## 3 The Acquisition Method Based on PIC  
### The Improved Algorithm Based on PIC and Coherent Accumulation  
In this subsection, we will focus on the presentation of the proposed acquisition algorithm based on the MUD algorithm and coherent accumulation algorithm. Given that MAI holds significant influence over the performance and capacity of multi-user systems, the interference cancellation algorithms can effectively mitigate its impact. Furthermore, coherent accumulation can significantly improve the acquisition performance in low-SNR scenarios. The improved algorithm is based on the following idea.  
As shown in Figure 3, the received signal first undergoes the parallel K-user acquisition module. From this module, we obtain the time bias and frequency bias information of all users. It should be noted that we optimize the coherence peaks of received signals here using the coherent accumulation module. Subsequently, reconstruction is carried out based on the aforementioned information of the strong signals. Simultaneously, by subtracting the reconstructed interfering signal from the original received signal, we can effectively eliminate the MAI. The detailed algorithm for reconstructing the interference signal will be explained in Section 3.3 of this paper.  
In DS-CDMA systems, the PIC method can be regarded as a practical multi-user detection technique that strikes a balance between algorithmic performance and complexity. Because of the reduced reliance on power control and MAI elimination order, PIC, surpassing SIC, is more efficient in eliminating interference. Consequently, PIC becomes the  
Figure 4: MAI suffered by weak signal.  
Figure 3: Receiver.  
more suitable method for implementation within acquisition modules, enhancing system detection efficiency. Figure 5 exemplifies one stage of the PIC-based acquisition algorithm.  
Further analysis of the on-board receiver is also required. As expounded in Section 2.1, we mainly focus on acquisition methods for non-data-modulated segments. Thus, it becomes more convenient to estimate the power of the received signal and eliminates the issue of bi-phase ambiguities, which occurs when the received sequence occupies half of the front and back PRN codes.  
The specific flow of the PIC-based spread spectrum acquisition algorithm is delineated as follows.  
1. Initially, the demodulated received signal \(y_{in}(iT_{s})\) is concurrently fed to independent acquisition modules for \(K\) users. Through correlating \(y_{in}(iT_{s})\) with individual user's local PRN code and accumulating the outcomes, a comprehensive two-dimensional search, including time and frequency for \(K\) groups is executed. The obtained outcomes are defined as \(z_{1}(n,m),z_{2}(n,m),...,z_{K}(n,m)\).
2. By identifying the maximum correlation value within the aforementioned search results, with its corresponding frequency and time deviations, the signal for each user is \(x^{\dagger}(k),x^{2}(k),...,x^{K}(k)\). Subsequently, the reconstructed signals, except the target user, are accumulated. This summation enables the extraction of all the MAI information associated with the target user.
3. By subtracting the previously reconstructed MAI from the original input signal, the interference-canceled signals \(y_{out}(iT_{s})\) are obtained. Following this, another round of acquisition operation is conducted for all users to obtain the interference-canceled K-group time-frequency two-dimensional search results \(z_{1}(\hat{n},m),z_{2}(\hat{n},m),...,z_{K}(\hat{n},m)\). At this stage, a significant portion of the MAI is effectively eliminated, while simultaneously enhancing the prominence of peaks corresponding to weak signals. As a result, \(P_{cd}\) is substantially increased.
4. Steps 1-3 constitute one stage of the PIC-based acquisition module. Furthermore, it is feasible to put the output signal from step 3 into another stage of the PIC module. By repeating steps 2 and 3, MAI can be further diminished, consequently leading to an enhancement in the detection performance of the system.