Efficient Methods for Time Synchronization in Distributed Radar Systems Damodarin Udhaya Mugil1 , Federico Di Girolamo1 and Samuele Tanzini1 1 Department of Electronic Engineering, Tor Vergata University of Rome, 00133 Rome, Italy Abstract Recently, the push to develop high-performance antenna arrays for space applications has underscored the economic and technical constraints associated with satellite missions. One cost-reducing strategy involves deploying a swarm of smaller, lighter satellites, though this approach introduces synchronization complexities. This paper evaluates two time synchronization techniques for distributed radar systems: the Two Way Time Transfer (TWTT) based Inter-Satellite Link (ISL) method and a Phase-Locked Loop (PLL) based method. The TWTT method utilizes Time Division Multiple Access (TDMA) for signal exchange among satellites, ensuring time alignment via delay filters. Conversely, the PLL method involves a primary satellite transmitting a reference signal to secondary satellites, which then recover the clock signal. Both techniques are analyzed for their implementation feasibility and effectiveness in maintaining synchronization, with simulation results demonstrating their potential in improving satellite communication performance. Keywords Time synchronization, distributed radar systems, satellite swarm, Two Way Time Transfer (TWTT), Inter-Satellite Link (ISL), Phase-Locked Loop (PLL). 1. Introduction 2. TWTT Based ISL Link Method In recent years, a new technical trend has been spread- The TWTT Based ISL Link is a Method used to reach the ing throughout the world. The objective is to develop time synchronization between sensors in a multistatic increasingly high-performance antenna arrays for space system. The basic idea is to broadcast signal flight times applications from both a technological and an applica- and offset delays among various local oscillators informa- tional point of view. The greatest economic impact of tion between nodes and exploit this information to align each mission is established by the weight of the launcher the flow of transmitted or received data with true delay and the payload; therefore, implementation constraints filters. The ISL is performed using a Time Division Multi- are often also established to find the optimal compromise ple Access (TDMA) method: to each node is assigned the between weight and technology [1] used to perform the time intervals to listen to and transmit data within the satellite or to improve its performance [2]. A possible formationas as reported in [11] and [12], for which the solution to reduce satellite launch costs is to use a satel- implemented software has been refactored accordignly lite swarm [3, 4] composed of many smaller and lighter [13]. In order to carry out the TDMA technique and to satellites [5]. Although the implementation of these sys- ensure that the time intervals will be respected, all nodes tems has the advantage of decreasing launch costs, they must first achieve coarse synchronization. This can be have the disadvantage of complexity of synchronization achieved by using a highly stable frequency source and [6, 7, 8, 9, 10]. In this paper, two different synchronization GPS pulse-per-second (PPS) tamed crystal oscillator. techniques are analyzed. The first one is based on a direct To achieve fine synchronization, the i-th node must first Inter-Satellite link (ISL) using Two Way Time Transfer broadcast a chirp signal, denoted as 𝑠𝑖 (πœπ‘– ), which is mod- (TWTT), and the second is based on the transmission ulated on a carrier of frequency 𝑓𝑐 and phase 𝛾𝑖𝑑π‘₯ : of a reference signal from a primary to one or multiple 𝑑π‘₯ secondary that recover the clock with a PLL. 𝑀𝑖 (πœπ‘– ) = 𝑠𝑖 (πœπ‘– ) Β· π‘’βˆ’π‘—2πœ‹π‘“π‘ (πœπ‘– ) Β· 𝑒𝑗𝛾𝑖 We can represent the signal received by the j-th sensor at a certain distance and sampled at 𝑓𝑠 as: [οΈ‚ (οΈ‚ )οΈ‚]οΈ‚ 𝑅𝑖,𝑗 𝑅𝑖,𝑗 err π‘Ÿπ‘–,𝑗 [𝑛] = 𝑠𝑗 𝑛 βˆ’ 𝑓𝑠 πœ™π‘– βˆ’ πœ™π‘— + π‘’βˆ’π‘—2πœ‹π‘“π‘ (πœ™π‘– βˆ’πœ™π‘— + 𝑐 ) 𝑒𝑗𝛾𝑖,𝑗 𝑐 ICYRIME 2024: 9th International Conference of Yearly Reports on Informatics, Mathematics, and Engineering. Catania, July 29-August To compute the time of arrival (and thus the delay time) 1, 2024 during reception, it is necessary to perform the following $ Udhaya.Mugil.Damodarin@uniroma2.it (D. U. Mugil); federico.digirolamo@alumni.uniroma2.eu (F. D. Girolamo); correlation: samuele.tanzini@alumni.uniroma2.eu (S. Tanzini) Β© 2024 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0). 𝑑𝑖,𝑗 (πœπ‘– ) = π‘Ÿπ‘–,𝑗 (πœπ‘– ) * 𝑠*𝑗 (βˆ’πœπ‘– ) 47 CEUR ceur-ws.org Workshop ISSN 1613-0073 Proceedings Damodarin Udhaya Mugil et al. CEUR Workshop Proceedings 47–52 Figure 1: Simulink block diagram of sensor Rx section. The maximum of this convolution correspond to the delay In this study, the classic Quadratic Least Squares method value associated with the clock temporal delays and the was used because it was found to have acceptable perfor- time of flight (TOF). mance as shown in [14]: 𝑦2 βˆ’ 𝑦0 π‘‘π‘π‘˜:𝑖,𝑗 = π‘Žπ‘Ÿπ‘”π‘šπ‘Žπ‘₯πœπ‘– |𝑑𝑖,𝑗 (πœπ‘– )| ˜ π‘π‘˜ = π‘›π‘π‘˜ βˆ’ 𝑛 2𝑦0 βˆ’ 4𝑦1 + 2𝑦2 = πœ™π‘– βˆ’ πœ™π‘— + 𝑇 𝑂𝐹𝑖,𝑗 2.2. Simulation results Once the time corresponding to the peak of the correla- tion has been found, the sample corresponding to this During the simulation, the correlation peaks initially time can be determined using the sampling frequency 𝑓𝑠 : appear separated because the average value of the pre- transmission shift has not yet been processed. These π‘›π‘π‘˜:𝑖,𝑗 = 𝑓𝑠 Β· π‘‘π‘π‘˜π‘– ,𝑗 peak separations indicate the delay of different transmis- sion epochs (Fig. 3). This delay prevents synchronous transmission, making the system unusable. Subsequently, 2.1. Simulation model synchronization epochs will be performed to observe The core issue is not the implementation of BPSK or how the peaks’ distances converge, as shown in Fig. 2.2. QPSK encoding, but the conversion of arrival times into This algorithm is continuously iterated so that the chirps information suitable for use as a modulating signal for overlap as much as possible. Only in this way can we transmission. The chosen method involves converting compensate for delays caused by temporal clock drifts these temporal values into voltage levels, which could be among the various nodes. utilized with an encoder before transmission. The proposed Rx architecture is shown in Fig. 1. Fol- In Fig. 2, the iteration of the algorithm throughout the en- lowing the correlation using the matched filter, there is a tire working period is shown; it is clear that it is possible comparison process aimed at resetting a set/reset counter to correct a few tenths of a sample. in free-counting mode. The counter continues to count indefinitely until reset by an external signal correspond- ing to the correlation peak. The conversion to amplitude 3. PLL Based ISL Method was achieved by implementing a memory that contains various delay values in terms of samples. This memory The second method analyzed is an implementation of is scanned by the previously introduced counter, and a PLL based architecture [15, 16, 17]. This architecture through the "hit" signal generated by the counter itself, has a primary sensor and 𝑛 secondary sensors; each sec- it becomes possible to sample the time value as ampli- ondary sensor receives a wave from the primary and tude. While in Simulink the transmission and reception synchronizes its clock on it. When all clocks are syn- process was simulated, in Matlab the iterative true peak chronized each node will be in phase depending on the detection algorithm was employed. This iterative process distance from the primary sensor [18, 19]. generates πœ™ Λ† 𝑖 at each step, which will be applied to dif- ferent chirps before transmission. The goal is to achieve 3.1. Simulation model perfect synchronization by aligning all signals ideally; The simulated PLL transfer function, responsible for en- where: 1 βˆ‘οΈ gaging the phase of the signal transmitted by the primary πœ™ ˆ𝑖 = Φ̂𝑖,𝑗 sensor, is: 𝑁 𝑗 1 + 𝑠8.1 Β· 10βˆ’ 3 7 𝐺0 (𝑠) = 5.78 10 𝑠2 48 Damodarin Udhaya Mugil et al. CEUR Workshop Proceedings 47–52 Figure 3: Iteration 1 Figure 2: Algorithm convergence. After a period of synchronization, the primary and sec- ondary nodes have the same clock time. In this work, Figure 4: Iteration 3 we used a carrier wave of 1 𝐺𝐻𝑧 modulated with a 1.5 𝑀 𝐻𝑧 sinusoidal wave. After clock synchronization, the next step is to synchro- nize the phases of the waveforms. This is important be- cause in relation to the distance from the primary sensor, all nodes must create a beam with constructive interfer- ence on the target. The formula used to adjust the phase contribution is [15]: 𝑑 πœ‘π‘Žπ‘‘π‘— (πœƒ) = 2πœ‹ [1 βˆ’ sin(πœƒ)] πœ†π‘…πΉ The simulated system is composed by 2 nodes, a block Figure 5: Iteration 6 that simulates an instantaneous phase noise, and the phase shift blocks, which are controlled by a high pre- cision ranging system [18]. In fig.7 the PLL structure is shown while the complete system is shown in fig.8. 3.2. Simulation results In the final step, we assessed the nodes’ performance by comparing the outputs of the phase shifters with the inputs. In Fig.9 and 10 we note that the system converges across all distances tested and remains resistant to small Figure 6: Iteration 8 phase disturbances. Method" we have the opportunity to develop both soft- 4. Conclusions ware, to face any implementation challenges, and hard- In this work, two different methods have been analyzed; ware, to speed up algorithm processing. This algorithm after the implementation study and the simulation results convergence is ensured mathematically, indeed, it is well- we are able to determinate the advantages and disadvan- known that the arithmetic mean can influence a set of tages for both paths taken. The "TWTT Based ISL Link data, improving its precision as well. A problem could 49 Damodarin Udhaya Mugil et al. CEUR Workshop Proceedings 47–52 Figure 7: PLL block diagram. Figure 8: Complete system be the rising of complexity in defining a communication neural approaches will be explored [20, 21, 22] protocol with increasingly large system. For the "PLL Based ISL Method" we are able to perform beamforming without DSP, which is an worth implementation sem- References plification, but we need an high precision measurement [1] L. M. Marrero, J. C. Merlano-Duncan, J. Querol, system in 𝑋 or π‘Š band which could be difficult in ISL S. Kumar, J. Krivochiza, S. K. Sharma, S. Chatzinotas, systems. A. Camps, B. Ottersten, Architectures and synchro- In future works, new optimization methods based on 50 Damodarin Udhaya Mugil et al. CEUR Workshop Proceedings 47–52 Figure 9: 40/50 m distance Figure 10: 10/50 m distance nization techniques for distributed satellite systems: Information Technology (NMITCON), 2023, pp. 1–6. A survey, IEEE access 10 (2022) 45375–45409. doi:10.1109/NMITCON58196.2023.10276347. [2] R. Giuliano, E. Innocenti, F. Mazzenga, A. Vizzarri, [3] D. PoΕ‚ap, M. WoΕΊniak, C. Napoli, E. Tramontana, L. Di Nunzio, P. B. Divakarachari, I. Habib, Trans- R. DamaΕ‘evičius, Is the colony of ants able to rec- former neural network for throughput improve- ognize graphic objects?, Communications in Com- ment in non-terrestrial networks, in: 2023 Inter- puter and Information Science 538 (2015) 376 – 387. national Conference on Network, Multimedia and doi:10.1007/978-3-319-24770-0_33. 51 Damodarin Udhaya Mugil et al. CEUR Workshop Proceedings 47–52 [4] C. Napoli, G. Pappalardo, E. Tramontana, Z. Marsza- ultrawideband software-defined radar networks, lek, D. Polap, M. Wozniak, Simplified firefly algo- IEEE Transactions on Microwave Theory and Tech- rithm for 2d image key-points search, in: IEEE SSCI niques 68 (2020) 4787–4804. 2014 - 2014 IEEE Symposium Series on Computa- [15] R. L. Schmid, T. M. Comberiate, J. E. Hodkin, J. A. tional Intelligence - CIHLI 2014: 2014 IEEE Sym- Nanzer, A distributed rf transmitter using one- posium on Computational Intelligence for Human- way wireless clock transfer, IEEE Microwave and Like Intelligence, Proceedings, 2014. doi:10.1109/ Wireless Components Letters 27 (2017) 195–197. CIHLI.2014.7013395. doi:10.1109/LMWC.2017.2648510. [5] D. Tuzi, T. Delamotte, A. Knopp, Satellite swarm- [16] I. E. Tibermacine, A. Tibermacine, W. Guettala, based antenna arrays for 6g direct-to-cell connec- C. Napoli, S. Russo, Enhancing sentiment anal- tivity, IEEE Access (2023). ysis on seed-iv dataset with vision transformers: [6] G. Borowik, M. WoΕΊniak, A. Fornaia, R. Giunta, A comparative study, in: ACM International C. Napoli, G. Pappalardo, E. Tramontana, A soft- Conference Proceeding Series, 2023, p. 238 – 246. ware architecture assisting workflow executions doi:10.1145/3638985.3639024. on cloud resources, International Journal of Elec- [17] F. Fiani, S. Russo, C. Napoli, An advanced solu- tronics and Telecommunications 61 (2015) 17 – 23. tion based on machine learning for remote emdr doi:10.1515/eletel-2015-0002. therapy, Technologies 11 (2023). doi:10.3390/ [7] C. Napoli, G. Pappalardo, E. Tramontana, A hy- technologies11060172. brid neuro-wavelet predictor for qos control and [18] J. E. Hodkin, K. S. Zilevu, M. D. Sharp, T. M. stability, in: Lecture Notes in Computer Sci- Comberiate, S. M. Hendrickson, M. J. Fitch, J. A. ence (including subseries Lecture Notes in Arti- Nanzer, Microwave and millimeter-wave rang- ficial Intelligence and Lecture Notes in Bioinfor- ing for coherent distributed rf systems, in: 2015 matics), volume 8249 LNAI, 2013, p. 527 – 538. IEEE Aerospace Conference, 2015, pp. 1–7. doi:10. doi:10.1007/978-3-319-03524-6_45. 1109/AERO.2015.7118937. [8] E. Iacobelli, S. Russo, C. Napoli, A machine learning [19] E. Iacobelli, V. Ponzi, S. Russo, C. Napoli, Eye- based real-time application for engagement detec- tracking system with low-end hardware: Devel- tion, in: CEUR Workshop Proceedings, volume opment and evaluation, Information (Switzerland) 3695, 2023, p. 75 – 84. 14 (2023). doi:10.3390/info14120644. [9] C. Napoli, G. Pappalardo, E. Tramontana, Improv- [20] G. Lo Sciuto, G. Capizzi, R. Shikler, C. Napoli, Or- ing files availability for bittorrent using a diffu- ganic solar cells defects classification by using a sion model, in: Proceedings of the Workshop on new feature extraction algorithm and an ebnn with Enabling Technologies: Infrastructure for Collab- an innovative pruning algorithm, International orative Enterprises, WETICE, 2014, p. 191 – 196. Journal of Intelligent Systems 36 (2021) 2443–2464. doi:10.1109/WETICE.2014.65. [21] G. Lo Sciuto, G. Susi, G. Cammarata, G. Capizzi, A [10] D. PoΕ‚ap, M. WoΕΊniak, C. Napoli, E. Tramontana, spiking neural network-based model for anaerobic Real-time cloud-based game management system digestion process, in: 2016 International Sympo- via cuckoo search algorithm, International Journal sium on Power Electronics, Electrical Drives, Au- of Electronics and Telecommunications 61 (2015) tomation and Motion (SPEEDAM), IEEE, 2016, pp. 333 – 338. doi:10.1515/eletel-2015-0043. 996–1003. [11] S. Niranjayan, A. F. Molisch, Ultra-wide bandwidth [22] G. Capizzi, G. Lo Sciuto, C. Napoli, E. Tramontana, timing networks, in: 2012 IEEE International Con- An advanced neural network based solution to en- ference on Ultra-Wideband, IEEE, 2012, pp. 51–56. force dispatch continuity in smart grids, Applied [12] M. Segura, S. Niranjayan, H. Hashemi, A. F. Soft Computing 62 (2018) 768–775. Molisch, Experimental demonstration of nanosecond-accuracy wireless network synchro- nization, in: 2015 IEEE International Conference on Communications (ICC), IEEE, 2015, pp. 6205–6210. [13] C. Napoli, G. Pappalardo, E. Tramontana, Using modularity metrics to assist move method refactor- ing of large systems, in: Proceedings - 2013 7th International Conference on Complex, Intelligent, and Software Intensive Systems, CISIS 2013, 2013, p. 529 – 534. doi:10.1109/CISIS.2013.96. [14] S. Prager, M. S. Haynes, M. Moghaddam, Wireless subnanosecond rf synchronization for distributed 52