Vector Bundle Model of Complex Electromagnetic Space and Change Detection

Complex Electromagnetic Space (CEMS), which consists of physical space and the complex electromagnetic environment, plays an essential role in our daily life for supporting remote communication, wireless network, wide-range broadcast, etc. In CEMS, the electromagnetic activities might work differently from the ideal situation; the typical case is that undesired signal would disturb the echo of objects and overlap into it resulting in the mismatch of matched filter and the reduction of the probability of detection. The lacking mathematical description of CEMS resulting from the complexity of electromagnetic environment leads to the inappropriate design of detection method. Therefore, a mathematical model of CEMS is desired for integrating the electromagnetic signal in CEMS as a whole and considering the issues in CEMS accurately. This paper puts forward a geometric model of CEMS based on vector bundle, which is an abstract concept in differential geometry and proposes a geometric detector for change detection in CEMS under the geometric model. In the simulation, the proposed geometric detector was compared with energy detector and matched filter in two scenes: passive detection case and active detection case. The results show the proposed geometric detector is better than both energy detector and matched filter with 4∼5 dB improvements of SNR (signal-to-noise ratio) in two scenes.