# Microwave Ghost Imaging via LTE-DL Signals

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Microwave Ghost Imaging via LTE-DL Signals Ziqian Zhang∗ , Ruichen Luo† , Xiaopeng Wang‡ and Zihuai Lin§ ∗†‡§ School of Electrical and Information Engineering The University of Sydney, Sydney, N.S.W. 2006, Australia ∗ Email: ziqian.zhang@sydney.edu.au † Email: rui.luo@sydney.edu.au ‡ Email: xiaopeng.wang@sydney.edu.au § Email: zihuai.lin@sydney.edu.au Abstract—In this paper, we propose a long-term-evolution LTE-DL signal to perform microwave GI has been deduced. (LTE) downlink (DL) signal-based microwave ghost imaging (GI) Then a signal selection scheme is proposed to transform the scheme. Motivated by its waveform structures and base stations existing LTE communication system into a LTE-DL based (BSs) distributions, LTE-DL signals conventionally employed for microwave GI system. Numerical simulation results show that communication applications are transformed and adopted into the proposed scheme can effectively achieve the reconstruction the scenario of microwave GI. Numerical simulation validates that the proposed LTE-DL based microwave GI scheme can of objects. Since the requirement of the purposely deployment effectively obtain the reconstruction of objects. Since the proposed of transmitters and receivers is avoided, the microwave GI system takes the advantage of existing LTE BSs as its transceivers, system complexity and operational cost has been significantly microwave GI system complexity and operational cost have been reduced. To the best of our knowledge, this is the first time for significantly reduced. microwave GI to be implemented by non-purposely designed illuminating signals and sources. It is also the first time Keywords—Long-term-evolution (LTE), LTE-downlink (LTE- for LTE signals which are originally designed and used for DL) signals, microwave ghost imaging. communications to be applied in the scenario of microwave GI. I. I NTRODUCTION The remaining of this paper is organized as follows. In Microwave ghost imaging (GI) is originated from quantum Section II, the motivation about applying LTE-DL signals for and optical areas [1], [2], [3], [4], [5], [6]. Compared with microwave GI is presented, followed by a typical LTE-DL- conventional microwave imaging methods, it possesses some based GI scenario in Section III. In Section IV, the signal unique features such as nonlocal reconstruction [6], non- selection method is presented together with the reconstruction scanning [7], super-resolution [8], [9], etc. Besides, it also process of the proposed LTE-DL signal based microwave GI benefits from the penetration ability of microwave spectrum, system. Then in Section V, numerical simulation results are which enables microwave GI systems with a immunity towards shown to verify the effectiveness of the proposed scheme. weather and illumination conditions [9], as well as obstacles Finally in Section VI, some conclusion remarks are drawn. [10]. However, due to incoherent requirements of the illumina- tion fields, both signal waveforms and transmitter deployment II. M OTIVATION should be deliberately designed [11] in such a system. Thus, the system complexity and operational cost for previously Time-space incoherent fields are essential to both optical proposed microwave GI schemes [9], [10], [11] should be and microwave GI [17]. In order to satisfy this requirement, further reduced. signals that are used for illumination should (1) possess a randomly modulated waveform; (2) be orthogonal to each Long-term-evolution (LTE) is a representative technology other when waveforms are from different transmitters [11]. which is widely used in the fourth generation (4G) wireless Microwave GI systems previously discussed in the literature communication system [12]. LTE-downlink (LTE-DL) sig- are employing signals obtained from stochastic processes, such nals are orthogonal-frequency-division-multiplexing (OFDM) as Gaussian random processes [11] and nonlinear chaotic structured, with an operating frequency varying from 800MHz processes [18]. However, theses deliberately designed signals to 3.5GHz and a bandwidth upto 20MHz [13]. Although are not easy to be generated [9]. Thus the system complexity the LTE-DL signal is originally designed for communication and operational cost of conventional microwave GI schemes usage, it has been adopted into many other applications re- still need to be further optimized. cently. For example, due to deterministic features contained in the signal, it is proposed to perform range and Doppler Besides, waveforms that already exist in the environment estimation in [14], [15]. As another example, based on the also possess a similar random feature, especially for those forward scattering radar technique, it is also used for vehicle employed in mobile communications such as FDD-LTE and recognition in [16]. TDD-LTE in the 4G systems. Both FDD and TDD based LTE systems contain two independent links for data transfer, Motivated by its pseudo-random feature, we propose a namely the LTE-up-link (LTE-UL) and the LTE-DL. LTE-UL LTE-DL signal based microwave GI scheme in this paper. refer to the links from battery powered mobile devices to their Based on a further analysis of both the signal structure and individually associated BSs while LTE-DL are those links from distribution of LTE base stations (BSs), the feasibility of using BSs to mobile devices. In this paper, we only consider using

Radio frames BS BS One Radio frame = 10 ms BS OFDM Symbols Only Contain Scrambled Dat Objects BS Base Stations 0 1 2 4 5 6 . . . . . . . . . . 18 19 BS One Slot = 0.5 ms z BS B Subcarrier (Frequency) 0 1 2 3 4 5 6 y x One OFDM Symbol Fig. 2. A typical 3D scenario of the proposed LTE-based microwave GI Cyclic prefix OFDM Symbol Data scheme. Symbol time duration T Time period of OFDM symbol data Fig. 1. LTE-DL signal structure. 1 st CP OFDM Symbol Data CP OFDM Symbol Data 2 nd CP OFDM Symbol Data CP OFDM Symbol Data Delay LTE-DL signals as the illumination sources for microwave GI Last CP OFDM Symbol Data CP OFDM Symbol Data OFDM Symbols (Time) as BSs always have stable power supply. As illustrated in Fig. Time Useable time duration Useable time duration 1, a typical LTE-DL signal radio frame consists of 10 sub- frames. Each of the sub-frame lasts for 1ms. One sub-frame Fig. 3. LTE-DL signals time selection. can be further divided into 2 slots, while each slot contains 7 OFDM symbols for short cyclic prefix (CP). Data requested by mobile users are contained in those OFDM symbols together IV. T HE LTE-DL S IGNAL - BASED M ICROWAVE GI with other repeated signal elements for identification, channel estimation, synchronization, etc. In order to perform microwave GI by using LTE-DL signals, the illumination fields should satisfy the time-space In order to evenly distribute energy upon the carrier band independent requirement [17]. Since the generation of fields and decrease the error probability, users’ requested data is are characterised by both LTE-DL signals and the localizations processed by the scrambler before being passed to the OFDM of corresponding BSs, in this section, we mainly discuss the modulator. A scrambler is to convert the original input data into selection of LTE-DL signals and the distribution of BSs. a pseudo-random state to avoid long data sequences appear the same values. Denote scrambled data symbols in the kth subcarrier by Xk , k ∈ {1, 2, ..., K}, where K is the total A. LTE-DL Signal Selection number of sub-carriers, the resulting data part waveform can In order to generate the incoherent field for microwave GI, be written as, the signal source should be random [11]. However, due to K−1 the LTE-DL signal structure, the coherent components such as pilots and synchronization sequences containing in the signal X v(t) = Xk ej2π(fc +k∆f )t (1) will lead to the incoherence destruction of the illumination k=0 fields and the quality of reconstruction. Although the scram- where fc is the carrier frequency and ∆f is the subcarrier bling process introduces randomness in the generated LTE-DL spacing. signals, not all the OFDM symbols contain the scrambled data. For instance, the CP is a repetition of each OFDM symbol’s Apparently that since Xk is processed by the scrambler, the end. Obviously this repetition will decrease the randomness of generated waveform can be recognized as a randomly mod- the resulting time domain LTE-DL signals. Similarly, repetitive ulated signal. In addition, according to the LTE regulations, modulated signals contained in sub-frames, such as the syn- different scrambling sequences will be assigned to different chronization sequence [19], will also reduce the randomness. users in different BSs. In other words, signals transmitted by different BSs are orthogonal to each other. Consequently, the In order to ensure that the EM fields used for reconstruction condition of performing microwave GI is satisfied. only consist of the data part of LTE-DL signals, here we propose a signal selection method. As illustrated in Fig. 3, only OFDM symbols containing users data are considered while the III. S YSTEM M ODEL CP part should be avoided. This usable time duration can be A typical three-dimensional (3D) LTE-based microwave expressed as GI scenario is shown in Fig. 2. The investigation area B is inhomogeneous and contains several objects to be imaged. The objects in B are distinguished by their scattering coefficients τu = τdata − τmax (2) σ(ro ), ro ∈ B, where ro is a vector containing the locations where τdata is the time period of the OFDM symbol data, for all the objects in the area of B. The investigation area B τmax is maximum propagation delay from BSs to pixels on is under the illumination from LTE BSs whose locations are the imaging plane B. Assuming each OFDM symbol with the expressed as ri , i = 1, 2, ..., I, where I is the total number of scrambled data only has a time duration of T , then the window BSs. The deployment height from BSs to B are identical and period twindow suitable for microwave GI reconstruction can denoted as h. Signals transmitted from the ith BS is denoted be written as by Si . Reflected signals from objects are collected by a single receiving BS located in the centre of B. τmax + τCP < twindow < T (3)

TABLE I. PARAMETERS OF SIMULATION In other words, measurements should be conducted within the above window period, in order to obtain a high quality Parameters Settings reconstruction of objects. Frame Structure Type FDD-LTE-DL Bandwidth 20 MHz Central Frequency 2.6 GHz B. Distribution of Base Stations Number of Resource Blocks 100 Although the LTE BSs distributions are normally modelled Sub-carriers Spacing 15 KHz by placing the BS on a regular hexagonal lattice or a square CP Type Normal lattice in standard regulations [20], distribution of base stations Constellation Mapper 256-QAM is difficult to remain uniform in practice [21]. Instead, BSs Average ISD 50 m distribution is normally modelled as Poisson point process (PPP) with an intensity η, which can be written as, 1 2 η=( ) (4) 2dε where dε is the average inter-site distance (ISD). Consider the EM field on plane B under the illumination by the LTE BSs, (a) (b) I X E(∆x, t) = Si (t − τi,∆x )`i,∆x (5) i=1 where E(∆x, t) is the EM state of the single point ∆x on the imaging plane B, ∆x ∈ B, τi,∆x is the propagation delay from the ith signal transmitter to ∆x, and `i,∆x is the propagation attenuation. Apparently, the background EM field is not only affected by the illumination signal, but also determined by (c) (d) the propagation delay induced by the BSs distribution. Thus the spatial incoherence of the generated EM field can be further enhanced by the randomness introduced by the irregular Fig. 4. Normalized correlation results with and without proposed signal selection method. (a) Autocorrelation result of the original LTE-DL signal. propagation delays provided by non-uniform distributed BSs. (b) Autocorrelation result after the proposed method is applied. (c) Cross- correlation result of the original LTE-DL signal from different transmitters. (d) Cross-correlation result after the proposed method is applied. C. Image Reconstruction Assuming the imaging area B is divided into N pixels with P rows and Q columns, where N = P × Q. According to the where k · k22 represents for the square of the Euclidean norm, Born approximation [22], the overall imaging equation can be and [σo ] is the unknown optimization variable. For solving this expressed as optimization problem, algorithms such as gradient projection [y] = [E][σ][ρ] (6) [24], genetic algorithm [25], singular-value decomposition [26], and iteratively reweighted norm algorithm [27] can be where 1 used here. 1 1 E1,1 E2,1 . . . EP,Q 2 2 2 E1,1 E2,1 . . . EP,Q V. S IMULATION R ESULTS [E] = .. .. .. .. (7) . . . . In this section, numerical simulation results are presented N E1,1 N E2,1 N . . . EP,Q to validate the effectiveness of our proposed scheme. The investigation area B is set to be 420m×420m and discrete into sub-grids with a size of 10m×10m. The total number of [σ] = [σ1,1 , σ2,1 , ..., σP,Q ]T (8) BSs is 19 with a distance of h = 10m. The distribution of BSs [ρ] = diag[ρ1,1 , ρ2,1 , ..., ρP,Q ] (9) is configured according to the PPP model [21]. Other details of the simulation are listed in the Table I. [y] = [y1 , y2 , . . . , yN ]T (10) n Self-correlation of the LTE-DL signal and cross-correlation where Ep,q is the background EM field at the corresponding between LTE-DL signals transmitted by different BSs are eval- pixel in the nth measurement, σp,q the scattering coefficient, uated and as shown in Fig. 4. We can see from Fig. 4(a) that yn is the receiving signal from the nth illumination and ρp,q the original LTE-DL signal suffers greatly from the repeated is the propagation attenuation from the pixel to the receiver. signal elements, resulting in a series of significant side-lobes. Assuming ρp,q is known, then the image reconstruction of However, after the proposed signal selection method is applied the object can be achieved by solving the following convex to the LTE-DL signal, those side-lobes have been effectively optimization problem [23] compressed and the signal self-correlation level has been dramatically increased, as shown in Fig. 4(b). In addition, from minimize k[y] − [E][σo ][ρ]k22 (11) the result shown in Fig. 4(c) and (d) we can see that the cross-

400 is applied as a quantitive evaluation metric, the reconstruction Normalized Spatial Correlation 1 300 0.75 performance of the proposed LTE-based microwave GI is shown in Fig. 6(d). We can see that the proposed method is Y(m) 0.5 200 not sensitive to the signal-to-noise ratio (SNR) condition when 100 0.25 SNR is high but the MSE performance decreases dramatically 0 especially when SNR is lower than 5dB. 400 0 200 400 0 200 0 100 200 300 400 -200 0 -400 -200 -400 X(m) Y(m) X(m) VI. C ONCLUSION (a) (b) In this paper, we proposed a novel LTE-DL signal based microwave GI scheme. To the best of our knowledge, this Fig. 5. BSs distribution and spatial-correlation of the generated illumination is the first time for LTE-DL signals which are originally field. (a) PPP-based BSs distribution. (b) Spatial-correlation of the illumination designed for communication purposes to be adopted in the field. framework of microwave GI. It is also the first time for 0 0.5 1 0 0.5 1 microwave GI to be implemented by using signals and trans- mitters that originally designed for communication purpose. 400 400 Numerical simulation results showed that the proposed LTE- 300 300 DL signal based microwave GI scheme can effectively obtain the image of objects. Compared to conventional microwave GI, Y(m) Y(m) 200 200 the proposed method possesses a significantly reduced system complexity and operational cost, since the purposely deployed 100 100 signals and transceivers are avoided. 0 0 0 100 200 300 400 0 100 200 300 400 X(m) X(m) R EFERENCES (a) (b) [1] T. Pittman, Y. Shih, D. Strekalov, and A. Sergienko, “Optical imaging 0 0.5 1 by means of two-photon quantum entanglement,” Physical Review A, vol. 52, no. 5, p. R3429, 1995. 0.2 400 [2] J. Cheng and S. Han, “Incoherent coincidence imaging and its appli- cability in x-ray diffraction,” Physical review letters, vol. 92, no. 9, p. 0.15 300 093903, 2004. [3] G. Scarcelli, V. 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