II. COHERENT RADIOMETRIC IMAGING

The proposed approach to coherent radiometric imaging consists of using BR and moving of the antennas for realizing synthetic apertures. This scheme enables obtaining range resolution of emitting objects at distances comparable with bistatic baseline. This is possible due to the fact that shifting of one antenna of interferometric radiometer with respect to stable emitting object changes phase relations between received signals. For different positions of the emitting object these phase relations will depend on antenna positions in different way. This fact can be used for building a reference function (a function of antenna position) and performing co-variation of radiometer returns with it. This gives a chance to improve the resolution and to some limit to generate 2D images. The paper is devoted to investigation of possibility and constraints of generation of 2D images using this approach at short ranges.

For realization of spatial scanning we use ABS [Reference Lukin1, Reference Lukin2]. Phase centers of antennas are moved along a real aperture in stepped like manner and signals are being recorded only when the antennas are stationary. This enables using common in SAR principle of splitting of the processing into two parts. The first step of coherent radiometric imaging is to perform cross-correlation between signals received in two channels. This will give information concerning mutual path length difference between signals. The second stage consists of co-variation of those signals obtained in different positions of ABS with corresponding reference function.

TDOA of the signal Δτ(x, y) coming to receiver and to the auxiliary receiver equals to ${{\Delta l\;\left( {x,\;y} \right)} / c}$ , where $\Delta l\;\left( {x,\;y} \right)={l_1}\;\left( {x,\;y} \right) -{l_2}\;\left( {x,\;y} \right)$ is path length difference between the emitting object with range-cross range coordinates (x, y) to the receiving antennas [Reference Dulevich3]. Mutual path length difference Δl(x, y) cannot exceed the bistatic baseline l _B . At each of antenna positions a the value of TDOA equals:

(1) $$\Delta {\tau _a}\left( {x,\;y} \right) = {{\Delta {l_a}\;\left( {x,\;y} \right)} / c}.$$

Cross-correlation function between signals received by reference channel of imager ${S_{1,a}}\left( {t + \tau} \right)$ and the auxiliary receiver $S_{2,a}^* \left( {t + {\tau _a}} \right)$ can be estimated as:

(2) $${R_a}\left( {\tau, \;T} \right) = \displaystyle{1 \over T}\int_0^T {{S_{1,a}}\left( {t + \tau} \right)} S_{2,a}^{\ast} \left( {t + {\tau _a}} \right)d\tau,$$

where T is the integration time; $\tau \in \left[ {{{ - {l_B}} / c};\;{{{l_B}} / c}} \right]$ is the mutual delay of the signals introduced for compensation of (1); symbol ^* denotes complex conjunction. The delay τ introduced in (2) may compensate TDOA value τ _a which may exceed the incoming signal coherence time. Thus the bistatic baseline is not limited by the coherence length of the signal.

Compression of the signals by path length difference consists of estimation of cross-correlation R _a (τ, T) for the required TDOA values and for all antenna positions.

Movement of phase center of ABS [Reference Lukin1, Reference Lukin2] causes change in path of the radio waves in waveguide. This change has to be taken into account during signal processing. Estimation of phase shift is easier to perform in frequency domain by adding corresponding phase shifts to all of the frequency components of the signals. Using known [Reference Nikolskiy and Nikolskaya10] relation for the main wave of rectangular waveguide this phase shift can be estimated using the following relation:

(3) $${\phi _a}\left( {{\lambda _i}} \right) = 2\pi \;{l_a}\;\sqrt {\displaystyle{{\xi \;\mu} \over {\lambda _i^2}} - \displaystyle{1 \over {{{\left( {2\,p} \right)}^2}}}},$$

where ${\lambda _i} = {c / {{f_i}}}$ is the wavelength of the given frequency f _i in free space; l _a is waveguide length corresponding to antenna position a; ξ, μ are the relative electric and magnet permittivity; p is the width of wide wall of the waveguide.

For effectiveness, correlation processing (2) has been performed in frequency domain using a fast Fourier transform. Taking into account (3) the cross-correlation (2) of the received signals is:

(4) $${R_a}\left( \tau \right) = \left\langle {S_{1,\;a}^{\ast} \left( {{\omega _i}} \right)\;{S_{2,\,a}}\left( {{\omega _i}} \right)\;\exp \left( {j{\phi _a}\left( {{\omega _i}} \right) + j{\omega _i}\tau} \right)} \right\rangle,$$

where ${\omega _i} = 2\pi \,{f_i}$ is the circular frequency of the received waveform spectrum limited by the BR band pass ${\omega _i} \in \left[ {{\omega _{\min}} ;\;{\omega _{\max}}} \right]$ ; symbols 〈〉 denote statistical averaging over ω _i .

The second step of the processing uses the results of correlation processing (3). It consists of estimation of the base of theoretical response from current point of space an expected variation of radar returns as a function of antenna position. Then, the received signals are compared with this reference function via co-variation. Relation for the generation of coherent radiometric image I(x, y) in time domain and with common simplification consisting of neglecting of amplitude term of reference function has the following form:

(5) $$I\left( {x,\;y} \right) = \left\langle {{R_a}\left[ {\Delta {\tau _a}\left( {x,\;y} \right)} \right]} \right\rangle \;\exp \left[ { - j{\omega _c}\;\Delta {\tau _a}\left( {x,\;y} \right)} \right],$$

where ω _c is the circular carrier frequency of the received waveform spectrum; and symbols 〈〉 denote averaging over antenna positions in the performed scan.

Thus, coherent radiometric image generation (5) consists of (a) matched filtration of the received signals and (b) the signals averaging up with taking into account phase difference between emitting object signals received by the BR antennas.

III. KA-BAND BR WITH ANTENNAS WITH BEAM SYNTHESIZING

The current work is devoted to the experimental evaluation of the possibility to obtain range resolution on coherent radiometric images with the Ka-Band Bistatic Ground-Based Noise Waveform SAR equipment modified for operation in the radiometric mode. The Ka-band BR (Fig. 1) uses the new type of antennas – ABS [Reference Lukin1, Reference Lukin2].

Fig. 1. Picture of the Ka-band BR with antennas with beam synthesizing.

A) Antennas with beam synthesizing

This is a special type of antennas phase center of which is moved along a real aperture (Fig. 2). As a real aperture antenna, a waveguide with a non-radiating half-wavelength longitudinal slot in its wider wall is used. The wall is covered with a metallic tape having a half-wavelength transverse resonant slot. In order to enhance its efficiency we placed a sliding plunger tied to the tape at the proper distance from the radiating slot. The tape moves along precise guides. Position of the slot is controlled by angle sensor. In the work, phase centers of antennas are moved in stepped like manner and signals are processed only when the antennas are stationary.

Fig. 2. Ka-band ABS: (a) general view of the reception point; (b) sub-units of the antenna.

B) The BR processing gain test

The Ka-band BR with ABS enable the generation of coherent radiometric images in 36.0–36.5 GHz band. The estimated bandwidth of receivers equals to 465 MHz. The noise factor of each receiver is 3 (noise temperature is 600 K). Estimated gain of receivers is up to 97 dB. Each receiver output signal is fed to 8-bit ADC with bandwidth 500 MHz (GaGe CS22G8-1 GHz) and saved to HDD for post-processing.

Received signals of thermal radiation of emitting objects are quite weak that leads to necessity of increasing the processing gain. The leakage of signals between two receivers (represents interchannel interference) limits opportunity of signal-to-noise ratio (SNR) improvement via processing gain increasing. We have carried out estimation of the leakage in Ka-band BR with ABS. Namely we have investigated dependence of output SNR on integration time in the limits of the processing gain of 20–70 dB. This has been done using two schemes shown in Fig. 3. The first scheme enabled to evaluate processing gain for the case of two correlated signals input to the digital correlator. Output SNR is close to input SNR multiplied by the processing gain. The second one consisted of feeding two uncorrelated signals to the correlator. It was done in order to estimate the correlator output signal power decrease along the integration time increasing. The output SNR showed good agreement with the expected processing gain. It proved that the leakage of the Ka-band BR with ABS is low enough for our radiometric experiments. This isolation level is provided by the down converter scheme where the oscillations frequency of common X-band oscillator is multiplied by 4 separately for each channel [Reference Lukin8, Reference Lukin11]. The receivers’ synchronization is provided by: (a) the down converter oscillator that is common in two receivers and (b) the ADC clock generator that is common in two receivers. The oscillator signal is transferred to the auxiliary receiver via coaxial cable. The baseline extension can affect the transferred signal performance that will decrease the system performance.

Fig. 3. Block-schemes for the estimation of the leakage of signals between two receivers.

IV. EXPERIMENTAL SETUP

The aim of the experiment was to generate coherent radiometric images using Ka-band BR with ABS.

A) The BR performance estimation

In order to validate ability of the radiometer to detect emitting objects on the background of the intrinsic noise of the receivers and to detect difference in thermal radiation of emitting objects it is necessary to measure the minimal increase of the signal amplitude which can be registered by the equipment. To check operation of the equipment in radiometric regime we used two stable dish antennas with 0.34 m diameter and regime of interferometric radiometer without spatial scanning with ABS [Reference Lukin1, Reference Lukin2]. To compare the output levels with the noise floor we used to switch matched loads to the inputs of the receivers between measurements with dish antennas. The experiment cycle was as following: (a) matched loads are connected to the receivers’ inputs, (b) two Ka-band dish antennas are connected to the inputs and directed to the sky, (c) matched loads are connected to the receivers’ inputs, and (d) the antennas are connected to the receivers’ inputs and directed to the concrete room ceiling. The integration time of 4 s was used in the cycle. In order to compare different realizations of these responses the cycle was repeated three times. That is why the Fig. 4 shows three realizations for the radiometer responses on sample emitting objects as the sky and the ceiling and 6 realization for the noise floor. Temporal intervals for re-connection of antennas and their direction affected total measurement time about few hours. The output levels of the radiometer (Fig. 4(b)) show that the difference in intrinsic noise level, the sky and the ceiling can be recognized, but changing in time the radiometer equipment parameters lead to some variations in the output levels for each of the emitting objects.

Fig. 4. The radiometer output signal level: intrinsic noise, sky, and room ceiling: (a) the experiment scheme; (b) the radiometer output signal levels, three experiment cycles results.

B) Coherent radiometric imaging experiment

For the coherent radiometric imaging experiment the equipment was placed inside a laboratory room. The phase delay of signal passes along antennas and receivers has been taken into account by calibration measurements using noise waveform generator placed. Ka-band noise waveform generators were used for the indoor preliminary experiments. They showed good concordance between the generators positions and coordinates of the generated radiometric images’ peaks. The experiments showed intersection of sidelobes of the Ka-band BR with ABS.

For proof of concept of indoor coherent radiometric imaging two absorbers were placed behind a window (Fig. 5). The room inside temperature was about 293 K.

Fig. 5. Generated images of the room interior for different threshold levels: (a) threshold equals to −3 dB; (b) threshold equals to −12 dB.

Correlation processing of received signals has been performed in frequency domain. The sidelobe level can be improved by applying weighting function to spectrums of received. Coherent radiometric imaging has been done taking into account the TDOA of the emitted signals to each receiver antenna (5). Step-like moving of phase centers of the ABS and the approach to generation of coherent radiometric images enabled to generate coherent radiometric image. The image contains amplitude and phase information along coordinates (range and cross-range directions). Logarithmic values of amplitude in each pixel are shown (Fig. 5). This amplitude information corresponds to apparent temperature of the objects in the scene. Semitransparent scheme of objects location inside is shown in the figure as well. The −3 dB threshold was applied to the color scheme (Fig. 5(a)) in order to analyze the image. Two peaks coincide the absorbers positions. The peaks positions are shifted from the absorbers centers. Another two peaks (in range span up to 2 m) do not coincide the absorbers positions.

The numerical simulation was provided to check the essence of the shifts. The simulation included the experiment geometry and the Ka-band BR with ABS parameters. It showed that the shift may be explained by close separation between the absorbers. The responses interaction does not lead to shift of their maxima at larger distances. The simulation showed the sidelobes interaction mentioned above as well. The interactions may cause false peaks on images. The peaks in range span up to 2 m may be explained by combination of sidelobes of two targets. Threshold by −12 dB was applied to color scheme (Fig. 5(b)). The scheme shows low amplitude (low apparent temperatures) with tints of blue color and high amplitude with tints of reds.

The strongest response in the image (Fig. 5(b)) corresponds to the object with rough surface (absorber 2). Absorber range is 2.6 m and cross-range is 3.7 m. The weaker responses in the image correspond to false peaks as well as to objects with smooth surfaces (the painted concrete wall, the window, the linoleum-covered floor). The response from object with smooth surface (related to the range 2.7 m and cross-range 3 m) is lower than the response from the object with rough surface by 19.7 dB. The object with rough surface emissivity ε _R equals to 0.98 and the object with smooth surface emissivity ε _S equals to 0.95 when zenith angle is 20° [Reference Dulevich3]. This provides an expected brightness temperature contrast of $\Delta T = T\left( {{\varepsilon _R} - {\varepsilon _S}} \right) \approx 9\,{\rm K}$ . With respect to the radiation efficiency of the antenna and scene temperature measured by the antenna pattern sidelobes, the minimum detectable temperature change on the image equals to ${{9 / {10}}^{1.97}} \approx 0.1\,{\rm K}$ . The calculated sensitivity value matches the experimentally obtained value well enough. Generally, cleaner images may be obtained in the case of increasing of SNR of the radiometric system.

The possibility of coherent radiometric images generation using Ka-band BR with ABS is shown. Its range resolution depends on the antennas apertures length and position of emitting object.

V. ESTIMATION OF RESOLUTION CELL DIMENSIONS OF GENERATED IMAGES

Angular resolution of interferometric radiometer is well known. Angular resolution provided by the ABS is also known from theory of SAR. The current work investigates unusual combination of these techniques which provides the range and azimuth measurement. This section is devoted to estimation of the resolution in both coordinates. Estimation of the position of emitting object in the range-azimuth plane requires data on the emitter of thermal radiation azimuth β and path length difference R. The provided coherent radiometric imaging focuses the target positions on the equal TDOA area by the ABS. The response of the coherent radiometric imager may be considered as intersection of the synthesized beam maxima with maxima of path length difference hyperbolic response R. The point of the maxima intersection is denoted as T (Fig. 6). Distance (slant range) r to point T can be defined using law of cosines as follows:

(6) $$r_1^2 = {r^2} + {B^2} - 2rb\;\cos \left( \beta \right),$$

where r ₁ = r − R; b the baseline of the BR. Then reduction of similar terms of this expression enables to express r as follows:

(7) $$r = \displaystyle{{{R^2} - {B^2}} \over {2\left[ {R - B\;\cos \left( \beta \right)} \right]}}.$$

Thus, the range to the emitter is calculated based on the distance between the phase centers of the receiving antennas b, the result of estimation of the path length difference R and the result of estimation of the azimuth β.

Fig. 6. Explanation to the estimation of coordinates in the range-azimuth plane.

Let us denote dimensions of resolution cell according to the position of the emitting object. These dimensions are limited by both width of the hyperbola (between DA and CB, Fig. 6) and by the width of the synthesized beam (between OA OD, Fig. 6). Azimuth increasing affects the range size of the curvilinear quadrangle ABCD.

Dimensions of the curvilinear quadrangle ABCD (Fig. 6) can be estimated by means of its projections on the axes of coordinates. Equation (7) is suitable for calculations of distances to its vertices A, B, C, and D. The measured values of azimuth allow calculating projections of segments OA, OB, OC, and OD to the specified axis. This calculation approach takes into account data on carrier wavelength and wave propagation velocity, azimuth and corresponding size of synthesized apertures, bandwidth of received signals, paths difference of arrival and bistatic baseline. The desired dimensions of the curvilinear quadrangle ABCD are defined as distances between the maximum and minimum coordinates of its vertices.

Numerical simulation of the dimensions of the curvilinear quadrangle ABCD had been provided. The simulation was provided using parameters of existing equipment. It was shown that its range size varies on propagation paths difference, bandwidth, antenna aperture, baseline, and others. For the system with one ABS, the curvilinear quadrangle ABCD range size got better with widening of the bandwidth, with shortening the range and for some azimuth values. The latest depends on the position of the ABS. Enlarging the baseline improves the range size of the quadrangle as well. For such geometry of the system, the range size of curvilinear quadrangle ABCD does not exceeds 0.6 m threshold only for some path lengths difference values and azimuth values from 10° to 40° approximately. Defining the limitation of such resolution cell (curvilinear quadrangle ABCD) as well as system parameters is suitable in order to estimate some limitations of a field of view.

It should be mentioned that the accuracies of estimation of both azimuth and path lengths difference are limited by existing SNR as well as by losses in the BR equipment. That is why both resolution cell position and dimensions can be not equal to described ones.