Abstract: In satellite navigation systems, regenerative Pseudo-Noise (PN) is usually adopted to range but its navigation signal power is low, along with large external interference. In order to achieve real-time PN ranging, tracking loop lock detection becomes crucial. In conventional loop lock detection method, loop decision threshold (including discriminator and counter threshold) can’t adapt received Signal to Noise Ratio (SNR) which results in false positives. For the forementioned problem, this study proposes an optimized chip tracking loop locking detection method which derives composite code SNR based on the relationship between residual carrier, composite code signal and total signal power, then adaptively selects a suitable locking threshold according to the SNR estimation. Through the simulation analysis, the feasibility of the optimization method is verified, with the conclusion that loop quickly runs into detection lock under high SNR and judges if it is locked after stabilized tracking under low SNR.
INTRODUCTION
In satellite navigation system, traditional methods of loop lock detection use fixed decision threshold and fixed counter threshold but its signal propagation range is long, causing low user receiving signal power which is susceptible to interference, so detection is prone to false positives and it increases detection time (Xie et al., 2011). Regeneration PN ranging is realized through regenerating uplink PN ranging signals and re-modulating it onto the downlink carrier. This brings considerable SNR gain for ranging signals (Tu et al., 2011; Chen et al., 2012). Therefore, in-depth study of locking detection method of Chip Tracking Loop (CTL) in regenerative PN ranging system has important and practical meaning for satellite navigation system.
Predecessors have done a lot of research on the loop lock detection issues. Literature (Fu et al., 2005) studying on method of carrier locking detection, shows the method of solving locking parameters and draws relationship between locking threshold and SNR. Literature (Liu and Ma, 2009; Ma and Hu, 2009) which is about the design of OFDM symbol synchronization, aimed at the problem that threshold is unable to adapt SNR, uses known experimental data to aid estimation in, respectively different algorithms which makes the system adaptively select thresholds under different SNRs. Literature (Song et al., 2009) which is about improving convergence speed and reducing angle of lock error, proposes a multi-polarity decision threshold about carrier recovery algorithm for QAM demodulation.
In regenerative PN ranging system, CTL lock detection is related to the chip tracking processing time. This study highlights the common methods of loop locking detection firstly and then designs an optimized locking detection method of CTL based on the effect of noise on the common loop and CTL inputs, whose locking judgment method has certain adaption to noise.
NORMAL LOOP LOCKING DETECTION
Either Frequency Locking Loop (FLL), Phase Locking Loop (PLL), Code Loop (CL) or Digit Loop (DL), normal detection algorithms all use threshold comparison of discriminator output. The results of comparisons dominate the counters adding or decrementing which decides locking or unlocking. They are different for different discriminator results. The structure diagram of normal loop locking detection units is showed in Fig. 1.
In reality, when sudden signal interrupt or sudden Signal to Noise Ratio (SNR) drop occurs caused by some reason, the signal correlation will suddenly drop which will affect correct signal tracking. To prevent unfavorable lock or unlock detection caused by noise, jamming or other accidental factors, a one-order low pass filter is directly used to smooth the computed loop discriminator result, followed by lock detection on the smoothed results. Smoothing filter is as follow:
| (1) |
where, yi denotes filtered result applied on lock detection, xi is output of current loop discriminator, α is smoothing coefficient.
Similarly, discriminating result after filter is not decided by single detection but by multiple detections. When filter result is lower than threshold value, that is, discriminating error is small, lock detection counter accumulates forward. Otherwise, when detection result is larger than threshold (discriminating error is large), lock detection counter decreases backward, until lock detection counter passes counter threshold which represents locking detection finishes. The detection flow is showed in Fig. 2. Due to the initial unstable loop, the first N discriminating outputs may be very large, unable to hold the locking detection property, thus the yi-1 of the filters is the mean of the first N results.
OPTIMIZATION OF CODE LOOP LOCKING DETECTION
Known from the loop features, when the loop band widths are the same, in the condition of high SNR, loop oscillation is relatively small, with faster converging speed and smaller tracking errors; in the condition of low SNR, loop oscillation is larger, with slower converging speed and larger tracking error. In traditional space measuring and controlling communication system, since signal receiver has relatively high SNR, the low SNR in deep space measuring and control environment won’t happen, therefore, traditional loop lock detection methods utilize fixed detection threshold and fixed counter threshold. Whereas in deep space measuring and controlling communication system, noise interferences are obviously larger, thus a new locking detection method suitable for regenerating PN code ranging system is needed.
| Fig. 1: | Normal loop locking detection structure |
| Fig. 2: | Normal loop locking detection work flow |
Table 1 showed when input code phase difference is 1/4 chip, in conditions of different CNR the discriminating results, from which the output results of CTL discriminators change greatly with the noise. If CTL locking detection threshold is selected based on high CNR, then when CNR drops and chip offset is largest, output of discriminator after filtering may be smaller than the discriminating threshold. After a period of accumulations, locking detection counter may reach the threshold, leading to detection lock. In reality, meanwhile CTL is not really locked which results in misjudging. At the same time, if discriminating threshold and counter threshold of CTL is selected in condition of low SNR, when SNR is high, discriminating error is smaller than locking detection threshold but due to higher counter threshold value, loop can’t be detection locked in a while, making the system unable to switch to the composite sub-code regenerating state.
The former situations can be attributed to inability problem of adaption between CTL detection threshold and SNR. In real environment, noise power and signal power in channel fluctuate all the time, giving rise to mismatch between loop detection threshold (including discriminating threshold and counter threshold) and received signal SNR (Ma and Hu, 2009), thus optimized design of code loop locking detection in the chapter is to make the CTL detection threshold changeable with SNR.
| Fig. 3: | Optimized locking detection structure |
| Table 1: | Impacts on identification of code phase difference of carrier to noise ratio |
Modulation in regenerating PN ranging system is Phase Modulation (PM). Signal processor first tracks medium-frequency carrier, followed by composite sub-code regenerating after carrier track is stable. Vestigial carrier is related to composite code signal power and composite code modulation degree. Based on composite code SNR deduced from vestigial carrier SNR, combined with the optimized detection threshold in all SNR conditions, detection time can be shortened using adaptive selection of current loop detection threshold. Before optimization, the structure resembles Fig. 1. After optimization, CTL locking detection structure is showed in Fig. 3.
Computing method of vestigial carrier SNR: Learned from Fig. 3, attaining adaptive lock threshold, composite signal SNR needs estimating. Before that, vestigial carrier SNR needs to be calculated, herein vestigial carrier SNR must be analyzed briefly and computed.
Vestigial carrier SNR computation is done by carrier loop I/O two-path integrate/dump results. When input medium frequency signal is stripped, I path integrate/dump result can be denoted as:
| (2) |
In the Eq. 2, A is carrier amplitude, Δθ is carrier tracking error, n is noise. Assuming phase error and Doppler error has been removed completely, I path integrate/dump can denoted as:
| (3) |
That is, I path integrate/dump result has included carrier signal amplitude info. and noise info. of the in-phase component. By the way, Q path integrate/dump result can be denoted as:
| (4) |
After errors removed, it can be:
| (5) |
That is, Q path integrate/dump result merely contains noise info. of the quadrature component.
Normally, noise in the channel is white noise. Therefore, when assumed noise mean value equaling to zero, through a while of accumulation of I path integrate/dump results, wiping out noise, only vestigial carrier signal left. What’s more, by disposal of I path and Q path integrate/dump results, vestigial carrier signal power and I path and Q path noise power can be computed. Usually the sum of I path and Q path noise power is taken as actual noise power. Then, dividing computed vestigial carrier to noise power, vestigial carrier SNR can be attained.
Composite code SNR computational method: When carrier is modulated by composite code and data at the same time, according to two path performance demands, up and down linking signal powers need to be distributed properly. When two signals co-exist, uplink or downlink carrier signals’ equations are:
| (6) |
| (7) |
In Eq. 6 the data D(t) first BPSK modulated to subcarrier, then modulated subcarrier is modulated to carrier by PM. Equation 7 presents data directly modulated to carrier. In Eq. 6 and 7, P is carrier signal power, ω0 represents carrier angle frequency, θr is ranging signal modulation degree, R(t) is composite code signal, θd is data signal modulation degree, ωsc is data subcarrier angle frequency, D(t) is data signal (±1), n(t) is Gaussian white noise, whose normal data modulation is direct PM and subcarrier PM.
Because downlink composite code is regenerating, composite code signal modulated downlink is immune from the uplink noise and as the same processing model, thereby downlink chain power distribution is the same with uplink chain. Among them, the ratio of vestigial carrier power to carrier total power is:
| (8) |
Composite code signal power to carrier total power ratio is:
| (9) |
Data signal power to carrier total power ratio is:
| (10) |
In the former equation, α(ψ) and β(ψ) represent the amounts composite code power and data power account for, respectively. The two parameter value are decided by the composite code waveform and data modulation methods. The relationship between waveform, modulation and α(ψ) and β(ψ) is showed as Table 2. Among them, ψ is composite code signal or data index modulation degree. J0(·) and J1(·) are the 0-order and 1-order first kind Bessel Function.
If carrier signal is merely modulated with composite code, without modulating data index, thus θd = 0, α(θd) = 1. Moreover, data modulation elements in Eq. 8 and 9 can be ignored, meanwhile Eq. 10 is no longer available due to θd, β(θd) and PD/PT not equal to 0.
After vestigial carrier SNR has been gained, composite code signal SNR can be deduced by Eq. 8 and 9, the details are as following: It can be presumed total carrier signal SNR is PT/N0, vestigial carrier SNR is PC/N0, composite signal SNR is PR/N0. Assuming the system does not modulate data index, merely modulate composite code signal to carrier, thus Eq. 8 and 9 can attain the ratio of vestigial carrier SNR to composite signal CNR:
| (11) |
| Table 2: | α (ψ) and β (ψ) definition |
| Fig. 4: | Work flow of SNR switched to detection threshold |
According to the relation between CNR and SNR, composite code SNR can be denoted as:
| (12) |
where, fc is composite code bit rate, B is loop bandwidth through carrier loop integrate/dump.
Learned from Eq. 11, the computation of transferring vestigial carrier SNR to composite code signal SNR is very complicated in real application. In order to reduce workloads and save device resources, table look-up is usually adopted. First set several possible vestigial carrier signal SNRs, save the set vestigial carrier SNR in a look-up table in advance. When signal processor receives carrier signal, vestigial carrier SNR can be computed. Afterwards, compare SNR by real computation and in table. According to comparison results, changes in address can be manipulated. For computational result is larger than that in table, table look-up addresses iterate; for computational result is smaller than that in table, then current vestigial carrier SNR can be taken as value in the table, outputting the current addresses in table which is switched to code loop detection threshold. The signal processing flow is showed as Fig. 4.
Normal locking detection noise performance: To further illustrate how the locking detection method in the chapter is different from normal locking detection method, noise performance of normal locking detection is first analyzed.
PLL usually utilizes such locking detection method that inputting the ratio of Q path integrate/dump result to I path integrate/dump result, in condition of no noise or high SNR, I path integrate/dump result is much larger than Q path integrate/dump result, that is, the value sent to locking detection is smaller; but with the noise augmenting, ratio of Q to I path integrate/dump result increases as well as locking detection value. The relations between Q path and I path ratio and noise are shown in Fig. 5. The underlying reason of Fig. 5 is when noise increases, discriminating phase error increases alongside, giving rise to Q path and I path ratio increase.
| Fig. 5(a-d): | Impact of noise on PLL Q path and I path ratio, (a) No noise, (b) CNR = 70 dBHz, (c) CNR = 60 dBHz and (d) CNR = 50 dBHz |
| Table 3: | Loop tracking errors under different CNR |
Locking detection algorithm of FLL is to send result of discriminator to locking detection unit, filtering and detecting discriminated frequency. Noise impacts on filtered discriminating result are showed as Fig. 6. Learned from the diagram, as noise augments, discriminating errors become larger, leading to filtered detection value increase.
For the code loop of normalized dot product discriminator, frequent method is to input discriminator output as code loop locking detection, followed by filtering and detection. The impacts of noise on code loop are showed as Fig. 7. Similar to PLL and FLL, with noise augmenting, output phase error of code loop discriminator becomes larger.
Figure 4-7 illustrates PLL, FLL and code loop discriminating result simulations under CNR equal to 70, 60 and 50 dBHz in condition of no noise. Corresponding loop tracking errors is shown in Table 3.
Learned from simulations and tracking errors, when loop discriminating results are large, corresponding loop tracking errors are also large. Therefore, if loop can attain stable tracking state, in certain tolerant spectrum, discriminating threshold can be risen appropriately to adapt to different noise environments.
| Fig. 6(a-d): | Impact of noise on FLL filtered discriminating result, (a) No noise, (b) CNR = 70 dBHz, (c) CNR = 60 dBHz and (d) CNR = 50 dBHz| |
| Fig. 7(a-d): | Impact of noise on code loop discriminator, (a) No noise, (b) CNR = 70 dBHz, (c) CNR = 60 dBHz and (d) CNR = 50 dBHz |
| Table 4: | Loop locking detection optimized simulation parameters |
| Table 5: | CTL tracking errors under different CNR |
Optimized design of locking detection: To properly select CTL detection threshold, the loop is first simulated. The detailed parameters are set in Table 4.
Table 5 illustrates, CTL tracking errors under different CNR, Fig. 8a-c illustrate code phase errors output by discriminator under different CNR, horizontal value is ±0.004. Comparing discriminator outputs and DTL loop tracking errors, different CNR has different corresponding tracking errors, though discriminator outputs are all stabilized between -0.004 to +0.004. In low CNR, discriminator output is around threshold but tracking errors are large; in high CNR, discriminator output is around threshold but real corresponding tracking errors are small. Therefore, it is redundant to set different discriminating threshold value according to different noises, whereas it is favorable to set threshold directly.
Meanwhile, from Fig. 8a-c simulation results, if discriminating threshold value is set as ±0.004 chip, in low CNR, to ensure loop is at stable tracking state, counter threshold is set larger; in high CNR, although discriminator outputs are around discriminating threshold, since real tracking error is small and loop is certain in stable tracking state, counter threshold can be decreased properly to shorten CTL locking detection time. Thus, a suitable counter threshold can be a dynamic choice based on composite code signal CNR (or SNR).
METHODS OF THE OPTIMIZED CTL LOCKING DETECTION METHOD
Optimized CTL locking detection method: In this study, optimized locking detection methods used by conventional tracking loop. In the case, composite code SNR is deduced according to residue carrier and power relation between composite code signal and total signal, followed by SNR-adaptively selecting a suitable locking threshold, based on which adaptive loop locking detection can be finished. The study compares conventional loop locking detection methods and proposed adaptive loop detection method:
| • | Conventional loop locking detection methods: Those methods utilize fixed detection threshold and fixed counter threshold to detect loop locking. First, they tend to judge the loop-filtered results, if which are less than the locking threshold value, counter adds 1, whereas, subtracts 1. When counter value is larger than counter threshold, loop is detected as “locked” |
| • | Proposed adaptive loop locking detection method: The study adopts SNR-related adaptive threshold detection method to implement loop locking detection. A loop SNR calculator unit is added in loop, based on whose calculated SNR detection threshold can be determined. Then we judge loop-filtered results, if which are less than the locking threshold value, counter adds 1, whereas, subtracts 1. When counter value is larger than counter threshold, loop is detected as “locked” |
| Fig. 8(a-c): | Under (a) 30, (b) 40 and (c) 50 dBHz CNR code phase errors output by discriminator |
Thus residue carrier SNR can be used to calculate signal SNR of composite code. It assumes total carrier signal CNR being PT/N0, residue carrier SNR being PC/N0, SNR of composite code being PR/N0. Supposing the system doesn’t modulate data indices, it only modulates composite code signal carrier which results in SNR of composite code:
| (13) |
where, fc denotes composite code rate and B denotes carrier loop integrate/dumped loop bandwidth.
| Algorithm 1: Proposed adaptive optimized loop locking detection algorithm |
SIMULATION ANALYSIS
According to former analyses, after optimized design of locking detection method, the concrete relation of discriminating threshold value and counter threshold value with noise is shown in Table 6.
Figure 9a-c illustrate tracking errors curve and locking detection time under different CNR. When CNR is 30 dBHz, optimized loop is detection locked at 4.9 sec, meanwhile the tracking errors is relatively small, detection locking is still available, contrarily if loop is detection locked at 2.1 sec before optimization, the tracking errors are relatively large, estimated code clock and real code clock shift is large which is not reasonable; when CNR is 50 dBHz, optimized loop is detection locked at 1.3 sec, meanwhile loop almost does not oscillate, with small tracking errors which can switch to the next working state. However, before optimization, loop is detection locked at 3.6 sec, when actually loop reaches stable tracking state at 1 sec or so, thus detection time is not rational. Simulation result verifies the feasibility of the optimization algorithm.
In the normal locking detection methods, discriminating threshold is usually selected according to maximum noise and the value is relatively high, with counter threshold set as fixed value. Discriminating threshold value of the optimized locking detection method mentioned in the study is selected according to maximum noise but the value is small, counter threshold is evaluated according to different noise setting. Based on impacts of noise on the discriminator result, in high noise situation, CTL’s converging speed is slow, discriminator output is around threshold, corresponding tracking errors are large, so it takes longer time to judge whether CTL is at the stable tracking state; when noise is small, CTL converging is relatively fast, despite discriminating result is also around threshold, the actual corresponding is already very small and CTL must be at the stable tracking state, so continuing to use longer detection time is not appropriate. So, counter threshold in high CNR can be shortened to shorten chip tracking processing time.
When noise is large, optimized locking detection adopts longer detection time. Only if discriminator results are smaller than discriminating threshold in a long time, it is testified that loop errors are within the spectrum of regulation. Until now the switched sub-code regenerating working state can be viewed efficient, that is, errors between actual code clock and estimated code clock is acceptable. When noise is small, discriminating result is smaller than discriminating threshold in a short period which can be interpreted loop errors are within error tolerance and estimated code clock has very small offset with actual code clock. Thus in condition of small noise interference, shorter detection time can be used.
RESULTS AND DISCUSSION
Experiment results and analysis: The proposed adaptive loop locking detection algorithm and optimize calculating complexity of the algorithm was analyzed and simulated here.
| Table 6: | Optimized detection threshold under different SNR |
| Fig. 9(a-c): | Tracking error curve under (a) 30, (b) 40 and (c) 50 dBHz SNR |
| Table 7: | Comparison of different loop locking detection methods |
| • | Optimized CTL locking detection model: Table 5 shows CTL tracking errors in different CNR conditions. Figure 8a-c describe phase errors outputted by discriminators in different CNR conditions which show that in low CNR, counter threshold value can be increased to secure stable tracking of the loop; in high SNR, counter threshold value can be decreased to shorten loop locking detecting time. Figure 9a-c describe tracking error curve and locking detecting time in different CNRs. As it shows, when CNR is relatively lower (30 dBHz), optimized loop tracking error is relatively small; when CNR is relatively higher (50 dBHz), optimized loop not only holds the small tracking error but also cuts down locking time. Table 7 shows the comparison of different loop locking detection methods in literature in comparison to the presented study. Therefore, the simulated results verify feasibility of the proposed optimized adaptive loop locking detection method |
CONCLUSION
In the regenerating PN ranging system, CTL locking detection relation is concerned with chip tracking processing time etc. If discriminating threshold is set too high, loop will be detected as lock in advance but current loop oscillation is relatively very severe, errors are large. If counter threshold is too high, it leads to too long loop detection locking time, slow to jump to the next step, prolonging loop tracking processing period. The chapter first analyzes normal loop locking detection methods, then researches locking detection method based on impacts of noise on locking detection input, finally puts forward an optimized CTL locking detection method: Regenerating ranging system initially strips carrier, meanwhile estimates vestigial carrier SNR. According to relation between vestigial carrier, composite code signal and total signal power, composite code signal SNR is deduced, finally a appropriate locking threshold is selected according to estimated composite code signal SNR, in low SNR, higher counter threshold is used, in high SNR, smaller counter threshold is used. Simulation result shows the locking detection method has some adaptivity to noise which can ensure loop makes quick detection locking in high SNR and is detection locked after loop is at stable tracking state in low SNR.
ACKNOWLEDGMENT
This study is supported by Youth Foundation, National Natural Science Foundation of China (61102130), “Innovation Project of Academy of Opto-Electronics”, Chinese Academy of Sciences (Y12414A01Y).