# Method of Calculating Desynchronization of DVB-T Transmitters Working in SFN for PCL Applications
## 1 Introduction  
The idea of using non-cooperative transmitters as an illuminator of opportunity (IO) for a passive radar receiver is not a new one. The history of passive radar goes back to the 1930s, when [PERSON] made the first demonstration of this technology utilizing a BBC radio transmitter as an illuminator of opportunity [1]. The technology was further developed during World War II, when the Germans built a passive radar named Klein Heidelberg which used Chain Home British radars as illuminators of opportunity [1]. After the Second World War, passive radar had no major research interest until the 1990s due to the limited computing power available. Nowadays, after nearly three decades, passive radar technology is in a stage of maturity. It provides many applications, from air surveillance [2; 3; 4] to target imaging [5; 6], where different kinds of IOs are used, from commercial transmitters (e.g., FM radio, DAB, DVB-T, GSM, among others) [7] to utilize other radars as IOs [8]. Recently, DVB-T transmitters of opportunity became one of the most frequently used as IOs for passive coherent localization (PCL) systems [9; 10; 7; 11], as they are characterized by relatively wide bandwidth (8 MHz) and relatively high power transmitters, which allows for medium range operation up to 100 km with a bistatic range resolution of ca. 36 m [7]. DVB-T can operate in multi-frequency network (MFN) or single frequency network (SFN) configurations. One of the problems of an SFN in passive radars is ghost targets. This phenomenon is a result of the number of signal copies acquired by a single receiver. There are several scientific works in the literature that focus on problems of passive localization systems utilizing SFNs [9; 12; 13]. A common assumption in most of these works is that SFN transmitters are time-synchronized. In reality, this condition is almost never fulfilled. Most commercial SFN transmitters experience a time shift between each other by design [14]. This fact seems unexplored by passive radar studies, therefore no attempts to cope with it were made. This is unfortunate because SFN desynchronization may introduce major errors in passive radar target localization. The authors of this article recognize a gap in passive radar signal processing studies, and propose a novel method ofcalculating the time shift between transmitters to compensate for this desynchronization, which might be used in passive radar signal processing to correct target localization error. In previous publications [15], the authors described a low-cost system designed and developed to localize any source of a signal (an emitter) which might be used for the localization of transmitters of opportunity within the area of passive radar operations. Based on the results of this work, further analysis was made. While positioning a chosen DVB-T transmitter, additional detections occurred through using Time Difference of Arrival (TDoA) techniques. It was discovered that there were two transmitters broadcasting in the SFN, and additional detections were caused both by another transmitter working in the SFN, and the correlation byproduct of two transmitters. In this article, an analysis of the origin of all the detections is made. Furthermore, the impact of transmitter desynchronization on these detections is explored. Finally, a novel method of calculating the desynchronization between transmitters working in an SFN based on detected TDoA peak positions is presented. The authors believe that this method is a solid addition to any passive radar operating in an SFN, and will be a triggering factor for further studies of the impact of SFN transmitter desynchronization on PCL applications. In the second chapter of this article, passive radar geometry is described. The third chapter provides a brief description of an SFN. In the next chapter, the problem of localizing transmitters used in passive radars is formulated. The next two chapters provide a concise explanation of TDoA. In the seventh chapter, the experiment scenario and setup are presented.