Abstract
Existing methods are unable to achieve high detection rates and low false alarm rates of satellite-based Automatic Dependent Surveillance-Broadcast (ADS-B) signal preambles at extremely low signal-to-noise ratios (SNRs) using limited on-star resources. In this paper, a dual-hierarchy synchronization method is proposed, including a first-level coarse synchronization and a second-level fine synchronization. The coarse synchronization process involves three steps: (1) detection of unknown signals, (2) soft decision, and (3) adaptive interval output. The first step introduces the threshold () of the minimum signal energy to be detected to guarantee a high detection rate. In the soft decision step, a value () designed to improve the robustness of the system curbs false detection caused by noise interference. In the last step, the coarse synchronization interval radius () is mapped out according to the SNR to reduce resource consumption. The fine synchronization process is based on the coarse synchronization output, and the correlation peak is calculated to complete the synchronization of the signal preambles. The results show that the proposed method achieves a high detection rate of 96% at an extremely low SNR using a low sampling frequency of 10 MHz. Furthermore, the adjustment of allows this method to be applied to ADS-B receivers with different sensitivities. The comprehensive performance of this method to achieve high detection rates and acceptable false alarm rates at extremely low SNRs with limited on-star resources is verified by final simulations to be superior to other methods.
1. Introduction
As the number of aircraft present in the airspace rapidly grows, the Automatic Dependent Surveillance-Broadcast (ADS-B) system is becoming a key surveillance tool for next-generation air traffic management due to its flexible surveillance mode and high-accuracy data-updating ability [1, 2]. However, the traditional ground-based ADS-B system cannot provide seamless global surveillance due to blind zones at ground stations [3]. In order to solve this problem, researchers have focused on satellite-based ADS-B systems to achieve real-time, continuous, and seamless surveillance globally [4–7].
The signal preamble detection of satellite-based ADS-B receivers is severely limited by extremely low signal-to-noise ratio (SNR) and fewer on-star resources [8], due to the fact that ADS-B systems were not originally designed for applications on satellites [9]. Several methods have been proposed to alleviate the various problems of signal detection that come with it. On the one hand, the initial detection of a 4-pulse preamble was used to judge the existence of the header and to calculate the arrival time of the signal, as was described in a previous study [10]. This method results in a low detection rate and a high false alarm rate due to the low SNR [11]. In order to make the false alarm rate acceptable, Ren et al. [12] proposed a novel preamble detection algorithm that follows four criteria: false alarm rate (CFAR) detection, deterministic symbol matching, consistent power testing, and null symbol validation. This method can guarantee a detection rate higher than 90% only if the SNR is not lower than 10 dB. However, the SNRs of satellite-based ADS-B signals are much lower than 10 dB based on the analysis of the communication link [5]. On the other hand, Qin and Yang [13] pointed out the importance of saving computational resources when processing signals on satellites. They designed a detection algorithm based on the preamble correlation to save resources. However, this method is not suitable for processing poorly correlated satellite-based ADS-B signal preambles. To obtain sufficient correlated information, Delovski et al. [14] directly detect signal frame headers at a high sampling frequency during intermediate frequency (IF). Although a detection rate of over 90% was achieved at a low SNR, the high sampling frequency of 105 MHz being used resulted in a significant increase in resource consumption. The application of this method is impractical on satellites with limited resources. Based on the above, the demand for a comprehensive algorithm that can robustly guarantee high detection rates and low false alarm rates at extremely low SNRs while consumes fewer on-star resources in satellite-based ADS-B signal detection attracts our attention.
We propose a dual-hierarchy synchronization method that incorporates three important steps: (1) detection of unknown signals, (2) soft decision, and (3) adaptive interval output. It enables the satellite-based ADS-B system to simultaneously meet the requirements of high detection rates, acceptable false alarm rates, fewer on-star resources consumed, and high robustness, even at extremely low SNRs. Our unique contributions are compared boldly and explicitly with the latest levels in Table 1 and further detailed as follows. (1)We propose the first comprehensive synchronization method for extremely weak ADS-B signals that achieves high detection rates even at a low sampling frequency(2)We introduce the threshold () of the minimum signal energy to be detected to achieve high detection rates at extremely low SNRs. This parameter can be adjusted to even ensure that the required detection rate is maintained for any ADS-B receiver with a different sensitivity(3)We add a system robustness value () that not only reduces false alarm rates but also robustly handles adjacent ADS-B signals with different dynamic ranges(4)We reduce the computational redundancy by mapping the relationship between the SNR and coarse synchronization interval radius () in addition to using a low sampling frequency
The first column of Table 1 represents the challenges faced in synchronization of satellite-based ADS-B signals, including extremely low SNRs, limited on-star resources, high detection rates, and low false alarm rates, with high robustness and strong applicability as additional advantages. The last column reflects which task of our method was used to address these challenges.
This paper is organized as follows. In Section 2, we build the mathematical model of the baseband signal of a satellite-based ADS-B system based on an analysis of the SNR. Section 3 describes the dual-hierarchy synchronization method for detecting satellite-based ADS-B signal preambles and the three key steps this method includes. In Section 4, the three important steps proposed in the method are simulated and validated. Furthermore, we also compared the simulation results with other methods in this section. The concluding remarks and potential future research topics are provided in the final section.
2. SNR and Mathematical Model of Digital Baseband Signals for Satellite-Based ADS-B
2.1. SNR Analysis of Baseband Signals
The sensitivity of the receiver is defined as the lowest signal energy required to ensure normal operation [15]. To determine the SNR of the baseband signal when the preamble is detected, we need to calculate the sensitivity of the satellite-based ADS-B receiver using the link budget without changing the transmitter power. is the free-space propagation loss of the signal and is given by [16, 17] where is the transmission distance of the signal in kilometer and is the carrier frequency of the signal in megahertz. According to the actual situation [18, 19], we initially estimate that the vertical distance between the vehicle and satellite is , and the farthest distance that the satellite can cover is . The ADS-B signal carrier frequency is MHz. By substituting the above values into (1), the range can be estimated as .
Without changing the ADS-B transmitter power ( dBm), the received radio frequency (RF) power of the satellite-based ADS-B receiver can be obtained from where is the sum of the gain of the transmitting antenna and receiving antenna and is the absorption loss caused by the atmosphere, rain, clouds, and fog in the carrier wave propagation process. By substituting these values of dB, dB, and into (2), the peak power range of the satellite-based ADS-B receiver can be obtained as . This range is consistent with the results of the simulated received signal described in the literature [5]. Thus, the system design and index allocation for the RF component and baseband signal processing component of the receiver should be based on this range.
The minimum peak power is -102 dBm, and the duty cycle of pulse position modulation (PPM) is 50%, so the average power .
The noise of the receiver can be calculated using where is the Boltzmann constant, the Kelvin temperature is equal to 290 K, is the bandwidth, and dBm is the base noise of the receiver.
Assuming that the RF link has a receiver noise figure (RNF) of 2.5 dB and the bandwidth is 4 MHz [20], then the minimum SNR of the baseband signal for preamble detection can be expressed as
This metric implies that the synchronization method for satellite-based ADS-B signals needs to achieve the desired performance at a SNR of 0.479 dB, including high detection rates, acceptable false alarm rates, fewer on-star resources consumed, and high robustness.
2.2. Mathematical Model of Digital Baseband Signals
The ADS-B signal has undergone PPM with 120 bits per signal and a duration of 120 microseconds. The energy of one bit can be defined using where is the amplitude of the digital signal.
First, the preamble of the signal is composed of the initial 8 microseconds, and its corresponding position characteristic array is .
Then, the other 112 microseconds are data bits, which can be expressed as follows:
These data bits have two forms that and can be represented using
Finally, the position characteristics of one signal can be expressed as .
The unipolar pulse signal can be expressed as follows: where μs is the duration of a code element, is a rectangular pulse, and . The analog IF signal passing through the RF link is denoted as . The term can be expressed as the product of the unipolar pulses and a sinusoidal carrier, as shown in where MHz is the IF carrier corner frequency, is the carrier initial phase (assumed to be 0), and is the additive Gaussian white noise expressed as . With as the input, the ADS-B digital baseband signal is obtained following the processing steps outlined in Figure 1.
As shown in Figure 1, with the sampling frequency MHz, the digital IF signal can be obtained after conducting an analog-to-digital conversion. The signal can be expressed using where μs.
First, is multiplied by the cosine and sine data generated by the numerically controlled oscillator (NCO).
Then, the obtained results are passed through low-pass filters and sampled to obtain the in-phase component and the quadrature component , as expressed in where is the discrete data of after filtering and sampling and is the number of samples per code element.
Finally, can be expressed as follows: where the noise satisfies based on Parseval’s theorem [21, 22] and .
3. Proposed Dual-Hierarchy Synchronization Method
3.1. Design of the Dual-Hierarchy Synchronization Method
The dual-hierarchy synchronization method, which is performed by superimposing coarse synchronization on fine synchronization, is designed to overcome the detection rate problems associated with satellite-based ADS-B signals due to extremely low SNR and limited on-star resources. Figure 2 shows the operational framework for this method, and then, more detailed algorithms are described in Sections 3.2 and 3.3.
As show in Figure 2, after the coarse synchronization, the radius () of the interval in which the signal exists is calculated with a certain probability, and the position () corresponding to the maximum energy within that interval is obtained. Thus, a certain signal preamble is judged to fall in interval . Based on the , the fine synchronization locates to the position () of the signal preamble by filtering-matching and passes it to the next function to complete the signal preamble synchronization process [23]. The coarse synchronization plays the most important role in the proposed method and is the main contribution of this paper.
3.2. First-Level Coarse Synchronization Algorithm
The function of coarse synchronization is to find the approximate position of the signal preamble and output it to fine synchronization in the form of an interval. Its performance is required to achieve a high detection rate and a low false alarm rate. The challenge is the extremely low SNR of the signal and the limited resources available on the satellite. As shown in Figure 3, the coarse synchronization process consists of three main steps: the unknown signal detection in step 1, the soft decision in step 2, and the adaptive interval output in step 3. The first step is aimed at identifying the existence of the signals, the second step is responsible for extracting the complete signals, and the last step calculates the potential interval of the signal preamble. The details of each step are described as follows.
3.2.1. Step 1: Detection of Unknown Signals
In the detection of unknown signal step as shown in Figure 3, the energy accumulation of the signal is first described. The filter expression is , where satisfies , the array is the preamble feature array as described in Section 2.2, and the array is an all-one array with a length of 224. Because the number of samples of a single code element is , is an all-one array of length . For the matrix with 5 columns and 240 rows, the elements of each row are reconstituted into an array according to the row numbers in turn. By convolving and , we can obtain the accumulation energy of one signal, as expressed by where is the square of the amplitude of the signal with noise.
Because the ADS-B signal is modulated through PPM, the accumulated energy can also be expressed using where and represent the number of low electrical level and high electrical level bits that have been convolved, respectively, and . conforms to the noncentral chi-square distribution [24], and fits the central chi-square distribution [9]. When the signal preamble is fully synchronized, and .
Then, the term is introduced to determine whether a signal is present or not, as shown in where and represent the presence and absence of the signal.
When the energy accumulation length is sufficiently large (usually ≥30), according to the central limit theorem (CLT), the multiple independent random variables must obey the Gaussian distribution expressed as follows [25]:
Thus, the false alarm probability and detection probability are calculated as follows [26]:
The can be computed by (17), as shown in where can be obtained according to the system requirements. When the preamble of the signal is synchronized, , , and . The can be adaptively determined according to the receiver sensitivity, as described in Section 2.1. Thus, the can be adjusted exactly to the needs of different situations. This is one of the advantages of this method: it is suitable for ADS-B signal receivers of different sensitivities. This parameter is verified in Section 4.1.
Finally, decision 1 is addressed using and , as shown in Figure 3. This step is aimed at determining whether the accumulated energy is greater than the value based on (15). We delimit , which is continuously determined to be greater than , within an interval defined as the signal existence interval (SEI). This result is passed to the step 2 (soft decision) as input.
3.2.2. Step 2: Soft Decision
Although the signal was judged to be present and the SEI was obtained, it is not possible to determine how many signals exist within this interval. The soft decision step is used to solve this problem and obtain the interval in which a single signal exists, denoted as SSEI. The key to this soft decision step is decision 2 as shown in Figure 3, which can be expressed in where is the value that guarantees the robustness of the system and is the length of .
If both inequalities in (19) are satisfied, the corresponding is recognized as . The position corresponding to the maximum energy in is recognized as . It will be passed on as output to the step 3 as shown in Figure 3.
If the second inequality is satisfied, but not the first, this means that this is misclassified as a signal due to excessive noise. This detection should be abandoned. Therefore, is important to reduce false alarms.
If the first inequality is satisfied but not the second, this means that, due to the filter length, this decision combines multiple signals shorter than 120 microseconds into the same signal interval. Thus, the signal separation described next is necessary.
The must be separated dichotomously until (19) is satisfied, giving multiple single signal intervals . Assuming that the position corresponding to the maximum energy in is , the signal separation rules are described as follows.
If , then
If , then
Here, the and are the new intervals obtained by signal separation. These intervals must be again verified by decision 2 until multiple are obtained.
3.2.3. Step 3: Adaptive Interval Output
Due to the presence of noise, there is a certain probability that is not a true preamble [27]. Fine synchronization consumes many resources if the processing is performed using the whole . Based on these two factors, we have to provide a shorter fine synchronization interval where the signal preamble exists. The radius of this interval is noted as , and the center point remains the output of the previous step 2. Because the dispersion measures of the signal preambles differ among different SNRs [28], we establish a mapping relationship between the coarse synchronization-output interval and SNR. The modeling details are explained in Section 4.3, and the mapping relationship is summarized in Table 2.
By estimating the SNR, is obtained. Combined with , the more accurate interval of the signal preamble is transmitted to the fine synchronization level as shown in Figure 3, which is noted as .
3.3. Second-Level Fine Synchronization
To fully utilize the position characteristics of the signal preambles, the bipolar matching filter defined as is chosen. The correlation coefficient () is obtained through a sliding correlation process using the output signal interval of the coarse synchronization results and the filter , as shown in
When is taken to be the maximum, the corresponding position is identified as the actual arrival point of the signal and is denoted as . At this point, the proposed synchronization method is completed with as the result.
4. Validation and Results
4.1. Simulation and Verification of
As mentioned in the first step in Section 3.2, for ADS-B receivers with different sensitivities, high detection rates can theoretically be maintained by adjusting the , which is one of the advantages of the dual-hierarchy synchronization method. It is necessary to simulate and verify the detection rates for different SNRs as in (17).
The first is a simulation of the operation of . Assuming that the noise following a Gaussian distribution satisfies and the system requires a detection rate of 96%, the of ADS-B receivers with different sensitivities can be calculated using (18) (as drawn in Figure 4).
Figure 4 shows that when the receiver sensitivity is -102 dBm, the result of calculating the is
According to (23), the relationship between the SNR and the detection rate can be expressed as where and . This means that a receiver with a sensitivity of -102 dBm can achieve a detection rate of 96% by setting a threshold of . This section will subsequently default the ADS-B receiver sensitivity to -102 dBm. Based on the above, the SEI can be obtained according to decision 1 in step 1 of Section 3.2, as shown in Figure 5.
In Figure 5, the solid blue line depicts the cumulative energy of the signal in (14). The purple pentagram is the cumulative energy assuming only noise, which can be used as a reference.
is indicated by the yellow line. Last, the orange dashed line depicts the SEI generated by the judgment of (15), which is the resulting set when is greater than .
Then, the verification process of the detection rate of this is described. A Monte Carlo experiment was set up using MATLAB to verify the synchronization performance of the system under different SNRs. Based on the analysis in Section 2.1, ten thousand pieces of data were generated randomly when the SNRs satisfied . The detection rates resulting from this method processing for are shown in Figure 6.
The blue line in Figure 6 represents the detection rates using the proposed method to process random data, and the red represents the theoretical one. The results justify the following conclusions. First, the detection rate reaches 95.98% when the SNR of the received signal is 0.479 dB. This result is almost consistent with (24). Secondly, the detection rates are all higher than 96% when the SNRs are higher than 0.479 dB and even reach 100% after the SNRs are higher than 3.479 dB. This proves that this method meets the requirement of high detection rate for satellite-based ADS-B systems. Thirdly, the processing results for signals with SNRs higher than 0.479 dB match the theory, but their results for signals with lower SNRs are worse than the theoretical values. This means that setting is well suited for receivers with a sensitivity of -102 dBm, while this parameter can be adjusted to apply to receivers with higher sensitivities. This also demonstrates the necessary study of the correlation between the in this method and the sensitivity of the satellite-based ADS-B receiver.
4.2. Simulation and Verification of the Soft Decision Step
The power of the receiving signals is different because the satellite-based ADS-B system has different coverage. Furthermore, the decision 1 leads to false alarms due to the effect of noise. The minimum value of the in (19) determines the false alarm rate, while its maximum value determines the maximum dynamic range of the signals that can be processed. This section will focus on verifying the robustness of the soft decision for processing signals with different dynamic ranges. The low false alarm rate will be verified in Section 4.4. The SEI may still satisfy (19) when two signals with high and low powers are adjacent to each other and their head-to-tail distance is less than the filter length. This phenomenon indicates the presence of more than one signal in this SEI (only the presence of two signals is considered here), as shown in Figure 7.
For the six signals shown in Figure 7, the signal powers are -95 dBm, -98 dBm, -95 dBm, -100 dBm, -95 dBm, and -102 dBm. The signals with powers of -95 dBm and -98 dBm are located in the same SEI, which is typical of those that need to be processed by step 2. We make the following assumptions. The system sensitivity is the minimum power , and the maximum power of the signal that can be processed can be represented by the dynamic range . The linear system is set up so that (25) is satisfied. where and are the powers of the baseband signals with RF signal powers and , respectively.
We provide an example in Figure 8 to verify the effect of the . Assume that the received RF signals are at powers of dBm (left) and dBm (right), that the time interval between them is μs, and that the noise conforming to the Gaussian distribution satisfies , as shown in Figure 8(a). Since this interval is less than the length of the filter (1200 bits), these signals are often judged by (15) to be in the same SEI, as shown in Figure 8(c).
In Figure 8, since is the starting point for the convolution energy of the signal and the filter in (13), it is noted as the coordinate origin. Point and point are used to assist in completing the signal separation. Point and point represent the intersections of the convolution energy and the threshold , which also denote the start and end points of the . Therefore, we establish the following equation: where and are the horizontal coordinates of these two points, which also represent the distance the filter moves. The and are the baseband powers of the received signals, which can be expressed in terms of the SNR as and , where . Then, μs is the period length of the filter. When , the derived from the first equation in (26) are listed in Table 3.
Assume that in (26) is set to zero, which is the limit of the soft decision; otherwise, the problem will turn into a solution interleaving. The and corresponding to signals of different received powers can be calculated using
Furthermore, according to (19), we obtain
Combining (27) and (28) yields
Assume that the minimum power of the received RF signal is -102 dBm and the maximum power is -95 dBm. By combining Table 3 and (29), we can obtain
Of course, if there is a requirement to process signals with a greater dynamic range, turning down the can make this method applicable. This is one of the advantages of the proposed method when applied according to the above scenario.
4.3. Simulation and Verification of the Adaptive Interval Output
According to the description of step 3 in Section 3, applying the adaptive interval derived based on the statistical detection criteria can reduce the computational effort because the length of the coarse synchronization interval output can be adjusted. The following two tasks will be done in this section. The first is to model the mapping relationship between the SNR and the adaptive interval output, which leads to the results in Table 2 in step 3 of Section 3.2. The second is to compare the effect on resource consumption before and after using the adaptive interval output through simulation experiments.
The first task reflects that the lengths of the adaptive output intervals differ under different SNRs. The model is built as follows. First 10,000 signal pieces are randomly generated of these seven SNR points (-2 to 4 dB with 1 dB step) using the Monte Carlo method. Then, the value of each signal in the SSEI is determined for further use according to the method described in Section 3.2. Most critically, after continuously calculating the absolute distance () of each signal between the and the known actual leading code position, the probability distribution of the at each SNR point is statistically determined. Finally, the probability distributions of for 10,000 signals at each SNR point are statistically shown in Figure 9. These probability statistic results also imply that the probabilities of falling within the output interval of these SNRs should also satisfy the requirements of this method when the detection rate of the system is sufficiently high. Therefore, this probabilistic model is also called the “mapping of the SNR to the coarse synchronization interval output when the detection rate is satisfied.”
The horizontal coordinate in Figure 9 indicates the absolute distance of the from the actual preamble position, and the vertical coordinate represents the probability that falls within the range centered on the actual preamble with as the radius. The orange line shows that if the required detection rate is 96% at a SNR of 1 dB, the corresponding horizontal coordinate should be 35, which is the radius of the adaptive interval output of the coarse synchronization process. If the number of Monte Carlo experiments is sufficiently large, the curve is smoothed, and the test results are closer to the theoretical values. The corresponding of the adaptive output interval derived under different SNRs at a detection rate of 96% are shown in Table 4.
The second task is to compare the resources consumed before and after the application of the above results. The five signals from 0 dB to 5 dB are generated separately based on MATLAB, and the effect achieved by step 3 is shown visually in Figure 10.
The orange lines in Figure 10 represent the derived without any adaptive adjustment, and the black lines represent the coarse synchronization interval outputs . As can be seen, the using of adaptive intervals significantly reduces the coarse synchronization output. An example will be given below to quantify the amounts of resources saved.
A Monte Carlo experiment was used to randomly generate 10,000 signals with the received signal power of -102 dBm. At first, after processing using step 1 and step 2 described in Section 3.2, the probability distribution of the lengths of the SSEI was statistically calculated, as shown in Figure 11. The statistical average of these SSEI lengths is denoted as . Finally, the coarse synchronization adaptive interval outputs are obtained using step 3. Comparatively, the probability distributions of these interval outputs were counted, and the results are presented in Table 5. The statistical average of these lengths can be calculated using
Combining the above statistics, the average lengths of the interval outputs before and after adaptive adjustment are 144 and 850, respectively. These results indicate that the application of step 3 reduces the computational burden by about 83.1% at a received RF signal power of -102 dBm, which is critical for resource-limited satellite systems.
4.4. Comparative Experiments and Results
Since several parameters of this method have been verified above, this section will compare the performances with reference to Table 1. Specifically, the first is the comparison of detection rate, the second is the comparison of resource consumption, and the third is the comparison of false alarm rate at the SNR for effective operation of the satellite-based ADS-B system. These comparison experiments will be performed based on the simulation conditions detailed below. Firstly, assuming that the powers of the received RF signals range from -102 dBm to -95 dBm, so the SNRs of the baseband signals obtained according to Section 2.1 range from 0.479 to 7.479 dB. Then, 10,000 baseband ADS-B signals are randomly and separately generated using the Monte Carlo method at each of these eight SNR points (0.479 to 7.479 dB with 1 dB step). Finally, these packets are used as homologous data for the comparison experiments described below.
The first is a comparison of the detection rates for each method. A detection rate of 96% is the requirement for the satellite-based ADS-B system to be popularized. The detection rates of these signals were obtained separately using different experimental methods, such as four-pulse detection [10], multicriterion detection [12], coherent detection [14], and the proposed dual-hierarchy synchronization method. The results of these experiments are shown in Figure 12.
In Figure 12, the blue line represents the detection rates derived using the dual-hierarchy synchronization method. These detection rates were above 96% when the powers of the received RF signals were no less than -102 dBm. The green line shows the results of the four-pulse detection method [10] in a ground-based system, and the purple line represents the results of the multicriterion detection method developed by Ren et al. The detection rates of these two methods are both less than 96% when the powers of the received RF signals range from -102 dBm to -95 dBm [12]. The orange line represents the results of the coherent detection method proposed by Delovski et al. [14]. The detection rates of this method are similar to the results of our proposed method.
Then, the resource consumption should be compared due to the limited on-star resources. As presented in Section 1, the coherent detection in [14] was accomplished using a sampling frequency of 105 MHz for 112 data bits. Compared to other methods with sampling frequencies of 10 MHz, 12.5 MHz, and 18 MHz, this method consumes extremely large amounts of resources. Moreover, step 3 of our method reduces the resource consumption even further. Therefore, the coherent detection, which uses a lot of hardware resources in exchange for high detection rates, is not suitable for satellite-based ADS-B systems.
Finally, the suitability of the dual-hierarchy synchronization method for satellite-based ADS-B systems was assessed by determining whether its false alarm rate was acceptable. The detection rate of the method [12] using CFAR fails, although its false alarm rate is acceptable. The coherent detection [14], which does not have the false alarm rate taken into account, is defective. Therefore, using the homologous data described above, Figure 13 shows the false alarm rates for the literature [10, 13] and the proposed method.
The green and orange lines in Figure 13 represent the false alarm rates obtained by the methods of literature [10, 13], respectively. The blue line represents the false alarm rates obtained by the method proposed in this paper. Clearly, the results of our method are more satisfactory, with lower false alarm rates at low SNRs and near-zero false alarm rates at higher SNRs. This effect is accepted by satellite-based ADS-B systems.
In summary, only the dual-hierarchy synchronization method achieves such a comprehensive performance, which uses limited resources to achieve a detection rate of 96% with an acceptable false alarm rate at an extremely low SNR.
5. Conclusions
In this work, the SNR analysis for the baseband signal of the satellite-based ADS-B system in Section 2 is also applicable to satellites at other orbital altitudes. This section clarifies that the extremely low SNR is one of the difficulties in the synchronization of satellite-based ADS-B signal preambles. Another dilemma is the apparently limited on-star resources.
It is a challenge to achieve a high detection rate and a low false alarm rate with these two dilemmas.
Notably, the presented dual-hierarchy synchronization method can satisfy the detection rate requirements for signal preambles with limited resources at extremely low SNR. This cannot be achieved without the role of several important steps in Section 3.2. The proposed in step 1 guarantees high detection rates at low SNRs, while providing value for strong applicability, and these results are verified in Section 4.1 and the first points of Section 4.4. The soft decision in step 2 guarantees low false alarm rates and can robustly handle signals with a high dynamic range. These results are verified in Section 4.2 and point 3 of Section 4.4. The use of a low sampling frequency and the mapping relations of step 3 both save on-star resources in varying degrees. These are demonstrated in Section 4.3 and the second part of Section 4.4, respectively. In summary, it is remarkable that this method achieves high detection rates and acceptable false alarm rates at extremely low SNRs with limited on-star resources, with such a comprehensive performance.
In addition, the proposed method utilizes only signal amplitude information and not signal phase information, allowing this method to avoid being affected by the Doppler frequency bias caused by high-speed satellite movements. However, if this phase information was effectively used for the coherent processing of the satellite-based ADS-B, it would improve the SNR of the baseband signal by 3 dB, and this would subsequently increase the probability of successful decoding the satellite-based ADS-B signal. Therefore, determining how to effectively use the phase information contained in satellite-based ADS-B signals is another likely area of improvement.
Data Availability
The data presented in this study are available on request from the corresponding author.
Conflicts of Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
This work is supported by the Ministry of Industry and Information Technology (No. 23100002022102001).