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SECTION I

For electronic warfare (EW) and radar systems, it is of critical importance to acquire parameters of incoming microwave signals, including the frequency, the pulse amplitude (PA), the pulse width (PW), the angle of arrival (AOA) and the time-difference of arrival (TDOA). Among these parameters, the estimation of frequency information has attracted lots of attention. The electrical approaches can provide high measurement resolution and large dynamic range, but its frequency measurement range is limited due to the electronic bottleneck, especially when the frequency of microwave signals in use or to be used is extending up to 300 GHz.

Photonic approaches are considered as promising solutions for microwave frequency measurement which are characterized by large instantaneous bandwidth, low loss, compact size, and immunity to electromagnetic interference [1]. Recently a number of photonic approaches have been proposed to perform instantaneous frequency measurement (IFM), for a single microwave frequency component or multiple ones [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17]. For a single frequency component, the IFM is usually realized by monitoring two frequency-dependent optical powers [2], [3], [4], [5], [6], [7], [8] or microwave powers [9], [10], [11], [12], [13], via the use of optical mixing, complementary optical filters, and dispersive element. A large frequency measurement range and a relative high resolution are usually resulted. For the measurement of multiple frequency components, photonic microwave channelized receivers are considered to be a powerful solution. A light array or an optical frequency comb serves as optical carriers, in combination with F-P etalons, which can be employed to realize the channelized receiver [14], [15], [16], [17]. In the above photonic-assisted approaches, the output results of frequency measurement are derived in analog format. However, digital outputs are preferred in modern IFM system, since they are compatible with commercially available digital signal processing devices and easy to be stored. Thus, in [18] a photonic frequency measurement system with digital outputs based on optical phase-shifted filter array was proposed. However, the coding efficiency and the number of effective bits need to be further improved.

We propose a novel photonic approach with digital outputs, which can not only extend the measurement range, but also increase the number of efficient bits. In the proposed approach, an optical filter array which consists of N filters is designed as the key device. In the filter array, the first $N - 1$ optical phase-shifted filter have a phase increment $\pi/(N - 1)$ but an identical FSR in the transmission responses, while the last one optical filter has a doubled FSR. By using frequency-amplitude mapping in the optical domain and post processing, we can achieve an $N$-bit binary code in the unambiguous measurement range of $2\times FSR$. In the experiment, 5-bit digital outputs are demonstrated for IFM within the range of 10 $\sim$ 40 GHz, with the number of effective bits being enhanced to be 4.

SECTION II

The schematic diagram of the proposed approach is shown in Fig. 1. The light wave from a laser diode (LD) is modulated by a microwave signal to be measured under the carrier-suppressed single sideband (CS-SSB) modulation, leading to the generation of one optical sideband which is then coupled to the optical filter array and a reference branch. The outputs from the filter array and the reference branch are detected and compared for the decision and the coding, such that the frequency value being measured is labeled by an $N$-bit binary digital output.

Under the CS-SSB modulation, the optical field can be expressed by TeX Source $$E_{1}(t)\propto\exp\ j\left[2\pi(f_{c} + f_{m})t\right]\eqno{\hbox{(1)}}$$ where $f_{c}$, $f_{m}$ are the frequencies of the optical light wave and the incoming microwave signal, respectively.

To implement frequency-to-amplitude mapping for the generated signal in (1), a filter array consisting of $N$ optical filters is used. The transmission response of the first $(N - 1)$ filters is expressed as TeX Source $$H_{k}(f) = \left[1 + \cos(2\pi f/FSR + \theta_{k}) \right]/2\eqno{\hbox{(2)}}$$ where $k$ represents the order of the filters, $f$ is the optical frequency, $FSR$ is the free spectral range, $\theta_{k} = \pi/(N - 1)$ is the initial phase of the $k$-th filter. Here, $N$ is only equal to $2^{n} + 1$, and $n$ is a positive integer. For the last optical filter, its transmission response can be written as TeX Source $$H_{N}(f) = \left[1 + \cos(\pi f/FSR)\right]/2.\eqno{\hbox{(3)}}$$

It is noted that the FSR of the $N$-th transmission response is twice those of the first $N - 1$ responses, while in [18] N transmission responses with identical FSR were employed. This difference will lead to the improvement in coding efficiency and the extension in the measurement range. At the outputs of the filter array, the optical powers are detected and sent to the division and decision module. A division operation between the optical power of the filter array and the reference arm is then performed. While the frequency of the laser is aligned with the zero-phase point of the first and the $N$-th transmission response, the power ratio corresponding to $k$-th filter is derived as TeX Source $$R_{k}(f_{m}) = {1 + \cos(2\pi f_{m}/FSR + \theta_{k}) \over 2}, \qquad(1 \leq k \leq N - 1)\eqno{\hbox{(4)}}$$ and the power ratio for the $N$-th optical filter can be written as TeX Source $$R_{N}(f_{m}) = {1 + \cos(\pi f_{m}/FSR) \over 2}.\eqno{\hbox{(5)}}$$

Based on the power ratios, an analog-to-digital conversion can be done. For the $k$-th filter, the output bit is labeled as “1” if the power ratio is not less than 0.5; otherwise, the bit is encoded as “0”. Therefore, we can obtain an $N$-bit binary-encoded result to indicate the frequency value. In this way, an unambiguous measurement range is extended from $FSR$ to $2\times FSR$, which is divided into $4\times(N - 1)$ sub-ranges. To show the improvement on the encoding efficiency, a comparison between the proposed approach and that in [18] is presented. In both cases, the digital outputs with 5-bit digitals are achieved as five optical filters are used. Here, 16 codes are available since the unambiguous measurement range is divided into 16 sub-ranges. With regarding to [18], only 10 effective codes can be provided because an unambiguous measurement range is divided into 10 sub-ranges. Therefore, both the coding efficiency and the number of effective bits are improved.

SECTION III

To verify the proposed approach, experiments are performed. As shown in Fig. 2, the combination of a polarization modulator (PolM) and a polarizer is used to suppress the optical carrier. Then the two optical sidebands go through the optical bandpass filter with steep edge to filter one sideband. A polarization maintaining fiber (PMF), an optical mirror, an optical circulator, and five polarizers are employed to implement the optical filter array. When the incidence polarization angle of the optical sideband is adjusted to be $\pi/4$ with respect to one principal axis of the PMF, the two components (i.e., $E_{f}(t)$ and $E_{s}(t)$) corresponding to the two principal axes of the PMF are produced, and then reflected by the optical mirror. Due to the second polarization decomposition, four components with relative time delays of 0, $\tau$, $\tau$, and $2\tau$ can be achieved, where $\tau = 1/(2\times FSR)$ is the relative time delay between the fast and slow axis of the PMF. The first two components are parallel with the fast axis of the PMF, while the last two components are parallel with the slow axis of the PMF. By adjusting the polarizer controllers (PCs) connected to the filter array, the transmission responses $H_{k}(f) = 1/2\ast[1 + \cos(2\pi f/FSR + \theta_{k})]$, for the $N - 1$ filters can be achieved [18]. In particular, a time delay of $\tau$ can be generated to implement the transmission response (i.e., $H_{N}(f) = 1/2\ \ast [1 + \cos(\pi f/FSR + \theta_{N})]$) with a doubled FSR for the $N$-th filter. For instance, the transmission response of the $N$-th filter together with that of one of the first $N - 1$ filters is shown in Fig. 3, indicating an achieved doubled FSR.

A microwave signal with a center frequency of 10 GHz is firstly applied to the PolM. Under the condition of carrier suppression, only two sidebands can be observed and the optical spectrum is shown in Fig. 4(a). It can be seen that the suppression ratio between the optical carrier and the two sidebands is about 28 dB. Then the optical sidebands are amplified by the erbium doped fiber (EDFA). A tunable optical filter is employed to filter one optical sideband, and the optical spectrum can be observed as shown in Fig. 4(b).

Next, a microwave signal with its frequency being swept at a 2-GHz step inside the range of 10 $\sim$ 40 GHz, is applied to the PolM. The optical powers detected at the outputs of five filters and the reference branch, are depicted in Fig. 5(a). After comparison, the optical power ratios are shown in Fig. 5(b), indicating the initial phase shift of 0, $\pi/4$, $\pi/2$, $3\pi/4$, but an identical $FSR$ for the first four filters, and $2\times FSR$ for the fifth filter.

Then the data of the optical power ratios are normalized for the purpose of comparison with the theoretical values as shown in Fig. 6. It is clear that the normalized optical power ratios agree well with the theoretical values. Based on the normalized optical ratios and the decision threshold of “0.5”, the digital outputs with binary code are derived to show the microwave frequency. As shown in Fig. 6, the range of 10 $\sim$ 40 GHz are divided into 9 sub-ranges. The input frequencies are labeled by 5-bit digital outputs: “00001”, “00011”, “00110”, “01110”, “11110”, “11100”, “11000”, “10000” or “00000”. It is deduced that a measurement range of 30 GHz and a resolution about 3.9 GHz are obtained in the proof-of-concept experiment. Noted that the measurement range of 30 GHz is less than $2\times FSR$ of 62.5 GHz, due to the limit of the operation frequency on the microwave signal generator. In fact, a full measurement range of $2\times FSR$ can be achieved in the proposed approach when a modulator with a larger bandwidth is available. Meanwhile, the number of efficient bits is improved to 4, compared with the value of 3.32 in [18].

The accuracy of this measurement approach is affected mainly by the system stability, and the number of the optical filters used. In the proof-of-concept experiment, the PMF and polarizers are employed to implement the filter array. To avoid the encoding errors induced by environmental conditions, a commercially available temperature controller can be employed. More importantly, if more filters are employed to provide digital outputs with more bits in the optical filter array, higher measurement resolution can be achieved theoretically. This increases complexity of the optical filter array on the other hand.

SECTION IV

A novel photonic approach to IFM with high-coding-efficiency digital outputs and large measurement range has been proposed and verified. By using $N - 1$ optical phased-shifted filters with identical but phase-shifted filtering responses and one optical filter with doubled $FSR$, an $N$-bit digital output was derived for the frequency measurement of an incoming microwave signal. The measurement range was extended to $2\times FSR$ and the resolution was $FSR/(2N - 2)$. Moreover, the number of efficient bits increases to $2 + \log_{2}^{(N - 1)}$. In the experiment, 5-bit digital outputs with an efficient bit of 4 were derived for microwave frequency measurement up to 40 GHz.

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