Proposed transceiver design

The proposed broadband reconfigurable transceiver antenna comprises of two stacked configurations fabricated on a single substrate, operating in a switched mode using two pin diodes. The design is shown in Fig. 1. When diode 1 is switched ON, the antenna operates in the C-band region with 3 GHz bandwidth from 5.5 to 8.5 GHz. When diode 2 is switched ON, the antenna operates in the X-band region with 3 GHz bandwidth from 8.5 to 11.5 GHz. The peak measured gain in C-band is 8 dBi while in X-band it is 7.7 dBi. The common 50 Ω feed line is connected to both the stacked configurations through a switch (pin-diode) for each. A regulated DC voltage supply can be connected to each diode, with the positive terminal connected to diode's anode and the negative terminal connected to common feed line to make it a common ground. In the experiments, a potentiometer connected with DC batteries, with its common pin connected to common ground, is used. This arrangement makes the system flexible to be applicable in the imaging setup. The fabricated circuit is shown in Fig. 2 and the microwave imaging setup is demonstrated in Fig. 3. The separation between two antennas is such that s > λ/4 (larger λ) and s ≠ nλ, so that their radiation patterns do not interfere with each other (s = 4.5 cm). In the fabricated transceiver, l ₁ = 1.1 cm, while l ₂ = 3.1 cm. The transceivers are designed such that their combined response in the frequency domain is a continuous wideband response. Response of the reconfigurable antenna for both the states is shown in Figs 4(a) and 4(b), respective gains are depicted in Fig. 5, and radiation patterns at different frequencies are shown in Fig. 6. Design parameters of the X-band antenna [Reference Katyal and Basu25] and C-band antenna are listed in Tables 1 and 2, respectively. Here W ₁, L ₁ represent width and length of first (driven) patch and so on for three patches, W_f is feed width, S_w and S_l are slot width and length, respectively, in C-band antenna design.

Fig. 1. Reconfigurable antenna/transceiver design.

Fig. 2. Fabricated transceiver circuit.

Fig. 3. Measurement setup employing reconfigurable stacked antenna as transceiver.

Fig. 4. (a) S ₁₁ response of reconfigurable antenna for C-band antenna ON, (b) S ₁₁ response of reconfigurable antenna for X-band antenna ON.

Fig. 5. Measured and simulated gains of C-band and X-band antennae.

Fig. 6. Measured radiation patterns of reconfigurable stacked microstrip antenna at different frequencies at: (a) C-band antenna ON and (b) X-band antenna ON.

Table 1. X-band antenna design parameters [Reference Zhou, Shen, Xu, Tang, Wang, Zhang, Ye, Huangfu, Li and Ran22]

Table 2. C-band antenna design parameters

Microwave imaging setup

The microwave imaging setup consists of the proposed broadband reconfigurable antenna as transceiver units, placed two-dimensionally in front of the target under investigation. For laboratory experiments, one transceiver unit is displaced at multiple locations and a vector network analyzer is used as signal generation and data acquisition unit. Here, a bistatic system is employed for 2D scanning of target under test. Microwave imaging measurement setup comprising of reconfigurable stacked antennas as transmitter and receiver (transceiver) is shown in Fig. 3. The reconfigurable antenna is functioning in switching mode, where diode 1 switches ON C-band stacked antenna and diode 2 switches ON X-band stacked antenna in the transceiver. At any instant, C-band antenna is switched ON in both transmitter and receiver, to capture target's spectral information in C-band and similarly it captures spectral information of the target in the X-band, when X-band antenna is switched ON in both the transmitter and receiver units. This reconfigurable transceiver allows collecting target's information in two frequency bands under same environmental conditions for both the states of its operation. The target is kept in the E-plane of both the stacked antennas of the transceiver. The distance between the target and the system's origin is “d,” which is kept equal to 1.1 m in the experiments. The DC supply (batteries) and potentiometer connections are attached to the transceiver support unit. The complete microwave imaging setup is kept in an open lab environment without the use of anechoic chamber or any absorber/s around. The system ensures rejection of backside clutter as the proposed reconfigurable antenna has unidirectional radiation patterns throughout the operating range. The reflections/scattering due to other nearby objects (in front) in the lab is rejected in the image reconstruction algorithm as described in the next section. Non-planar and irregular-shaped objects have been used as targets. The center of the target is aligned with the center of the transceiver, keeping the environment conditions constant for both the operating states while measuring scattered signal from the target. With this we can obtain the target's spectral information in both the frequency bands through the scattered signal received in each state of operation. This information is then combined in the frequency domain to obtain an equivalent wideband response, which is then processed to obtain target's image.

Image reconstruction

Scattered electric field is calculated and analyzed for multi-point illumination of the target for solving the inverse scattering problem. The investigation domain containing target is scanned two-dimensionally by illuminating the target from different point/angles; conceptually through multiple transceivers, while in experiments by displacing the single transceiver unit at multiple locations. The total electric field is given by:

(1)$$E = E_{inc} + E_{scat}$$

In the inverse scattering problem, we find unknown E_scat to obtain the target's information, which can be obtained by (2) [Reference Pasterino26].

(2)$$E_{scat} = j\omega \mu \mathop \smallint \limits_S^. J_sG( {r, \;\;r} ) dr{\rm ^{\prime}}$$

(3)$$\forall \;\;J_S = \tau ( {{r}^{\prime}} ) E( {r{\rm^{\prime}}} ) $$

which essentially is solved for the unknown $\tau ( {{r}^{\prime}} ) = j\omega ( \varepsilon _{obj}\unicode{x2013} \varepsilon _b)$, called as object function or scattering potential, with the object permittivity ɛ_obj and the background permittivity ɛ_b. This is the analytical solution for the unknown target's information. In the present work quick qualitative solution is applied to obtain target's information using the SAR algorithm for image reconstruction. Moreover, the spectral information of the target obtained in two different (but continuous) frequency bands is combined to provide an equivalent wideband response of target in the given scenario. The target placed in the investigation domain is scanned using transceiver in X- and C-band frequency regions. Target's response in both the frequency bands is combined according to (4), where [S(f ₁)]_C is the transceiver response in the C-band and [S(f ₂)]_X is the transceiver response in the X-band region of operation. This gives wideband spectral information of the target which is processed further to reconstruct the target's image. Initially, the obtained wideband data (target's response) are converted into the time-domain form. Furthermore, background subtraction is done where system's response without the target is obtained in the given scenario, along with considering any scattering from target's support system. Time gating is applied to the signal to remove the direct signal (from the transmitter to the receiver) and the any other clutter due to surrounding objects:

(4)$$S( f ) = [ S( {\,f_1} ) ] \_{\rm C} + [ S( {\,f_2} ) ] \_{\rm X}$$

(5)$$S( t ) = \displaystyle{1 \over {2\pi }}\mathop \sum \limits_{-\infty }^\infty S( f ) e^{\,j\omega t}$$

(6)$$S_{target}( t ) = S( t ) -S_{without\;target}( t ) $$

∀ S _{without target}(t) is obtained similar to S(t), by just removing the target from the given scenario (investigation domain):

(7)$$S_{time \hbox{-} gated}( t ) = \mathop \sum \limits_{\tau _1}^{\tau _2} S_{target}( t ) $$

The range τ ₁–τ ₂ needs to be properly chosen/optimized (based on the location of the setup) so as to contain only target's information and rejecting all the clutter due to nearby objects, as the system is operating in a real open environment. In the present case, measurements are done in a normal lab environment containing several objects near the setup, with many of them being very strong reflectors. Furthermore, this also ensures rejection of high amplitude direct signal, directly reaching the receiver from the transmitter. The averaging operation is performed using Savitzky–Golay filter on the time-domain signal to reduce the effect of noise. Let's say N signal samples lie in the time-gated signal and a frame length of m is considered for signal smoothening, then signal amplitude at different time instants (samples) is given by:

(8)$$( t_i, \;\;A_i) ; \;i\;\in \{ {1, \;\;2, \;\ldots , \;m} \} $$

These samples are operated with convolution coefficients C_j according to below equation:

(9)$$A_i = \mathop \sum \limits_{\,j = ( 1-k) /2}^{( k-1) /2} C_jA_{i + 1}$$

$$\forall \displaystyle{{k-1} \over 2} \le i \le m-\displaystyle{{k-1} \over 2}$$

Here, the convolution coefficients are obtained based on selection of filter order and frame length according to [Reference Schafer27]. In the above equations “k” is the order of the filter and “m” is the frame length. These two parameters need to be optimized properly when working in an open environment for satisfactory noise reduction along with no signal loss. In the present work, after optimization, the values are chosen as: k = 3 and 20 < m < 30 (optimized in case of slight changes in background scenarios). The given target image is obtained using the SAR algorithm for image reconstruction and the algorithm implementation is given by (10) and (11). Let the image matrix be M where initially each matrix cell value is initiated to zero. Then each cell of the matrix M_j (l, m), for jth sensor location and cell location as x = l and y = m, is incremented by amplitude A_i (A_i is the signal amplitude at time instant t_i):

(10)$$M_j( {l, \;\;m} ) = M_j( {l, \;\;m} ) + A_i$$

(11)$$t_i = \tau _1 + ( {i-1} ) \left({\displaystyle{{\tau_2-\tau_1} \over N}} \right)$$

$$\forall t_{i\;}\approx T( {l, \;\;m} ) ; \;\quad T( {l, \;\;m} ) = 2( D/c) $$

Here, t_i is the value in time vector closest to the time of flight of each cell, i.e. T(l, m), within the limits of 0.1–0.5 ns. Furthermore, D is the distance between jth sensor with location (x_j, y_j, z = 0) and the cell (l × Δx, m × Δy, z = d); Δx and Δy are the dimensions of each unit cell. Similarly each matrix element is incremented by the amplitude value corresponding to the time-of-flight from the jth transceiver to that element and these amplitude levels keep adding up in each matrix element for j = 1, 2,… up to the number of transceivers used for scanning. In our previous work [Reference Malhotra and Basu23], the primitive work of combining information in two operating bands has been carried out by simple image matrix addition in both the bands. However, this method also allows addition of noise/clutter or any error in the image matrix rather than canceling it out. This is, however improved in the proposed novel method of combining frequency domain information, where the background subtraction is done properly over the combined equivalent broadband frequency range to minimize the effect of noise and any clutter signal due to surroundings.