WO2022258138A1

WO2022258138A1 - Method for operating a gpr device

Info

Publication number: WO2022258138A1
Application number: PCT/EP2021/065180
Authority: WO
Inventors: Daniel Marco TREYER; Samuel LEHNER; Antonio Caballero
Original assignee: Proceq Sa
Priority date: 2021-06-07
Filing date: 2021-06-07
Publication date: 2022-12-15

Abstract

The invention relates to a method for operating a GPR device having a single-sideband up-converter (3) and to the GPR device itself. The GPR device further comprises a transmit antenna (1) connectable to the up-converter (3) and configured to transmit radar waves, a receive antenna (2) configured to receive radar waves, a down-converter (11) connectable to the receive antenna (2), and a monitor mixer (12) connectable to the up-converter (3) via a mixer calibration path (6). The monitor mixer (12) comprises a nonlinear element (22, 32, 32a) with a nonlinear transfer characteristic and a low-pass filter. The method comprises calibration steps for calibrating the single-sideband up-converter (3). The calibration steps comprise: (a) mixing, by means of the up-converter (3), a local oscillator signal (v_LO) at frequency f_LO and an intermediate signal (v_IF) at frequency f_IF, thereby generating a transmit signal (v_RF) comprising a desired frequency component in the upper sideband (USB) at f_LO + f_IF or in the lower sideband (LSB) at f_LO - f_IF, and at least one undesired frequency component, wherein an amplitude of the desired frequency component is larger than an amplitude of the least one undesired frequency component; (b) measuring, by means of the monitor mixer (12) connected to the up-converter (3), a monitor signal, (c) using the monitor signal to reduce an amplitude of the at least one undesired frequency component by adjusting the intermediate signal (v_IF).

Description

Method for operating a GPR device

Technical Field The invention relates to a method for operating a ground- penetrating radar (GPR) device having a single-sideband up-converter and to a GPR device.

Background Art

In the field of non-destructive testing GPR devices are conventionally used for probing the subsurface, e.g. a construction, concrete, reinforced concrete, a pavement or the ground or soil. For this purpose, the GPR device transmits radar waves, e.g. in a frequency range between 400 and 4000 MHz, into the subsurface and receives a back-reflected echo of the transmitted radar waves. Since the radar waves are reflected at changes of the electro-magnetic properties of the subsurface, such as a defect, a rebar, a pipe, etc., the echo may be used to reconstruct an image of the subsurface. For a better reconstruction of the image, it is useful to precisely control the transmitted radar waves, e.g. in terms of their frequency content.

A class of conventional GPR devices, e.g. implementing the stepped-frequency continuous wave (SFCW) method, comprises an up-converter, such as an IQ modulator for mixing a local oscillator signal at frequency f_LO and an intermediate signal at frequency f_IF < f_LO, thereby generating the transmit signal transmitted by a transmit antenna. Such method and device are e.g. known from WO2018161183A1.

GPR devices with an up-converter often exploit only one sideband of the up-converted signal, i.e. either the upper sideband (USB) at frequency f_LO + f_IF or the lower sideband (LSB) at frequency f_LO - f_IF. Hence, it is advantageous that other frequency components are ideally not present, or at least suppressed as much as possible, in the transmit signal. In conventional single sideband up-converters, the desired sideband is larger than undesired frequency components by at least 10 to 30 dB. Undesired frequency components present in the transmit signal typically comprise the lower sideband (or, respectively, upper sideband) and a local oscillator (LO) leakage at frequency f_LO.

Such undesired frequency components may lead to artefacts in the reconstructed image of the subsurface, in particular in the GPR A-scan, thereby deteriorating image quality. Further they may limit the data acquisition speed and/or acquisition depth, and they may require elaborate post-processing algorithms for reconstructing the image of the subsurface.

Disclosure of the Invention

The problem to be solved by the present invention is therefore to provide a method for operating a GPR device having a single-sideband up-converter which leads to a better quality of a reconstructed image of the subsurface and/or which allows a higher data acquisition speed and/or acquisition depth.

According to a first aspect of the invention, this problem is solved by the method for operating a GPR device having a single-sideband up-converter according to claim 1. According to a second aspect of the invention, the problem is solved by the GPR device of claim 14. All features described below are meant to define the method as well as the device, where applicable.

The GPR device comprises

- the single-sideband up-converter: The single-sideband up- converter in particular generates a transmit signal with a desired frequency component either in an upper sideband (USB) or in a lower sideband (LSB), which is larger than any other, undesired frequency component in the transmit signal, e.g. by 10 or 30 dB. In particular, the up-converter is a multiplicative mixer, e.g. an IQ modulator or a serrodyne modulator.

- a transmit antenna connectable to the up-converter and configured to transmit radar waves: “Connectable” in particular means connected or connectable by a switch, e.g. by a multiplexer. The transmit antenna may be one transmit antenna, or it may in particular comprise several transmit antennas operable in sequence, e.g. by a first multiplexer.

- a receive antenna configured to receive radar waves: Also the receive antenna may be one receive antenna, or it may in particular comprise several receive antennas operable in sequence, e.g. by a second multiplexer.

- a down-converter connectable to the receive antenna: The down- converter may be connected to the receive antenna through the second multiplexer. Further, an electrical path between the receive antenna and the down-converter may comprise a first amplifier and/or a low-pass filter.

- a monitor mixer connectable to the up-converter via a mixer calibration path: The monitor mixer comprises a nonlinear element with a nonlinear transfer characteristic and a low-pass filter. In the following, the term “mixer calibration” is used synonymously with “up-converter calibration”.

The monitor mixer in particular is configured to facilitate a detection of undesired frequency components, such as an undesired (e.g. lower) sideband or an LO leakage. In case, the detected undesired frequency component is the undesired (e.g. lower) sideband only, the monitor mixer may also be called image detector. Advantageously, the monitor mixer is arranged in parallel to the down- converter, in particular with two switches, allowing to either switch the down- converter in a receive signal path, typically in a measurement routine, or the monitor mixer, typically in an up-converter calibration routine, which is detailed below. This has the advantage that both, the down-converter and the monitor mixer may use the same analog and digital electronics, e.g. amplifiers, a filter bank, an ADC and an FPGA, in the receive signal path. In other words, the same elaborate components used for the measurement routine may also be used for the calibration routine, which saves costs and space in the device.

Alternatively, the mixer calibration path may be any connection between the up-converter and the monitor mixer, e.g. an antenna calibration path, given that a signal level in the connection are adequate.

In a further embodiment, the monitor mixer may not be switched in and out of the circuit. Rather, the monitor mixer may be connected, in particular permanently, to the up-converter, e.g. by means of a power splitter configured to provide a part of the transmit signal from the up-converter to the monitor mixer, in particular via dedicated filters and/or amplifier(s).

The method for operating a GPR device comprises calibration steps for calibrating the single-sideband up-converter, e.g. in the calibration routine. The calibration steps comprise

- mixing, by means of the up-converter, a local oscillator signal (v_LO) at frequency f_LO and an intermediate signal (v_IF) at frequency f_IF, thereby generating a transmit signal (v_RF) comprising a desired frequency component in the upper sideband (USB) at f_LO + f_IF or in the lower sideband (LSB) at f_LO - f_IF, and at least one undesired frequency component, wherein an amplitude of the desired frequency component is larger than an amplitude of the least one undesired frequency component,

- measuring, by means of the monitor mixer connected via the mixer calibration path to the up-converter, a monitor signal,

- using the monitor signal to reduce an amplitude of the at least one undesired frequency component by adjusting the intermediate signal (v_IF). Such method facilitates a suppression of undesired frequency components in the transmit signal. In particular, it may increase a difference between the desired frequency component and the at least one undesired frequency component to 40 dB, in particular 60 dB, or more. In this way, the quality of the image reconstructed from received radar signals is improved, in particular artefacts in the GPR A-scan, e.g. due to the lower sideband or to LO leakage, are avoided. Further, a data acquisition speed of the GPR device may be increased, thereby increasing productivity of the GPR measurements. Additionally or alternatively, the above method facilitates a greater acquisition depth, i.e. evaluating the received radar signal at greater distance from the GPR device.

Nonlinear element

In an embodiment, a first derivative of a transfer characteristic of the nonlinear element increases or decreases with increasing voltage. The transfer characteristic in particular is a relation between an input of the nonlinear element, e.g. an input voltage, and an output of the nonlinear element, e.g. an output current. In particular, the transfer characteristic may be exactly or approximately piecewise linear with different derivatives in at least two linear pieces.

Advantageously, the nonlinear element has an input Ie and at least one output Oe. A signal derived from the signal received by the receive antenna is applied to the input Ie. The output Oe is fed to the low-pass filter.

The output carries a signal (a voltage or a current) that is a function of the input, with

Oe = f(Ie).

Advantageously, the non-linear element is progressively nonlinear. For a progressively nonlinear element, the function f is progressive in the sense that f (Iel) / f (Ie2) > k, wherein f is the derivative of fin respect to Ie, and f is positive,

Iel is any voltage in a high-voltage range RH,

Ie2 is any voltage in a low-voltage range RL.

RL and RH are distinct voltage ranges with RH comprising higher voltages in respect to a zero signal of the input Ie than RL, and k is a constant of at least 10, in particular of at least 100. Advantageously, another suitable non-linear element may be symmetric with respect to Ie = 0, i.e. a mathematically odd function, with finite derivatives. A possible realization thereof is an ideal rectifier, i.e. Oe ~ |Ie|, or an approximation thereof.

In case the transfer characteristic is symmetric to the origin, e.g. of a diagram output current vs. input voltage, i.e. an odd function in mathematical terms, an operating point of the nonlinear element is advantageously chosen such that an integral of an area under the transfer characteristic in operation is non-zero.

If the input signal Ie comprises several frequency components with one being significantly stronger than the other(s), the non-linear transmission of such a non-linear element causes that a DC component of the signal after the low-pass is predominantly governed by the amplitude of the strongest frequency component, i.e. the desired frequency component.

In an embodiment, the nonlinear element comprises at least one of a diode and a transistor. Diodes typically are progressively nonlinear in the above sense since they exhibit a reverse range of high (ideally infinite) resistance, e.g. for an input voltage below 0, and a forward range of low resistance, where the output current increases exponentially with increasing input voltage, typically for low positive input voltages. Advantageously, the nonlinear element has an operating range of at least up to the frequency f_LO, e.g. up to 4000 MHz. An example for such nonlinear element is a Schottky diode.

In a further embodiment, the nonlinear element comprises at least two diodes in differential configuration. This means that two diodes are arranged in the circuit in parallel for the input signal but reversely to each, in particular in series for the output signal, such that a first diode operates in the forward range when a second diode operates in the reverse range, and vice versa. Such two diodes form a singly balanced down-converting mixer with differential output. Further, the diodes may be arranged as a full-wave rectifier. Such differential configuration improves detection efficiency of the monitor mixer.

Advantageously, the low-pass filter of the monitor mixer comprises a capacitor. In particular, the capacitor may comprise a capacitive transmission line stub. Thus, an output of the nonlinear element will charge the capacitor. Further, the low-pass filter may comprise an inductor, e.g. capacitor and the inductor forming the low-pass filter. Thus, the capacitor may be discharged via the inductor. In particular, the low-pass filter is configured to have a cut-off frequency between 2*f_IF and f_LO, such that f_LO is filtered out of the monitor signal. In a way, such monitor mixer acts as an envelope detector. A simple example of such monitor mixer is a classical diode detector. Calibration of IQ modulator

In an embodiment, the up-converter comprises an IQ modulator. In that case, the intermediate signal (v_IF) comprises an in-phase component (i(t)) and a quadrature component (q(t)), wherein the in-phase component (i(t)) and the quadrature component (q(t)) have frequency components at the frequency f_IF. For single-sideband generation, the quadrature component (q(t)) is shifted with regard to the in-phase component (i(t)) by a phase shift of +90° or -90°, depending on which sideband is desired. In particular, this means for an ideal IQ modulator that 1(f) / Q(f) = +/-j, i.e. either +j or -j with j being the imaginary unit, in frequency domain, wherein 1(f) and Q(f) are Fourier transforms of i(t) and q(t), respectively.

In general, the transmit signal (v_RF) generated by an ideal IQ modulator has the following form

In the ideal case, when i(t) and q(t) are in quadrature as stated above, v_RF(t) has only non-zero frequency components at the upper- or lower sideband, i.e. at f_LO + f_IF or f_LO - f_IF, depending on the phase relation of 1(F) with respect to Q(f). In any practical analog implementation of an IQ modulator, there will be a residual component of the undesired sideband and a residual component of the LO signal (LO leakage) present at its RF output.

Adjusting the intermediate signal (v_IF) comprises the step of changing at least one of the in-phase component (i(t)) and the quadrature component (q(t)) to reduce the amplitude of the at least one undesired frequency component.

For a real IQ modulator, the non-idealities responsible for the undesied sideband and LO leakage may be accounted for by introducing error terms referenced to the I and Q inputs. In frequency domain, the effective in-phase and quadrature components (1(f), Q(f)) have at the frequency f_IF the following complex amplitudes

with amplitude imbalance e, phase imbalance Q, and I_f_IF / Q_f_IF = +/-j. In particular I_f_IF and Q_f_IF have an arbitrary but equal amplitude. At the frequency f=0, 1(f) and Q(f), in frequency domain, have the constant offsets oi and oq l(f=0) = oi, and Q(f=0) = oq.

In particular, at the output of the IQ modulator, the amplitude of the residual undesired sideband with respect to the desired sideband is proportional to sqrt(e² + Q²), and the amplitude of the LO leakage is proportional to sqrt(oi² + oq²). Thus, adjusting the in-phase and quadrature components (i(t), q(t)) advantageously comprises deliberately introducing at least one of the amplitude imbalance (s c), the phase imbalance (0_c) and the offsets oi_c and oq_c, onto the complex input signal v_IF(t) = i(t) + j*q(t) of the IQ modulator, to counter-act or compensate for the respective error quantity (e, Q, oi, oq) inherent to the IQ modulator.

Undesired sideband In a first case, the at least one undesired frequency component comprises an undesired sideband. The undesired sideband may be the upper sideband, contaminating the transmit signal at frequency f_LO + f_IF, or the lower sideband at f_LO - f_IF. Particularly, the desired component corresponds to the upper sideband, and the undesired sideband is the lower sideband (LSB). In such case, using the monitor signal to reduce an amplitude of the at least one undesired frequency component comprises

- determining an image component (u_2IF) at frequency 2*f_IF in the monitor signal: The image component (u_2IF) corresponds to the undesired frequency component, i.e. the undesired sideband, which, in frequency domain, has a distance of 2*f_IF from the desired sideband. Advantageously, the image component is determined by digital processing means, such as an FPGA, connectable to the monitor mixer via an analog-to-digital converter (ADC).

- adjusting the intermediate signal (v_IF), in particular the in-phase and quadrature components (i(t), q(t)), as a function of an amplitude (amp(u_2IF)) and/or a phase (phase(u_2IF)) of the image component (u_2IF): Also this step may be performed by the digital processing means.

- iterating the previous steps and minimizing an absolute value (abs(u_2IF)) of the image component (u_2IF). In other words, an optimization problem is solved, wherein i(t) and q(t) are modified to i_mod(t) and q_mod(t), and the modified i_mod(t) and q_mod(t) are fed to the input of the IQ modulator. Thus, a modified monitor signal is generated, which may again be evaluated according to the above steps. In particular, for the case of an undesired sideband, adjusting the in- phase and quadrature components (i(t), q(t)) comprises changing at least one of the amplitude imbalance (e) and the phase imbalance (Q). Advantageously, the amplitude imbalance (e) is adjusted dependent on the complex -valued signal u_2IF or on an amplitude (amp(u_2IF)) of the image component (u_2IF). Further advantageously, the phase imbalance (Q) is adjusted dependent on the complex -valued signal u_2IF or on an amplitude (amp(u_2IF)) in particular in connection with a phase (phase(u_2IF)) of the image component (u_2IF). In particular, a correction coefficient (e_c) for the amplitude imbalance may be used to generate modified i_mod(t) and q_mod(t), having deliberately imposed amplitude imbalance (a_c) to compensate the amplitude imbalance (e) of the IQ modulator. Further, a correction coefficient (6_c) for the phase imbalance may be used to generate further modified i_mod(t) and q_mod(t), having deliberately imposed phase imbalance (0_c) to compensate the phase imbalance (Q) of the IQ modulator.

For iteratively minimizing the absolute value (abs(u_2IF)) of the image component (u_2IF), any suitable optimization algorithm may be used, e.g. Newton’s method or a gradient descent method or a bisection method modified for complex numbers or a random search.

In a particular embodiment, iterating the steps comprises per iteration changing only the amplitude imbalance (e) or only the phase imbalance (Q). In particular, in subsequent iterations the amplitude imbalance (e) and the phase imbalance (Q) may be changed altematingly. This makes the implementation simpler and the computations less expensive, while the solutions still converges to an optimal state, i.e. the undesired sideband being suppressed and e.g. weaker than the desired sideband by at least 40 to 60 dB.

In such embodiment, an iteration for determining a next correction coefficient a c next for the amplitude imbalance (e) may comprise the following steps

- keeping the correction coefficient 0_c for the phase imbalance (Q) constant,

- measuring the monitor signal for different values a_c_i of the correction coefficient for the amplitude imbalance (e),

- determining the next correction coefficient e c next as value of e_c, which minimizes the absolute value (abs(u_2IF)) of the image component (u_2IF).

Analogously, an iteration for determining a next correction coefficient 9_c_next for the phase imbalance (Q) may comprise the following steps - keeping the correction coefficient e_c for the amplitude imbalance

(e) constant,

- measuring the monitor signal for different values 9_c_i of the correction coefficient for the phase imbalance (Q),

- determining the next correction coefficient 9_c_next as value of 9_c, which minimizes the absolute value (abs(u_2IF)) of the image component (u_2IF).

In general, the optimization needs to finish after a finite number of iterations. In particular, the iteration of the steps may be terminated dependent on fulfilling at least one of the following stop criteria

- the absolute value (abs(u_2IF)) of the image component (u_2IF) is below a defined first threshold,

- a change of the absolute value (abs(u_2IF)) of the image component (u_2IF) compared to a previous iteration is below a defined second threshold,

- a defined number of iterations is reached.

For a continued re-calibration, as e.g. needed to adapt to temperature changes and drift, the initial calibration may be updated by taking only a few measurement points at long time intervals.

In general, adjusting the intermediate signal (v_IF), in particular the in-phase and quadrature components (i(t), q(t)), as a function of both, the amplitude (amp(u_2IF)) and the phase (phase(u_2IF)) of the image component (u_2IF), as described above, has several advantages over just using the amplitude (amp(u_2IF)). In the latter case, a first derivative of the optimized quantity (abs(u_2IF)) is zero at the minimum, and the optimization problem is nonlinear. This makes it computationally more difficult to solve.

When using both, the amplitude (amp(u_2IF)) and the phase (phase(u_2IF)), the monitor signal may be expressed as a complex -valued voltage. In this case, the first derivative does not disappear at the minimum of the optimized quantity (abs(u_2IF)). Rather, different values of the correction coefficient e_c while 9_c is constant, or respectively 9_c while e_c is constant, form orthogonal lines in the complex plane of u_2IF. This leads to a linear optimization problem, wherein an optimal e_c, or respectively 9_c, is the one with the smallest distance from an origin of the complex plane of u_2IF. Such optimization converges faster, is less susceptible to noise and computationally less expensive. In theory, as few as two points in the complex plane, i.e. measurements of amp(u_2IF) and phase(u_2IF) at two distinct values of e_c or 9_c, are sufficient to determine the minimum at a particular iteration step. In practice, however, due to noise and possible nonlinear effects, it is advantageous, that the two points are located at opposite sides about the origin in the u_2_IF planes, in particular the correction coefficients of two trial points are e_c_2 = -e_c_l, and 6_c_2 = 9_c_l, respectively.

In general, it is a requirement for the above described steps of using not only the amplitude (amp(u_2IF)) of the undesired frequency component but also its phase (phase(u_2IF)) that all involved signals are phase-locked with regard to each other, in particular the intermediate signal (v_IF), in particular the in-phase and quadrature components (i(t), q(t)), the local oscillator signal (v_LO), and the ADC and DAC clock signals. In particular, a phase shift between a phase of an envisioned common subharmonic frequency of these signals is constant over time.

Undesired LO leakage

In a second case, the at least one undesired frequency component comprises a local oscillator (LO) leakage component at frequency f_LO. Such case may be combined with the first case above, i.e. both, the undesired sideband and the undesired LO leakage may be minimized simultaneously. Features of the optimization described above with respect to the first case are also applicable here.

If the at least one undesired frequency component comprises a local oscillator (LO) leakage component at frequency f_LO, using the monitor signal to reduce an amplitude of the at least one undesired frequency component comprises

- determining a leakage component (u_IF) at frequency f_IF in the monitor signal: Such leakage component (u_IF) corresponds to the undesired frequency component since, in frequency domain, it has a distance of IF from the desired (upper or lower) sideband.

- adjusting the intermediate signal (v_IF), in particular the in-phase and quadrature components (i(t), q(t)), as a function of an amplitude (amp(u IF)) and/possibly also a phase (phase(u_IF)) of the leakage component (u_IF),

- iterating the previous steps and minimizing an absolute value (abs(u IF)) of the leakage component (u_IF).

In particular, adjusting the in-phase and quadrature components (i(t), q(t)) in this case comprises changing at least one of the offsets (oi, oq). Correction coefficients oi_c and oq_c for the offsets minimizing the abs(u IF) component and therefore the LO leakage level may be iteratively determined in the same way as the correction coefficients e_c and 9_c to minimize the abs(u_2IF) component and therefore the undesired sideband level, see above.

Further signal processing

In an embodiment, the method comprises filtering out harmonics of f_LO and sidebands thereof from the transmit signal between the up-converter and the down-converter, and in particular in a calibration routine between the mixer calibration path and the monitor mixer, in particular by a low-pass filter having a cut off frequency between f_LO and 2*f_LO. This is useful for reducing artefacts in the received signal, originating from the harmonics and sidebands of the harmonics. In a sense, this reduces self-interference and thereby improves the quality of the reconstructed image.

For this purpose, the GPR device may in particular comprise a filter bank with switchable low-pass filters, wherein the low-pass filters have different cut off frequencies. Such filter bank is advantageous if f_LO is changed during a measurement routine, as it is e.g. the case in the SFCW method mentioned in the Background Art section. An alternative realization would be an electronically tunable low-pass filter, having continuously or discretely adjustable cut-off frequency.

Further, the transmit signal coming from the mixer calibration path and the received signal from the receive antenna are advantageously amplified by a first amplifier before being input to the down-converter or, respectively, the monitor mixer. Such first amplifier may comprise an additional low-noise amplifier and may be arranged at the output of the receive antenna calibration switches and/or at the input of the filter bank.

Advantageously, measuring the monitor signal at the monitor mixer is done by an analog-to-digital converter, and adjusting the intermediate signal (v_IF), in particular the in-phase and quadrature components (i(t), q(t)), is done in digital domain. The method then further comprising the steps of

- analog-to-digital converting the mixing signal and in particular determining the image component (u_2IF) and/or the leakage component (u_IF) in the monitor signal, before adjusting the intermediate signal (v_IF), and

- digital-to-analog converting the adjusted intermediate signal (v_IF), in particular the corrected in-phase and quadrature components (i(t), q(t)), before supplying them to the up-converter.

For this purpose, the device further comprises - an analog-to-digital converter (ADC) connectable to the monitor mixer,

- a digital -to-analog converter (DAC), in particular two digital-to- analog converters, one for the in-phase component (i(t)) and one for the quadrature component (q(t)), connected to the up-converter.

Further and as mentioned above, the device may comprise an FPGA connected with its input to the analog-to-digital converter (ADC) and with its output to the digital-to-analog converter(s) (DAC). The FPGA is in particular configured to generate and adjust the intermediate signal (v_IF), in particular the in-phase and quadrature components (i(t), q(t)), e.g. as described above.

Operation

In general, the method for operating the GPR device advantageously has a measurement routine, wherein GPR data are acquired from a subsurface, and a mixer calibration routine, wherein the single- si deb and up-converter is calibrated as described above. Further calibration routines may include a calibration of the transmit and receive antennas. Antenna calibration paths in the device configured for this purpose typically have more damping, e.g. at least 10 dB more damping, than the mixer calibration path.

In an embodiment, the method thus comprises the steps of

- upon initiating the mixer calibration steps, connecting the up- converter and the monitor mixer to the mixer calibration path. For this purpose, the device may comprise a first and second multiplexer, respectively.

- upon initiating measurement steps, connecting the up-converter to the transmit antenna and the receive antenna to the down-converter. This may, again, be effected by switching the first and second multiplexers.

In particular, when a filter bank (and first amplifier) is present, the input of the filter bank (or, respectively, the first amplifier) is selectably connectable to the receive antenna and to the mixer calibration path via the second multiplexer. The output of the filter bank is then selectably connectable to the down-converter and to the monitor mixer, e.g. via a switch.

Advantageously in the measurement routine, the method further comprises measurement steps comprising

- changing a value of f_LO in discrete steps, in particular between 400 and 4000 MHz, - for each discrete step, changing a value of f_IF, in particular according to the equation f_IF = x + n*y.

Example values are x = 2 MHz, y = 0.4 MHz and n = (0,1,...,5). Such shifting of frequency components in the transmit signal, in other words a frequency sweep, is done e.g. in the SFCW method. This helps to acquire more information about the subsurface, improving signal and image quality. Further, this increases acquisition depth and improves spatial resolution.

In an embodiment, a mixer calibration routine for such GPR device comprises a further calibration step as follows

- for each combination of f_LO value with f_IF value, determining the correction coefficients (e_c, 9_c) for the amplitude imbalance (e) and the phase imbalance (Q), and/or determining the correction coefficients (oi_c, oq_c) for the offsets (oi, oq). This may be necessary since the optimal correction coefficients are frequency-dependent.

In a simpler embodiment, calibration may only be performed for selected combinations of f_LO value with f_IF value. Optimal correction coefficients for the remaining value pairs f_LO and f_IF may then e.g. be found by interpolation.

In general, it may be sufficient to perform calibration of the single sideband up-converter once when manufacturing the GPR device, then storing the correction coefficients in a memory, e.g. of the FPGA. However, a degree of suppression of the at least one undesired frequency component typically varies over time, in particular due to temperature variations. Thus, optimal correction coefficients may vary over time, and particularly between start-up of the device and during operative measurements.

Hence, in an advantageous embodiment, the method comprises performing the calibration steps at start-up of the GPR device. Further, it may be advantageous to perform the calibration steps after a heat-up time of the GPR device, e.g. between 1 and 10 min after start-up, or in regular time intervals, e.g. every 5 min. Advantageously, the calibration steps are performed or quasi-continuously between measurement sweeps, one or more iteration step at a time, before advancing to the next measurement sweep. In this way, the at least one undesired frequency component is optimally suppressed, e.g. by at least 40 to 60 dB compared to the desired frequency component, at every time. GPR device

According to the second aspect of the invention, the initially described problem is described by a GPR device. The above described specifications and embodiments of features of the method shall also apply to the GPR device, and vice versa. Such GPR device comprises

- a single-sideband up-converter,

- a transmit antenna connectable to the up-converter and configured to transmit radar waves,

- a receive antenna configured to receive radar waves,

- a down-converter connectable to the receive antenna,

- a monitor mixer connectable to the up-converter via a mixer calibration path, wherein the monitor mixer comprises a nonlinear element with a nonlinear transfer characteristic and a low-pass filter, and

- processing means, which in particular are adapted to execute the steps of the above-described method.

As described before, such GPR device may be calibrated, in particular at least one undesired frequency component in the transmit signal generated by the up-converter may be suppressed, e.g. by at least 40 to 60 dB compared to the desired frequency component, i.e. the desired (upper or lower) sideband. Thus, the GPR device delivers better quality data and hence clearer images of the subsurface. Further, the acquisition speed and/or acquisition depth may be increased. In particular, either of acquisition speed or depth alone may be increased by a factor of up to two, respectively.

In an advantageous embodiment, a first derivative of a transfer characteristic of the nonlinear element increases or decreases with increasing voltage. Further, the nonlinear element may comprise at least one of a diode and a transistor, in particular two or four diodes or transistors in differential configuration at the input or/and at the output. In an embodiment, the low-pass filter of the monitor mixer comprises a capacitor and in particular an inductor. The capacitor may comprise a capacitive transmission line. The inductor may comprise an inductive transmission line. Further, the low-pass filter advantageously has a cut-off frequency between 2*f_IF and f_LO, such that f_LO and harmonics of f_LO are filtered out. For details see the above description as well as the examples in the section Modes for Carrying Out the Invention. In a particular embodiment, the monitor mixer comprises two diodes and two low-pass filters in differential output configuration. Such series diode pair together with the low-pass filter at the output forms a singly balanced down converting mixer with differential output. This makes the detection of the monitor signal more efficient and more robust against noise and interference in the circuit downstream the monitor mixer.

Further, the monitor mixer may comprise a shunt inductor at its output. Such shunt inductor provides a DC return for the diodes, which improves detection sensitivity. The shunt inductor also has a DC resistance, resulting in a residual DC voltage at the output of the monitor mixer that is proportional to a level of the dominant frequency component in the input signal, i.e. the desired sideband. Further, the impedance of the shunt inductor at frequencies IF and 2*IF advantageously is large enough in order not to load these frequency components. In an advantageous embodiment, the up-converter comprises an IQ modulator. In such embodiment, the device further comprises a local oscillator (LO) configured to generate a local oscillator signal (v_LO) at frequency f_LO and connected to a first input of the IQ modulator. The processing means, in particular an FPGA, are connected to a second input of the IQ modulator via two digital-to-analog converters (DAC), one for i(t) and one for q(t), and configured to generate an intermediate signal (v_IF), in particular the in-phase component (i(t)) and the quadrature component (q(t)), at frequency f_IF.

In an embodiment, such as a GPR device implementing the SFCW method, the local oscillator (LO) is configured to sequentially switch the frequency f_LO, in particular stepwise to discrete values between 400 and 4000 MHz. The digital signal processing means are configured to sequentially switch the frequency f_IF, in particular stepwise to discrete values between 2 and 4 MHz. The sequential stepwise switching of f_LO and f_IF may be in various orders, in particular linearly ascending, linearly descending, or arbitrary (pseudo-random). Advantageously, the local oscillator (LO) comprises two wideband synthesizers configured to be alternatingly connected to the first input of the IQ modulator. This allows a faster switching of the LO signal: While one synthesizer is providing the LO signal at f_L01 to the IQ modulator, the other synthesizer is prepared and set to a next value of f_L02, such that it directly provides the correct signal when switched, and vice versa. This increases the acquisition speed and/or acquisition depth by allowing more or finer frequency steps in a given time interval.

A typical LO switching period is 20 or 40 micro seconds. Further, the device may comprise a filter bank comprising switchable low-pass filters or a tunable filter. An input of the filter bank or the tunable filter is selectably connectable either to the receive antenna or to the mixer calibration path. An output of the filter bank or the tunable filter is selectably connectable either to the down-converter or to the monitor mixer. In particular, the low-pass filters of the filter bank have cut-off frequencies between f_LO and 2*f_LO adapted to the different discrete values of f_LO. Such filter bank facilitates filtering out harmonics of f_LO, each comprising its own sidebands, which otherwise may be mirrored to lower frequencies and appear as artefacts in the acquired data.

In an embodiment, the GPR device comprises an analog-to-digital converter (ADC) selectably connectable, in particular via an amplifier, either to an output of the mixing monitor or to an output of the down-converter, and connected to an input of the processing means, in particular of the FPGA. This means that either the down-converter or the mixing monitor may be connected to the receiver path, such that both may use the same elaborate analog and digital components.

Antenna array In an advantageous embodiment, the GPR device is configured to acquire radar data on at least two measurement lines quasi-simultaneously. For this purpose, the GPR device comprises

- n transmit antennas selectably connectable to the up-converter via a first multiplexer and configured to transmit radar waves, and m receive antennas selectably connectable to the down-converter via a second multiplexer and configured to receive radar waves, in particular wherein m = n-1 or n or n+1.

The transmit antennas and the receive antennas are advantageously arranged in a staggered arrangement. This saves space, thereby leading to a smaller form factor of the GPR device, while reducing cross-talk between neighbouring antennas. In an embodiment, the n transmit antennas are arranged on a first straight line, and the m receive antennas are arranged on a second straight line, wherein position of the antennas on the first and second lines are parallel but offset from each other. In particular, the transmit antennas and the receive antennas are equally spaced. In general, such arrangement of n transmit and m receive antennas, in other words an antenna array, leads to n+m-1 measurement lines if measurements are performed with pairs, in which each transmit antenna is only combined with the neighbouring two receive antennas. In an example with n=3 and m=4, 6 measurement lines may be measured quasi-simultaneously, meaning the pairs of transmit and neighbouring receive antennas are sequentially activated, in particular with different values of f_IF, leading to different frequencies of the desired sideband f_LO + f_IF or f_LO - f_IF. In a way, the frequency sweep is distributed not only over the different f_LO frequencies but additionally over the different measurement lines.

Accordingly, first and second multiplexers may be configured to activate combinations of pairs of a transmit antenna with a neighbouring receive antenna sequentially. In particular, the transmit antennas may be configured to sequentially transmit transmit signals (v_RF) with different frequencies, in particular f_LO and f_IF, of the desired frequency component. This facilitates a fast acquisition of radar data on more than one line, while maintaining a high data quality, as well as an efficient use of the transmit and receive hardware. Computer program

A third aspect of the invention relates to a computer program and/or a field programmable logic device (FPGA) comprising instructions to cause the GPR device described before to execute the steps of the above-described method.

Other advantageous embodiments are listed in the dependent claims as well as in the description below.

Brief Description of the Drawings

The invention will be better understood and objects other than those set forth above will become apparent from the following detailed description thereof. Such description makes reference to the annexed drawings, wherein: Fig. 1 shows a circuit diagram of a GPR device according to an embodiment of the invention;

Figs. 2 and 3 show circuit diagrams of a monitor mixer according to embodiments of the invention;

Figs. 4a and 4b show schematic frequency spectra of a transmit signal and a monitor signal, respectively, according to an embodiment of the invention; Fig. 5 shows a block diagram of digital processing means according to an embodiment of the invention;

Fig. 6 shows a flow diagram of a method for operating a GPR device according to an embodiment of the invention.

Modes for Carrying Out the Invention

Fig. 1 shows a circuit diagram of a GPR device with an array of three transmit antennas 1 and four receive antennas 2, in particular a GPR device implementing the SFCW method. In general, the device may comprise a different number of transmit and receive antennas, in the simplest case one transmit antenna 1 and one transmit antenna 2. By means of the three transmit antennas 1 and four receive antennas 2, quasi -simultaneous measurement of six measurement lines is facilitated as described before. The six measurement lines are formed by pairs of each of the three transmit antennas with its two neighbouring receive antennas. For each of the antenna pairs, the GPR device comprises an antenna calibration line 7, which may be switched into the circuit by transmit antenna calibration switches 5a and receive antenna calibration switches 8a instead of the transmit and receive antennas in order to calibrate the antenna path. The purpose of having multiple parallel measurement lines is to increase the lateral spatial resolution of the reconstructed image of the subsurface within a single survey scan.

In order to reduce cross-talk between the antennas and make the form-factor of the device smaller, the transmit and receive antennas are advantageously arranged in a staggered arrangement, e.g. as shown in Fig. 1.

In a measurement routine, the transmit antennas 1 are connected to an IQ modulator 3, which is a single-sideband up-converter, on a transmit side 19 of the GPR device. The IQ modulator 3 provides a transmit signal RF (at radar frequencies, such as between 400 and 4000 MHz) to the transmit antennas 1, e.g. via a filter. In the depicted case of several transmit antennas 1, the transmit signal RF is switched to the different transmit antennas 1 sequentially via a first multiplexer 5.

The IQ modulator 3 has three inputs, one for a local oscillator (LO) signal and two for the intermediate signal consisting of an in-phase component I and a quadrature component Q. The LO signal is generated by a wideband synthesizer 4, in particular two switchable wideband synthesizers as shown, at frequency f_LO.

Before being supplied to the IQ modulator 3, the LO signal is advantageously filtered, e.g. lowpass-filtered to suppress harmonics of f_LO. In the embodiment of Fig. 1, the GPR device comprises two synthesizers 4. In operation, one synthesizer is connected to the LO input of the IQ modulator 3, while the other synthesizer is prepared and set to a next value of f_LO, and then the other synthesizer is routed to the LO input of the IQ modulator. In this way, a frequency sweep, as e.g. required in the SFCW method, may be performed faster.

Further, the GPR device comprises two digital-to-analog (DAC) converters 17 and 18, which are connected upstream to the I and Q inputs of the IQ modulator 3. The DACs 17 and 18 convert the in-phase component I and a quadrature component Q of the intermediate signal TX IF (v_IF), which are generated and adjusted in the digital domain, into the analog domain. Generating and adjusting I and Q may be done in an FPGA, see also Fig. 5.

On a receive side 20 of the GPR device, a first amplifier 9 is advantageously connected to the receive antennas 2 via a second multiplexer 8. Advantageously, low-noise amplifiers 9a are connected between the receive antennas 2 and the second multiplexer 8. The low-noise amplifiers 9a reduce noise that is due to the signal losses of the transmission lines between transmit antenna 2 and the second multiplexer 8, and noise due to the signal losses of the second multiplexer 8. The low noise-amplifiers 9a also help to improve the input matching seen by the receive antennas 2. By switching the first multiplexer 5 and the second multiplexer 8, all pairs of transmit and receive antennas may be operated. Alternatively, the antenna calibration lines 7 or a mixer calibration line 6 may be connected between the transmit side 19 and the receive side 20 of the device. The mixer calibration line 6 is switched in the circuit, in particular in connection with a monitor mixer 12, for calibrating the IQ modulator 3, in particular for adjusting the in-phase and quadrature components I and Q of the intermediate signal TX IF (v_IF), and thereby the transmit signal RF, in order to suppress undesired frequency components in the transmit signal RF.

Further, the received radar signal is supplied to a filter bank 10. The filter bank 10 comprises several, in particular four, switchable low-pass filters, which have cut-off frequencies between f_LO and 2*f_LO, for filtering out harmonics of the fundamental frequency f_LO. The cut-off frequencies of the several low-pass filters differ from each other and are configured to fulfil the above condition for any value of f_LO used in the frequency sweep, e.g. for f_LO between 400 and 4000 MHz. Example values for the cut-off frequencies of the four low-pass filters are around 800, 1400, 2300 and 4000 MHz. Assuming that the transmit signal, at a point of time during the measurement routine or during the calibration routine, has the stepped frequency component of 700 MHz. The harmonics would be at 1400, 2100, 2800, 3500 MHz. These in turn have LO leakage and sidebands. However, a frequency spacing, and amplitude and phase ratios of the sidebands around the harmonics are not the same as for the fundamental 700 MHz. Since the monitor mixer 12 is broadband (in order to cover frequencies up to a maximum value of f_LO, e.g. 4000 MHz), the down- converted products of the down-converter 11, or the down-mixed products of the monitor mixer 12 of the harmonics would overlap with those of the fundamental wave at its output. As a result during measurement routine, the output of the down- converter 11 could no longer be interpreted as radar wave echo of frequency f_LO probing the subsurface alone, but also from harmonics thereof, although at reduced intensity, thereby degrading the reconstructed image. Further, during mixer calibration, the output signal of the monitor mixer 12 could no longer be interpreted in terms of a minimization of the LO leakage and sideband exclusively of the fundamental wave.

Therefore, the filter bank 10 is configured to filter out the harmonics from the received signal, thereby improving a detection and suppression of the at least one undesired frequency component, e.g. the undesired (lower or upper) sideband or the LO leakage. Advantageously, the filter bank 10 is configured to suppress the harmonics for each value of f_LO to at least 40 dB below the fundamental component f_LO.

From the output of the filter bank 10, the signal is supplied either to a down-converter 11 or to the monitor mixer 12. The down-converter 11 and the monitor mixer 12 are arranged in parallel and may selectively be connected with the filter bank 10 and the further electronic components, e.g. a second amplifier 15, by two switches 13 and 14.

During a measurement routine, i.e. when the transmit antennas 1 and receive antennas 2 are used to acquire radar data, the received signal from the receive antennas 2 is routed via the down-converter 11. The down-converter 11 is further connected to the output of the synthesizer(s) 4 generating the LO signal at frequency f_LO. The down-converter 11 is configured to down-convert the received signal in order to retrieve the frequency component at f_IF. The down-converted signal, in particular in comparison with the original intermediate signal at f_IF, in general contains information about a travel path of the radar waves between transmit antenna 1 and receive antenna 2, i.e. in particular about the subsurface. For retrieving an image of the subsurface, the down-converted signal may be filtered and further amplified by a second amplifier 15. Then, the signal is converted to digital domain by an analog-to-digital converter (ADC) 16. The ADC 16 supplies the digitized signal RX IF to digital processing means (not shown in Fig. 1), in particular an FPGA. Advantageously, this is the same digital processing means as the one generating and adjusting the intermediate signal TX IF, in particular the components I and Q, see also Fig. 5.

During a calibration routine, in particular for the IQ modulator 3, the mixer calibration path 6 connects the transmit side 19 and the receive side 20 (instead of the transmit antennas 1 and the receive antennas 2). Further, switches 13 and 14 are switched to the monitor mixer 12. Thus, the monitor mixer 12, instead of the down-converter 11, is connected to the circuit on the receive side 20.

In general, the monitor mixer 12 is configured to detect at least one undesired frequency component in the signal supplied to its input, i.e. in particular the transmit signal from the IQ modulator 3 conducted via the mixer calibration line 6. In an embodiment, the mixer calibration line 6 has a lower damping, e.g. by at least 10 dB, than the antenna calibration lines 7. This is because the particular monitor mixer is less sensitive at its input compared to the particular down-converter employed. The monitor mixer 12 then generates a monitor signal from the transmit signal. In general, also the monitor signal is a down-converted signal. Possible setups and the function of the monitor mixer 12 are described in detail with respect to Figs. 2 to 4b.

During a calibration routine, the monitor mixer 12 is connected to the further signal processing components, such as the second amplifier 15, the ADC 16 and the digital processing means, via the switch 14. In this way, the same components are used in the calibration as well as in the measurement routine.

Figs. 2 and 3 show different embodiments of the monitor mixer. In particular, the monitor mixer is configured to separate the at least one undesired frequency component, e.g. a lower (or upper) sideband or LO leakge, from the desired frequency component, typically the upper (or lower) sideband, in the transmit signal supplied to an input 21 and, respectively, 31 of the monitor mixer. For that purpose, the monitor mixer comprises a nonlinear element.

Fig. 2 shows a classical diode detector as monitor mixer comprising a diode 22 as nonlinear element, a capacitor 23 and an resistor 24. The capacitor 23 and the resistor 24 are connected, on one side, to the diode 22, and on the other side to ground 25. The capacitor 23 and the resistor 24 together form a low-pass filter. The low-pass filter advantageously has a cut-off frequency between 2*f_IF and f_LO, such that frequency components at f_LO and above are filtered out of the monitor signal. At an output 26 of the monitor mixer, the monitor signal is output, in particular having a dominant DC component corresponding to the desired dominant frequency component, and frequency components at f_IF and/or 2*f_IF corresponding to the undesired LO leakage and undesired sideband components, respectively. In other words, the monitor mixer acts as an envelope detector. For more details, see Figs. 4a and 4b and the corresponding description.

In general, the diode 22 has an operating range at least matching that of the LO frequency range, e.g. 400 to 4000 MHz. Suitable diodes are e.g. Schottky diodes. Alternatively, a similar monitor mixer may be implemented by using a transistor as nonlinear element. Due to the amplification by a transistor, such monitor mixer is very sensitive.

Fig. 3 shows a singly-balanced detector or monitor mixer with differential output 36, 36a as monitor mixer. The upper half of the circuit, leading to output 36, again comprises a diode 32, in particular a Schottky diode, a capacitor 33 connected to ground 35, and an inductor 34. The capacitor 33 and the inductor 34, again, form a low-pass filter. The lower half of the circuit is symmetric to the upper half with an identical diode 32a, capacitor 33a and inductor 34a. However, the polarity of the diode 32a is reversed compared to the one of the diode 32. In particular when the signal at the input 31 is a positive voltage, diode 32 is forward biased and thus conducting, and diode 32a is reverse biased and thus blocking, and vice versa. Together with the low-pass filtering properties of capacitor 33 and inductor 34, and respectively capacitor 33a and inductor 34a, this leads to a differential signal at the outputs 36 and 36a. Such differential monitor mixer is in particular more efficient than the monitor mixer of Fig. 2.

Example values for the electronic components in Fig. 3 are: capacitors 33, 33a - approx. 50 pF, inductors 34, 34a - approx. 50 nH. Further, the signal at input 31 may advantageously be impedance matched, e.g. by a transmission line network.

Further, the monitor mixer of Fig. 3 advantageously comprises a shunt inductor 37, e.g. with approx. 70 uH and a DC resistance of approx. 15 Ohms, between the outputs 36 and 36a. Such shunt inductor 37 provides a DC return for the diodes 32, 32a, which improves detection sensitivity. The impedance of the shunt inductor 37 at the AC components f_IF and 2*f_IF advantageously is large enough not to load these frequency components. In particular, the impedance of the shunt inductor 37 is significantly larger than an impedance of the inductors 34 and 34a, e.g. by a factor of at least 100, in particular at least 1000. In particular, the differential loading of the monitor mixer at the terminals 36-36a by the following circuits may be approx. 200 Ohms. Advantageously, the signal chain from the output of the down- converter 11 and the output of the monitor mixer 12 to the input of the ADC 16 is realized differentially.

Figs. 4a and 4b show schematic frequency spectra of a transmit signal and a monitor signal, respectively, i.e. in particular the signal at the input 21,

31 and the signal at the output 26, 36-36a, respectively, of the monitor mixer. The transmit signal in Fig. 4a has a dominant component at f_LO + f_IF, which corresponds to the desired upper sideband that is in particular exploited to retrieve information about the subsurface. “Dominant” shall in particular mean larger than any other, undesired frequency components by at least 10 dB, in particular at least 30 dB before, and by at least 40 dB, in particular 60 dB, after calibration of the up- converter. Further, the transmit signal comprises frequency components at f_LO - f_IF and at f_LO, which in this context are undesired frequency components and correspond to the lower sideband (also called “image”, not to be confused with the reconstructed image of the subsurface) and the LO leakage, respectively.

In general, the dominant frequency component, in this example the desired upper sideband, acts as a pumping or clocking signal for the nonlinear element, here for the diode(s). In other words, the dominant frequency component switches the diode(s) between conducting and blocking, while the weaker undesired frequency components hardly affect a conducting or blocking state of the diode(s).

Thus, the transmit signal is rectified, clocked by the dominant frequency component, here f_LO + f_IF. Further, the low-pass filter of the monitor mixer filters out frequencies f_LO - f_IF and above. In general, the monitor mixer acts as an envelope detector. Hence, in the monitor signal, the desired frequency component (in particular the pumping or clocking signal) appears as DC signal at frequency 0, see Fig. 4b. The undesired frequency components LO leakage and undesired (lower) sideband appear at f_IF and 2*f_IF, respectively. This is advantageous because their relative distance to each other is larger in the monitor signal than in the transmit signal, namely e.g. f_IF / f_IF = 100% instead of f_IF / f_LO which may be in the range of 0.05 to 1%. This facilitates exact measurements of amplitudes and phases of the different components. Measurement of the phases works only of all the involved clocks and LOs are phase locked to each other, or derived in a phase coherent way from a common reference clock. A further advantage is that the upper and lower sideband are distinguishable, and in particular not imaged together, e.g. on one frequency component at f_IF, as would be the case with the downconverter mixer 11.

Fig. 5 shows a block diagram of the digital processing means, in particular an FPGA 50, connected to both, the ADC 16 as well as the DACs 17 and 18, e.g. of Fig. 1. This means that the FPGA 50 has the digitized monitor signal RX IF as input, wherein the monitor signal may in particular be further low-pass filtered and/or amplified still in the analog domain as depicted in Fig. 1. According to the schematic drawing of Fig. 5, the FPGA 50 comprises an amplitude and phase detector 51 configured to measure at least the amplitude and possibly also the phase of the at least one undesired frequency component, in particular in the calibration routine. In case of the undesired frequency component comprising the (lower) sideband appearing in the monitor signal as u_2IF at frequency f_2IF, the measured values are amp(u_2IF) and phase(u_2IF). The amplitude and possibly also the phase are then supplied to a feedback (F) unit 52, either directly or e.g. as real and imaginary part, Re(u_2IF) and Im(u_2IF), derived from amp(u_2IF) and phase(u_2IF). Alternatively, Re(u_2IF) and Im(u_2IF) may be measured in the amplitude and phase detector 51.

The feedback unit 52, which is advantageously implemented in software, not in the FPGA, is configured to determine correction coefficients e_c and 9_c for the amplitude imbalance e and the phase balance Q, respectively, in the in- phase and quadrature components i(t) and q(t) based on amp(u_2IF) and phase(u_2IF), as described in section Disclosure of the Invention. If the undesired frequency, alternatively or additionally, comprises the LO leakage appearing as u_IF at frequency f_IF in the monitor signal, the feedback unit 52 is configured to determine correction coefficients oi_c and oq_c based on the amplitude and phase amp(u_IF) and phase(u IF). In general, the correction coefficients e_c and 9_c are adapted to minimize the undesired sideband, and the correction coefficients oi_c and oq_c are adapted to minimize the undesired LO leakage. This may be done in an iterative optimization scheme, as described before, until optimal correction coefficients are found.

The FPGA 59 further comprises an intermediate signal generator 53, which is configured to generate the in-phase and quadrature components, I=i(t) and Q=q(t), of the intermediate signal. In particular, the intermediate signal generator 53 is configured to adjust i(t) and q(t) based on the applicable correction coefficients, (e_c, 9_c) and/or (oi_c, oq_c). In general, by applying the same principle and FPGA 50, it is possible to suppress not only an undesired sideband and the LO leakage in the transmit signal, but also further undesired frequency components, e.g. distortion products at distance n*f_IF from the desired sideband with arbitrary n.

As stated before, a fixed phase relation between the involved signals, in particular between the LO signal and the intermediate signal TX IF, but also between the monitor signal RX IF and the intermediate signal TX IF, is important for conducting phase measurements on the various frequency components. This fixed phase relation is achieved by deriving the involved signals from a common reference clock 55 using frequency dividers and phase-locked loops. Therefore, the FPGA 50 further comprises a master (M) clock 54 connected to both, the amplitude and phase detector 51 and the intermediate signal generator 53. This facilitates the adjustment of the intermediate signal, in particular of i(t) and q(t), and hence a reliable suppression of undesired frequency components.

The FPGA 50 is also configured to process received data during a measurement routine. In such case, the input signal RX IF coming from the ADC 16 represents a received radar signal that was down-converted by down-converter 11 in Fig. 1. The amplitude and phase detector 51 may then measure amplitude and phase of the received radar echo signal at each frequency step. The feedback unit 52 is configured to provide the optimal correction coefficients, in particular as determined in the last calibration routine. The intermediate signal generator 53 is configured to generate i(t) and q(t) based on these optimal correction coefficients. In this way, the up-converted transmit signal (depicted as RF in Fig. 1) that is transmitted by the transmit antennas contains only very weak undesired frequency components, which are in particular weaker than the desired frequency component by at least 40 to 60 dB.

Fig. 6 shows a flow diagram of the method for operating a GPR device, in particular a schematic mixer calibration routine with calibration steps Cl to C4 and a schematic measurement routine with measurement steps Ml to M4.

Advantageously, the GPR device up-converter is calibrated before its first use, e.g. in a manufacturing-site test.

In step Cl, the up-converter and the monitor mixer are connected to the mixer calibration path. In step C2, the local oscillator signal v_LO at frequency f_LO and an intermediate signal v_IF, in particular i(t) and q(t), at frequency f_IF are mixed by means of the up-converter. Thereby, the transmit signal v_RF is generated, comprising a desired frequency component in the upper sideband (USB) at f_LO + f_IF or in the lower sideband (LSB) at f_LO - f_IF. Further the transmit signal v_RF comprises at least one undesired frequency component, wherein an amplitude of the desired frequency component is larger than an amplitude of the least one undesired frequency component.

In step C3, the monitor signal is measured by means of the monitor mixer connected to the up-converter.

In step C4, the monitor signal is used to reduce an amplitude of the at least one undesired frequency component by adjusting the intermediate signal v_IF, in particular by correction coefficients (e_c, 9_c) and/or (oi_c, oq_c), as described above.

Steps C2 to C4 are then iterated while adjusting the correction coefficients according to an optimization scheme, until optimal values of the correction coefficients is reached, e.g. according to one of the afore-described stop criteria. The optimal values of the correction coefficients are then stored for use in the measurement routine.

In case of different values of f_LO and different values of f_IF, the optimization of the correction coefficients may be performed for each pair (f_LO, f_IF) in order to achieve an optimal suppression of the undesired frequency component s), e.g. throughout a full frequency sweep. In the flow diagram of Fig. 6, this means further iterations over C2 to C4 for each pair (f_LO, f_IF). Alternatively, optimal correction coefficients may only be determined for some pairs of (f_LO, f_IF), and then be interpolated for the remaining pairs of (f_LO, f_IF). Advantageously, the optimal correction coefficients for each pair (f_LO, f_IF) are stored. Then, a measurement routine may be started.

In measurement step Ml, if not already done, the up-converter is connected to the transmit antenna, and the receive antenna to the down-converter. Further, the local oscillator, e.g. the first synthesizer 4 of Fig. 1, is set to a first value of f_LO, e.g. 400 MHz.

In step M2, the intermediate signal generator 53 is set to a first value of f_IF, e.g. 2 MHz. The intermediate signal generator 53 then generates i(t) and q(t) adjusted by the stored optimal correction coefficients for (f_LO, f_IF) from the last calibration routine. By IQ modulating the LO signal at f_LO and i(t), q(t) at f_IF, the up-converter generates the transmit signal v_RF with a dominant frequency component, e.g. in the upper sideband at f_LO + f_IF, here at 402 MHz. The transmit signal v_RF is transmitted by the transmit antenna(s) into the subsurface, and the echo is received as received radar signal by the receive antenna(s).

In step M3, the received signal is down-converted by down- converter 11 of Fig. 1. Further, the down-converted signal is processed by the FPGA.

In case of more than one transmit and/or receive antenna, in step M4, a next pair of transmit antenna and neighbouring receive antenna is connected in the circuit, e.g. by the multiplexers 5 and 8 of Fig. 1.

Then, steps M2 to M4 are repeated with the intermediate signal generator 53 set to a next value of f_IF, e.g. 2.4 MHz, resulting in a transmit signal with a desired upper sideband at 402.4 MHz. In case of six quasi-simultaneous measurement lines, e.g. as in Fig. 1, steps M2 to M4 may be repeated five times, e.g. with values of f_IF further set to 2.8, 3.2, 3.6 and 4 MHz.

In general, the intermediate signal generator 53 is advantageously set to as many values of f_IF for each value of f_LO as there are quasi-simultaneous measurement lines. This is due to the fast switching time of the signal generator 53 in the digital domain, while the local oscillator in analog time needs longer for switching to a different value of f_LO. In this way, a fast data acquisition speed is facilitated.

After such iteration over, e.g. six, different values of f_IF, the measurement routine is started again at step Ml : The local oscillator is set to the next value of f_LO, e.g. 420 MHz. In case of two synthesizers as local oscillator, the LO signal is now advantageously provided by the second synthesizer, which has been prepared before and is instantly operable. Then steps M2 to M4 are iterated again for different values of f_IF, and so on.

By means of this method, a full frequency sweep, e.g. from 400 MHz up to 4000 MHz, over all transmit/receive antenna pairs of interest, i.e. pairs 0 to 5, may be conducted very fast, i.e. in less than 1 s, in particular less than 0.1 s, more particularly in less than 5 ms. This enables very efficient radar data acquisition, e.g. at walking speed of around 1 m/s, on several measurement lines quasi-simultaneously and with high spatial resolution, in particular of 5 mm along the direction of the survey path.

Claims

1. A method for operating a GPR device having a single-sideband up-converter (3), wherein the GPR device further comprises

- a transmit antenna (1) connectable to the up-converter (3) and configured to transmit radar waves,

- a receive antenna (2) configured to receive radar waves,

- a down-converter (11) connectable to the receive antenna,

- a monitor mixer (12) connectable to the up-converter (3) via a mixer calibration path (6), wherein the monitor mixer (12) comprises a nonlinear element (22, 32, 32a) with a nonlinear transfer characteristic and a low-pass filter, the method comprising calibration steps for calibrating the single sideband up-converter (3), wherein the calibration steps comprise

- mixing, by means of the up-converter (3), a local oscillator signal (v_LO) at frequency f_LO and an intermediate signal (v_IF) at frequency f_IF, thereby generating a transmit signal (v_RF) comprising a desired frequency component in the upper sideband (USB) at f_LO + f_IF or in the lower sideband (LSB) at f_LO - f_IF, and at least one undesired frequency component, wherein an amplitude of the desired frequency component is larger than an amplitude of the least one undesired frequency component,

- measuring, by means of the monitor mixer (12) connected to the up-converter (3), a monitor signal,

- using the monitor signal to reduce an amplitude of the at least one undesired frequency component by adjusting the intermediate signal (v_IF).

2. The method of claim 1, wherein a first derivative of a transfer characteristic of the nonlinear element (22, 32, 32a) increases or decreases with increasing voltage.

3. The method of any of the preceding claims, wherein the nonlinear element (22, 32, 32a) comprises at least one of a diode (22) and a transistor, in particular two diodes (32, 32a) in differential configuration, in particular wherein the low-pass filter comprises a capacitor (23,

33, 33a).

4. The method of any of the preceding claims, wherein the up-converter (3) comprises an IQ modulator, wherein the intermediate signal (v_IF) comprises an in-phase component (i(t)) and a quadrature component (q(t)), wherein the in-phase component (i(t)) and the quadrature component (q(t)) have frequency components at the frequency f_IF, wherein the transmit signal (v_RF), in particular in ideal form, has the following form

wherein adjusting the intermediate signal (v_IF) comprises the step of changing at least one of the in-phase component (i(t)) and the quadrature component (q(t)) to reduce the amplitude of the at least one undesired frequency component.

5. The method of claim 4, wherein, in frequency domain, the in-phase and quadrature components (i(t), q(t)) have at the frequency f_IF the following complex amplitudes I(f=f_IF) = I_f_IF*(l+e_c/2)*exp(+j*9_c/2), and

Q(f=f_IF) = Q_f_IF*(l-e_c/2)*exp(-j*9_c/2) with correction coefficients for amplitude imbalance e_c and phase imbalance 9_c, and

I_f_IF / Q_f_IF = +/-j, and at the frequency f=0 correction coefficients for offsets oi_c and oq c l(f=0) = oi_c, and Q(f=9) = oq c, wherein adjusting the in-phase and quadrature components (i(t), q(t)) comprises changing at least one of the correction coefficients for amplitude imbalance (s c), phase imbalance (9_c) and offsets oi_c and oq c.

6. The method of any of the preceding claims, wherein the at least one undesired frequency component comprises an undesired sideband, wherein using the monitor signal to reduce an amplitude of the at least one undesired frequency component comprises - determining an image component (u_2IF) at frequency 2*f_IF in the monitor signal,

- adjusting the intermediate signal (v_IF), in particular the in-phase and quadrature components (i(t), q(t)), as a function of an amplitude (amp(u_2IF)) and/or a phase (phase(u_2IF)) of the image component (u_2IF),

- iterating the previous steps and minimizing an absolute value (abs(u_2IF)) of the image component (u_2IF), in particular wherein adjusting the in-phase and quadrature components (i(t), q(t)) comprises changing at least one of the correction coefficients for amplitude imbalance (s c) and phase imbalance (0_c).

7. The method of claim 6, wherein the correction coefficient for the amplitude imbalance (s c) is adjusted dependent on an amplitude (amp(u_2IF)) and in particular additionally on a phase (phase(u_2IF)) of the image component (u_2IF), and/or wherein the correction coefficient for the phase imbalance (0_c) is adjusted dependent on the amplitude (amp(u_2IF)) and in particular additionally on the phase (phase(u_2IF)) of the image component (u_2IF).

8. The method of any of claims 6 to 7, wherein iterating the steps comprises per iteration changing only the correction coefficient for the amplitude imbalance (s c) or only for the phase imbalance (0_c), in particular in subsequent iterations altematingly changing the correction coefficients for amplitude imbalance (s c) and phase imbalance (0_c).

9. The method of any of the preceding claims, wherein the at least one undesired frequency component comprises a local oscillator leakage component at frequency f_LO, wherein using the monitor signal to reduce an amplitude of the at least one undesired frequency component comprises

- determining a leakage component (u_IF) at frequency f_IF in the monitor signal,

- adjusting the intermediate signal (v_IF), in particular the in-phase and quadrature components (i(t), q(t)), as a function of an amplitude (amp(u_IF)) and/or a phase (phase(u_IF)) of the leakage component (u_IF),

- iterating the previous steps and minimizing an absolute value (abs(u IF)) of the leakage component (u_IF), in particular wherein adjusting the in-phase and quadrature components (i(t), q(t)) comprises changing at least one of the correction coefficients for offsets (oi_c, oq_c).

10. The method of any of the preceding claims, further comprising

- filtering out harmonics of f_LO and sidebands thereof from the transmit signal (v_RF) between the mixer calibration path (6) and the monitor mixer (12), in particular by a low-pass filter having a cut-off frequency between f_LO and 2*f_LO, in particular wherein the GPR device comprises a filter bank (10) or a tunable filter comprising switchable low-pass filters, wherein the low-pass filters have different cut-off frequencies.

11. The method of any of the preceding claims further comprising the steps of

- upon initiating the calibration steps, connecting the up-converter (3) and the monitor mixer (12) to the mixer calibration path (6),

- upon initiating measurement steps, connecting the up-converter (3) to the transmit antenna (1) and the receive antenna (2) to the down-converter (11).

12. The method of any of the preceding claims, further comprising measurement steps comprising

- changing a value of f_LO in discrete steps, in particular between 400 and 4000 MHz,

- for each discrete step, in particular, for each pair of transmit antenna (1) with neighbouring receive antenna (2), changing a value of f_IF, in particular according to the equation f_IF = x + n*y, in particular wherein x = 2 MHz, y = 0.4 MHz and n = (0,1,...,5), in particular wherein n is a number of the antenna pair.

13. The method of claim 12, wherein the calibration steps comprise

- for each combination of f_LO value with f_IF value, determining the correction coefficients (e_c, 0_c) for the amplitude imbalance (e) and the phase imbalance (Q), and/or the correction coefficients (oi_c, oq_c) for the offsets (oi, oq).

14. A GPR device comprising

- a single-sideband up-converter (3),

- a transmit antenna (1) connectable to the up-converter (3) and configured to transmit radar waves, - a receive antenna (1) configured to receive radar waves,

- a down-converter (11) connectable to the receive antenna,

- a monitor mixer (12) connectable to the up-converter (3) via a mixer calibration path (6), wherein the monitor mixer (12) comprises a nonlinear element (22, 32, 32a) with a nonlinear transfer characteristic and a low-pass filter, and - processing means, in particular adapted to execute the steps of the method of any of the preceding claims.

15. The GPR device of claim 14, wherein a first derivative of a transfer characteristic of the nonlinear element (22, 32, 32a) increases or decreases with increasing voltage.

16. The GPR device of any of claims 14 to 15, wherein the nonlinear element (22, 32, 32a) comprises at least one of a diode (22) and a transistor, in particular two diodes (32, 32a) in differential configuration.

17. The GPR device of any of claims 14 to 16, wherein the low-pass filter of the monitor mixer comprises a capacitor (23, 33, 33a) and in particular an inductor (34, 34a), in particular wherein the low-pass filter has a cut-off frequency between 2*f_IF and f_LO.

18. The GPR device of any of claims 14 to 17, wherein the monitor mixer (12) comprises two diodes (32, 32a) and two low-pass filters in differential configuration, in particular wherein the monitor mixer (12) further comprises a shunt inductor (37) at its output.

19. The GPR device of any of claims 14 to 18, wherein the up-converter (3) comprises an IQ modulator, the device further comprising - a local oscillator (LO) (4) configured to generate a local oscillator signal (v_LO) at frequency f_LO and connected to a first input of the IQ modulator, wherein the processing means, in particular an FPGA (50), are connected to a second input of the IQ modulator via two digital-to-analog converters (DAC) (17, 18) and configured to generate an intermediate signal (v_IF), in particular an in-phase component (i(t)) and a quadrature component (q(t)), at frequency f_IF.

20. The GPR device of claim 19, wherein the local oscillator (LO) is configured to sequentially switch the frequency f_LO, in particular to discrete values between 400 and 4000 MHz, wherein the digital signal processing means are configured to sequentially switch the frequency f_IF, in particular to discrete values between 2 and 4 MHz.

21. The GPR device of any of claims 19 to 20, wherein the local oscillator (LO) comprises two wideband synthesizers (4) configured to be altematingly connected to the first input of the IQ modulator.

22. The GPR device of any of claims 20 to 21, further comprising

- a filter bank (10) comprising switchable low-pass filters or a tunable filter, wherein an input of the filter bank (10) or the tunable filter is selectably connectable to the receive antenna (2) and to the mixer calibration path (6), and wherein an output of the filter bank (10) or the tunable filter is selectably connectable to the down-converter (11) and to the monitor mixer (12), in particular wherein the low-pass filters of the filter bank (10) have cut-off frequencies between f_LO and 2*f_LO adapted to the discrete values of f_LO.

23. The GPR device of any of claims 14 to 22, further comprising

- an analog-to-digital converter (ADC) (16) selectably connectable, in particular via an amplifier (15), to an output of the mixing monitor (12) and an output of the down-converter (11), and connected to an input of the processing means, in particular of the FPGA (50), in particular wherein the analog-to-digital converter (ADC) (16) is configured to measure the monitor signal.

24. The GPR device of any of claims 14 to 23, comprising n transmit antennas (1) selectably connectable to the up-converter

(3) via a first multiplexer (5) and configured to transmit radar waves,

- m receive antennas (2) selectably connectable to the down- converter (11) via a second multiplexer (8) and configured to receive radar waves, wherein the transmit antennas (1) and the receive antennas (2) are arranged in a staggered arrangement, wherein m = n-1 or n or n+1, in particular wherein n=3 and m=4.

25. The GPR device of claim 24, wherein the first and second multiplexers (5, 6) are configured to activate combinations of pairs of a transmit antenna (1) with a neighbouring receive antenna (2) sequentially, in particular wherein the transmit antennas (1) are configured to sequentially transmit transmit signals (v_RF) with different frequencies of the desired frequency component.

26. A computer program comprising instructions to cause the GPR device of any of claims 14 to 25 to execute the steps of the method of any of claims 1 to 13.