Gating technique for SFGPR

signal is amplified prior to being gated by the switch in the receiver antenna. The quadrature receiver determines the amplitude of the re- ceived signal and its phase relative to the refer- ence signal for each frequency step. The receiver system has a noise figure of 8 dB. Frequency domain data from the quadrature receiver is transformed to the time domain using a fast Fourier transform algorithm on a dedi- cated DSP. The time domain response is dis- played on a PC in real-time. The 10–620 MHz radar has been designed and built specifically for GPR applications. Un- Ž like other SFGPR systems e.g., Hamran et al., . 1995 , this radar is not based around a commer- cial network analyser. A fast switching synthe- sizer together with a fast settling quadrature receiver is used to enable approximately 50 depth profiles to be collected per second. Inter- changeable antenna subsystems can be used to change the operational frequency. The main radar subsystem is housed in a shock-mounted, portable 19 Y rack that can be accommodated in the back of a 4-wheel drive vehicle. Electrical power can be supplied either at 12 VDC or 240 VAC. Rechargeable batteries power the antenna subsystem providing suffi- cient capacity for a typical day of operation in the field. System performance is defined as the ratio of mean transmitted power to minimum detectable Ž . signal power Plumb et al., 1998 . It is typically used as a ‘‘figure-of-merit’’ for the penetration performance of GPR systems. The minimum detectable signal power should be specified in relation to some acceptable signal to noise ratio Ž . SNR and integration time. Throughout this paper we adopt the convention of assuming a 10 dB SNR and a 10 ms integration time unless otherwise stated. Bench tests of the 10–620 MHz SFGPR Ž measured through coaxial attenuators antennas . bypassed have confirmed a system perfor- mance of 175 dB in ungated mode and 170 dB in gated mode. In comparison, Wright et al. Ž . 1994 estimated the system performances of conventional impulse GPR systems to be in the range 100–130 dB without stacking. Impulse GPR system performance can be improved significantly by using real-time digi- tisers and stacking successive waveforms, and increasing the duty cycle of impulse transmit- ters. In addition, a fast sensitivity time control Ž . STC is required before the real-time digitiser to utilise the improved system performance. Ž . Wright et al. 1990 reported an experimental impulse GPR system operating around 10 MHz with these improvements to obtain a theoretical Ž system performance for 100 ms integration . time of 160 dB, although in practice it was about 145 dB. Coherently summing waveforms during a 10 ms integration time should give a theoretical system performance of 180 dB. However, these improvements to impulse GPR system performance become much more diffi- cult as the operating frequency increases.

3. Gating technique for SFGPR

The details for the application of gating for stepped-frequency GPR were first described by Ž . Hamran et al. 1995 . The technique involves the pulsing of the transmitter and gating of the receiver for each frequency step. The timing of the receiver gate is delayed relative to the trans- mit gate to avoid strong signals from the leak- age signal between the transmitter and receiver Ž . antennas Fig. 2 . The delay between the trans- Fig. 2. Typical gating functions applied to the transmitter and receiver gates. The receiver gate is delayed relative to the transmitter gate. The delay between the gates should be varied to match the return travel time to reflectors of interest. Note that the transmitter and receiver gating have the same repetition interval. Fig. 3. Variation of received signal strength with delay to target for gated SFGPR. Transmitter and receiver gates both have width of 10 ns. The gate repetition interval Ž . GRI is 50 ns and receiver delay is 20 ns. Note that peak system performance is less than the system performance of Ž . an ungated system by 1r duty cycle , which in this case is 7 dB. mit and receive gates must be adaptive so that targets at different depths can be imaged. Four important gating parameters illustrated in Fig. 2 are Gate Repetition Interval GRI, Receiver Gate Delay D , Receiver Gate Width W , and Trans- R R mitter Gate Width W . The duty cycle of the T transmitter gate is g s W rGRI and of the T T receiver gate is g s W rGRI. R R Assume that there is a single target with two-way delay of t seconds. Further, consider Ž . only a single frequency vr2p . In ungated mode, the received signal after the receive gate can be written as: S s a sin v t y t q f 1 Ž . Ž . Ž . ungated where a is a constant and f is a phase angle. In gated mode, the received signal after the receive gate can be written as: t y D t y D R R S s III = P gated ž ž GRI W R = t y t t y t III = P ž ž GRI W T =S 2 Ž . ungated Ž . ` Ž . where III t s S d t y i for all integer i; isy` Ž . P t s 1 for y0.5 - t - 0.5, 0 elsewhere; = the convolution operator. To simplify the algebra, assume that the transmitter and receiver gates have equal widths Ž . W s W s W and hence equal duty cycles T R Ž . g s g s g . Combining the comb functions T R result in: t y V t y V S s III = P gated ž ž GRI W c = a sin v t y t q f 3 Ž . Ž . Ž . where V s t q D r2 and W s W y t y D if R c R t y D - W; W s 0 otherwise. R c If there is overlap between the transmitter gate and the delayed receiver gate, then the received signal is a gated sinusoid. Outside of the overlap is no received signal. In the fre- quency domain a gated sinusoid is a windowed line-spectra centred on the frequency of the Fig. 4. A synthesized pulse extracted from the radar image of Fig. 5. The reflection from the water table appears at 50 ns. The weaker reflection at 100 ns is a double bounce between the ground surface and water table reflector. Note that the phase of the double bounce is inverted compared with the water table reflector. gated sinusoid. A filter within the quadrature receiver rejects all frequencies except that of the ungated sinusoid. Therefore, it is helpful to find the frequency component of the received signal that has the same frequency as the ungated sinusoid. An approximate expression for this component is: S gated original component W c f a sin v t y t q f Ž . Ž . ž GRI W c f S 4 Ž . ungated ž GRI Thus, the useful received power from a gated system reaches a maximum when the delayed transmitter gate and the receiver gate coincide in time. The reduction in received power verses Ž . 2 target delay t is proportional to, W rGRI , c the square of the duty cycle of S . Fig. 3 gated shows the ‘‘window’’ relationship where trans- mitter and receiver gates are 10 ns wide, the gate repetition interval is 50 ns and the receiver gate delay is 20 ns. Targets with delays outside the gating ‘‘window’’ are suppressed relative to targets with delays inside the gating ‘‘window’’. The ‘‘window’’ can be moved out in range by changing the receiver gate delay. Ž The system performance described in Sec- tion 2 as the ratio of the mean transmitter power . and the minimum detectable signal of a gated system is less than that of an ungated system. For a gated system the mean transmitter power is decreased by the transmitter gate duty cycle Ž g s W rGRI assuming the peak transmitter T T . power remains unchanged . The resulting fre- quency domain is a series of line-spectra, of which the quadrature receiver uses only a single frequency line. Hence, the useful received power Fig. 5. Ungated image of the shallow underground water table on the sand island. The radar was stepped in frequency from 50 MHz to 350 MHz. In the grey scale images of this paper, the negative swings of the synthesized pulses are associated with dark grey and the positive swings with light grey. is also reduced by the transmitter gate duty cycle g . T In most circumstances the minimum de- tectable signal for a gated system MDS will gated be decreased relative to the minimum detectable signal for an ungated system MDS . An ungated important criterion is that the dominant contri- bution to the background noise in the quadrature receiver is from a source located before the receiver gate. This noise source should remain the dominant noise source irrespective of whether the radar is gated or ungated. Typically this source is the thermal noise arising within the first receiver amplifier. The above criterion is usually met provided that the receiver ampli- Ž . fier gain in dB plus the receiver amplifier Ž . noise figure in dB is much greater than 1rg R Ž . in dB , where g s W rGRI is the receiver R R gate duty cycle. Given this criterion, the back- ground noise power of the quadrature receiver in a gated system will decrease by 1rg com- R pared to an ungated system. Combining the reductions associated with mean transmitter power, useful received power and minimum detectable signal of a gated sys- tem, results in a system performance degrada- tion of g 2 rg over an ungated system. If the T R duty cycles of the transmitter and receiver gates Ž . are the same i.e., g s g s g , then the sys- T R tem performance of a gated system degrades by a factor of g over an ungated system. This is the reason for the peak of the gating ‘‘window’’ in Fig. 3 being 7 dB below the system perfor- mance of an ungated system. The system performance of the 10–620 MHz SFGPR in gating mode is 170 dB. Tests have also showed that strong targets can be sup- pressed by at least 80 dB through gating. Fig. 6. Gated image taken along the same survey line as Fig. 5. Note the electromagnetic double bounce has an inverted phase compared with the water table reflection. The radar was stepped in frequency from 50 MHz to 350 MHz.

4. SFGPR field tests