## 1 Introduction
In particular, submarine and UAV satellite communication systems have the special conditions of low SNR and large carrier frequency offset application [3; 4]. In order to achieve the correct synchronization of the carrier, usually a long synchronization header is needed, that is, long auxiliary data for capturing and synchronizing the carrier must be included in a burst frame. This will increase the synchronization overhead of the burst communication system, affect the communication efficiency, increase the signal space exposure time, and increase the probability of being intercepted. Removing the overhead of the synchronous head can greatly improve the transmission efficiency, shorten the airborne exposure time of the signal, and further improve the anti-interception performance of the communication. At present, most burst spread spectrum systems realize synchronization based on synchronization overhead. Paper [5; 6; 7; 8; 9; 10; 11] uses the synchronization overhead of the leading code, frame header, special synchronization sequence and pilot frequency to realize system synchronization. However, no synchronization overhead is only realized in multiple-input multiple-output (MIMO) systems, which can achieve no synchronization overhead through the correlation of multiple signals [12]. The removal of the synchronization cost in single-input single-output spread spectrum systems only focuses on the carrier synchronization part, such as by using non-data-assisted methods [13], or it just focuses on removing frame synchronization overhead, as in paper [14]. The proposed method in this paper can improve the frame transmission efficiency by removing the synchronization overhead of the physical layer, and better complement the gaps in related fields. The length and complexity of synchronization overhead are related to the acquisition mode, frequency offset, dynamics, SNR and so on. Burst spread spectrum communication has the characteristics of low power spectrum density, short burst time and random transmission time. Therefore, the system response time is required to be short enough, that is, the receiver should be able to quickly acquire the signal, demodulate the original signal, and wait for the arrival of the next signal. This puts forward a high requirement for the real-time operation and probability of spread spectrum code acquisition. To remove the physical layer synchronization overhead and ensure synchronization, an aperiodic long code spread spectrum is used. However, the acquisition of aperiodic long  
Figure 3: The processing flow of burst spread spectrum signal based on synchronous overhead. codes has the problem of high hardware resource usage, so it is necessary to ensure the capture success rate and reduce the hardware resource usage. Typical acquisition methods include sliding correlation, a matching filter, FFT, PMF-FFT, and so on. However, the sliding correlation method is slow and the search time is long, which can meet the requirement of fast acquisition set in this paper. The hardware complexity of the matching filter method is high, and the time domain correlation value is large, which is proportional to the square of the code period length, so it is not suitable for the long code acquisition in this paper. The FFT algorithm mainly deals with the acquisition of spread spectrum signals under the condition of high dynamic and high SNR [15], and is not applicable to the situation of low SNR in this paper. The PMF-FFT method can shorten the length of a single matching filter by increasing the number of matching filters, but it cannot effectively reduce the hardware resource consumption [16; 17]. Aiming at long code acquisition, paper [18; 19; 20] studies the indirect acquisition method of short-code-assisted long code acquisition. However, when indirect acquisition is adopted, the short code with poor anti-interference ability is easily disturbed.