1. Introduction
In active radar system, the target identification ability is closely associated with average transmission power. Limited by the finite peak power, the promotion of target identification ability usually depends on the increase of transmission pulses’ bandwidth. However, the increase of transmission pulses’ bandwidth will degrade the range resolution. To resolve the contradictions between the identification ability and the range resolution, a process of broadening the pulses’ bandwidth in transmitter and compressing them in receiver is utilized. This technique is called pulse compression [
1] and its schematic diagram is shown in
Figure 1. The input measured signal is mixed with the chirp modulation signal to expand its bandwidth, then the modulated signal is compressed into pulses by a digital pulse compression method or an analog dispersive device. An analog dispersive device of surface acoustic wave (SAW) filter was previously used for pulse compression; nowadays, methods of digital pulse compression are frequently utilized for signal expansion and pulse compression instead of SAW filters [
2,
3].
As early as in 1960s, the technology of radar pulse compression was firstly utilized to represent Fourier transform by Klauder [
4]. Afterwards, a much more detailed discussion of spectral analysis utilizing the radar pulse compression was described by Darlington [
5]. Nowadays, the Darlington’ system is known as the chirp transform spectrometer (CTS). In a CTS system, the pulse compression is usually realized by using the SAW filters and this makes it possible to apply to real-time spectrum measurement. The CTS system was later spread to the field of atmospheric radiation measurement by Hartogh and Hartmann [
6], Hartogh and Lis et al. [
7,
8,
9], and Hartogh and Osterscheck [
10]. An improved CTS system with a novel digital dispersive matching network instead of the SAW devices for signal expansion helped to improve the accuracy of the measured spectrum and the system’s linear response, which greatly improved the system’s performance [
11]. As a new passive detection method, the CTS back-end was developed into a mature tool widely used in weather and astronomical observation. Early in the 1990s, CTS back-end had been applied for ground-based submillimeter observation of planets [
12] and comets [
13]. Subsequently, CTS was used for atmosphere components investigation of Comet Chyruymov Gerasimenko in Rosetta Orbiter, which was launched in 2004 for deep-space detection [
14]. With the advantage of high spectral resolution and high stability, the CTS back-end was mounted on the high-resolution spectrometer of the German Receiver for Astronomy at Terahertz Frequencies (GREAT) on board the Stratospheric Observatory for Infrared Astronomy (SOFIA) for planetary and cometary research in recent years [
15,
16,
17,
18,
19].
Compared to fast Fourier transform (FFT) algorithm, the CTS has relatively low weight and power consumption, high spectral resolution and extremely high stability, which makes it quite suitable for space/airborne applications to make a study of comets, planetary atmospheres, interstellar medium, and even early universe. In the classical CTS system, a push–pull arrangement with two uniform channels are adopted to make up the bandwidth mismatch between the expander and compressor. This two-channel arrangement helps to guarantee the maximum sensitivity that can be obtained for the instrument. However, the frequency accuracy and amplitude consistence are directly affected by the match between the two channels. This matching problem, especially the match between different SAW filters, may increase the difficulty of hardware implementation. Meanwhile, the doubled devices also increase the mass and power consumption of the CTS system.
In this paper, a new conception of single-channel CTS system with less components was developed. One channel was replaced by only adding a source, a mixer, a splitter, and a combiner in the novel structure, which helps to avoid the matching problem between the two channels in the classical structure with acceptable system performance. In addition, in the novel structure, the sequential control of the output pulses is simplified for the later digital sampling and storage. The structure and detailed principle of the classical CTS is described in
Section 2. The description and principle of the novel single-channel CTS system is shown in
Section 3. The simulation verification with ideal and nonideal devices and the experiment analysis of the obtained results are presented in
Section 4 and
Section 5, respectively. Finally, a brief conclusion is drawn in the last section.
3. Design of Novel Single-Channel Structure for CTS
To deal with the matching problem and simplify the structure, a single-channel arrangement is developed. The circuit frame diagram of the developed novel single-channel arrangement is demonstrated in
Figure 5. In the new structure, one channel is replaced by only adding a small number of devices. The front part used for signal expansion is the same as the classical CTS structure, and the extension signal is then divided into two parts by the power divider. One is used for signal mixing, and the outputs have both the up-and-down conversion signals. This part is then combined with another part to obtain a complete signal distribution over the entire measuring time. At last, the complete modulated chirp signals resulting from the combiner are delivered to the SAW device for pulse compression. The signal send to the LO port of the mixer is a sine signal with a fixed frequency that is equal to the compression bandwidth. A matching network is added to adjust the little difference of the line delay and eliminate the influence of the added mixer. Usually, in real hardware implementation, the dispersion of mixer, power splitter, and combiner is very small and the introduced mismatch can be ignored.
In the
arrangement, the real input signal is firstly premultiplied by the chirp signal
for signal expansion, then passed though the SAW filter
. The output of the filter is given by a convolution integral
Considering that the impulse response of the premultiplying chirp
and the SAW filter
are both of the form
where
is a rectangular gating function with duration
centered on time
.
is an arbitrary weighting function and here it is set to be unity. Notation
is the chirp rate of the chirp signal and
is a phase term. Thus, Equation (
5) can be rewritten as
where
Multiplication of the cosine terms produces integrals that involve terms in
and
. Ignoring those terms depends on
; Equation (
7) can be expanded in the form
where
and
The notation * means complex conjugation. Since
is real, Equation (
10) can be written as [
20]
where
is the Fourier transform of
; and Equation (
12) can be further written as
where Re means the real part and
is the Fourier transform of
. Considering
in form of the magnitude and phase angle
Equation (
15) indicates that the envelope of the signal
resulting from the SAW filter is the amplitude spectrum of the (truncated) real input signal
. It is important to stress that the gating function shown in Equation (
15) is sliding across
, only embracing different parts of
while at the same time performing Fourier transformation in a time-ordered manner [
20]. For the classical CTS structure described in [
22], the time duration of the premultiplying chirp signals (20 us) is twice that of the SAW filters (10 us), thus, only half of the input signal is measured according to Equation (
15) for one
arrangement. So, the push–pull two-channel structure is adopted to obtain the full duty cycle of the expander–compressor arrangement.
In the single-channel structure, an additional up-and-down conversion mixing process is adopted. So, the output of the SAW filter for the additional up-and-down conversion signals can be written as
where
means the added mixer with a fixed LO input frequency of
. Equation (
16) can be further written as
where
Let
and
; Equation (
17) can be written as
where
is the Fourier transform of
. This indicates that
arrangement with the additional up-and-down conversion mixing process essentially represents the Fourier transform of
—meaning the previous and later parts of
with time interval of
. This actually has the same effect with the push–pull two-channel structure of obtaining the full duty cycle of the expander–compressor arrangement.
Here, we assume that the working parameters are the same as that in [
22]. The schematic diagram with corresponding temporal relations of the novel structure is shown in
Figure 6.
In
Figure 6, two input signals with frequencies of 2.3 GHz and 2.1 GHz are modulated by a chirp signal firstly and then are up-and-down converted. The obtained up-and-down conversion modulated chirp signals will be compressed into output pulses though the SAW filter. These output pulses are just identical to that resulting from one channel of the classical CTS system. For the measured signals, if the frequencies are equal to the boundary of the measured bandwidth (i.e., 1.9 GHz and 2.3 GHz), the output pulses from the novel single-channel structure will be completely the same as that from the classical two-channel structure, as shown in the left part of
Figure 6. In general, there would be some little differences between the output pulses at the first and last time period of the compression procedure (see the right part in
Figure 6). However, these little differences become insignificant in consideration of the digital process of data accumulation for noise elimination in practical application.
For the introduced power combiner, some possible interferences of the three modulated chirp signals may exist at the output of the power combiner. A possible solution is to put two bandpass filters in front of the power combiner and remove the bandpass filter just before the SAW filter. Even though the three modulated chirp signals coexist in the proposed single-channel structure, after passing though the bandpass filter, the time arriving at the power combiner would be different for the three modulated chirp signals. This can minimize the possible interferences of the three signals.
5. Experiment and Analysis
To test the applicability and performance of the novel structure, we build an experiment with hardware implementation on real chains shown in
Figure 10. Limited by the processing difficulty and high-cost manufacturing of the SAW filter, an S2P file is instead used to produce the SAW filter. As shown in
Figure 10, an arbitrary waveform generator (AWG7082C) is used for the generation of the chirp signal
and the input measured signal
. Frequency of the chirp signal starts from 2.5 GHz to 3.7 GHz, the time duration is 20 us, and the chirp rate is 60 MHz/us. The measured signal with four frequencies of 1.8 GHz, 1.9 GHz, 2.0 GHz, and 2.1 GHz is generated by the AWG. The measured signal is first mixed with the chirp signal though the mixer 1 to get the modulated signal
. The modulated signal is then divided into two channels shown in
Figure 10. Signals of channel 2 are mixed with a fixed frequency signal (600 MHz) generated by an analog signal generator and then combine with channel 1. Signals from the combiner are then filtered by the bandpass filter with band-pass width ranging from 700 MHz to 1.3 GHz. Then, a digital phosphor oscilloscope (DPO) with 2-GHz bandwidth is used to sample and store the output signals for the final pulse compression. At last, the sampled signals from DPO are sent to the ADS for pulse compression.
Figure 11 shows the final compression results. The pulses appearing at m1, m2, m3, and m4 result from the pulse compression of channel 1. It can be seen that there are some differences in the amplitudes of these pulses. This is mainly caused by two aspects. One is the different convention loss for different input RF signals of mixer 1. Another is that the insertion loss of the power splitter and combiner changes slightly over the input frequency range. The pulses appearing at m5, m6, m7, and m8 result from the pulse compression of channel 2. The amplitudes of these pulses are much lower than that of pulses resulting from channel 1, and the difference ranges from roughly 10 dB to 12 dB. Not only are they influenced by mixer 1, power splitter, and combiner, but the amplitude differences between these pluses are also affected by the difference convention loss for different input RF signals as well as the difference convention loss between up-conversion and down-conversion of mixer 2. The up-conversion loss and down-conversion loss are shown in
Figure 12 and
Figure 13, respectively. The horizontal axes of
Figure 12 and
Figure 13 show the sweep range of RF input signal when the LO input signal is fixed to 600 MHz. It can be seen that the conversion loss of mixer 2 is approximately equal to the amplitude differences between pulses at m1, m2, m3, m4, and pulses at m5, m6, m7, and m8. The influence on amplitudes due to the mixers, power splitter, and combiner can be compensated in the later digital signal processing.
Usually, there are two ways to retrieve the instrument’s spectral resolution. One is to obtain the time difference between the maximum value and the first zero-crossing point from the amplitude envelope of the output pulses, and the spectral resolution is approximately equal to the product of the time difference and the chirp rate. Another is to derive the full-width half-maximum (FWHM) to obtain the average FWHM [
15]. Here, we use the FWHM method to retrieve the spectral resolution. Firstly, the response of the novel single-channel CTS system to a sinusoidal input is measured at different input frequencies. Then, the relative half-width half-maximum (HWHM) to the right and left could be obtained from the measurements and thus, the full-width half-maximum (FWHM) is derived.
Figure 14 shows the measured average FWHM to be 90.503 kHz. This value is particularly close to the maximum achievable spectral resolution (
kHz) of the expander–compressor arrangement, which is determined by the compressor’s working bandwidth.
6. Conclusions
A novel design of a single-channel arrangement for the CTS system is introduced in this paper. By adding an additional source, a mixer, and a splitter\combiner, one channel of the classical CTS system is replaced. The output pulses from the two simulation models with ideal devices match well. Considering the introduced nonideal devices of the mixer and power splitter\combiner, the main influence is that differences exist between the amplitudes of the output pulses, which have been observed both in results of the simulation model with nonideal devices and in the real hardware circuit experiment. Generally, the amplitude differences of output pulses can be compensated in the later digital signal processing. The dispersion of the introduced mixer, power splitter, and combiner is usually very small, and its influence on signal resolution can be ignored. In addition, the experimental results indicate that the retrieved instrument’s spectral resolution is particularly close to the maximum achievable spectral resolution of the expander–compressor arrangement.
Compared to the classical two-channel arrangement CTS structure, the novel single-channel structure can save three amplifiers, two filters, a SAW filter, and a switch. The structure of the CTS system is simplified due to the saved active devices. The matching problem between the two channels is ignored and the sequential control system can be simplified. This indicates that the novel single-channel CTS system may have the potential feasibility for practical application. However, as the simulation and experiment only focus on the signal detection and fundamental spectral analysis without real SAW filter and the subsequent signal processing, there still exists some main characteristics (such as the system linearity and power spectral density accuracy) of the CTS system needing further investigation. Even though the single-channel structure is simple, the introduced mixer and power splitter\combiner may cause uncertain signal interference influencing the system performance, which would not occur in the classical two-channel structure. An additional data compensation procedure is also needed in the subsequent signal processing which will increase additional power consumption. Further research will be focused on compensating actual measured data in the later digital signal processing; investigating the implementation of the novel signal-channel CTS system with real SAW filter and subsequent signal processing; and evaluating system performance with other main characteristics of power spectral density accuracy, linearity, and sensitivity, along with the front-end antenna system and the retrieval algorithm.