Evaluation of C/N 0 estimators performance for GNSS receivers
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1 International Conference and Exhibition The 14th IAIN Congress 2012 Seamless Navigation (Challenges & Opportunities) October, Cairo, Egypt Concorde EL Salam Hotel Evaluation of C/N 0 estimators performance for GNSS receivers ABSTRACT Ondrej Kútik, Martin Orejas Honeywell International Tuřanka 100, Brno, Czech Republic ondrej.kutik@honeywell.com; martin.orejas@honeywell.com In GNSS receivers the estimation of the Carrier-to-Noise ratio (C/N 0 ) of the signals being tracked is an important function not only because it is a measure of the input signal strength in a given environment but also because it is a fundamental measurement exposing the status and performance of the tracking system. Traditionally, GNSS receivers have been employing the narrowband-wideband power ratio method (NWPR) to estimate the C/N 0 of the signals being tracked. The increased number of signals that future GNSS receivers will need to track in addition to intrinsic limitations of this method has drawn interest in more computationally efficient alternatives. Several C/N 0 estimators for GNSS receivers, usually adapted from SNR estimators used in the field of digital communications have been proposed over the last years. Various studies have analyzed the estimators performance, namely in term of bias and noise, as a function of parameters like residual carrier phase, coherent predetection integration time, SNR, and number of samples utilized. This paper expands the analysis by investigating the impact of crosscorrelation between signals from different SVs as well as between data and pilot signals on the estimators performance. The estimation techniques of interest were implemented and tested in a hardware GPS/Galileo receiver prototype developed by the team. The results show that the impact of cross-correlation is reflected by the estimators if used with appropriate predetection integration time. The standard deviation of the estimate on various C/N 0 estimators differs significantly and is also dependent on the length of predetection integration time. KEYWORDS: GNSS, C/N 0, estimator, receiver, cross-correlation 1 INTRODUCTION With the introduction of the new GNSS signals, the commonly used narrowband-wideband power ratio (NWBP) estimator faces new challenges. In a traditional GNSS receiver design the coherent predetection integration time is a multiple of the primary code period (see Table 1). In a later tracking state, after symbol or secondary code synchronization, the integration time can be prolonged, what improves the sensitivity and accuracy (Kaplan and Hegarty 2006). Additionally it decreases the computational burden by reducing the update rate of the control loops. The computational efficiency might become important with the increasing number of tracked signals. The maximum length of integration period is constrained by design of the control loops and, for signals containing the navigation message by symbol period (assuming no data prediction). The NWBP estimator requires input with two different integration times. This is not available for traditional receiver tracking GALILEO E1b signal which has primary code duration equal to symbol period. Furthermore, the estimator request of various integration times is a limitation for GNSS receiver architectures where the integration is done in HW, as the HW cannot integrate the longest period possible. To other considerations in the choice of C/N 0 1
2 estimator belongs the utilization of the estimated C/N 0 to determine the frequency lock status. In this case the estimator needs to operate properly without phase lock. Table 1: Primary code and data symbols periods for various civilian GPS/GALILEO signals. Signal type Primary code [ms] Data symbol [ms] GPS L1 C/A 1 20 GPS L5I 1 10 GPS L5Q 1 - GALILEO E1b 4 4 GALILEO E1c 4 - GALILEO E5aI 1 20 GALILEO E5aQ 1 - GALILEO E5bI 1 4 GALILEO E5bQ 1 - The above mentioned limitations call for search of alternative estimators. Summary and comparison can be found in various sources (e.g. Pauluzzi and Beaulieu 2000, Falletti et al. 2011). A key factor in the selection process of the C/N0 estimators studied within this paper has been their complexity and suitability for the new expected signals. Section 2 explains the means to compute the estimate of Carrier-to-Noise ratio. List of considered C/N 0 estimators is summarized in section 3, together with formulas to compute the C/N 0 estimate. Section 4 describes how the cross-correlation among different SVs, and also between data and pilot signals, affects the effective C/N0. This is confirmed by tests done with the GPS/Galileo receiver prototype developed by the team. In section 5 the performance comparison of implemented estimators is shown for various coherent predetection integration times. 2 SIGNAL MODEL Figure 1 shows a model of the GNSS receiver. The incoming IF signal r l is downconverted to the baseband by estimated carrier frequency and multiplied with the local replica of the code. For simplicity only the prompt replica used for C/N 0 computation is shown. The C/N 0 is estimated using the output of the correlators r c. The coherent predetection integration time of the correlators is further referred as. Estimated carrier rate prompt Integrate & Dump r c,re Control loops r l 90 PRN code generator Estimated chip rate prompt Integrate & Dump r c,im C/N0 estimator Figure 1: GNSS receiver tracking model with C/N 0 estimator The output signal of the correlators (Integrate & Dump blocks) is modelled as (1) 2
3 bmwhere is data symbol, is complex noise, is useful signal power and is the noise power. Signal-to-Noise ratio is defined as The C/N 0 represents the Carrier-To-Noise Density ratio and relates to the SNR by the following formula (Falletti et al., 2011) Where the equivalent noise bandwidth 3 C/N 0 ESTIMATORS 3.1 Narrowband Wideband Power Ratio (NWBP) This traditional approach estimates the power at two different bandwidths. Wideband power WBP with bandwidth and narrowband power NBP with bandwidth (Van Dierendonck A.J., 1996). ( ) (5) (2) (3) (4) ( ) ( ) ( ) (6) (7) Notes: Needs to be symbol synchronized, saturates at high C/N 0 levels. 3.2 Moments Method (MM) Using the second (M 2 ) and forth (M 4 ) order moment the following relations can be revealed for carrier and noise strength (Pauluzzi and Beaulieu, 2000) The moments are estimated as (11) (8) (9) (10) SNR is finally estimated according equation (2). Notes: Robust, but computationally expensive. 3.3 Squared Signal-to-Noise Variance Estimator (SNVE) Based on the first absolute moment and the second moment of samples (Pauluzzi and Beaulieu, 2000) [ ] (12) 3
4 (13) (14) SNR is estimated according equation (2). Notes: Needs to be phase locked, saturates at high C/N 0 levels. 3.4 Beaulieu s Method The method estimates the carrier and signal strength for a BPSK modulated signal as (Beaulieu et al. 2000) ( ) (15) ( ) (16) [ ] (17) Notes: Needs to be phase locked. 4 CROSS-CORRELATION INTERFERENCE GNSS systems using Code-Division-Multiple-Access (CDMA) multiplexing technique are subject to intrasystem interference due to cross-correlation among the different PRN codes, which directly influences the effective C/N 0. For a perfectly phase tracked signal i interfered with signal j the output of correlators can be described as (Elrod and Van Dierendonck, 1996) (18) (19) where A is a signal amplitude is a product of PRN codes is carrier frequency difference is signal phase From the above equations it can be observed the cross-correlation interference is maximized when the interfering signal amplitude is high. Less obvious condition for maximized interference is the need of signals delta frequency to be multiple of code repetition rate (Elrod and Van Dierendonck, 1996 for GPS L1 C/A). The power of the interfering signal is {[ ( ) ] [ ( ) ] } (20) 4
5 Delta frequency [Hz] Carrier Phase SD [m] C/N0 [db] Typically is integer multiple of primary code period (inverse of code repetition rate). The integration over each code period is identical for Doppler differences of multiples of code repetition rate. If the Doppler difference is integer multiple of code repetition rate, the interfering signal power reaches its maxima peaks, as all fractions are added without cancellation. The receiver s tracking system perceives the cross-correlation interference as a noise, thus the effective C/N 0 is degraded. For the new signals that contain data and pilot components the cross-correlation between these is another source of interference. Unlike the case when the interference is between signals from different SVs, in which the degradation is maximum at certain delta frequency (function of the primary code s repetition rate), in this case, because both signals have the same frequency, the degradation occurs at all times.. Both cases have been tested in the scenarios using the HW GPS/GALILEO receiver prototype. 4.1 Cross-correlation of two SVs As explained before the cross-correlation peaks at delta frequencies multiples of 1 khz. A test with the aforementioned GPS/Galileo HW receiver prototype and HW GNSS simulator confirms the theory. A smooth decline of estimated C/N 0 of two SVs can be seen in Figure 2a where the maximum drop is at delta frequency 6000Hz. The impact of the cross-correlation on tracking can be observed by noisier estimate of the carrier phase (Figure 2b) x 10-3 SV3 SV11-2 Figure 2: Degradation of estimated C/N 0 due to cross-correlation between two SVs. a) estimated C/N 0 using Moments Method. b) Imact of the cross-correlation on carrier phase tracking performance c): Delta carrier frequency 4.2 Data/pilot cross-correlation GPS L1, Integration 20ms, MM C/N0 estimator Because the cross-correlation between data and pilot signals is constant over all frequencies but varies for each data/pilot pair, due to the cross-correlation properties of the codes used, each SV will observe a different C/N 0 even though the signal power received is the same. This is shown in Figure 3 when all SVs transmit signals with equal power level for the whole scenario duration. 5
6 C/N0 [db-hz] C/N0 [db-hz] C/N0 [db-hz] db below full correlation C/N0 [db-hz] Galileo E1, MM C/N0 estimator, 4ms integration Figure 3: Degraded C/N 0 due to data/pilot cross-correlation. All SVs transmit equal power signal The C/N 0 degradation is constant and depends on the cross-correlation level and pilot signal, which is computed as SV#5 SV#12 SV#7 SV#8 SV#6 SV#13 between data (21) where N is the code length, d and p are the PRN sequences of data and pilot channel respectively. The cross-correlation levels of GALILEO E1 signals are shown in Figure Galileo E1 data/pilot cross-correlation SV Figure 4: Galileo E1 data/pilot cross-correlation The observation is supported by estimating the C/N 0 of data signal with pilot signal disabled or enabled. For SV13, where the data/pilot cross-correlation is one of highest of E1 PRN sequences, the effective C/N 0 is degraded by approximately 3dB (for given signal power). On the other hand, SV5 with better cross-correlation properties remains unaffected. It is important to notice that this degradation manifest for signal with high C/N0 and is not visible at lower C/N 0 (Figure 5c), as the cross-correlation interference is buried in other noise SV SV Figure 5: Galielo E1 C/N 0 estimation degraded by data/pilot cross-correlation. MM 4ms estimator SV13 low C/N0 Data Only Data (D+P) Pilot (D+P) 6
7 Estimated C/N0 [db-hz] Delta Doppler frequency [Hz] Estimated C/N0 [db-hz] Estimated C/N0 [db-hz] 5 SIMULATIONS C/N 0 estimators from section 3 were implemented in the HW GPS/GALILEO receiver prototype. GPS L1 C/A signal has been selected for tests, due to large range of possible integration time (1-20ms) and short PRN sequences resulting in lower cross-correlation protection. To maximize the crosscorrelation interference scenario with delta frequency equal to integer multiple of code repetition rate has been used. Parameters of interest are the standard deviation and mean. The averaging length was set to 1 second, leading to configuration parameters listed in Error! Reference source not found.. The C/N 0 in Figure 6 for steady state (t > 600) unsaturated estimates (MM, Beaulieu) using short integration time is lower compared to estimates using longer integration time. When the integration time is short, each integration cycle will contain part of interfering signal degrading the C/N 0. On the other hand, with longer integration the interfering signal can partially or completely cancel itself. For example, if the delta Doppler frequency would be 1/, the total integrated power of interfering signal would be zero, as the codes would be flipped. = 1ms = 10ms MM SNVE B NWBP = 20ms Delta frequency with interfering signal Figure 6: Comparison of estimated C/N 0 for various estimators and integration times on SV3 GPS L1 C/A signal. Applyed smoothing with moving average of length 10. Bottom right: Delta Doppler frequency with the interfering signal (SV11) Table 2: C/N 0 estimator parameters for various integration periods C/N 0 estimator = 1ms = 10ms = 20ms MM N = 1000 N = 100 N = SNVE N = 1000 N = 100 N = Beaulieu N = 1000 N = 100 N = 7
8 Estimated C/N0 [db-hz] Delta Doppler frequency [Hz] Estimated C/N0 [db-hz] Estimated C/N0 [db-hz] NWBP M = 20, N = M = 2, N = - Table 3 together with Figure 6 show the simulation results. For better readability smoothing with moving average of length 10 samples has been applied on plots in Figure 6. Statistics is computed from time when the impact of cross-correlation is neglidgable (t = 600s). NWBP and MM estimators give less noisy estimate. Some estimators tend to saturate at high level of C/N 0, leading to underestimate of C/N 0 (Falletti et al., 2011). From the implemented estimators the saturation effect is visible for NWBP and SNVE estimators, namely when longer predetection integration time is used. The C/N 0 in Figure 6 for steady state (t > 600) unsaturated estimates (MM, Beaulieu) using short integration time is lower compared to estimates using longer integration time. When the integration time is short, each integration cycle will contain part of interfering signal degrading the C/N 0. On the other hand, with longer integration the interfering signal can partially or completely cancel itself. For example, if the delta Doppler frequency would be 1/, the total integrated power of interfering signal would be zero, as the codes would be flipped. = 1ms = 10ms MM SNVE B NWBP = 20ms Delta frequency with interfering signal Figure 6: Comparison of estimated C/N 0 for various estimators and integration times on SV3 GPS L1 C/A signal. Applyed smoothing with moving average of length 10. Bottom right: Delta Doppler frequency with the interfering signal (SV11) Table 2: C/N 0 estimator parameters for various integration periods C/N 0 estimator = 1ms = 10ms = 20ms MM N = 1000 N = 100 N = SNVE N = 1000 N = 100 N = Beaulieu N = 1000 N = 100 N = 8
9 NWBP M = 20, N = M = 2, N = - Table 3: C/N 0 estimator statistical performance, N = 0 C/N 0 = 1ms = 10ms = 20ms estimator STD MEAN STD MEAN STD MEAN MM SNVE Beaulieu NWBP CONCLUSION Trying to apply conventional NWBP C/N 0 estimator to a new GNSS signals schemes reveals its intrinsic limitations. Alternative C/N 0 estimators have been evaluated in terms of standard deviation and mean values. The selection of C/N 0 estimator is a trade-off among various parameters such as belong accuracy, computational burden, HW vs. SW integration, asymptotic behaviour and ability to operate without phase lock or symbol synchronization. The effective C/N 0 is affected by the cross-correlation interference. The amount of crosscorrelation interference will depend on the amplitude of the involved signals, the cross-correlation between the codes, and for cross-correlation between different SVs also the delta frequency. The crosscorrelation interference manifests at high signal power levels and has impact on the tracking performance. It has been shown that NWBP estimator in a common M = 20, N = configuration is not able to reveal the impact of cross-correlation interference. REFERENCES Beaulieu N.C, Toms A.S, Pauluzzi D.R, (2000), Comparison of Four SNR Estimators for QPSK Modulations, IEEE Communications Letters, 4, 2, pp Elrod B.D., Van Dierendonck A.J. (1996). Interference caused by cross-correlation between C/A codes. In: Parkinson B.W., Spilker J.J. Global Positioning System: Theory and Applications, Vol II. American Institute of Aeronautics and Astronautics, Washington, DC, pp Falletti E., Pini M., and Lo Presti L. (2011), Low Complexity Carrier-to-Noise Ratio Estimators for GNSS Digital Receivers, IEEE Transactions on Aerospace and Electronic Systems, Volume 47, pp Falletti E., Pini M., and Lo Presti L. (2010), Carrier-to-Noise Algorithms, Inside GNSS, January / February 2010, pp Kaplan ED and Hegarty CJ (2006) Understanding GPS: Principle and Applications 2 nd ed, Artech House, Norwood, MA, pp Pauluzzi D.R. and Beaulieu N.C (2000), A comparison of SNR estimation techniques for the AWGN channel, IEEE Transactions on Communications, Volume, 10, pp Van Dierendonck A.J. (1996). GPS Receivers. In: Parkinson B.W., Spilker J.J. Global Positioning System: Theory and Applications, Vol I. American Institute of Aeronautics and Astronautics, Washington, DC, pp
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