1. Introduction
A radar is a nondestructive sensor that was first used for military applications. Nowadays, radars can be found in industrial applications, healthcare and medical applications, remote sensing, and subsurface investigation [
1]. Depending on how the radar signal is generated, radars can be divided into time and frequency domain groups [
2]. First mentioned was the impulse radar, which works in the time domain [
3], and its advantage is its simple hardware design and signal processing. The representatives of the frequency domain radars are the Frequency-Modulated Continuous Wave (FMCW) radar [
4] and the Stepped-Frequency Continuous Wave (SFCW) radar [
5]. The popularity of these radars has increased, as they demodulate a high-frequency signal to an Intermediate Frequency (IF) signal, which does not require high-speed Analog-to-Digital Converters (ADCs). Additionally, these radars have higher sensitivity and a wider dynamic range compared with time domain radars [
6,
7]. Therefore, their use can been found in different fields, and the current focus is highly on automotive applications [
8,
9,
10].
As both the SFCW and FMCW radars work in the same domain, the acquired data bins have to be transformed from the frequency to the time domain. Nevertheless, despite the data acquisition similarity, the signal generator and receiver work differently. Therefore, the SFCW radar shows better performance in applications where a lower operating frequency band has to be used, and, at the same time, high resolution is required with a low noise figure. A drawback compared with FMCW radars is the acquisition time, which is longer. A popular use of the SFCW radar principle is in Ground-Penetrating Radar (GPR) applications [
11,
12,
13,
14,
15], where small objects‘ detection was presented. Due to the fact that the signal travels through a highly lossy medium—soil—the sensitivity of such a sensor is crucial. Another scenario where the observed scene and required performance are similar would be in through-wall imaging radar applications [
16,
17,
18,
19]. The sensor sensitivity also has to be high, since the signal is attenuated strongly through the wall, as it may contain metal pieces or multiple air slots. An even more drastic scenario would be in an air-coupled antenna system [
20,
21,
22,
23], where the signal has to travel through an additional medium—air. This kind of system has become especially popular, since no physical contact is needed between the investigated medium and the antenna. In this scenario, not only does attenuation cause a problem, but also the fact that the Radar Cross-Section (RCS) of the observed surface can be several times larger than the RCS of the target of interest; RCS is a measure of the object‘s ability to reflect the signal back to the direction of the receiver and does not relate directly on the object‘s area, but also considers frequency, aspect angle, and polarization [
24]. This explains the large differences in the single-echo amplitudes. By increasing transmit power to amplify a weak echo signal, this can cause the receiver saturation because of the strong echo signals. To find a solution for this problem, large RCS targets—e.g., ground surface reflection or reflections from the wall—have to be categorized. A main assumption is that the ground surface or the wall is homogeneous. In this case, even if the radar moves, the distance to the surface could be controlled easily, and remain relatively constant during the whole measurement. Due to this, such a target could be categorized as a static target. Other targets of interest that appear during the measurement are then considered as dynamic, which separates them from static targets.
In this paper, we present a complete SFCW radar design with an integrated Echo Cancellation (EC) system, which is able to cancel multiple static targets with a combination of active and passive components. The first implementation of digital CW signal cancellation was presented and implemented in 1994 [
25], where a bandwidth of 200 MHz could be achieved. Recent work has shown that the bandwidth could already be increased to above a few GHz [
26] with the use of measuring equipment such as Vector Network Analyzers (VNAs). The proposed system is based on the previously developed compact SFCW radar [
27], and its extension represents an integrated EC system that affects the size of the radar and the power consumption minimally. The proposed method is highly suitable for battery-powered devices and applications where weight is critical.
The EC signal is generated with an RF synthesizer [
28] that is synchronized with the transmitter and can perform a phase shift all the way up to
radian or more, without modifying the hardware itself. As the amplitude of the echo signal can change at each frequency step, the EC system must match it in order to achieve the highest efficiency. Therefore, a digital attenuator is used to perform attenuation of the EC signal in uniform steps. Before the EC system can be used, a calibration procedure is needed and requires a measurement of the static scene. This step provides the information about the required EC signal phase and amplitude through the whole used frequency spectrum.
The proposed EC method was applied to the SFCW radar using implementation on multiple boards to speed up the prototyping process. The performance of the EC system was tested through a frequency band between 500 MHz and 2.5 GHz, which covers a popular range for GPR or through-wall imaging applications. The first experiment was performed with direct connection of the transmitter and receiver using a cable with a known length. This allowed us to measure the system delay and simulate a single target. Further experiments have been performed in a scene with a large homogeneous static target and a smaller dynamic target. TEM flared antennas were used for transmitting and receiving the signal. To obtain a B-scan, these were moved over a scene with the use of a motorized rail.
The proposed system is not only suitable for an SFCW radar system, but also for any other CW system, e.g., Doppler radar. An important fact to note is that the system cannot be implemented in another pre-existing SFCW radar, since the transmitter and EC system depend on each other. The bandwidth could be increased further, but was limited due to the components, such as RF amplifiers and antennas.
2. SFCW Radar
The principle of SFCW radar is based on stepping through a definite frequency span in uniform frequency steps
[
5]. The range resolution performance is equal to the very similar and widely used FMCW radar, and also relates to the bandwidth
B as
where
is the velocity of the Electromagnetic (EM) wave through a given medium, and its permittivity
and permeability
define the value.
The output frequency of such a radar is defined as
where
is the start frequency and
N defines the number of frequency steps. The value
N also defines the theoretical maximum range which can be obtained as
At least,
N defines the measure time of one complete frequency sweep, or also named range bin (
) as
where
is the time of a single-frequency transmission. In practice, this parameter is the SFCW radar‘s biggest disadvantage, since to detect long-range targets, the number
N needs to be high and
cannot be short as the hardware needs a certain amount of time to lock the desired frequency.
If a target is present, the receiver will obtain an echo signal with the time delay
, corresponding with the two-way travel time to the target, and an amplitude
. The signal in a complex-valued form can be expressed as
where
. The signal could be sampled directly with a high-speed ADC. To avoid this, the signal can be demodulated further to an In-Phase (I) and Quadrature (Q) signal, using a quadrature-demodulator, where the output can be described in a vector form as
represents the phase between the transmitted and received signals and is related directly with the time delay as
. To represent the target as a single response, an Inverse Discrete Fourier Transform (IDFT) has to be applied on the vector
C, where the result can be expressed as
Since the value N defines the number of range points, the length of vector C can be increased by adding zeros. This will result in an increase of the range points and provide better range accuracy. The result of the IDFT needs to be represented in the absolute form as . A synthetic pulse will occur in the location corresponding with the time delay caused by the target and make it visible.
Echo Response
The received radar’s EM signal is time delayed for the two-way travel time to the target. Equation (
5) describes the received signal for a single target for the SFCW radar principle. In practice, the received signal is a sum of multiple targets, which is described with Equation (
8).
where
U defines the number of all targets,
is the total amplitude, and
is the total time delay of the summed echo signals.
Figure 1 shows an example of multiple echo signals and their sum from targets at different locations for frequency
. To take the most advantage of the receiver dynamic range, the received signal has to be scaled through the whole available ADC range. This can be achieved by accordingly amplifying or attenuating the transmit or receive signals. Otherwise, if the received single echo signals with the smallest and highest amplitudes have a great difference between each other, the sensitivity of such a system is greatly limited.
3. Echo Cancellation
In the case of a time-domain radar, an echo that is strong enough to saturate the receiver does not have a critical effect on the final radargram compared with the frequency-domain radar. An impulse radar is a representative of time-domain radars, and transmits short pulses that are time-delayed by a relation between the EM speed in a given medium and the distance at the receiver’s site [
29]. Different target echoes, therefore, do not interfere with each other at the receiver, even if, at a certain point, some of them would saturate the receiver. This is not the case in Continuous Wave (CW) radars such as the SFCW or FMCW radars. The transmitting time is much longer than the echo response time of the most distant target, which means that all echoes are summed together and cannot be separated once received by the antenna.
At a certain frequency
, it is impossible to separate a single echo from the summed signal
. One of the possible solutions would be to subtract—cancel it physically, directly on the receiver input. This could be achieved with physical summing
with a replica version, which we name the Echo Cancellation (EC) signal, is matched by amplitude, and has a phase difference of
radian. For a simplified scenario where only stationary targets are present, the summed result is described with Equation (
9).
where
is the EC signal amplitude, which is expected to be closest to
, and
is the phase offset between the EC signal and transmit signal. If there is no difference in the distances between the transmitted signal and the EC signal, then
radian. In an ideal case scenario, the result would be
.
In a real environment where the radar platform is usually moving, it would be challenging to track and cancel only specific echoes, as the signal is changing constantly with the distance. In applications such as GPR or through-wall imaging, the most problematic echoes are stationary. Considering this, an echo signal of this type of target would remain the same through the whole measurement, even if the radar platform is moving. The EC System, therefore, removes only static echoes and keeps dynamic targets visible. The proposed EC system is not only limited to GPR or through-wall imaging applications, but can also be used for similar problem solving. For instance, instead of reducing antenna coupling with an RF circulator [
30], the proposed system achieves a similar effect, as the coupling has the same performance as an echo signal of a static target.
In practice, the applications that use the EC system should be calibrated each time the static scene changes, e.g., the distance of the radar has changed. Calibration is the process where a static scene is recorded, and the appropriate phase and echo power are obtained for each frequency. If, during the measurement, any other captured dynamic echo appears, after the system calibration, it will change the value , and make the target visible.
4. The Proposed Hardware Implementation and System Workflow
The EC system can be implemented as an extension to the previously developed SFCW radar [
27], with a receiver’s design changes. The proposed system’s block diagram is shown in
Figure 2. The main part of the radar systems are the three frequency synthesizers boards (SYN. 1—TX synthesizer; SYN. 2—EC synthesizer; SYN. 3—LO1 synthesizer), which generate all the necessary signals. The hardware for SYN 1-3 is the same, therefore, the single board is shown in
Figure 3a. All frequency synthesizer boards use the same clock buffer as a reference source, which enables phase synchronization, and performs a phase shift of the signal within a few picoseconds. To achieve phase synchronization, an additional line has to be provided to deliver a time-critical phase sync pulse.
Figure 2 shows the TX synthesizer that generates the transmit signal, the EC synthesizer that generates the EC signal, and the LO1 synthesizer that is used on the receiver and generates the Local Oscillator (LO1) signal source for the Intermediate Frequency (IF) down-converter. The transmitted signal is filtered by a Low-Pass Filter (LPF) to suppress higher harmonics. In the proposed system, the transmitted signal is, after filtering, coupled directly with the antenna, but could, if needed, also be amplified optionally with a Power Amplifier (PA).
The EC signal has, compared with the received signal (echo signal), a higher amplitude, and needs to be attenuated. A digital attenuator was used to achieve variable attenuation. Control of all digital devices such as the synthesizers, the ADC, the attenuator, and the RF switch is performed using a Field-Programmable Gate Array (FPGA).
The receiver is designed in a super-heterodyne architecture [
31] with an analog IF down-converter and a digital Intermediate-Quadrature (IQ) demodulator, where
Figure 3b shows the receiver and processing unit. Before the signal is coupled with the Low-Noise Amplifier (LNA), a digital switch selects the acquisition of the RX port or REF port. The REF port is connected directly with the TX port over a coaxial cable, while the RX port guides the sum between the echo signal received with the antenna and EC signal. Either the signal that goes through the RX port or the REF port is then amplified with an LNA. The RX—REF signal is demodulated further to an IF signal with frequency
MHz, and filtered additionally with an LPF to reject the higher harmonics that are caused by the transmitter. Afterwards, the IF signal is amplified and sampled with a 14-bit at 40 MSa/s ADC. The selected sampling rate matches the value of the frequency, which also feeds all three synthesizers and the FPGA. As all devices share the same clock, coherence is ensured, which is necessary for the IQ demodulation [
27]. Further, IQ demodulation and low-pass filtering are performed on an FPGA. The much higher ADC sample rate compared with the frequency
additionally prevents aliasing, which could potentially be caused by the higher harmonics of the synthesizers. The final result is a complex-valued vector
, where the number of frequency steps defines its length.
4.1. The Proposed Echo Cancellation and Calibration Workflow
A calibration procedure is proposed to achieve the best performance of the EC system. The calibration procedure is the most important step that has to be accomplished before starting the normal operation mode. The efficiency of the EC can be determined directly through the magnitude
of the acquired signal
. The goal of the EC algorithm at this stage is to remove the transmitter’s signal at the receiver’s site. This is achieved by amplitude matching and phase estimation between the signals generated with the EC synthesizer and TX synthesizer at the point where they are coupled with the combiner. In this paper, we propose using a brute force method to determine the unknown parameters
, which represent the phase shift offset of the EC synthesizer with an additional phase shift of
radian,
, which represents the attenuation amount of the digital attenuator in dB. Attenuation of the EC signal is performed, as we assume that the amplitude of the EC synthesizer is always greater than the amplitude of the TX synthesizer. The phase shift step
and attenuation step
are software selected, and limited by the hardware capability. The calibration operation mode is described in Algorithm 1.
Algorithm 1: Echo Cancellation calibration |
- 1:
Set the RF switch port to RX input - 2:
for; do - 3:
Set TX synthesizer and EC synthesizer to frequency - 4:
Set LO1 synthesizer to frequency - 5:
Set predefined value of digital attenuator - 6:
for Set EC synthesizer phase shift to ; do - 7:
Store data to a temporary array - 8:
end for - 9:
Find phase shift index at minimum magnitude as
- 10:
Change EC synthesizer phase shift to value and store it as - 11:
for Set digital att. to ; do - 12:
Store data to a temporary array - 13:
end for - 14:
Find attenuation shift index at minimum magnitude as
- 15:
store the attenuator value as - 16:
end for
|
After a complete frequency sweep, when and are obtained, the EC system can be enabled in normal operation mode.
4.2. The Proposed Normal Operation Mode Workflow
In normal operation mode, the proposed radar sweeps through the available frequency band and acquires complex-valued data. The EC system can be disabled or enabled, where, in the latter case, the calibration values and are used. In normal operation mode, an additional step is required, and it is not related with the EC system. The reference signal is needed because the signals of the LO1 synthesizer and TX synthesizer have different frequencies and phase lock times. Therefore, for each frequency step, the initial phase of the generated signal is unknown. The problem was solved by using a coaxial cable to feed the REF port of the RF switch, and guide the signal to its common output port, since the cable has a fixed length and causes a constant delay between the TX and RX ports. The obtained complex-valued signal represents the reference signal . The normal operation mode of this radar can be described with Algorithm 2.
The denotes the complex conjugate operator—it should be noted that the result does not correlate directly with the actual distance to the target, but has a constant offset caused by the reference line length and the phase response of the directional coupler. However, since it is only an offset, it does not have any other influence on the quality of the measurement. Due to this, in the experimental results, the radargram range is also expressed as relative.
4.3. Hardware Overview
The SFCW radar with EC was developed using widely available IC components, which can be controlled digitally. For speeding up the prototyping process, the radar was divided into the following sub-boards:
Transmitter (TX) synthesizer—Synthesizer board 1;
Echo Cancellation (EC) synthesizer—Synthesizer board 2;
Local Oscillator 1 (LO1) synthesizer—Synthesizer board 3;
Receiver board (IF down-converter, IQ demodulator, ADC, clock buffer);
FPGA board;
Digital attenuator board.
Algorithm 2: Normal operation mode |
- 1:
for; do - 2:
Set TX synthesizer and EC synthesizer to frequency - 3:
Set LO1 synthesizer to frequency - 4:
if EC is enabled then - 5:
Change EC synthesizer phase shift to - 6:
Change the digital attenuator value to - 7:
else - 8:
Disable the EC synthesizer - 9:
end if - 10:
Set the RF switch port to REF input - 11:
Obtain - 12:
Set the RF switch port to RX input - 13:
Obtain - 14:
Calculate the complex-valued IQ signal as - 15:
end for
|
All boards that include high-frequency RF signals were realized on a 4-Layer substrate for simpler impedance matching between wave-guide ports. Additional small modules were used, such as an RF Combiner, RF switch, directional coupler, amplifier, and attenuator. The hardware was designed according to the block scheme shown in
Figure 2. A Transverse Electromagnetic (TEM) flared antenna [
32], was used to transmit and receive the RF signal. A summary of the selected relevant parameters of the SFCW radar with an integrated EC system is shown in
Table 1.
As stated before, the start frequency and stop frequency were limited mainly by the amplifiers and antennas. With a different selection of these components, the frequencies could be extended to the range between 12.5 MHz to 6.4 GHz. The IF frequency has a constant value of = 2 MHz and is generated indirectly with LO1, whose output is defined as .
The PC was connected to the FPGA board, and communicates over a serial communication. This communication includes the control of digital configurable devices, such as transferring the raw IQ data back to the PC. The acquired data are then processed further on the PC. The PC itself could be replaced by using a storage device, where the needed configuration would be read-out directly by the FPGA, and also the acquired data would be written back to it.
6. Conclusions
The SFCW radar design with an integrated EC system is proposed in this paper. The system is especially suitable for GPR and through-wall imaging applications, where the difference in the echo power of different targets is usually large. The methodology of operation of such a system is known and has been presented in recent works, but the main difference is reflected in the implementation of such a system. This means that the system could mostly be suitable for power and size critical applications. Nowadays, this is crucial, due to the need to implement various sensors into, e.g., robots or Unmanned Aerial Vehicles (UAVs).
The experimental results showed that the proposed method is able to suppress the stationary signals using the proposed procedures. To verify the operation of the system in a real environment, a measurement was performed that included the use of antennas and a polygon with a static target. As an antenna with a certain frequency response was used, the results were not expected to be as successful as with the coaxial cable. However, the measurements showed that the removal of reflections was still successful at frequencies where the magnitude was high, which confirms the efficiency of the proposed system in practice. Attention must be given to a scenario where the stationary target disappears or the RCS changes. In these cases, the EC system would operate in the opposite manner and add artificial targets.
Future work could also include techniques that are currently implemented in automotive radars, such at the orthogonal noise waveforms method, and, additionally, increasing the visibility of targets with small RCS [
33]. Furthermore, adding an antenna frequency response block would increase the success of the EC system and allow use of a higher transmit power.
Since the system used CW signals, this means that the proposed method could also be applied to other radars that use the same working principle.