## 2 QPSK-Oriented All-Optical Matching System and Noise Analysis  
### QPSK-Oriented All-Optical Matching System  
[PERSON] et al. proposed a QPSK-oriented all-optical matching system based on PSA using HNLF [16]. Figure 1 shows the structure of the matching system. First, the input QPSK data are split into two identical optical signals using a 1:2 power splitter. The first optical signal passes through the PSA module, and symbols with phases of \(\{0\}\) and \(\{\pi\}\) are amplified, whereas the power of symbols with phases of \(\{\pi/2\}\) and \(\{3\pi/2\}\) is compressed to 0, resulting in the signal\({}_{1}\) to be matched. The other optical signal also passes through another PSA module, which amplifies symbols with phases of \(\{\pi/2\}\) and \(\{3\pi/2\}\), while symbols with phases of \(\{0\}\) and \(\{\pi\}\) have their power compressed to 0, resulting in the matching of signal\({}_{2}\). Target signals are then generated by controlling the two BPSK signal sources, Targets 1 and 2. When the target symbol is \(\{0\}\) or \(\{\pi\}\), Target 1 outputs the signal, and Target 2 outputs 0. When the target symbol is \(\{\pi/2\}\) or \(\{3\pi/2\}\), only Target 2 outputs the signal, and Target 1 outputs 0. The upper and lower parts of the symbol-matching module are identical. The upper part matches signal\({}_{1}\) with Target 1. Signal\({}_{1}\) is split into two paths by the 1:2 power splitter. One path is input into a frequency converter to obtain a signal with frequency \(f_{1}\), and the other path is multiplexed with one of the signals obtained from Target 1 after passing through the 1:2 power splitter. After multiplexing,the result is combined with the frequency-converted signal and passes through the first AND gate. The output signal of the first AND gate is then combined with another signal obtained by splitting Target 1 and input into the second AND gate to eliminate the impact of mismatching positions. The lower part follows the same principle to match signal\({}_{2}\) with Target 2. By multiplexing the outputs of both parts, the symbol-matching results can be obtained. Based on the order and number of symbols in the target sequence, the symbol-matching module sequentially outputs \(N\) frames of the symbol-matching signals. The signals output by the symbol-matching module are input to a recirculating loop composed of an AND gate and a regenerator. The first frame of the symbol-matching signal is subjected to an AND logic operation with the initial pulse to obtain the first frame-matching result. After regeneration and delay, the first frame-matching result is subjected to an AND logic operation with the second frame of the symbol-matching signal output by the symbol-matching module to output the second frame-matching result. This process continues in sequence, and the all-optical matching system outputs a total of \(N\) frames of matching results. The matching result of the \(k_{i}h\) frame represents the match between the sequence \(\{a_{1},a_{2},\ldots,a_{k}\}\) formed by the first \(k\) symbols of the target sequence and the data sequence. The number of high-power optical pulses in the matching result indicates the number of times the sequence appears in the data sequence, and the position of the high-level pulse corresponds to the last symbol of the sequence in the data sequence. The \(N_{i}h\) frame result indicates the overall matching result of the system for the entire target sequence. The design of this system focuses primarily on achieving a match without optimizing its noise resistance. Input and amplifier noise introduced by the extensive use of erbium-doped fiber amplifiers (EDFAs) affect the matching performance of the system and may lead to errors in the output results. Therefore, there is a need to evaluate the impact of noise on the system matching effects and to develop appropriate noise-suppression schemes to overcome this challenge.