Microwave instantaneous frequency measurement (IFM) has attracted widespread research interest due to its numerous applications in national defense, satellite communication, electronic warfare, radar et al. Traditional electronic solutions face challenges in achieving IFM due to their reliance on frequency scanning within a limited frequency range. These solutions often encounter difficulties such as a restricted measurement range, high power consumption, and poor resistance to electromagnetic interference (EMI). With the increasing complexity of the electromagnetic environment and the continuous growth in bandwidth demand for radio frequency (RF) signal transmission, IFM with high precision, high resolution, and the ability to measure multiple microwave frequencies within a wide frequency range have significant prospects for application. Compared to traditional electronic solutions, a photonic-assisted microwave IFM scheme is an effective method for achieving a wider measurement range, lower measurement error, and higher resolution [1–4].

According to the measurement principle, photon-assisted microwave IFM schemes can be categorized into frequency-power mapping (FPM), frequency-time mapping (FTM), and frequency-space mapping (FSM). The FPM-based method [5–14] constructs a monotonic function between power ratio and an unknown microwave signal for a one-to-one correspondence between measured powers and unknown frequencies. While such methods can achieve IFM by simply constructing the amplitude comparison function (ACF), they are limited to detecting a single frequency at a time and cannot detect multiple frequencies simultaneously.

In [15], the unknown frequencies are mapped to the time intervals, which exhibits a measurement error of ±510 MHz within a 25 GHz measurement range, and a multi-frequency measurement resolution of approximately 5 GHz. In [16], Singh et al. introduced an FTM-based method for dynamic photon IFM. The system has a resolution of less than 1 MHz within a frequency range of 10 GHz, with a measurement accuracy of ±0.4 MHz. In [17], Chen et al. mixed unknown microwave signals with bidirectional chirp microwave probing signals through a dual-drive Mach-Zehnder modulator (MZM), and the unknown frequencies were measured by calculating the pulse time intervals. In the range of 2 to 14 GHz, the measurement error is less than ±3 MHz. Liu et al. [18] proposed a photonic-assisted multiple microwave frequency measurement approach based on stimulated Brillouin scattering (SBS) and FTM with high accuracy and a wide frequency measurement range. Within the frequency range of 6–18 GHz, the measurement error this approach is less than ±1 MHz. In [19], a simultaneous angle-of-arrival (AOA) and frequency measurement system based on microwave photonics has been proposed. By measuring the time intervals and the normalized amplitudes of the output electrical pulses, the AOA and the frequency can be obtained simultaneously. Within the frequency measurement range of 5 to 15 GHz, the measurement error is less than ±12 MHz. In [20], a narrowband optical filter implemented based on a frequency-shifted recirculating delay line loop and the SBS effect is used to achieve a multi-frequency measurement resolution of 250 MHz from 0.1 to 20 GHz. Although the FTM-based schemes have the capability of measuring multiple microwave frequencies, the measurement range needs to be further expanded while maintaining a higher measurement accuracy.

In order to achieve a wide frequency measurement range and higher measurement accuracy, FSM-based schemes are proposed. In [21], by using a coherent two-electron optical frequency comb (OFC) and a circular optical frequency shifter, the measurement system can simultaneously realize wavelength-division and time-division multiplexing, which enables high-speed spectral scanning from 1 to 8 GHz with a spectral resolution of 1.2 MHz. Using the Fabry-Perot interferometer as a periodic optical bandpass filter, different frequency signals fall into distinct channels [22, 23]. However, the number of microwave signals that can be simultaneously detected is limited by the comb lines of the OFC. Additionally, the instability of the Fabry-Perot filter (FPF) and the difficulty in precisely aligning wavelengths impose constraints on measurement performance. Channelized reception based on dual OFCs [24, 25] offers a solution to the wavelength misalignment issue inherent in FPF by modulating unknown signals onto the signal OFC while the coherent OFC, with a fixed frequency difference from the signal OFC, is used as the local oscillator light. The local oscillator light is then coupled with the signal OFC, followed by channel segmentation. However, the frequency measurement range is constrained by the comb line spacing, and there is the issue of mirror image blurring [25]. Although the use of image-rejection mixers can address the mirror image blurring issue, system complexity is increased. A frequency measurement method using OFC and photonic multichannel reception has also been proposed in [26–29]. Among them, in [26], the unknown signal needs to be determined by measuring two beat frequency values. In [27–29] the unknown frequency is determined by comparing the power of a pair of beat frequencies. However, when unknown signals appear at the midpoint of the channel, or the multiple unknown signals appear at positions symmetric to the midpoint of the channel, the system experiences frequency ambiguity, making it difficult to differentiate. While the frequency ambiguity issue can be addressed by adjusting the channel spacing and re-measuring a pair of beat frequency values, the beat frequency needs to be measured twice to ascertain the unknown frequency.

For the aforementioned issue, a wideband reconfigurable instantaneous microwave multi-frequency measurement system based on an optical frequency shifter and optical frequency comb has been proposed in this paper. The received unknown signals are segmented and allocated to separate channels as signal light through a demultiplexer. The local oscillator light carriers generated using an OFC are divided using a demultiplexer. The signal light and local oscillator light are mixed through a 90° optical hybrid coupler (OHC). The result is that each channel contains only one local oscillator light carrier with an unknown signal located to the right of it. Therefore, the frequency ambiguity caused by the beating frequencies generated between an unknown signal and a pair of local oscillator optical carrier with different powers is solved. Also, the measurement system can be reconfigured by simultaneously adjusting the comb spacing of the OFC and the channel bandwidth of DEMUXs.

A schematic diagram of the proposed instantaneous microwave multi-frequency measurement system is illustrated in Fig. 1. As shown in Fig. 1, the proposed measurement scheme is composed of a continuous wave (CW) laser, an optical splitter (OS), an optical bandpass filter (OBPF), three intensity modulators (IM), a dual-parallel Mach-Zehnder modulator (DPMZM), two erbium-doped fiber amplifiers (EDFA), two demultiplexers (DEMUX1 and DEMUX2), n 90° optical hybrid couplers (OHC), and n post-processing modules (PPM) consisting of a balanced photodetector (BPD) and an electrical spectrum analyzer (ESA). Among them, the BPD modules consist of a pair of BPDs and an electrical phase shifter (EPS). The output optical signals from DEMUX1 and DEMUX2 are called the signal and local oscillator light, respectively.

Figure 1. Schematic diagram of the proposed system.

Assuming that the output of the CW laser is E_in(t) = E_c exp (j2πf_c t), where E_c and f_c represents the amplitude and frequency of the optical carrier signal, respectively, j represents the imaginary number, and t represents the time. In the upper branch, the optical carrier output from the OS is inputted into the optical frequency shifter (OFS), which is composed of IM1 and OBPF. V₁(t) = V₁cos (2πf_s t) denotes the input radio frequency RF1 signal, where V₁ and f_s = 12f₃ (f₃ is the frequency of RF3) represents the amplitude and frequency of RF1. Since IM1 operates in the push-pull mode and the orthogonal transfer point, its output can be represented as

where J_n(•) represents the nth-order first kind Bessel function, ϕ₁ = πV_DC1/V_π1, ϕ₂ = πV_DC2/V_π1 respectively denote the phase shift caused by the bias voltages V_DC1 and V_DC2 on the upper and lower arms, V_π1 represents the half-wave voltage of the modulator, Δϕ = ϕ₂ − ϕ₁, and m₁ = πV₁/V_π1 is the modulation index of IM1. By adjusting V₁ to make m₁ small, ignoring the higher-order sidebands, the output of IM1 can be rewritten as

In Eq. (2), it can be seen that output of IM1 ultimately includes the carrier and ±1-order sidebands.

By using the OBPF, the carrier and the +1-order sideband are filtered, the output of IM1 can then be represented as

In Eq. (3), E₀ = E_c/4exp(jϕ₁)(1 − j)J₋₁(m₁) represents the optical signal amplitude output by IM1, and the output of IM1 incudes only f_c − f_s, as illustrated in Fig. 2-A.

Figure 2. Spectra at positions of A, B, C, D, and E in the measurement system shown in Fiig. 1.

The output optical signal frequency f_c − f_s from OBPF is employed as a new optical carrier input into the DPMZM. The DPMZM is composed of MZM1, MZM2, and an optical phase shifter (OPS). The output of the DPMZM can be represented as

where φ represents the phase shift of the OPS. The operating points of MZM1 and MZM2 are set at the minimum transmission points, and φ is the phase difference between the upper and lower arms of the DPMZM, resulting in the DPMZM operating in a carrier-suppressed single-sideband (CS-SSB) modulation state. When the unknown signal V_xn(t) = V_xn cos(2πf_xn t + φ₀) (where V_xn, f_xn and φ₀ represents the amplitude, frequency and initial phase shift of the unknown signal) is input into MZM1 and MZM2, then in Eq. (4)

where ꞵ = πV_xn/V_π, represents the modulation index of MZM1 and MZM2, V_π represents the half-wave voltage of MZM1 and MZM2. By substituting Eq. (5) into Eq. (4), Eq. (4) can then be rewritten as

By setting adjusting the electrical phase shifter (EPS) and OPS to ensure that φ₀ = −φ = ±π/2, carrier-suppressed upper sideband (CS-USB) signals are generated, and Eq. (6) can be reformulated as

The optical signal from the DPMZM is amplified by EDFA1 and channelized by the 1 × 25 DEMUX1 to allocate unidentified signals into distinct channels. The frequency of the optical carrier of the first channel (Channel 0) of DEMUX1 is f₀ = f_c − f_s = f_c − 12f₃, the output of DEMUX1 can be expressed as

where V_S = 1/2α₁E₀J₁(ꞵ) represents the amplitude of the optical signal output by DEMUX1, α₁ represents the amplification factor of EDFA1, and i denotes the channel number. The DEMUX1 output channelized optical spectra are illustrated in spetra position C of Fig. 2.

In the lower branch, the optical carrier is modulated by the RF2 signal in the dual-drive IM2 after being split by the OS. Denoting RF2 is V₂(t) = V₂cos(2πf₂t), where V₂ and f₂ represent the amplitude and frequency. The output of IM2 can then be expressed as

where V_π2, m₂ = πV₂/V_π2 denotes the half-wave voltage and the modulation index of IM2, ϕ₃ = πV_DC3/V_π2, ϕ₄ = πV_DC4/V_π2 are phases differences introduced by the bias voltages of V_DC3 and V_DC4, respectively, and θ is the initial phase of RF2.

By setting V_π2, θ, V_DC3, and V_DC4 to satisfy

Based on Eq. (10), under small-signal modulation and neglecting higher-order sidebands, Eq. (9) becomes

In Eq. (11), it can be observed that the output of IM2 forms a five-line OFC consisting of the 0^th, ±1^st, and ±2^nd-order sidebands where frequency spacing is f₂.

The five-line OFC performed as an optical multi-carrier is input into IM3. Assuming that the IM3 input RF3 signal is V₃(t) = V₃cos(2πf₃t) (where V₃ = V₂ and f₃ = 0.2 f₂ represent the amplitude and frequency), and the side-bands of IM3 also satisfy Eq. (10), the output of IM3 can be written as

where ϕ₅ = ϕ₃ represents the phase shift caused by the bias voltage of IM3, and m₃ = m₂ = πV₂/V_π2 denotes the modulation index of IM3. According to Eq. (12), it can be inferred that the IM3 output results in a 25-line OFC.

The 25-line OFC from IM3 is amplified by EDFA2 and then channelized by the 1 × 25 DEMUX2. Because the frequency of the first channel of DEMUX2 is the same as the carrier frequency of the input DPMZM, both are f₀. The output of DEMUX2 can then be expressed as

In Eq. (13), V_L = α₂E_c/8[exp(jϕ₃) + 1]²$J_0^2$(m₃) represents the amplitude of each optical comb output by DEMUX2, where α₂ represents the amplification factor of EDFA2, and f₀ + if₃ (0 ≤ i ≤ 24) denotes the channelized frequency. The DEMUX2 output channelized optical spectrum is illustrated in spectra position D of Fig. 2.

The output of DEMUX2 is input into the L port of the 90° OHC, while the DEMUX1 output channelized optical signal serves as the signal light and is input into the S port of the 90° OHC. The output spectra of the OHCs are illustrated in Fig. 2-E. The output of the 90° OHC is

If the outputs of DEMUX1 and DEMUX2 are directly coupled into a photodetector (PD) for optoelectronic conversion, each channel can only detect a single signal. When multiple signal frequencies occur in a channel, the spectrum aliasing phenomenon occurs, making it difficult to accurately distinguish unknown signals. The issue of spectrum aliasing can be addressed by combining a 90° OHC and a BPD.

To solve the frequency ambiguity problem caused by the beating frequencies generated between a single unknown signal and a pair of local oscillator optical carriers with different powers, the signal light and the local oscillator light are divided into two branches in this system, and are subsequently delineated by channelization. By adjusting the OFS, the input optical carrier frequency of the DPMZM is made equal to the local oscillator optical carrier frequency of the first channel of DEMUX2. By using the 90° OHCs to couple the outputs of the DEMUX1 and DEMUX2, all the unknown signals are located to the right of the local oscillator optical carrier, thus resolving the issue of frequency ambiguity.

The 90° OHC output optical signal is converted into electrical signals by the BPD, which can be represented as

In Eq. (15), V_S, V_L represents the amplitude of the unknown signal output from DEMUX1 and the amplitude of the local oscillator optical carrier output by DEMUX2, and ℜ is the responsivity of the BPD.

In Eq. (15), it can be observed that the unknown signal undergoes a frequency down-conversion through the i-th channel and can be detected by the i-th BPD. Therefore, if the i-th BPD detect frequency is f_PD = f_xn − (f₀ + if₃), the unknown signal f_xn can be expressed as

3.1. Simulation Results

Based on the schematic diagram shown in Fig. 1, an experimental simulation system is established using Optisystem 15.0. In the simulation, the sequence length of global variables is set to 1,024 bits, with 64 samples per bit, for a total of 65,536 samples, and a sample rate of 640 GHz. Also, the system noises such as thermal noise, shot noise, or amplifier spontaneous emission noise are included. The main parameters of the key devices of the system are shown in Table 1.

TABLE 1. Parameters of key devices.

Device	Parameter	Value
Laser	Frequency (THz)	193.100
	Power (dB)	13
	Linewidth (MHz)	1
IM1	Extinction Ratio (dB)	40
	Half-wave Voltage (V)	4
	Bias Voltage1 (V)	1
	Bias Voltage1 (V)	−1
MZM1/MZM2	Extinction Ratio (dB)	40
	Half-wave Voltage (V)	4
	Bias Voltage1 (V)	2
	Bias Voltage1 (V)	−2
IM2/IM3	Extinction Ratio (dB)	40
	Half-wave Voltage (V)	4
	Bias Voltage1 (V)	1.26
	Bias Voltage1 (V)	0
EDFA1/EDFA2	Gain (dB)	28
	Noise Figure (dB)	4
PD	Responsivity (A/W)	0.5
	Dark Current (nA)	5

The insertion loss of the modulators in this system are all set to 5 dB. The frequency of RF1 is set to f_s = 24 GHz, the modulation index of IM1 is set to 0.39, and the negative first-order sideband frequency of IM1 is f_c − f_s = 193.076 THz. For the DPMZM, the modulation indexes of MZM1 and MZM2 are both set to 0.39. The phase shifts of the EPS and OPS are set to −90° and 90°, respectively. The centre frequency of channel 0 of DEMUX1 is set to 193.077 THz. The channel bandwidth of DEMUX1 is set to 2 GHz, and the insertion loss of each channel is set to 3 dB. When the input unknown signal frequencies are 0.8 GHz, 1.7 GHz, 18.5 GHz, 20 GHz, 33.3 GHz and 49 GHz, the output spectrum of the DPMZM is as depicted in Fig. 3.

Figure 3. Output spectrum of the dual-parallel Mach-Zehnder modulator (DPMZM).

As indicated in Fig. 3, the frequency (f_c − f_s) of 193.0760 THz is suppressed and the signal frequencies of 0.8 GHz, 1.7 GHz, 18.5 GHz, 20 GHz, 33.3 GHz, and 49 GHz are moved to the optical domain corresponding to the frequencies of 193.0768 THz, 193.0777 THz, 193.0945 THz, 193.0960 THz, 193.1093 THz, and 193.1250 THz through the DPMZM. The output of the DPMZM is divided through the DEMUX1, which results in the frequencies 193.0768 THz and 193.0777 THz being allocated to the 0th channel, the frequencies 193.0945 THz and 193.0960 THz being allocated to the 9^th channel, and the frequencies 193.1093 THz and 193.1250 THz being allocated to channels 16 and 24 of DEMUX1, respectively.

In the lower branch, the frequency of RF2 is set to f₂ = 10 GHz, and the modulation index m₂ of IM2 is set to 2.75. The other parameter settings for IM2 are shown in Table 1. As a result, a five-line OFC with spacing of 10 GHz is generated and input into IM3. The modulation index m₃ of IM3 is set to 2.75. The other parameters of IM3 are shown in Table 1. By setting the frequency of the RF3 as 2 GHz, the half-wave voltage and bias voltage of IM3 are identical to IM2. Therefore, a 25-line OFC with spacing of 2 GHz is generated, as shown in Fig. 4.

Figure 4. Output spectrum of the 25-line optical frequency comb (OFC).

The channel bandwidth of DEMUX2 is set to 2 GHz, the insertion loss for each channel is set to 3 dB, and the center frequency of the first channel is 193.076 THz, which corresponds to the frequency of the first comb line of the 25-line OFC. As a result, the channelized output of DEMUX2 contains only one local oscillator optical carrier. The spectra of DEMUX2 are shown in Fig. 5.

Figure 5. DEMUX2 output spectra.

By using the 90° OHC, the frequencies in channels 0, 9, 16, and 24 of DEMUX1 are respectively coupled with the local oscillator optical carriers of channels 0, 9, 16, and 24 of the DEMUX2. The outputs of the OHCs are shown in Fig. 6.

Figure 6. Output spectra of the (a) 0^th, (b) 9^th, (c) 16^th, and (d) 24^th optical hybrid coupler (OHC).

In Fig. 6, it can be observed that the output of the 0^th 90° OHC comprises the local oscillator optical carrier frequency, which is 193.0760 THz, and the signal frequencies are 193.0768 THz and 193.0777 THz. The 9th 90° OHC comprises the local oscillator optical carrier frequency, which is 193.0940 THz, and the signal frequencies are 193.0945 THz and 193.0960 THz. The 16th 90° OHC comprises the local oscillator optical carrier frequency, which is 193.1080 THz, and the signal frequency is 193.1093 THz. The 24^th 90° OHC comprises the local oscillator optical carrier frequency, which is 193.1240 THz, and the signal frequency is 193.1250 THz.

The outputs of the 0^th, 9^th, 16^th, and 24^th 90° OHCs are respectively input into the 0^th, 9^th, 16^th, and 24^th BPDs to convert into electrical signals. The output spectra of BPDs are shown in Fig. 7.

Figure 7. Output spectra of the (a) 0^th , (b) 9^th, (c) 16^th, and (d) 24^th balanced photodetectors (BPD).

As shown in Fig. 7, it can be seen that by combining frequency calculation Eq. (16), the frequencies of the unknown signal detected in channel 0 are 0 × 2 + 0.8 = 0.8 GHz and 0 × 2 + 1.7 = 1.7 GHz. The frequencies of the unknown signal detected in channel 9 are 9 × 2 + 0.5 = 18.5 GHz and 9 × 2 + 2 = 20 GHz. The frequency of the unknown signal detected in channel 16 is 16 × 2 + 1.3 = 33.3 GHz. The frequencies of the unknown signal detected in channel 24 is 24 × 2 + 1 = 49 GHz. As a result, the measured frequencies agree with the input frequencies.

3.2. Analysis and Discussion

3.2.1. Mirror Image Blurring

Firstly, considering that the input optical carrier frequency f_c − f_s of the DPMZM is not equal to the 0^th channel center frequency of DEMUX2. For example, by setting f_c − f_s is 193.0750 THz, the 0^th channel center frequency of DEMUX2 is 193.0760 THz, the channel bandwidths of DEMUX1 and DEMUX2 are 2 GHz, and the 0^th channel center frequency of DEMUX1 is set to 193.0760 THz. As a result, when the input unknown signal frequencies are 0.5 GHz and 1.5 GHz, the output spectrum of the 0^th 90° OHC and BPD is shown in Fig. 8(a).

Figure 8. Output spectrum of (a) the 90° optical hybrid coupler (OHC) and (b) the balanced photodetector (BPD) with mirror image blurring.

In Fig. 8(a), it can be observed that the unknown 0.5 GHz and 1.5 GHz signals correspond to the frequencies of 193.0755 THz and 193.0765 THz and are symmetrically located on both sides of the local oscillator optical carrier (193.075 THz). Therefore, only the 0.5 GHz signal can be detected by the 0th BPD, as shown in Fig. 8(b).

Secondly, considering that the input optical carrier frequency f_c − f_s of the DPMZM and the 0th channel center frequency of DEMUX2 are both set to 193.0760 THz. Meanwhile, the 0th channel center frequency of the DEMUX1 is set to 193.0770 THz. As a result, as shown in Fig. 9(a), the input 0.5 GHz and 1.5 GHz unknown frequencies correspond to the frequencies of 193.0765 THz and 193.0775 THz and are moved to the right side of the local oscillator optical carrier (193.0760 THz). At the same time, after PPM processing, the signal is detected in the 0^th channel, and its spectrum is shown in Fig. 9(b).

Figure 9. Output spectra of (a) the 90° optical hybrid coupler (OHC) and (b) the balanced photodetector (BPD) without mirror image blurring.

In Fig. 9(a), it can be observed that the signal light and the local oscillator light carrier are separately allocated channels by using DEMUX1 and DEMUX2. Then, by using the 90° OHC each allocated channel contains only one local oscillator light carrier. Additionally, by setting the input optical carrier frequency f_c − f_s of the DPMZM equal to the 0th channel center frequency of DEMUX2, the local oscillator light carrier is associated only with the signal light to its right, while at the same time, the combination of PPM thereby addresses the issue of frequency ambiguity due to mirror images.

3.2.2. Measurement Resolution

To assess the measurement resolution, two sets of frequencies, 5.122 GHz and 5.132 GHz, and 5.123 GHz and 5.132 GHz, are input into the system. The BPD output spectra are shown in Fig. 10.

Figure 10. Balanced photodetector (BPD) output spectra with input frequencies of (a) 5.122 GHz and 5.132 GHz, and (b) 5.123 GHz and 5.132 GHz.

In Fig. 10(a), when the input frequencies are 5.122 GHz and 5.132 GHz (the spacing is 10 MHz), the BPD can detect two signals in channel 2. According to Eq. (16), the measured frequencies can be calculated as 2 × 2 + 1.122 = 5.122 GHz and 2 × 2 + 1.132 = 5.132 GHz. However, when the input frequencies are 5.123 GHz and 5.132 GHz (the spacing is 9 MHz), the BPD can only detect one signal in channel 2. Therefore, it can be seen that the resolution of the proposed measurement system is 10 MHz.

3.2.3. Measurement Error

Due to the down-conversion of unknown frequencies greater than 2 GHz to the 0–2 GHz range for measurement, the single-tone signals within the 0–2 GHz range with a step size of 0.1 GHz are input into the system to evaluate the measurement error. The measured and input frequencies are illustrated in Fig. 11. From Fig. 11, it can be observed that the measurement error of the system is within ±5 MHz.

Figure 11. The measurement error of the system.

Note that the duration of the signal is t = N / f_a (where N is the number of sampling points of the global parameter and f_a is the sampling rate), therefore when the sampling rate f_a is fixed, the longer the duration of the signal, the greater the number of sampling points, and thus the smaller the measurement error of the system. Table 2 illustrates the measurement errors at different durations for the input frequency is 1.5 GHz.

TABLE 2. Measurement error under different durations.

Durations (ns)	1.6	6.4	25.6	102.4
Measurement Error (|MHz|)	250.0	62.5	15.6	4.0

From Table 2, when the signal durations are 1.6 ns, 6.4 ns, 25.6 ns, and 102.4 ns, the measurement errors are −250 MHz, 62.5MHz, 15.6MHz, and 4.0 MHz respectively. Therefore, as the signal duration increases, the corresponding measurement error gradually decreases.

3.2.4. Measurement Reconfigurability

To demonstrate the reconfigurability of the proposed system, the input frequencies of IM1, IM2 and IM3 are change to 48 GHz, 20 GHz and 4 GHz respectively, while the channel bandwidth of DEMUX1 and DEMUX2 are set to 4 GHz, which results in the comb line spacing of the OFC is 4 GHz. Therefore, according to the comb spacing of the OFC and the channel bandwidth of DEMUX1 and DEMUX2 are changed from 0 to 2 GHz to 0 to 4 GHz, the number of lines in the optical frequency comb remains unchanged at 25 lines, the frequency measurement range has increased from 0.01–50 GHz to 0.01–100 GHz.

As an example, when the input unknown signal frequencies are 3.2 GHz, 93 GHz, and 95 GHz. The BPD output spectra are illustrated in Fig. 12. From Fig. 12(a), the measured frequency is 0 × 4 + 3.2 = 3.2 GHz. From Fig. 12(a), the measured frequencies are 23 × 4 + 1 = 93 GHz and 23 × 4 + 3 = 95 GHz respectively.

Figure 12. Output spectra of (a) channel 0 and (b) channel 23.

Similarly, due to the down-conversion of unknown frequencies (greater than 4 GHz) to 0–4 GHz for measurement, the single-tone signals within the 0–4 GHz range with a step size of 0.1 GHz are input into the system to evaluate the measurement error. The results are illustrated in Fig. 13.

Figure 13. Measurement error of the reconfigured system.

In Fig. 13, it can be observed that the measurement error of the system is 5–14.6 MHz. Therefore, although the measurement range can be extended from 0.01 to 50 GHz to 0.01 to 100 GHz by reconfiguring the comb spacing of the OFC and the channel bandwidth of DEMUX1 and DEMUX2, the measurement error increases. This comes from the fact that when comb spacing of the OFC and the channel bandwidth of DEMUX1 and DEMUX2 are changed to 4 GHz, there may be more unknown frequencies in the same channel, resulting in greater errors when passing through the BPD beat frequency.

For comparative analysis, the performances of various frequency measurement schemes in recent years are shown in Table 3. From Table 3, it can be observed that the FPM- based measurement schemes can only measure a single unknown frequency signal, and the measurement error is relatively large. In contrast, the FTM- and FSM-based methods can simultaneously measure the frequencies of multiple microwave signals. In [16], measurement accuracy was ≤±0.4 MHz and resolution was <3 MHz. However, the measurement range is limited to 0–10 GHz. In [29], the adjustable measurement ranges are 1–40 GHz or 1–72 GHz, with a measurement accuracy of 2 MHz. However, a secondary beat frequency process is required to address the issue of frequency ambiguity. In contrast, the proposed FSM-based method in this paper has an adjustable measurement range of 0.01–50 GHz and 0.01–100 GHz, with measurement accuracies of <±5 MHz and 5–14.6 MHz, respectively. Also, the frequency can be measured without secondary beat frequency operations and the mirror image blurring issue.

TABLE 3. Frequency measurement performance comparison.

Refs.	Technology	Range (GHz)	Accuracy (MHz)	Input	Resolution	Second Beat Frequency
5	FPM-based	7.5–20	<100	Single-tone	-	No
6		1.6–24.6	<±300		-	No
7		0.1–25	<3%		-	No
8		8–20	<110		-	No
9		8–18	<±150		-	No
15	FTM-based	0–25	<±510	Multi-tone	5 GHz	No
16		0–10	<±0.4		<1 MHz	No
17		2–14	<±3		-	No
18		6–18	<±1		-	No
19		5–15	<±12		-	No
20		0.1–20 (90)	-		250 MHz	No
22	FSM-based	0.5–11.5	±500	Multi-tone	0.5 GHz	No
23		0.5–39.5	±500		0.5 GHz	No
26		<70	-		-	Yes
27		0–32	-		-	Yes
28		2–12	2		-	Yes
29		1–40 (1–72)	2		-	Yes
This Work		0.01–50 (0.01–100)	<±5 (5–14.6)		10 MHz	No

In conclusion, a wideband reconfigurable instantaneous microwave multi-frequency measurement system based on an optical frequency shifter and optical frequency comb is presented and investigated. The system can achieve reconfigurability by tuning the comb line spacing of the OFC and the channel bandwidth of the DEMUXs. The signal and local oscillator light carriers, which have been separated by DEMUX1 and DEMUX2, are mixed using a 90° OHC. By using the 90° OHC, each channel contains only one local oscillator optical carrier, and the optical signal is consistently positioned to the right of the local oscillator light carrier. At the same time, the combination of PPM resulting there is without frequency ambiguity caused by the beat frequencies generated between the unknown signal and a pair of local oscillator optical carriers. Simulation experiments were conducted using Optisystem 15.0, which revealed that when the channel bandwidths of DEMUX1 and DEMUX2 are set to 2 GHz, the measurement range is 0.01–50 GHz, with a measurement error within ±5 MHz. When the channel bandwidths of DEMUX1 and DEMUX2 are both set to 4 GHz, the measurement range is 0.01–100 GHz, with a measurement error from 5 to 14.6 MHz.

This work was supported in part by the National Natural Science Foundation of China (Grant no. 62162034), and in part by Yunnan Fundamental Research Projects (Grant no. 202201AT070189).

The authors declare no conflicts of interest.

Data underlying the results presented in this paper are not publicly available at the time of publication, and may be obtained from the authors upon reasonable request.