Wideband High-Speed and High-Accuracy Instantaneous Frequency Measurement System

A new photonic-assisted instantaneous frequency measurement system is presented. It overcomes the latency problem in the reported structures based on the frequency-to-time mapping technique or the frequency-to-power mapping technique that involves a long length of fiber, and at the same time, enables the incoming microwave signal frequency to be measured over a wide frequency range with only small errors. The system generates three low-frequency signals. The phases of the three low-frequency signals are compared. One of the two low-frequency signal phase differences is used to estimate the incoming microwave signal frequency unambiguously over a wide frequency range and the other is used to provide accurate microwave signal frequency measurement. A proof-of-concept experiment is set up. Experimental results show, by measuring the phase difference of two low-frequency signals, the frequency of the input microwave signal can be determined unambiguously in 15 GHz and 500 MHz frequency ranges with errors below ±220 MHz and ±10 MHz respectively. Hence, by using two low-frequency signal phase differences, the input microwave signal frequency can be determined accurately over a wide frequency range. The new photonic-assisted frequency measurement system has a fast response time, which is an order of magnitude shorter than that of the systems based on the frequency-to-time mapping technique and the frequency-to-power mapping technique with a kilometer-long fiber.

electronic warfare, a microwave signal frequency needs to be captured instantaneously, so that a jammer can be tuned rapidly to jam against a frequency hopping signal [1].
Instantaneous frequency measurement systems are commercially available [2], [3]. Frequency measurement systems from AKON have a 2-18 GHz operating frequency range, 5 MHz measurement accuracy and 300 ns processing time [3]. Photonics provides a solution for wide frequency measurement range, immunity to electromagnetic interference (EMI) and small size. Many photonic-assisted frequency measurement systems have been developed in the past 15 years. The systems based on sweeping the wavelength of an optical source [4] or the frequency of a reference signal [5], [6] use the same principle as an electrical spectrum analyzer. Hence they have the latency problem and are not suitable for electronic warfare applications. The system that involves a delay line loop takes around 100 μs for measuring a microwave signal frequency up to 20 GHz [7]. The recent reported frequency-to-time mapping based frequency measurement systems have a measurement time of around 10 μs [8], [9], [10], [11]. This is still much longer than the processing time of the commercial instantaneous frequency measurement systems.
There are a number of frequency measurement systems operated based on the frequency-to-power mapping technique that involve a kilometer-long fiber [12], [13], [14]. Using a long length of fiber for frequency measurement not only increases the system size but the system time delay is in the order of tens of microseconds. Hence a photonic-assisted frequency measurement system with a fast measurement time cannot be implemented using a frequency-to-time mapping technique or a frequency-to-power mapping technique that involves a long length of fiber. It is worth to point out that although the frequency-to-time mapping based frequency measurement systems have the latency problem, they have multiple frequency measurement capability and small errors. Also note that it is not necessary for a frequency-to-power mapping based frequency measurement system to have a long length of fiber [15], [16], [17], [18]. However, most frequencyto-power mapping based frequency measurement systems have over ±100 MHz measurement errors, which is much larger than that of the commercial instantaneous frequency measurement systems. They also require high-speed photodetectors.
Recently there is a report on a frequency measurement system based on the frequency-to-phase mapping technique [19]. It has a simple and compact structure, and does not have the latency problem. However, the frequency measurement error is in the range of ±200 MHz, which is two orders of magnitude larger This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ Fig. 1. Topology of the wideband high-speed and high-accuracy instantaneous frequency measurement system. The bold lines represent polarization maintaining components. than that of the commercial frequency measurement systems [2], [3]. This prevents the frequency-to-phase mapping based frequency measurement system to be used in practice. In this paper, we present an instantaneous frequency measurement system that has a fast measurement time, a large frequency measurement range and small frequency measurement errors. The system uses two pairs of delay lines to produce two low-frequency (LF) signal phase differences. One of the signal phase differences is used for coarse signal frequency estimation over a wide frequency range without ambiguity and the other is used for fine frequency estimation. Experimental results are presented that demonstrate the concept of using two pairs of delay lines and two LF signal phase differences can determine the input microwave signal frequency accurately over a wide frequency range. Fig. 1 shows the structure of the proposed wideband highspeed and high-accuracy instantaneous frequency measurement system. A laser source generates a continuous wave (CW) light, which is traveled in the slow axis of a polarization maintaining fiber (PMF) before launching into an optical modulator. The optical modulator is a dual-polarization binary phase shift keying (BPSK) dual-drive Mach-Zehnder modulator (Fujitsu FTM7980EDA). It comprises a 3 dB coupler, two BPSK modulators, a 90°polarization rotator (PR) and a polarization beam combiner (PBC). Each BPSK modulator has two input RF ports and a DC port. An unknown microwave signal received by an antenna is equally split into four portions via a 4-way power divider. The four microwave signals at the power divider outputs are applied to the RF ports of the two BPSK modulators. As shown in the figure, the power divider Port 1 and 2 are connected to the two RF ports (RF 1 and RF 2 ) of the lower BPSK modulator (MZM 1 ). Note that there is a length difference ΔL 1 between the two electrical paths. Similarly, the power divider Port 3 and 4 are connected to the two RF ports (RF 3 and RF 4 ) of the upper BPSK modulator (MZM 2 ) with a path length difference ΔL 2 . The DC port of the two BPSK modulators are driven by a LF ramp waveform from a waveform generator (WG). The peak-to-peak amplitude of the ramp waveform is twice the BPSK modulator DC port switching voltage. This results in shifting the frequency of the light traveled in one arm of the BPSK modulator [20], [21]. The amount of the frequency shift is the same as the input ramp waveform frequency, which can be 50 kHz for example. MZM n output electric field is given by

II. TOPOLOGY AND OPERATION PRINCIPLE
where E in and ω c are the electric field amplitude and the angular frequency of the CW light into the dual-polarization modulator respectively, t ff is the insertion loss of the dual-polarization modulator, J m (x) is the Bessel function of mth order of the first kind, β RF = πV RF /V π ,RF is the modulation index, V RF is the amplitude of the unknown microwave signal received by the antenna into the modulator, V π ,RF is the modulator RF port switching voltage, ω S and ω RF are the angular frequency of the ramp waveform and the unknown microwave signal respectively, θ n = ω RF Δτ n + θ e , Δτ n is the signal time delay due to the electrical path length difference ΔL n , and θ e is the phase imbalance of the 4-way power divider used to split the incoming microwave signal. The spectra at the output of MZM 1 and MZM 2 are shown in Fig. 2(a) and (b) respectively. Note from the figure that the optical carriers at f c -f s and f c have the same phase whereas the sidebands with and without frequency shift have a phase difference depending on the time delay. Also note that ΔL 1 and ΔL 2 shown in Fig. 1 are different. Hence the two signal time delays (Δτ 1 and Δτ 2 ) are different and consequently θ 1 ࣔθ 2 . The polarization state of the optical signal at the output of MZM 1 is rotated by 90°via a PR. The two orthogonally polarized optical signals traveled in the two arms of the dual-polarization modulator are combined via a PBC. The electric field of the optical signal at the output of the dual-polarization modulator is given by wherex andŷ represent the two orthogonally polarized optical signal polarization states. The x-and y-polarization state optical signals are traveled in the fast and slow axis of a PMF and are launched into an optical circulator (OC), a fiber Bragg grating (FBG), an optical filter (OF) and a polarization beam splitter (PBS) as shown in Fig. 1. The center frequency of the FBG is the same as the laser source frequency. Hence the optical carriers are reflected by the FBG while the sidebands pass through the FBG. The OF filters out the upper sidebands. The two orthogonally polarized optical signals, which contain the lower sidebands, are split by the PBS. The xand y-polarization optical signals from MZM 1 and MZM 2 are detected by LF photodetectors (PD 1 and PD 2 ) respectively. The electric fields of the optical signals into PD 1 and PD 2 can be written as The optical carriers reflected by the FBG are routed from Port 2 to Port 3 of the OC into another LF photodetector (PD 3 ). Therefore the electric field of the optical signal into PD 3 can be expressed as The spectra of the optical signals into PD 1 , PD 2 and PD 3 are shown in Fig. 2(c)-(e) respectively. The optical signals with and without frequency shift are beat at the LF photodetectors (PD 1 , PD 2 and PD 3 ). This generates photocurrents with the frequency same as the input ramp waveform frequency. The photocurrents at the output of PD n , which is the product of the photodetector responsivity and the system output electric field square, can be expressed as where P in is the power of the CW light into the dual-polarization modulator and The photocurrents are fed into a digital signal processor (DSP), which performs phase comparison between the three LF signals. According to (6)-(8), the phase difference between the LF signals at PD 3 and PD 1 output is −φ 1 , and the phase difference between the LF signals at PD 3 and PD 2 output is −φ 2 . Under the small signal modulation condition, the second order sidebands are small, which can be neglected. Under an ideal situation, the power divider has no phase imbalance. Hence, according (9), the phase difference −φ 1 is θ 1 = 2πf RF Δτ 1 and the phase difference −φ 2 is θ 2 = 2πf RF Δτ 2 . Therefore the frequency of the unknown microwave signal into the system can be determined by either −φ 1 or −φ 2 .

III. SIMULATION RESULTS AND DISCUSSION
In practice, a phase detector can only measure a signal phase difference within 0°-360°. Therefore the electrical path length difference needs to be designed to obtain a time delay that results in a one-to-one mapping between a phase shift within 0°-360°and a microwave signal frequency in a given frequency measurement range. Fig. 3(a) shows the relationship between the frequency measurement range and the required signal time delay. As shown, the larger the frequency measurement range the smaller the time delay is needed. A 36 GHz frequency measurement range requires a time delay of 27.8 ps. Fig. 3(b) shows a unique mapping between a 4-40 GHz microwave signal frequency and a phase difference of 0°-360°, when the system is operated under the small signal modulation condition, the power divider has no phase imbalance, and Δτ 1 = 27.8 ps. In this case, for every 100 MHz change in the microwave signal frequency, there is a 1°change in the phase difference, which can be measured using a field programmable gate array (FPGA) based phase detector [22].
Note from Fig. 2(c) and (d) that, in addition to the first order sidebands, there are second order sidebands into the photodetectors. The second order sideband amplitude is dependent on the incoming microwave signal power, which is unknown. The presence of the second order sidebands causes the phase difference to deviate from θ 1 , which consequently causes deviation in the phase difference to microwave signal frequency relationship from that shown in Fig. 3(b). This leads to errors when determining the incoming microwave signal frequency using the phase difference. Another major cause of frequency measurement error in the proposed structure is the power divider phase imbalance θ e . The frequency measurement error f e is given by Fig. 4 shows the maximum amount of frequency measurement error, obtained using the phase difference of the LF signals at PD 3 and PD 1 outputs, for different frequency measurement ranges. As can be seen from Fig. 4(a), for a frequency measurement range of 36 GHz, which is realised by using a time delay of 27.8 ps, the frequency measurement error, caused by the presence of the second order sidebands, is within ±180 MHz for a modulation index of less than 0.7. As shown in Fig. 4(b), with the inclusion of ±3°power divider phase imbalance, the maximum amount of frequency measurement error is increased from ±180 MHz to ±480 MHz for the system having a 36 GHz frequency measurement range. Fig. 4 shows the frequency measurement error is small when the system is designed to have a small frequency measurement range. As the frequency measurement range increases, the error also increases. This indicates that a wide measurement range and a high measurement accuracy cannot be achieved at the same time. This limitation is present in many reported photonic-assisted frequency measurement systems. In the proposed structure, two different time delays (Δτ 1 and Δτ 2 ) are used to produce two phase differences (−φ 1 and −φ 2 ). The time delays Δτ 1 is designed to provide a coarse microwave signal frequency measurement over a wide frequency measurement range while Δτ 2 is designed so that the microwave signal frequency can be measured accurately. For example, as shown in Fig. 3, the time delay Δτ 1 = 27.8 ps is needed to measure a microwave signal frequency over the 4-40 GHz frequency range. According to Fig. 4(b), the frequency measurement error for the system with a 36 GHz frequency measurement range can be ±480 MHz. Hence the time delay Δτ 2 is designed to be 1 ns to provide a fine frequency measurement within a 1 GHz frequency measurement range, which is more than twice the maximum frequency measurement error of ±480 MHz for Δτ 1 = 27.8 ps. The corresponding phase difference to microwave signal frequency relationship and the maximum frequency measurement error versus the power divider phase imbalance are shown in Fig. 5. This shows a small frequency measurement error of less than ±13 MHz can be obtained for a power divider phase imbalance of less than ±3°and a modulation index below 0.7. This is a 36-time improvement in frequency measurement accuracy compared to that when using only one time delay of 27.8 ps for 4-40 GHz frequency measurement.
Assuming the incoming microwave signal frequency is 29.3 GHz, for Δτ 2 = 1 ns, the phase difference −φ 2 is 2πΔτ 2 f RF = 10548°. Since a phase detector can only measure a phase difference between 0°and 360°, a phase difference of 10548°c orresponds to 108°displayed on a phase detector under an ideal situation. Due to the presence of the second order sidebands and ±3°power divider phase imbalance, the phase difference −φ 2 obtained from the phase detector is within 108°± 4.7°. Hence, according to Fig. 5, the estimated incoming microwave signal frequency obtained from the phase difference −φ 2 is (k × 1 GHz) + 0.3 GHz with a maximum error of ±13 MHz, where k is an integer. The incoming microwave signal frequency is also estimated using the phase difference −φ 1 obtained from another phase detector in the DSP and Δτ 1 = 27.8 ps, and it is 29.3 GHz ± 480 MHz. This shows k can only be 29 in order for the estimated microwave signal frequency obtained from −φ 2 to be within the 29.3 GHz ± 480 MHz frequency range. Therefore, by using the two phase differences (−φ 1 and −φ 2 ) at the system output, a microwave signal frequency can be measured over a wide frequency range with small errors. For Δτ 2 = 1 ns and using a phase detector with a phase detection resolution of 1°, the frequency of a microwave signal can be measured with a resolution of 2.8 MHz. Hence the proposed structure also has a high frequency measurement resolution. Since the proposed frequency measurement system determines the incoming microwave signal frequency by measuring the signal phase differences, a phase detection error causes an error in frequency measurement. However, a phase detector can be made to have a high accuracy of better than 0.1° [23]. Hence the frequency measurement error caused by the phase detector detection error can be neglected.
The 1 dB compression point of the proposed frequency measurement system, which is defined as the input microwave signal power required to cause the loss of the output LF signal to increase by 1 dB, can be obtained from (6). It is between 6.9 dBm to 8.8 dBm for 0°to 360°phase difference. The proposed frequency measurement system has a wide frequency measurement range where the upper operating frequency is only limited by the power divider bandwidth. 2-40 GHz 4-way power dividers are commercially available. They have a typical phase imbalance of ±2.8° [24]. A wideband DC-67 GHz 4-way power divider [25] can be used in the proposed structure for microwave frequency measurement beyond the Ka band. The system lower operating frequency is determined by the reflection bandwidth of the FBG used to reflect the optical carriers, which can be made to be few GHz. The proposed frequency measurement system has a fast measurement time as it does not require sweeping a laser wavelength or a reference signal frequency, and does not involve a long length of fiber or use the frequency-to-time mapping technique.

IV. EXPERIMENTAL RESULTS
An experiment was set up similar to that shown in Fig. 1 to demonstrate the concept of the high-speed and high-accuracy instantaneous frequency measurement system. A tunable laser (Keysight N7711A) generated a CW light, which passed through a polarization controller (PC) into a dual-polarization BPSK dual-drive MZM (Fujitsu FTM7980EDA). Due to the lack of a 4-way power divider, a 2-way power divider was used to split a microwave signal from a 20 GHz microwave signal generator. The microwave signal at each power divider output passed through a phase shifter, which had an adjustable length of 6 mm. The output of one of the phase shifters was connected to a 30 mm connector adaptor. This results in a 30 mm with ±6 mm adjustable electrical path length difference between the two electrical paths from the power divider to the RF ports of MZM 1 in the dual-polarization modulator. A 50 kHz ramp waveform from a waveform generator was applied to MZM 1 DC port. The peak-to-peak amplitude of the ramp waveform was set to be 11.6 V, which is two times the modulator DC port switching voltage, to introduce 50 kHz frequency shift on the optical signal traveled in one arm of MZM 1 . The RF ports of MZM 2 were terminated by 50 Ω terminators. A DC voltage was applied to MZM 2 DC port to bias MZM 2 at the null point. The output of the dual-polarization BPSK dual-drive MZM was connected to an OC, a FBG, a tunable optical bandpass filter and a PBS as shown in Fig. 1. The reflection magnitude response of the FBG is shown in Fig. 6(a). As shown, the FBG has a center wavelength of 1550.1 nm, a narrow 3-dB reflection bandwidth of 8.5 GHz and a stopband rejection level of around 35 dB. A PC was connected to the tunable optical bandpass filter output. It was adjusted so that the x-polarization optical signal from MZM 1 and the y-polarization optical signal from MZM 2 were routed to two different PBS output ports.
The tunable laser wavelength was set at the FBG center wavelength. A microwave signal at 15 GHz frequency from the microwave signal generator was applied to the dual-polarization modulator. The center wavelength and the bandwidth of the tunable optical bandpass filter were adjusted so that the optical filter has a magnitude response as shown in Fig. 6(b) to filter out the lower sidebands in wavelength, which corresponds to the upper sidebands in optical frequency. The optical spectra at the OC Port 3 and at the output of the PBS that contains the optical signal from MZM 1 were measured on an optical spectrum analyzer. They are shown in Fig. 6(a) and (b) for two different microwave signal powers of −1.8 dBm and 4.85 dBm into the modulator. Since the RF port of MZM 1 has a switching voltage of around 3 V, the modulation indexes are 0.28 and 0.58 for the two input microwave signal powers. As shown in the figures, the optical carriers are reflected by the FBG (Fig. 6(a)) while the upper sidebands in wavelength are passed through the FBG and the tunable optical bandpass filter ( Fig. 6(b)). Fig. 6(b) also shows the optical carrier is largely suppressed, and for a modulation index of less than 0.58, the second order sideband is more than 18.7 dB below the first order sideband.
The carriers and sidebands shown in Fig. 6 were amplified by erbium-doped fiber amplifiers (EDFAs) before detecting by two photodetectors (PD 1 and PD 3 ) (Discovery Semiconductor DSC30S). The optical signals with and without 50 kHz frequency shift beat at the photodetectors. A 50 kHz LF signal was generated at each photodetector output. It was amplified by a LF electrical amplifier followed by a 50 kHz lowpass filter (LPF) for eliminating the harmonic components. The two amplified 50 kHz signals were injected into an FPGA based DSP, which has an LCD display showing the input signal phase difference. Due to the FBG used in the experiment has a 3-dB reflection bandwidth of 8.5 GHz and the microwave signal generator available for experiment has a bandwidth of 20 GHz, microwave signal frequency measurement can only be demonstrated in a frequency range of 5 to 20 GHz. Hence the length of the phase shifter was Fig. 7. Phase difference between the two system output 50 kHz signals generated by PD 3 and PD 1 for different microwave signal frequencies of 5-20 GHz into MZM 1 . adjusted so that the time delay of the two electrical signals into MZM 1 was 67 ps to obtain a unique mapping between 5-20 GHz input microwave signal frequency and 0°-360°output LF signal phase difference. Fig. 7 shows the phase difference measured on the DSP when the input microwave signal frequency was changed from 5 to 20 GHz with a step of 0.5 GHz. As shown, the phase difference has a linear relationship with the microwave signal frequency. More importantly, each microwave signal frequency within the 5-20 GHz frequency range has a unique phase difference. The figure also shows a reference phase line, which was obtained using the time delay introduced by the two electrical path length difference and a constant phase shift introduced by the LF electrical components connected to the photodetector output.
The input microwave signal frequency can be estimated using the phase difference measured on the DSP and the reference phase line. It is shown in Fig. 8(a). The difference between the estimated microwave signal frequency and the actual frequency of the microwave signal into the system is the frequency measurement error, which is shown in Fig. 8(b). As shown, the frequency measurement error is less than ±220 MHz for a microwave signal with different frequencies between 5-20 GHz and different powers of −1.8 dBm and 4.85 dBm into the system. The error is mainly caused by the phase detection error from the DSP and the power divider phase imbalance. Since the DSP only measures the phase difference of two system output LF signals and there is only little change in the power divider phase imbalance over the 5-20 GHz frequency range, the frequency measurement error does not increase with the input microwave signal frequency as can be seen in Fig. 8(b). To demonstrate the frequency measurement error can be reduced by designing the signal time delay, the microwave signal and the 50 kHz ramp waveform were applied to MZM 2 instead of MZM 1 . A short length of electrical cable was inserted to one of MZM 2 RF ports to introduce a time delay Δτ 2 = 2 ns to realise a 500 MHz frequency measurement range, which is more than twice the frequency measurement error of ±220 MHz for Δτ 1 = 67 ps. This results in a unique mapping between a microwave signal frequency of 0 to 500 MHz and a phase difference of 0°to 360°. This frequency to phase difference mapping relationship is repeated for every 500 MHz. The upper sidebands generated by MZM 2 passed through the OC, the FBG, the tunable optical bandpass filter, the PC and the PBS. They were amplified by an EDFA before detecting by a photodetector (PD 2 ). The optical carriers reflected by the FBG were routed from Port 2 to Port 3 of the OC into an EDFA and a photodetector (PD 3 ). As before, the 50 kHz LF signal generated by the photodetector was amplified by the 1 MHz bandwidth amplifier and passed through the 50 kHz LPF before injecting into the FPGA based DSP. Fig. 9 shows the system output 50 kHz signal phase difference measured by the DSP, for a microwave signal with different frequencies of 14.5 to 15 GHz and different powers of −1.8 dBm and 4.85 dBm into MZM 2 . A one-to-one mapping between a microwave signal frequency of 14.5-15 GHz and 0°-360°p hase difference can be seen. Note that the phase difference measurement shown in Fig. 9 was obtained by increasing the input microwave signal frequency from 14.5 to 15 GHz with a step of 20 MHz. As shown in the figure, there is an around 14°p hase change for every 20 MHz change in the input microwave signal frequency. This agrees with the phase difference to time delay relationship stated in Section II. Phase detectors with an accuracy of better than 1°and a phase detection range of 0°-360°h ave been reported [22], [23], [26]. Hence the input microwave signal frequency can be measured in high resolution by using these high-accuracy phase detectors in the proposed structure. As before, an estimated microwave signal frequency can be obtained using the measured phase difference and the reference phase line. It is shown in Fig. 10(a). Fig. 10(b) shows the frequency measurement error, which is the difference between the estimated and actual input microwave signal frequency, is within ±10 MHz. This shows the frequency measurement error is reduced from ±220 MHz to ±10 MHz when the frequency measurement range is reduced from 15 GHz to 500 MHz. The experimental results show, the proposed structure, which produces two LF signal phase differences (−φ 1 and −φ 2 ), can determine the input microwave signal frequency over a wide frequency range with small errors.
The input microwave signal frequency was fixed at 15 GHz. The phase difference displayed on the phase detector was recorded every 5 minutes over an hour. The measurement shows the phase difference has less than ±0.5°change throughout the one-hour measurement period. This shows the proposed frequency measurement system has a stable performance. The noise components in the system are the laser relative intensity noise, the signal-spontaneous beat noise, the shot noise and the thermal noise. The signal-spontaneous beat noise from the EDFA was found to be the dominant noise component in the system. The noise floor of the system was more than 80 dB below the LF signal at the phase detector input for an input microwave signal power of −1.8 dBm. It was found that the frequency measurement error increases as the input microwave signal power reduces to below −5 dBm. This is because, for a −5 dBm input microwave signal power, the power of the LF signal generated by the beating of the two first order sidebands at the photodetector is below 0 dBm, which is outside the DSP operating power range. The EDFA gain needs to be increased or a LF electrical amplifier with a higher gain needs to be used before the DSP in order for the frequency measurement system to operate at small input microwave signal powers.
The time delay for the microwave signal traveled from the power divider input to the photodetector output was measured to be 218 ns. It was mainly due to the instrument EDFA used in the setup, which has a time delay of around 130 ns. Phase detectors with a fast response time of around 1 μs have been reported [26], [27]. Using these phase detectors in the proposed structure to measure the LF signal phase differences, the incoming microwave signal frequency can be determined with an order of magnitude faster than the systems based on the frequencyto-time mapping technique and the frequency-to-power mapping technique with a kilometer-long fiber. This overcomes the latency problem in the reported photonic-assisted frequency measurement systems [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14]. Table I shows the performance comparison of the proposed and reported frequency measurement systems without the latency problem. As shown, most of the reported instantaneous frequency measurement systems have simple structures. However, they have high frequency measurement errors of above ±100 MHz. Note that recently there are few reports on frequency measurement systems implemented using integrated photonic technology that have fast measurement times [33], [34]. They operated based on the original frequency-to-power mapping technique, which requires a pair of high-speed photodetectors.
The system output microwave signal powers are measured, which are used to construct an amplitude comparison function (ACF) for estimating the incoming microwave signal frequency. The integrated photonics based frequency measurement systems have an over 30 GHz frequency measurement range and root mean square errors of 755 MHz [33] and 10.85 MHz [34].

V. CONCLUSION
A wideband, high-speed and high-accuracy instantaneous frequency measurement system has been presented. It is based on using two signal time delays in a microwave photonic structure to generate two LF signal phase differences. One of the signal phase differences is used to estimate the incoming microwave signal frequency unambiguously over a wide frequency range. The other is used to provide accurate estimation on the microwave signal frequency. The proposed instantaneous frequency measurement system overcomes the latency problem in many reported photonic-assisted frequency measurement systems. It also has high frequency measurement resolution and a compact structure, which can be implemented using off-the-shelf components or integrated photonic technology. Experimental results demonstrate, by using a signal time delay of 67 ps (2 ns) and measuring the phase difference of two system output LF signals, the input microwave signal frequency can be determined unambiguously in a 5 to 20 GHz (14.5 GHz to 15 GHz) frequency range with errors below ±220 MHz (±10 MHz). Hence the proposed structure, which has two different time delays and produces two LF signal phase differences, can determine the input microwave signal frequency accurately over a wide frequency range. A short optical signal time delay of 218 ns and a high frequency measurement resolution of 20 MHz have also been demonstrated. The proposed instantaneous frequency measurement system should find application in modern electronic warfare and electronic countermeasure systems.