure of merit is a signal-to-noise ratio (SNR) that divides the detector gain (i.e., “signal”) by the detector output noise with resulting units of dB-Hz. All else being equal, noise should be minimized, and SNR should be maximized.

Expressions for each figure of merit are as follows:

23

24

where F_I&D is the semicodeless integrate-and-dump rate consistent with Woo (2000); y_[n] is the PED output, sampled at F_I&D; Δθ is the baseband rotation angle in radians; G_PED is the gain in dB-(Hz/rad); and R_PED is the SNR in dB-Hz.

The input to the numerical simulation was the Averna recording in the desired configuration with weighted vote enabled (all codes) or disabled (C/A + P only). By adding synthetic AWGN at the appropriate level and repeating the simulation as needed, the effect on the PED can be evaluated under a range of receiver operating conditions. The resulting phase detection gains are shown in Figure 8. When weighted voting is off, there is no intrasatellite interference. Weighted voting introduces a small amount of intrasatellite interference that is detectable for received C/N₀ above 41dB-Hz. However, below this point, there is no distinguishable effect on the phase-detector gain.

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FIGURE 8

Phase-detector gain for weighted voting (WV) on and off scenarios

The SNR results are shown in Figure 9. For received C/N₀ up to 41 dB-Hz, the change to weighted vote combining has no distinguishable effect on the output of the MAP-motivated PED. At higher C/N₀, there is minor degradation in C/N₀ in concert with the simulation described in this paper.

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FIGURE 9

Phase-detector SNR for weighted voting (WV) on and off scenarios

7 LABORATORY TEST CONFIGURATION AND TEST PROCEDURE

A test campaign focused on the determination of weighted vote effects for industry-representative semicodeless receivers was conducted by Aerospace to expand and strengthen previous studies. The primary purpose of this testing was to determine the performance impact of the L1C weighted vote combined signal vs. no addition of L1C (only linear combination of C/A and P(Y)). It was not practical to compare the L1C weighted vote with interplex or other code combining schemes because this testing utilized preflight hardware that has only implemented weighted vote combining. Because the Aerospace direct analysis results described above are limited to one common semicodeless receiver architecture, the follow-on tests extend results to a variety of proprietary and non-proprietary architectures, spanning ground, civil aviation, and space-use cases for both government and commercial receivers. A primary focus of this test was to assess the backward compatibility with respect to legacy receivers. Several metrics that impact the Position, Navigation, and Timing (PNT) solution were examined, but since only a single signal was tracked, PNT solution performance was not directly assessed.

The backward compatibility test was comprised of two phases. During Phase I in April 2018, the backward compatibility test team obtained signal recordings from a GPS III Mission Data Unit (MDU), the component of the Navigation Payload that generates the radio-frequency navigation signals. Phase II, which was conducted May 29 – June 29, 2018 at Aerospace (El Segundo, CA), entailed playing back the recorded signals to 13 semicodeless receivers to observe the impacts of the weighted vote on tracking performance.

The objective of Phase I was to obtain a recording of the signals that replicate GPS III SV MDU with acceptable fidelity for playback use in Phase II tests, which allowed Phase II to be completed without the use of a production MDU. Thus, the performance of the Averna RF Record and Playback system was critical and appropriately analyzed prior to and during the test events. Prior to the tests of record, the Averna system was functionally tested using simulated GPS signals and rigorously calibrated for amplitude deviation over GPS frequencies of interest, phase offset between recording channels, and phase offset of the record and playback system. Further calibration information is detailed in Davidson et al. (2018). The Averna performance was verified during tests of record via exposure of two receivers both to the live MDU output and the recorded-and-played-back output. Comparison of the receivers’ performance ensured that the quality of the recordings made was sufficient to enable testing in Phase II. An additional benefit of exposing two receivers to live MDU signals was that the weighted vote trends observed later during Phase II (from the Averna recordings) were corroborated by the trends seen using the live MDU output.

Although the recordings during Phase I and subsequent playback during Phase II consisted of ten test cases, the results presented below focus on Test Case 5 (TC5) (weighted vote on) and Test Case 8 (TC8) (weighted vote off). In both of these test cases, the power level was set such that a reference receiver measured an L1 C/A code C/N₀ of 56dB-Hz, an L2C code C/N₀ of 56dB-Hz, and an L1 andL2 Y code C/N₀ of 53 dB-Hz. M code was not present. In TC5, the L1C pilot code had equivalent C/N₀ of 56.25 dB-Hz, and the L1C data code had equivalent C/N₀ of 51.5 dB-Hz. These high C/N₀ values were selected so that any degradation of the signal could be most readily discerned. In TC8, L1C was not present. Phase II of the test campaign used the test configuration shown in Figure 10.

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FIGURE 10

Phase II laboratory setup. Elements in gray were used during Phase I for recording

8 LABORATORY TEST RESULTS

This section summarizes the test results from Phase II of the GPS III backward compatibility test events. A complete report of test results is described in Allen et al. (2018). The laboratory test results agree with the predictions of analysis and simulation. Specifically, the laboratory test results show that there may be a detectable decrease in C/N₀ at higher power levels, but this decrease does not result in a detectable degradation of tracking performance. Additionally, it showed that only some receivers detect this degradation in C/N₀.

The metrics used to evaluate receiver tracking performance are listed in Table 3. Because only a single satellite is tracked, these metrics utilize differencing between the various pseudorange and carrier phases. The code consistency relies on the differences between the pseudoranges reported for the various codes on L2 and the L1 C/A pseudorange, the carrier noise is determined by the standard deviation of the difference between the various carrier phases on L2 and the L1 C/A carrier phase, and the code noise is the standard deviation of the difference between each codes’ pseudorange and carrier phase, respectively.

Multiple test cases were run on each receiver. Each of these test cases involved approximately one hour of playback at various power levels. Two such assessments are included herein, shown in Figure 11 and Figure 12. These figures respectively show the data used to evaluate the carrier noise and code consistency metrics listed in Table 3.

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FIGURE 11

Carrier noise for example receiver

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FIGURE 12

Code consistency for example receiver

In addition to the standard test cases, linearity tests were conducted to characterize the performance at various C/N₀ levels and to ensure receiver frontends were not saturated by typical test power levels. The linearity tests involved periodically changing the signal power levels to sweep through a range of C/N₀. The linearity tests used a reduced set of three metrics to evaluate the performance of the receivers. These metrics were the reported C/N₀ levels on different codes, the code noise, and the carrier noise. As in Table 3, the code noise is defined to be the standard deviation of the difference between the L2 P(Y) pseudorange and carrier phase. Similarly, the carrier noise is the standard deviation of the difference between the L2 P(Y) and L1 C/A carrier phases. The C/N₀ measurements used are the receiver-reported C/N₀ and, thus, use the receivers’ internal C/N₀ calculation. Although these metrics do not cover all the metrics in Table 3, they provide an adequate basis for the comparison to the simulation.

To collect the metrics from the linear tests, it is necessary to first partition the data based on the signal power level. The changing of the signal power level involves changing the setting of a variable attenuator. Whenever the variable attenuator is changed, the signal is momentarily blocked and distorted. For this reason, the receiver is allowed to stabilize at the new signal power level and before data collecting begins. Data collection ends shortly before the signal power level is changed again to account for the amount of time it takes to physically turn the dial of the variable attenuators.

As previously mentioned, only some of the receivers exhibited the reduced C/N₀ of the semicodeless tracking of P(Y)-code at high power levels. For the remainder of the linearity test results, two receivers are compared. “Receiver A” is a receiver that did not show degraded C/N₀ at high power levels, while “Receiver B” did show this degradation. This can be seen in Figure 13 and Figure 14. The abscissa in these figures is the receiver-reported C/N₀ for L1 C/A-code, and “MV” is used instead of “WV” in these and subsequent figures.

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FIGURE 13

Reported C/N₀ for Receiver A

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FIGURE 14

Reported C/N₀ for Receiver B

In both Figure 13 and Figure 14, the receivers reported that L2 P(Y) C/N₀ is comparable for both the weighted vote on and off cases below approximately 50 dB-Hz (L1 C/A C/N₀); however, above 50 dB-Hz (which is higher than what most receivers experience in real-world applications), Figure 14 shows a reduced L2 P(Y) C/N₀ when the weighted vote is on, although the degradation is not seen in Figure 13. This degradation is due to some combination of intrasatellite interference and weighted voting, since in this experiment there is no intrasatellite interference when the weighted vote is off. Notice that it is very similar to the predicted degradation shown in Figure 4 and Figure 5.

Figure 15 through Figure 18 show the code and carrier noise, respectively, for the same two receivers. If the reduced L2 P(Y) C/N₀ were to impact the tracking performance, one would expect to detect an increase in code noise and carrier noise above 50 dB-Hz. Figure 16 and Figure 18 show these metrics for a receiver that exhibits the C/N₀ degradation. In these figures, no difference in code or carrier noise can be seen related to weighted vote on or off, leading to a conclusion that weighted voting did not introduce any other unexpected behavior or degradation in these measurements. Thus, the only detected impact of the weighted vote was a reduced L2 P(Y) C/N₀, but only at higher power levels and only on some receivers.

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FIGURE 15

Code noise for receiver A

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FIGURE 16

Code noise for receiver B

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FIGURE 17

Carrier noise for receiver A

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FIGURE 18

Carrier noise for receiver B