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) downlink (DL) signal-based microwave ghost imaging (GI)scheme. Motivated by its waveform structures and base stations(BSs) distributions, LTE-DL signals conventionally employed forcommunication applications are transformed and adopted intothe scenario of microwave GI. Numerical simulation validatesthat the proposed LTE-DL based microwave GI scheme caneffectively obtain the reconstruction of objects. Since the proposedsystem takes the advantage of existing LTE BSs as its transceivers,microwave GI system complexity and operational cost have beensignificantly reduced.

Keywords—Long-term-evolution (LTE), LTE-downlink (LTE-DL) signals, microwave ghost imaging.

I. INTRODUCTION

Microwave ghost imaging (GI) is originated from quantumand optical areas [1], [2], [3], [4], [5], [6]. Compared withconventional microwave imaging methods, it possesses someunique features such as nonlocal reconstruction [6], non-scanning [7], super-resolution [8], [9], etc. Besides, it alsobenefits from the penetration ability of microwave spectrum,which enables microwave GI systems with a immunity towardsweather and illumination conditions [9], as well as obstacles[10]. However, due to incoherent requirements of the illumina-tion fields, both signal waveforms and transmitter deploymentshould be deliberately designed [11] in such a system. Thus,the system complexity and operational cost for previouslyproposed microwave GI schemes [9], [10], [11] should befurther reduced.

Long-term-evolution (LTE) is a representative technologywhich is widely used in the fourth generation (4G) wirelesscommunication system [12]. LTE-downlink (LTE-DL) sig-nals are orthogonal-frequency-division-multiplexing (OFDM)structured, with an operating frequency varying from 800MHzto 3.5GHz and a bandwidth upto 20MHz [13]. Althoughthe LTE-DL signal is originally designed for communicationusage, it has been adopted into many other applications re-cently. For example, due to deterministic features containedin the signal, it is proposed to perform range and Dopplerestimation in [14], [15]. As another example, based on theforward scattering radar technique, it is also used for vehiclerecognition in [16].

Motivated by its pseudo-random feature, we propose aLTE-DL signal based microwave GI scheme in this paper.Based on a further analysis of both the signal structure anddistribution of LTE base stations (BSs), the feasibility of using

LTE-DL signal to perform microwave GI has been deduced.Then a signal selection scheme is proposed to transform theexisting LTE communication system into a LTE-DL basedmicrowave GI system. Numerical simulation results show thatthe proposed scheme can effectively achieve the reconstructionof objects. Since the requirement of the purposely deploymentof transmitters and receivers is avoided, the microwave GIsystem complexity and operational cost has been significantlyreduced. To the best of our knowledge, this is the first time formicrowave GI to be implemented by non-purposely designedilluminating signals and sources. It is also the first timefor LTE signals which are originally designed and used forcommunications to be applied in the scenario of microwaveGI.

The remaining of this paper is organized as follows. InSection II, the motivation about applying LTE-DL signals formicrowave GI is presented, followed by a typical LTE-DL-based GI scenario in Section III. In Section IV, the signalselection method is presented together with the reconstructionprocess of the proposed LTE-DL signal based microwave GIsystem. Then in Section V, numerical simulation results areshown to verify the effectiveness of the proposed scheme.Finally in Section VI, some conclusion remarks are drawn.

II. MOTIVATION

Time-space incoherent fields are essential to both opticaland microwave GI [17]. In order to satisfy this requirement,signals that are used for illumination should (1) possess arandomly modulated waveform; (2) be orthogonal to eachother when waveforms are from different transmitters [11].Microwave GI systems previously discussed in the literatureare employing signals obtained from stochastic processes, suchas Gaussian random processes [11] and nonlinear chaoticprocesses [18]. However, theses deliberately designed signalsare not easy to be generated [9]. Thus the system complexityand operational cost of conventional microwave GI schemesstill need to be further optimized.

Besides, waveforms that already exist in the environmentalso possess a similar random feature, especially for thoseemployed in mobile communications such as FDD-LTE andTDD-LTE in the 4G systems. Both FDD and TDD basedLTE systems contain two independent links for data transfer,namely the LTE-up-link (LTE-UL) and the LTE-DL. LTE-ULrefer to the links from battery powered mobile devices to theirindividually associated BSs while LTE-DL are those links fromBSs to mobile devices. In this paper, we only consider using

One Radio frame = 10 ms Resource Element

Resource Block

One OFDM Symbol

OFDM Symbols (Time)

Subc

arrie

r (Fr

eque

ncy)

Cyclic PrefixCyclic Prefix

0 1 2 4 . . . . . . . . . . 18 195 60 1 2 4 . . . . . . . . . . 18 195 6

Cyclic prefix OFDM Symbol DataCyclic prefix OFDM Symbol Data

0 1 2 3 4 5 60 1 2 3 4 5 6

One Slot = 0.5 ms

One OFDM Symbol

Radio frames

OFDM Symbols Only Contain Scrambled Data

Fig. 1. LTE-DL signal structure.

LTE-DL signals as the illumination sources for microwave GIas BSs always have stable power supply. As illustrated in Fig.1, a typical LTE-DL signal radio frame consists of 10 sub-frames. Each of the sub-frame lasts for 1ms. One sub-framecan be further divided into 2 slots, while each slot contains 7OFDM symbols for short cyclic prefix (CP). Data requested bymobile users are contained in those OFDM symbols togetherwith other repeated signal elements for identification, channelestimation, synchronization, etc.

In order to evenly distribute energy upon the carrier bandand decrease the error probability, users’ requested data isprocessed by the scrambler before being passed to the OFDMmodulator. A scrambler is to convert the original input data intoa pseudo-random state to avoid long data sequences appearthe same values. Denote scrambled data symbols in the kthsubcarrier by Xk, k ∈ {1, 2, ...,K}, where K is the totalnumber of sub-carriers, the resulting data part waveform canbe written as,

v(t) =

K−1∑k=0

Xkej2π(fc+k∆f)t (1)

where fc is the carrier frequency and ∆f is the subcarrierspacing.

Apparently that since Xk is processed by the scrambler, thegenerated waveform can be recognized as a randomly mod-ulated signal. In addition, according to the LTE regulations,different scrambling sequences will be assigned to differentusers in different BSs. In other words, signals transmitted bydifferent BSs are orthogonal to each other. Consequently, thecondition of performing microwave GI is satisfied.

III. SYSTEM MODEL

A typical three-dimensional (3D) LTE-based microwaveGI scenario is shown in Fig. 2. The investigation area B isinhomogeneous and contains several objects to be imaged. Theobjects in B are distinguished by their scattering coefficientsσ(ro), ro ∈ B, where ro is a vector containing the locationsfor all the objects in the area of B. The investigation area Bis under the illumination from LTE BSs whose locations areexpressed as ri, i = 1, 2, ..., I , where I is the total number ofBSs. The deployment height from BSs to B are identical anddenoted as h. Signals transmitted from the ith BS is denotedby Si. Reflected signals from objects are collected by a singlereceiving BS located in the centre of B.

Base Stations

B

ObjectsBSBS

BSBS

BSBS

BSBS

BSBS

BSBS

xy

zxy

z

Fig. 2. A typical 3D scenario of the proposed LTE-based microwave GIscheme.

Time

st1nd2

Last

Useable time duration

CP OFDM Symbol DataCP OFDM Symbol Data OFDM Symbol DataCP OFDM Symbol DataCPCP OFDM Symbol Data OFDM Symbol DataCPDelay

CP OFDM Symbol DataCP OFDM Symbol Data OFDM Symbol DataCP OFDM Symbol DataCPCP OFDM Symbol Data OFDM Symbol DataCP

CP OFDM Symbol DataCP OFDM Symbol Data OFDM Symbol DataCP OFDM Symbol DataCPCP OFDM Symbol Data OFDM Symbol DataCP

Useable time duration

Symbol time duration T Time period of OFDM symbol data

Fig. 3. LTE-DL signals time selection.

IV. THE LTE-DL SIGNAL-BASED MICROWAVE GI

In order to perform microwave GI by using LTE-DLsignals, the illumination fields should satisfy the time-spaceindependent requirement [17]. Since the generation of fieldsare characterised by both LTE-DL signals and the localizationsof corresponding BSs, in this section, we mainly discuss theselection of LTE-DL signals and the distribution of BSs.

A. LTE-DL Signal Selection

In order to generate the incoherent field for microwave GI,the signal source should be random [11]. However, due tothe LTE-DL signal structure, the coherent components such aspilots and synchronization sequences containing in the signalwill lead to the incoherence destruction of the illuminationfields and the quality of reconstruction. Although the scram-bling process introduces randomness in the generated LTE-DLsignals, not all the OFDM symbols contain the scrambled data.For instance, the CP is a repetition of each OFDM symbol’send. Obviously this repetition will decrease the randomness ofthe resulting time domain LTE-DL signals. Similarly, repetitivemodulated signals contained in sub-frames, such as the syn-chronization sequence [19], will also reduce the randomness.

In order to ensure that the EM fields used for reconstructiononly consist of the data part of LTE-DL signals, here wepropose a signal selection method. As illustrated in Fig. 3, onlyOFDM symbols containing users data are considered while theCP part should be avoided. This usable time duration can beexpressed as

τu = τdata − τmax (2)

where τdata is the time period of the OFDM symbol data,τmax is maximum propagation delay from BSs to pixels onthe imaging plane B. Assuming each OFDM symbol with thescrambled data only has a time duration of T , then the windowperiod twindow suitable for microwave GI reconstruction canbe written as

τmax + τCP < twindow < T (3)

In other words, measurements should be conducted withinthe above window period, in order to obtain a high qualityreconstruction of objects.

B. Distribution of Base Stations

Although the LTE BSs distributions are normally modelledby placing the BS on a regular hexagonal lattice or a squarelattice in standard regulations [20], distribution of base stationsis difficult to remain uniform in practice [21]. Instead, BSsdistribution is normally modelled as Poisson point process(PPP) with an intensity η, which can be written as,

η = (1

2dε)2 (4)

where dε is the average inter-site distance (ISD).

Consider the EM field on plane B under the illuminationby the LTE BSs,

E(∆x, t) =I∑i=1

Si(t− τi,∆x)`i,∆x (5)

where E(∆x, t) is the EM state of the single point ∆x on theimaging plane B,∆x ∈ B, τi,∆x is the propagation delay fromthe ith signal transmitter to ∆x, and `i,∆x is the propagationattenuation. Apparently, the background EM field is not onlyaffected by the illumination signal, but also determined bythe propagation delay induced by the BSs distribution. Thusthe spatial incoherence of the generated EM field can befurther enhanced by the randomness introduced by the irregularpropagation delays provided by non-uniform distributed BSs.

C. Image Reconstruction

Assuming the imaging area B is divided into N pixels withP rows and Q columns, where N = P ×Q. According to theBorn approximation [22], the overall imaging equation can beexpressed as

[y] = [E][σ][ρ] (6)

where

[E] =

E1

1,1 E12,1 . . . E1

P,Q

E21,1 E2

2,1 . . . E2P,Q

......

. . ....

EN1,1 EN2,1 . . . ENP,Q

(7)

[σ] = [σ1,1, σ2,1, ..., σP,Q]T (8)[ρ] = diag[ρ1,1, ρ2,1, ..., ρP,Q] (9)[y] = [y1, y2, . . . , yN ]T (10)

where Enp,q is the background EM field at the correspondingpixel in the nth measurement, σp,q the scattering coefficient,yn is the receiving signal from the nth illumination and ρp,qis the propagation attenuation from the pixel to the receiver.

Assuming ρp,q is known, then the image reconstruction ofthe object can be achieved by solving the following convexoptimization problem [23]

minimize ‖[y]− [E][σo][ρ]‖22 (11)

TABLE I. PARAMETERS OF SIMULATION

Parameters Settings

Frame Structure Type FDD-LTE-DL

Bandwidth 20 MHz

Central Frequency 2.6 GHz

Number of Resource Blocks 100

Sub-carriers Spacing 15 KHz

CP Type Normal

Constellation Mapper 256-QAM

Average ISD 50 m

(a) (b)

(c) (d)

Fig. 4. Normalized correlation results with and without proposed signalselection method. (a) Autocorrelation result of the original LTE-DL signal.(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.

where ‖ · ‖22 represents for the square of the Euclidean norm,and [σo] is the unknown optimization variable. For solving thisoptimization problem, algorithms such as gradient projection[24], genetic algorithm [25], singular-value decomposition[26], and iteratively reweighted norm algorithm [27] can beused here.

V. SIMULATION RESULTS

In this section, numerical simulation results are presentedto validate the effectiveness of our proposed scheme. Theinvestigation area B is set to be 420m×420m and discreteinto sub-grids with a size of 10m×10m. The total number ofBSs is 19 with a distance of h = 10m. The distribution of BSsis configured according to the PPP model [21]. Other detailsof the simulation are listed in the Table I.

Self-correlation of the LTE-DL signal and cross-correlationbetween LTE-DL signals transmitted by different BSs are eval-uated and as shown in Fig. 4. We can see from Fig. 4(a) thatthe original LTE-DL signal suffers greatly from the repeatedsignal elements, resulting in a series of significant side-lobes.However, after the proposed signal selection method is appliedto the LTE-DL signal, those side-lobes have been effectivelycompressed and the signal self-correlation level has beendramatically increased, as shown in Fig. 4(b). In addition, fromthe result shown in Fig. 4(c) and (d) we can see that the cross-

0 100 200 300 400X(m)

0

100

200

300

400

Y(m)

(a)

0

0.25

400

0.5

No

rma

lize

d S

pa

tial C

orr

ela

tion

0.75

1

200 400200

Y(m)

0

X(m)

0-200 -200-400 -400

(b)

Fig. 5. BSs distribution and spatial-correlation of the generated illuminationfield. (a) PPP-based BSs distribution. (b) Spatial-correlation of the illuminationfield.

0 100 200 300 400X(m)

0

100

200

300

400

Y(m)

0 0.5 1

(a)

0 100 200 300 400X(m)

0

100

200

300

400

Y(m)

0 0.5 1

(b)

0 100 200 300 400X(m)

0

100

200

300

400

Y(m)

0 0.5 1

(c)

0 5 10 15 20 25SNR (dB)

0

0.05

0.1

0.15

0.2

MS

E

(d)

Fig. 6. Reconstruction results with PPP-based BSs distribution and proposedsignal selection method. (a) Original scenario. (b) Reconstructed results whenSNR = 10 dB. (c) Reconstructed results when SNR = 0 dB. (d) ReconstructionMSE curve.

correlations between LTE-DL signals transmitted by differentBSs without and with proposed method, respectively, stayslow and does not change significantly with the applications ofthe proposed signal selection method, indicating an inherentlyorthogonal relationship for LTE-DL signals.

The PPP-modelled BSs distribution and the spatial-correlation of the generated illumination fields are illustrated inFig. 5(a) and (b), respectively. It shows that when the proposedsignal selection method is applied, the resulting microwavefields on the investigation area B is incoherent, which satisfythe requirement of performing microwave GI.

In order to validate the effectiveness of the proposed LTE-based microwave GI, a single square shaped target is locatedin the center of the investigation area B, as shown in Fig.6(a). As shown in Fig. 6(b) and (c), the proposed method canobtain the object reconstruction when SNR=10 dB and 0 dBwith clear edges. In addition, when mean-square-error (MSE)

is applied as a quantitive evaluation metric, the reconstructionperformance of the proposed LTE-based microwave GI isshown in Fig. 6(d). We can see that the proposed method isnot sensitive to the signal-to-noise ratio (SNR) condition whenSNR is high but the MSE performance decreases dramaticallyespecially when SNR is lower than 5dB.

VI. CONCLUSION

In this paper, we proposed a novel LTE-DL signal basedmicrowave GI scheme. To the best of our knowledge, thisis the first time for LTE-DL signals which are originallydesigned for communication purposes to be adopted in theframework of microwave GI. It is also the first time formicrowave GI to be implemented by using signals and trans-mitters that originally designed for communication purpose.Numerical simulation results showed that the proposed LTE-DL signal based microwave GI scheme can effectively obtainthe image of objects. Compared to conventional microwave GI,the proposed method possesses a significantly reduced systemcomplexity and operational cost, since the purposely deployedsignals and transceivers are avoided.

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