###### Abstract
Finally, based on the decomposition matrix of the GPR target, [PERSON] and [PERSON] [22; 23] proposed a serial detection method. The GPR target form is very similar to the 8-way GPR target. However, the parameters at the four corners were calculated by multiplying the horizontal and vertical parameters. Therefore, the GPR target in [22; 23] is still not a real 8-way GPR target. In addition to the VA, we can use the Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm for detection in the BPMR system [24; 25]. In general, although the BCJR algorithm achieves high performance, its complexity is very high. Therefore, when researchers design detection schemes, they mostly focus on the VA. In this study, we analyzed various types of \(N\)-way GPR combined with detection. Based on the complexity problem of 2D Viterbi detection, we propose a 1D Viterbi detection scheme for an 8-way GPR target. In the detection of this GPR target, ITI information is supplied to convert the 2D detection into 1D detection with the same performance and reduced complexity. The proposed scheme extracts the ITI information supplied from multiple GPR targets instead of exploiting multi-head multitrack to subtract the ITI, as in [12; 26; 27; 28; 29]. The proposed model exploits multiple layers of GPR targets to estimate each layer of original data. In each layer, the accuracy of the estimated data gradually improved. Therefore, this model is close to the ideal case. The results demonstrate that our model improves the BER performance of the BPMR systems. Generally, detection is based on a GPR target. Therefore, well-designed GPR targets must fit the interference forms, and the final detection that removes the interference can improve the accuracy. The contributions of this study are as follows:  
* We propose an interference estimation method and design a simple 1D detection scheme for the 8-way GPR target instead of the 2- or 4-way GPR targets in the previous works. * We analyzed the latency and suggested a method to reduce it. * We compared the complexity of the proposed method with that of previous methods. \[\mathbf{G=} \begin{bmatrix}0&0&0\\ g_{0,-1}&1&g_{0,1}\\ 0&0&0\end{bmatrix} \text{ or }\mathbf{G=} \begin{bmatrix}0&g_{-1,0}&0\\ 0&1&0\\ 0&g_{1,0}&0\end{bmatrix} \quad:2\text{--way GPR target}\]  
\[\mathbf{G=} \begin{bmatrix}0&0&0\\ g_{0,-1}&1&g_{0,1}\\ 0&g_{1,0}&0\end{bmatrix} \text{ or }\mathbf{G=} \begin{bmatrix}0&g_{-1,0}&0\\ g_{0,-1}&1&g_{0,1}\\ 0&0&0\end{bmatrix} \quad:3\text{--way GPR target}\]  
\[\mathbf{G=} \begin{bmatrix}0&g_{-1,0}&0\\ g_{0,-1}&1&g_{0,1}\\ 0&g_{1,0}&0\end{bmatrix} \quad:4\text{--way GPR target}\]  
\[\mathbf{G=} \begin{bmatrix}g_{-1,-1}&g_{-1,0}&g_{-1,1}\\ g_{0,-1}&1&g_{0,1}\\ \mathcal{G}_{1,-1}&g_{1,0}&\mathcal{G}_{1,1}\end{bmatrix} \quad:8\text{--way GPR target}\]  
The remainder of this paper is organized as follows. In Section 2, we analyze \(N\)-way GPR with detection and interpret \(N\)-way detection. Based on Section 2, we propose a detection scheme for an 8-way GPR target in Section 3. The simulation results and discussion are presented in Section 4. Section 5 presents the complexity and latency issues of the proposed method compared with those of previous methods. Finally, conclusions are presented in Section 6.