# Passive Location for 5G OFDM Radiation Sources Based on Virtual Synthetic Aperture
## 1 Introduction
Orthogonal frequency-division multiplexing (OFDM) is an efficient multi-carrier transmission technology, which first appeared in the field of digital communication. The OFDM multi-carrier signal has the advantages of flexibility, large bandwidth, and good orthogonal characteristics, which are an important signal form of 5G communication. In addition to the universal passive localization method, there are several passive location methods specific to OFDM signals. Reference [19] proposes a DPD method based on the MLE for OFDM signals, and Reference [20] derives the least squares estimator (LSE) algorithm. Reference [21] constructs an optimization model based on the maximum likelihood estimator and the multi-carrier technology of OFDM signals and proposes a DPD method based on the spectrum. The DPD methods for OFDM signals have the same difficulty as the DPD methods for other signals. Article [22] introduced the long synthetic aperture technology into direct location. Article [23] analyzes the range resolution, azimuth resolution, and sensitivity of the algorithm. Compared with other passive location algorithms, the difference is that the range and azimuth distance between the radiation source and the satellite is used to replace the description of the location of the radiation source which can obtain the analytic solution of the radiation source, and the coherent accumulation of long-term data is used to obtain the high-precision location. However, the articles only introduce the algorithm for simple signal forms like the single-frequency signal or simple modulated single-frequency signal. On this basis, this paper proposes a passive location method based on a virtual synthetic aperture for OFDM signals, which uses long-term coherent data to synthesize a large virtual antenna azimuth aperture to improve the location precision. The paper utilizes the multi-carrier modulation technology of OFDM signals and the pilot technology of the communication systems to extract carrier phase information and compensate phase, obtaining the carrier Doppler signal in the form of linear frequency modulation (LFM)signal. The range and azimuth location of the radiation source can be obtained by range searching and azimuth focusing. In addition, a noise elimination method based on channel estimation is proposed based on the signal transmission model. The paper also derives the range and azimuth resolution, and a simple analysis on the effect of satellite vibration is discussed in this paper. Simulation results verify the effectiveness of the algorithm and show that tit can realize high-precision location for the OFDM radiation sources. This paper is organized as follows. The signal model of OFDM signals and the principle of passive location based on the virtual synthetic aperture for OFDM signals is presented in Section 2. Azimuth resolution, range resolution, the satellite vibration effect and computation complexity of the proposed method are investigated in Section 3. Simulation results are given in Section 4. Finally, the conclusion is drawn in Section 5. The notations related to this paper are shown in Table 1.