The M-sequence constituting the PSS enables cross-correlation in the time domain, facilitating the identification of time domain offsets. The PSS matched filter operates by accumulating correlation values at each time offset, storing these values in a buffer, and detecting the highest peak among them. Currently, peak detection uses a linear search accelerated by vector load store operations. Correlation values are searched using an integer type, with the potential for a short type search if a precise threshold is defined in the future.

#### Frequency Shift Cancellation Level Implementation
The frequency shift cancellation level determines the shift immediate values for accumulation and sum, adjusting based on the specified level (1, 2, 4, or 8). This helps in effectively canceling out frequency offsets during the correlation process.
![](Pasted%20image%2020240722120200.png)
The graph illustrates the changes in peak point detection with different frequency offset and cancellation levels (L1, L2, L3, L4). The actual peak point is 4854, while the FO_Unit represents manually induced frequency shift effects, such as Doppler shift.

L1, L2, and L3 show distinct patterns in the graph, indicating the algorithm's sensitivity to different cancellation levels. However, L4 did not show any difference with significant frequency offsets, so it is not detected. 

#### Feedback Algorithm Implementation
The feedback algorithm aims to reuse duplicates to eliminate unnecessary calculations, enhancing efficiency. This approach optimizes the detection of the PSS signal by leveraging selected PSS coefficients and frequency shift cancellation to reduce redundant computations. This implementation was developed in collaboration with algorithm engineers, with my role focused on the implementation aspect.

![](Pasted%20image%2020240719171956.png)


The key concern highlighted in this diagram is the feedback delay, $L$. Unlike traditional 5G UU transmission, 5G sidelink features continual PSS blocks located closely in the time domain. By utilizing the characteristics of this setup, we have successfully reduced the computational requirements by half. Since PSS correlation consumes a significant amount of time in signal processing, this reduction plays a crucial role in minimizing overall time consumption. However, implementing this delay feedback in hardware for a single symbol time and guard interval, given the numerology, poses a substantial challenge. Therefore, I provided support for this implementation as SW.

![](Pasted%20image%2020240719174605.png)

The table above presents the results of a test measuring the time taken to find the correlation in a long buffer of 8192 samples. This test assesses the processing efficiency at the same time domain location of the correlation point in the buffer. Notably, the introduction of feedback implementation significantly reduces the clock cycles required for correlation computations at various cancellation levels. This showcases the practical benefits of feedback mechanisms in signal processing.