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Abstract
A photonic method used to simultaneously measure the Doppler-frequency-shift (DFS) and angle-of-arrival (AOA) of microwave signals is proposed and experimentally demonstrated. At the remote antenna unit (RAU), the local oscillator (LO) signal and two echo signals are applied to a phase modulator (PM) and a polarization-division-multiplexed Mach-Zehnder modulator (PDM-MZM), respectively. After transmission over a fiber link, the DFS and AOA parameters can be obtained by processing the two low-frequency electrical signals at the central office (CO). Experimental results show that the DFS between ± 100-kHz with < ± 5 × 10−3-Hz error and the AOA from 1.82° to 90° with <0.85° error at 10 GHz are obtained over a 10-km single mode fiber (SMF) transmission. Moreover, the DFS direction can also be distinguished by comparing the phase difference of two electrical signals.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Microwave measurements have been widely used, such as mobile communications, radar and warfare systems, medicine and health care, high-speed railways, traffic and automotive control, and astronomy [1–4]. In general, such measurements are implemented by using electronic technology. However, signals with a large frequency range from MHz to hundreds of GHz are needed for certain applications, while electronic-based approaches may be difficult to implement due to various bottlenecks. Compared with electronic methods, photonic ones have attracted great attentions in the past few years, due to their intrinsic advantages in term of compact size, light weight, low insertion loss and immunity to the electromagnetic interference [5,6].
Up to now, a series of photonic methods have been investigated for the measurements of different parameters of microwave signals, such as instantaneous frequency [7–9], spectrum [10–12], phase noise [13–15], Doppler-frequency-shift (DFS) [16–20] and angle-of-arrival (AOA) [21–25]. Among these, the DFS and AOA have become one of the hot topics, as both parameters can be used to track the velocity and position of moving targets. In [17], the DFS between the transmitted microwave signal and the received echo signal is measured by using two cascaded electro-optic modulators (EOMs). In order to distinguish the direction of the DFS, an additional acousto-optic modulator (AOM) is added to use as an optical wavelength shifter [18]. On the other hand, the AOA of microwave signals can be calculated based on phase shifts between the received echo signals. In [21,25], the phase shifts can be estimated from the relative delay time that is obtained by measuring the transmission notch. In [23], the phase shifts are estimated by measuring the optical powers of the two optical components generated by using two Mach-Zehnder modulators (MZMs). The methods discussed above are proposed to measure either DFS or AOA. However, it is highly desirable to obtain both DFS and AOA in applications that require fast and accurate location. Consequently, a single photonic system that can simultaneously measure the DFS and AOA is of great importance. In addition, the transmission of the received echo signals from the remote antenna unit (RAU) to the central office (CO) has not been considered in the mentioned methods.
In this paper, we propose and experimentally demonstrate a photonic method to measure DFS and AOA simultaneously. At the RAU, the local oscillator (LO) signal is applied to a phase modulator (PM), and the two echo signals received by the antennas are applied to a polarization-division-multiplexed Mach-Zehnder modulator (PDM-MZM). After the transmission of a segment of single mode fiber (SMF), the orthogonally polarized optical signals are demultiplexed and divided into two paths at the CO. The DFS and AOA can be calculated by measuring the frequency and phase difference of the signals from two paths. Moreover, the direction of the DFS can also be obtained by comparing the phase difference of the two signals.
2. Principle
Figure 1 shows the schematic diagram of the proposed approach for the DFS and AOA measurements. At the remote antenna unit (RAU), a light wave emitted from a laser diode (LD) is sent into a phase modulator (PM) driven by a local oscillator (LO) signal. Under small signal modulation, the optical field at the output of the PM can be expressed as
where and are the amplitude and angular frequency of the input optical signal respectively, is the modulation index of the PM, and are the amplitude and angular frequency of the LO signal, is the half-wave voltage of the PM, is the n-th Bessel function of the first kind. Then the phase-modulated light wave is injected into a PDM-MZM driven by two received echo signals. The echo signals are obtained by two separate antenna elements with a distance of d. Consequently, we can obtain that where is the relative time delay of the received signals for two antenna elements, is the phase difference between the two received signals, is the angular frequency of the received signal, c is the speed of the light in vacuum, is the AOA of microwave signals. Afterwards, the modulated optical wave is sent to a tunable optical filter (TOF) to eliminate the −1-order sideband. Under small signal modulation, the optical field at the output of the TOF can be expressed aswhere m2 is the modulation index of the PDM-MZM. The two orthogonally polarized signals transmit over a segment of single mode fiber (SMF), which would introduce a phase shift to the optical signal. Thence, the output optical field can be written aswhere are the dispersion-induced phases of the optical carrier, + 1-order sideband of the LO and echo signals. After the transmission, the optical signals are demultiplexed and split into the upper and lower paths through a PBS. In each path, the optical signal is detected by a photodetector (PD) and then filtered by a low pass filter (LPF). After the LPFs, the electrical signals can be expressed as where and are the amplitudes of direct current (DC) and down-converted signal respectively, . As can be seen that the DFS and AOA can be obtained by processing the received electrical signals. Moreover, the direction of DFS can also be distinguished by comparing the phase difference of IUpper and ILower. When IUpper is delayed with respect to ILower, a negative direction is derived. In contrast, if IUpper is advanced with respect to ILower, a positive direction is obtained.
Fig. 1 Schematic diagram of the proposed approach for DFS and AOA measurements. LD, laser diode; PM, phase modulator; LO, local oscillator; PDM-MZM, polarization division multiplexing Mach-Zehnder modulator; PBC, polarization beam combiner; TOF, tunable optical filter; PBS, polarization beam splitter; PD, photodetector; LPF, low pass filter; DSP, digital signal processor; RAU, remote antenna unit; CO, central office.
3. Experimental setup and results
To verify the proposed scheme, we build an experimental setup as shown in Fig. 2. A continuous optical wave emitted from a narrow linewidth laser (PS-TNL, TeraXion,) has a center wavelength of 1550.9 nm and an optical power of 12 dBm. The optical wave is modulated by a PM (EOspace), which is driven by a radio frequency (RF) signal generated from a microwave signal generator (MSG, Anritsu, MS2840A). The PM has a 3-dB bandwidth of 20 GHz and a half-wave voltage of 3.8 V. Then the phase modulated optical signal is sent into a PDM-MZM (FTM7980EDA) via a polarization controller (PC). The PDM-MZM has an insertion loss of 9 dB and a half-wave voltage of 3.5 V at each electrode. Another RF signal is equally divided into two paths: one is directly applied to the upper MZM of the DP-MZM; the other one goes through an electronically controlled phase shifter (PS), and then is sent to the lower MZM of the DP-MZM. The modulated signals are filtered by a TOF, and then amplified by an EDFA (Amonics). After the transmission of a 10 km SMF, the orthogonally polarized optical signals are demultiplexed by a PBS. The demultiplexed signals are detected by two low speed PDs respectively, and then captured by a low speed oscilloscope (OSC, LeCroy, WaveJet 334A) with the bandwidth of 350 MHz and the sampling rate of 2 GS/s.
Fig. 2 Experimental setup of the proposed approach for DFS and AOA measurements. PC, polarization controller; MSG, microwave signal generator; PS, phase shifter; EDFA, erbium doped fiber amplifier; OSC, oscilloscope;
Firstly, two microwave signals at 10 and 10.001 (or 9.999) GHz are generated, serving as the LO and echo signal, respectively. The optical spectra before and after the TOF are captured by an optical spectrum analyzer (OSA, Yokogawa, AQ6370D) with the resolution of 0.02 nm as shown in Fig. 3. After the filter, the + 1-order sideband is suppressed by 37 dB, while the optical carrier and −1-order sideband are suppressed by 13 and 9 dB, respectively, which indicate that a single sideband (SSB) signal is generated.
Subsequently, the filtered optical signal is demultiplexed by a PBS and divided into two paths. The optical signal in each path is detected by a low-speed PD. When the frequencies of the echo signals are set to be 10.001 GHz, the temporal waveforms of the upper and lower path are shown in Fig. 4(a). As can be seen that the waveform of the upper path is advanced with respect to that of the lower path, which indicates that the direction of the DFS is positive. The output signals from the two paths have the same spectrum as shown in Fig. 4(c). The frequency of the received signal is 1 MHz that equals the DFS of the echo signals. When the frequencies of the echo signals are set to be 9.999 GHz, the measured temporal waveforms and electrical spectrum are shown in Figs. 4(b) and 4(d). The waveform of the upper path is delayed to that of the lower path, which indicates that the direction of the DFS is negative. The DFS of the echo signals are measured to be −1 MHz, which agrees well with the theoretical analysis. In addition, different DFSs are also experimentally investigated by tuning the frequency of the echo signals from 9.99999 to 10.00001 GHz with a step of 10 kHz, while the frequency of the LO signal is fixed to be 10 GHz. The values of DFS are measured by using an electrical spectrum analyzer (ESA) with a resolution bandwidth (RBW) of 30 Hz and a video bandwidth (VBW) of 30 Hz. The measurement errors can also be obtained by comparing the values of the measured DFS and practical frequency offsets. The measured results are plotted as a function of the practical frequency offsets as shown in Fig. 5. It can be seen that the measured values agree well with the theoretical ones, and the measurement errors are less than ± 5 × 10−3 Hz. To clearly show the experimental results, the electrical spectra at the DFSs of ± 50 kHz are also shown in the insets of Fig. 5 respectively.
Fig. 4 Temporal waveforms of the upper (blue line) and lower (red line) path for the DFS at (a) 1 MHz and (b) −1 MHz; Measured electrical spectra of the upper path for the DFS at (c) 1 MHz and (b) −1 MHz.
Fig. 5 Measured Doppler frequency shift from −100 kHz to 100 kHz at 10 GHz and corresponding errors.
In order to emulate the change of the AOA, an electrically controlled phase shifter is employed to introduce a phase shifter between the microwave signals at 9.999 GHz applied to two RF ports of the PDM-MZM. Figure 6 shows the phase shifts measured by vector network analyzer (VNA, orange-dotted line) and proposed method (blue-dotted line) as a function of the voltage and corresponding measurement errors (green-dotted line). As can be seen that the measurement errors are less than ± 1.9° with the range from 0° to 180°, compared with the results measured by VNA. Assuming that d = λ/2 = 0.015m, according to Eq. (2), we can calculate that the range of the AOA is from 1.82° to 90° with the errors less than ± 0.85°.
Fig. 6 Phase shifts measured by vector network analyzer (VNA, blue, dotted line) and proposed method (orange, dotted line), and corresponding measurement errors (green, dotted line) at 10 GHz
To verify the frequency tunability of the system, the frequencies of the LO signal and echo signals are set to be 18 and 18.001 GHz respectively. Figure 7(a) shows the results of the measured DFSs. Obviously, the measured DFS values keep consistency with the theoretical ones, and the measurement errors are less than ± 5 × 10−3 Hz. Figure 7(b) shows the measured phase shifts and corresponding measurement errors. As can be seen that the measurement errors are less than ± 2.6° with the range from 0° to 180°, compared with the results measured by VNA. In the same way, we can obtain the range of the AOA is from 4.35° to 90° with the errors less than ± 2.25°.
Fig. 7 (a) Measured DFS from −100 kHz to 100 kHz and corresponding errors, and (b) Phase shifts measured by vector network analyzer (VNA, blue, dotted line) and proposed method (orange, dotted line), and corresponding measurement errors (green, dotted line) at 18 GHz
4. Conclusion
In conclusion, we have proposed and experimentally demonstrated a photonic method to measure the DFS and AOA of microwave signals simultaneously. In the proposed method, the parameters of the DFS and AOA can be calculated by processing the two received electrical signals that obtained by beating the LO signal and echo signals. Moreover, the direction of the DFS can also be obtained by comparing the phase difference between the two signals. When the upper path is delayed to the lower path, the direction of the DFS is negative. On the contrary, when the upper path is advanced to the lower path, the direction of the DFS is positive. In the proof-of-concept experiment, the DFS between ± 100-kHz with < ± 5 × 10−3-Hz error, and the AOA from 1.82° to 90° with <0.85° error at 10 GHz and from 4.35° to 90° with <2.25° at 18 GHz are obtained. The proposed scheme has relatively lower cost and better tolerance to the chromatic dispersion, which may be used in modern radar systems.
Funding
National Natural Science Foundation of China (NSFC) (61335005, 61771438, 61860206006); Ministry of Education United Foundation of Equipment Pre-Research (6141A020334).
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