As an interdisciplinary topic, microwave photonics has important applications in fields of broadband optical wireless communications, radars, and electronic warfare, due to the intrinsic characteristics of large bandwidth, high resolution, tunability, reconfiguration, and immunity to electromagnetic interference. In recent years, demodulation techniques based on microwave photonics have attracted considerable research interest, through the sensing information conversion from the optical domain to the microwave domain and high-resolution electrical spectrum analysis and processing techniques. When microwave photonic demodulation technology is applied to multi-point or quasi-distributed fiber Bragg grating (FBG) sensing systems, the RF response curve of the sensing system is usually transformed from the RF domain to the time-domain by discrete inverse Fourier transform (IDFT). Meanwhile, the sensor demodulation is realized by analyzing the amplitude of the peak point of impulse response in the time domain or the position change on the time axis. When traditional microwave photonic demodulation technology based on frequency-time transformation is applied to the FBG sensor network, it is necessary to ensure that no superposition is generated in the corresponding time-domain response signal for guaranteeing accurate demodulation of each FBG. This puts forward strict requirements for the spatial interval and wavelength separation between FBGs and limits the application range of microwave photonic demodulation technology. To this end, an effective meta-heuristic algorithm, arithmetic optimization algorithm (AOA) is introduced into the microwave photonic demodulation technology based on frequency-time transformation to realize precise demodulation of multiple FBG peaks under the time-domain signal superposition.

AOA is a newly developed meta-heuristic search technique that simulates the distribution characteristics of the basic arithmetic operations of addition, subtraction, multiplication, and division and has been employed to solve some real-world optimization problems. It is mainly divided into three stages including initialization, exploration, and development. During the exploration stage, Math optimizer accelerated functions are adopted to select different search strategies. At the beginning of this stage, AOA takes advantage of the characteristic that the multiplication and division operators are widely distributed and are difficult to approach the target to complete the global optimization in the search space and thus jump out of the local optimum. At the end of the exploration stage, AOA leverages the characteristic that the addition and subtraction operators are lowly distributed and easy to approach the target to achieve local optimization in the search space and further improve demodulation accuracy in a more accurate search space.

In a proof-of-concept experiment, a sensor network consisting of six FBGs with different wavelengths is built. The scanning range of vector network analyzer (VNA) is set to 10 MHz-5 GHz, the sampling resolution is 5 MHz, and a total of 1000 sampling points are included. In the experiment, the two ends of the sensing FBG are fixed on the two 3-axis translation stages via AB glue, with the distance between the two fixed points being 10 cm. The strain applied on the sensing FBG can be adjusted by moving one of the two translation stages, and it is linearly increased from 0 με to 2000 με with a step size of 100 με. It should be pointed out that by changing the strain applied to the sensing FBG, the time-domain sinc peaks corresponding to two FBGs will experience three conditions of non-overlapping, partially overlapping, and completely overlapping. The experiment results show that AOA can determine the central wavelength of each FBG regardless of the overlapping situation of the time-domain pulse signal, indicating that this method is suitable for the demodulation of time-domain overlapping signals (Fig. 8). To further validate AOA's demodulation performance, we conduct a comparison between AOA and other six meta-heuristic methods. The results confirm that, compared with other meta-heuristic algorithms, AOA has better performance in convergence efficiency, demodulation speed, and demodulation precision. Additionally, AOA solves the defect that the traditional meta-heuristic algorithm is prone to fall into the local optimal solution (Fig. 9 and Table 4).

When traditional microwave photonic technology based on frequency-time transformation is employed in the demodulation of FBG sensor arrays, it is necessary to ensure that the pulse signals of the time-domain response curve do not overlap, otherwise, huge demodulation errors will be caused to severely limit the application range of microwave photonic demodulation technology. To solve this problem, we introduce a time-domain overlapping signal peak detection method based on an arithmetic optimization algorithm. The proposed method transforms the demodulation of time-domain overlapping signals into multi-parameter optimization and achieves precise demodulation of time-domain peaks under signal overlapping through mathematical modeling. Comparison with the other six meta-heuristic algorithms shows that AOA exhibits sound performance in convergence efficiency, demodulation speed, and demodulation accuracy. Meanwhile, it solves the defect that traditional meta-heuristic algorithms are prone to fall into local optima to improve the demodulation of microwave photonic demodulation technology for dense FBG sensing networks.