## 3 Optimization and Performance Evaluation
The random search method is employed to take some points  
Figure 4: Two-dimensional search results. Figure 3: Comparison of correlation results. from the grid for correlation operation every cycle. When a result exceeds the threshold, we obtain the optimal solution only by searching near the result. Otherwise, the search scope is traversed. In the third step, we assume that the motion state of the underwater moving target conforms to the Markov process. The Doppler factor of the current symbol is calculated only in the adjacent area of the previous Doppler estimation, and the search range is reduced. A detailed description of all optimization steps is given next. It can be seen from Figure 5 that if the search process is modeled as an extreme value optimization, the fitness function of correlations is a multimodal function. The simulation conditions are the same as before. When conducting correlation searching in the Doppler range of \([-0.008,0.008]\) in steps of \(0.0001\), we find the correlation result is a smooth and continuous three-dimensional surface. The peak position corresponds to the Doppler estimation and the estimation of the spread spectrum code number of the present symbol. The pseudo-random codes have an excellent correlation performance. They also have sharp peaks on the Doppler axis. These characteristics make it possible to estimate Doppler directly from the spreading signal without data assistance. Nevertheless, with such a Doppler step size and code numbers for only one symbol search, the correlation operations of 1e3 (\(8\times 161=1288\)) are required. The computations required for decoding are directly proportional to the symbols. Therefore, this paper first optimizes the search step size. We show that this optimization reduces the computations of correlation by an order of magnitude later. With the help of Doppler estimation, we generally use the CAF method to realize accurate symbol synchronization and to suppress the influence of motion state on the UWA signal. Actually, the accuracy of Doppler estimation is not strict in the spread spectrum communication system. In a conventional DSSS communication system, the code synchronization is carried out by the sliding correlation method [40]. After coarse synchronization, they perform correlation operations on the one-symbol-length received signal and the reference signal, and find the position of the maximum correlation value. Then, taking this position as the starting position, they slide back half the symbol length, intercepting the signal with one symbol length again. The above steps should be repeated until the correlation operations are achieved for the whole frame signal. In incoherent UWA spread spectrum communication, the Doppler has an obvious effect on signal compression/expansion. The sliding correlation method can only suppress the cumulative effect of synchronization error caused by a small Doppler factor. Hence, the large Doppler factor is, firstly, modified to a  
Figure 5: Three-dimensional correlation search graph. smaller one by Doppler coarse estimation and compensation, then the residual Doppler is processed by sliding search. The BER curves of the conventional MSS method under different motion scenarios are given in Figure 6. Assuming that the motion speed is constant within the duration of the whole frame signal, we simulate at the speeds of 0.6 m/s, 1.2 m/s, 1.8 m/s, and 2.4 m/s. The simulation results are shown as a blue dashed line, a purple solid line, an orange solid line, and an orange dashed line, respectively. We also give two comparisons of different conditions. One is that the relative motion speed changes continuously up and down at 1.5 m/s within the signal duration. The simulation result is shown as the black line at the top of Figure 6. The other is assuming that we perform accurate Doppler estimation and compensation processing at the receiver, when the uniform speed is 2.4 m/s.