## 2 Burst Spread Spectrum Signal Design Based on Aperiodic Long Code  
In order to improve the efficiency of frame transmission, this paper presents a signal design method to remove the synchronous overhead. To remove the synchronization overhead, the signal structure needs to be redesigned. The burst spread spectrum signal without physical layer synchronization overhead adopts an aperiodic long code spread spectrum. The baseband processing process at the signal sender (before shaping filter) is shown in Figure 4.  
Compared with the burst spread spectrum signal based on synchronous head, there are two main differences. First, there is no special synchronous head. Second, the spread spectrum code adopts an aperiodic length code, which does not repeat in a burst frame. Therefore, as long as the receiver realizes the synchronization of the spread spectrum code and locates the spread spectrum code, the beginning time of the burst signal and the position of the signal in the burst frame are determined. This enables bit synchronization and frame synchronization, and restores the signal structure. The receiver processing block diagram of the aperiodic long code spread spectrum burst signal without physical layer synchronization overhead is shown in Figure 5. The specific work flow is as follows:  
1. Cache the sampled data;
2. Spread spectrum code acquisition--Configure the matching filter parameters to start the spread spectrum code acquisition. The beginning time of the burst signal can be located after the spread spectrum code is captured;
3. Spread spectrum code tracking--After the spread spectrum code synchronization, the data of certain symbol length are taken from the cache for processing to complete the spread spectrum code tracking;
4. Carrier frequency offset correction--The best sampling point data corresponding to a certain symbol length are taken from the cache, and the local spread spectrum code is de-expanded. After the de-expanding, the carrier frequency offset is estimated based on the algorithm assisted by no data, and the estimated results are used to correct the frequency offset of the data in the cache;
5. Carrier phase recovery--After carrier frequency offset correction, the data are read from the cache for frequency conversion, de-expansion and carrier recovery. Because there is no data assistance, the phase ambiguity problem exists in the data after carrier recovery;  
Figure 4: Processing flow of aperiodic long code signal sender without synchronization overhead. Extract valid data for channel decoding--Phase ambiguity needs to be identified and corrected during decoding. The fast and reliable acquisition of an aperiodic long spread spectrum code is the key and most difficult point of receiving and processing burst spread spectrum signals without synchronization overhead of the physical layer. According to the application background of burst spread spectrum acquisition, the acquisition method based on matching filter is adopted. Compared with the burst spread spectrum receiving based on a synchronous head, a higher-order matched filter is needed and the hardware implementation complexity is higher. The basic principle of using matching filter to achieve spread spectrum code acquisition is as follows. The correlation between the input signal and the local spread spectrum code is carried out in a modulation symbol period, and then the test statistics are obtained by modularization and multiple incoherent accumulations. Then, the test statistics and the threshold are judged to determine whether the input signal and the local spread spectrum code are synchronized, and the acquisition performance is determined by the incoherent accumulation and the decision threshold. Due to the short duration of the burst spread spectrum signal, it is necessary to complete the acquisition quickly and ensure the correctness of the acquisition.