National University of Sciences & Technology,Pakistan
Abstract —Recently, microwave imaging has received a considerable amount of interest with respect to other imag-ing techniques. A large number of studies [1] rely on mi-crowaves, as a powerful electromagnetic tool to retrieve physical and electrical properties of penetrable and imetrable objects. The capability of microwave signals to pen-etrate light opaque materials and sense distant or inacces-sible objects with reasonable spatial resolution makes them attractive for different industrial, civil and medical applica-tions. Our Through-the-Wall Microwave Imaging (TWMI) radar system facilitates us to detect and localize objects be-hind the wall. Measurements with mono-static radar con-figuration are made with various sizes of metallic materials inside the room with wooden wall (of known thickness and dielectric constant) using 2D antenna positioning assembly and scattering data is recorded in frequency domain. The simple and fast algorithm for compensation of different wave velocity inside the wall is used and the measured raw data is processed with 2D SAR Beamforming algorithm in time domain to reconstruct the image of the targets behind wall. This paper provides an overview of the basic concepts, foun-dation prototype system of TWMI, SAR Beamforming algo-rithm and Comparison of Various matched filter approaches and their effects on quality of image are elaborated in detail.
I. Introduction
This paper presents detection and imaging capabilities of a simple 2D beamforming algorithm, applied to available open source experimental data sets that are obtained un-der various radar scene configurations (single- or multiple-target in free-space or through-the-wall). Data is collected with the wideband Radar Microwave Imaging System, which operates in 2 to 3 GHz by mechanically scanning a single Dual Ridge Horn antenna acting as a transceiver, thus avoiding the mutual coupling that occurs when an ar-ray is used.
Measurements are performed in the frequency domain at several discrete frequencies. The collected experimental data is processed by a 2D SAR beamforming algorithm to unravel the complicated multiple scattering affects and produce high resolution 2D digital images of the target objects in imaging domain. The algorithm processes the received signals in a supposedly known medium (either free-space or through-a-wall with known permittivity) to achieve effective imaging. Two configurations models for free-space and through-the-wall with and without targets are investigated and processed to calibrate the scenes.
Fig. 1 Prototype system
II. Prototype System Model
Fig 1. shows the prototype system consisting of antenna positioning assembly, Horn Antenna, RF cable, wooden wall, data acquisition and Positioner controller worksta-tion and the Vector Network Analyzer (VNA). Agilent’s VNA in the range 300 KHz-3 GHz is used to generate step frequency signals at Microwave frequencies, Our Radar sys-tem is working in the range 2-3 GHz for optimum reso-lution and penetration capability in through the wall sce-nario. Directional and broadband Dual ridge Horn antenna with 12dB gain is used to transmit and receive these sig-nals.
The whole system is controlled through a computer in-terface which is inin-terfaced over LAN to VNA and also programmed to direct the movement of antenna over 2D Positioner. A sliding wooden wall module of known per-mittivity is constructed.
Fig. 2 Side and top views for system setup
III. Geometry for Delay formulation
3D view and corresponding single 2D slice of the whole system configuration is shown in Fig 2. Axis x, z and y rep-resents cross-range, range and height of the room respec-tively. As in [4], geometry for computation of traveling distances for through wall scenario is described in terms of angle of incidence, referring to geometric illustration in [4,7], where i=pused for target location andi=qused for pixel location representing that target.
To compute the focusing delays between antenna and Im-age pixel location, we consider the three medium changes in the incident ray: between antenna and wall, within wall and between wall and targeted pixel as medium 1, 2 and 3 respectively as shown in Fig 3. Knowing the wall thickness and dielectric permittivity, we can apply Snell’s law, since wall have permittivity greater than air and therefore the ray undergoes refraction, given by [10]:
θwall=
arcsin(sinθair)
√
wall
(1)
Where θair is the angle of incidence at air-wall bound-ary and θwall is the angle of refraction, similarly in [10], traveling distances are formulated as following:
Lair1= zof f set cosθair
(2)
Lwall=
d
cosθwall
(3)
Lair2= zq−d cosθair
(4)
All above equations are in terms of angle of incidence. Us-ing the transcendental equation in [1,4,7], to computeθair, which is obtained by applying Law of Cosine to triangle
ABP :
(xq−(xtx+zof f settanθair))2+z2q =L 2 wall+L
2 air2
−2LwallLair2cos(π+θwall−θair) (5)
This equation can be solved by numerical methods. We have used this equation to calculated angles of incidences
Fig. 3 2D geometry
to all image pixels for each position of antenna and hence the traveling distances for all pixels to antenna position. Focusing delays at one pixel can be found by simple for-mula:
delay=2Lair1
c +
2Lwall
c/√wall
+2Lair2
c (6)
Where c and v are the speed of light in air and wall re-spectively. Focusing Delays are calculated for whole image grid and stored in form of a matrix for further processing the received vectors.
IV. Data Acquisition
We have used a step-frequency radar (SFR) approach [1] for generating a broadband pulse. Continuous wave mea-surements of both magnitude and phase are collected at several closely-spaced frequencies over a broad frequency band of 2-3 GHz. [9] Describes the direct advantages of the SFR approach, since the measurement system can be easily built around a microwave vector network analyzer with rel-atively few specialized components, which offers advantage of high signal to- noise ratio over impulse Radars due to narrowband electronics and the availability of extremely stable signal sources resulting in increased measurement accuracy and stability [9]. This allows for the removal of many sources of systematic (non time-varying) mea-surement error including the frequency-dependent magni-tude and phase variations of connectors, transmission lines, adapters and antenna. However, data collection time is generally increased. For high-resolution microwave imag-ing applications, the increased measurement time can often be justified since there will be additional time required to process the data. Our Radar uses the 1GHz band with step size of 5 MHz; data is collected at 69 positions at 201 frequencies between 2 and 3 GHz. It makes a sampling time of 1ns in time domain and 30 meters Radar range. Similar 2D data is acquired at different antenna heights and stored in form of matrices.
V. Beamforming
Fig. 4a Antenna beam capturing target
used for aperture synthesis. Either all the elements of the intended array can be physically present and share a single processing channel via a multiplexer, or a single transceiver can be used to realize the full M-element array by mov-ing this transceiver to different locations formmov-ing the array aperture [4,7]. The use of a calibration procedure, by in-corporating two measurement scenarios (through-the-wall and in-air), allows for the removal of many sources of pulse distortion in the time-domain data which occur due to the effective aperture, phase dispersion, and resonances of the antennas. Also the reflection from ceiling and floor are removed through this calibration. Further processing is performed over the calibrated data.
The basic 2D SAR spatial model is shown on Fig 4a. Trans-mitted wave is reflected from target to all directions uni-formly. Because antenna beam is wide, signal reflected from target is received not only when antenna system is exactly over the target but in all positions that allow to see the target [3]. As a result, pointed target will be rep-resented in B-scan as hyperbola as shown in Fig 4b. Time delay is the time when wave is flying from antenna to tar-get and from tartar-get back to antenna. The signals received in given time are actually representing the scattering from all points that lie on the locations where time delay is constant. Migration process is used to transform received A-scans data to B-scan image.
Using equation (6) for calculation of focusing delays for each pixel, we can apply these delays to the corresponding one of the 69 received vectors to actually time align these signals for target pixel location in range and cross-range resolution. This process in fact is focusing of points on hy-perbola with same time delay at transceiver position. After time aligning the signals for target pixel, these are summed over total antenna positions, which can be mathematically written as:
B(xq, zq) = M
X
m=1
R(xtxm, delaym) (7)
Bq(t) = M
X
m=1
wmR(xtxm, delaym) (8)
Fig. 4b Delay for single pixel at all antenna positions
WhereR(xtxm, delaym) represents the receive vector as a function of transmitter location (xtxm) and focusing delay (delaym). And B(xq, zq) is the corresponding pixel in B-scan, image is obtained by weighting the B-scan pixels so as to control the shape and side lobe structure of the sys-tem. We have used hamming weights such that the pixel, with minimum distance to antenna at certain position, gets the maximum weight. Repeating the same procedure for all pixels one by one, the complete B-scan is obtained; this is the beamformed image. This image contains some of the false targets which [5] explains as intersection of hyperbo-las, which can be removed by passing the signal through a filter matched to the transmitted pulse (T(−t)) and taking the output as:
Image(xq) = (Bq(t)∗h(t))|(t=0) (9)
VI. Gaussian Filter Approach
Gaussian function and its derivatives can be used to rep-resent the UWB pulses [2], in [5], the received vectors are processed with Gaussian filter. However we are us-ing the Beamformed data vectors to cross-correlate with the second derivative of Gaussian mono pulse, since sec-ond derivative has very close resemblance to the shape of target echoes than any other derivative [5]. Gaussian pulse and its second derivative are represented like this:
g(t) =− √
2
α exp−(
2Πt2
α2 ) (10)
g00(t) = (1−4πt
2
α2) exp−( 2Πt2
α2 ) (11)
Where α is pulse shaping factor, we have used its value as 9e−10 for optimum shape. The cross correlation of beamformed signals and the second derivative of Gaussian mono-pulse signals are represented as:
Tq(τ) =
Z ∞
−∞
Bq(t)g00(t−τ)dτ (12)
Fig. 5 Scene detail for single target
Fig. 6a Beamformed Image
of the targets in the image which is termed as envelop detection in [5] represented as:
Eq(t) = (Tq(τ))2∗h(t) (13)
The final step is to use Eq(t) as the weighting factor for Beamformed image. It will help us to eliminate the false targets appearing in image and to separate the closely spaced targets[5].
VII. Results
The results are shown for two configurations:
• Single target environment
• Multiple target environment
The rear and side walls are covered with 60×60 and four 20×40pieces of pyramidal radar absorbent modules respec-tively, so as to avoid the reflections from windows, walls and doors.
A. Single Target Detection
Single target environment consists of a metallic target placed at a specific location with respect to the axis system, as described in Fig 5. The results are shown as an image
Fig. 6b Image after Cross-Correlation
Fig. 6c Image after filtering (envelop detection)
Fig. 7 Scene detail for multiple targets
Fig. 8a Beamformed Image
after beamforming, cross correlation, Convolution with a matched filter and applying weighting factor in the Fig 6a to 6d respectively.
B. Multiple Target Detection
Multiple targets environment consists of six different tar-gets at known locations in range and cross range of the room as shown in Fig 7. Our Beamforming algorithm has exactly located all of them. Rear wall can be seen at 200 distance.The results are shown as an image after beam-forming, cross correlation, convolution with a matched fil-ter and applying weighting factor in the Fig 8a to 8d re-spectively.
VIII. Conclusion
In this paper, we have presented an approach towards 2D beamforming for our prototype through-the-wall mi-crowave imaging Radar. It is based on incorporating the smaller velocity inside wall of known permittivity and thickness. Gaussian filter approach with weighting factor is applied over the Beamformed image allowing effective and reliable imaging behind wall. Simulated results for
Fig. 8b Image after Cross-Correlation
Fig. 8c Image after filtering (envelop detection)
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