Algorithm 1 Direct Path Recognition (DPR)

Input: N: number of the antennas; K: number of the multipath signals; M: number of the estimation groups; v: number of the signal snapshots; Δϕ: angel step; $\left[\Theta ,\mathrm{P}\right]$: the DOA and power estimation joint set. $\left[\Theta ,\mathrm{P}\right]=\left[\begin{array}{cccc}\left({\theta }_{1,1},p_{1,1}\right)& \left({\theta }_{1,2},p_{1,2}\right)& \cdots & \left({\theta }_{1,K},p_{1,K}\right)\\ \left({\theta }_{2,1},p_{2,1}\right)& \left({\theta }_{2,2},p_{2,2}\right)& \cdots & \left({\theta }_{2,K},p_{2,K}\right)\\ ⋮& ⋮& \cdots & ⋮\\ \left({\theta }_{M,1},p_{\mathrm{M},1}\right)& \left({\theta }_{M,2},p_{\mathrm{M},2}\right)& \cdots & \left({\theta }_{M,K},p_{\mathrm{M},K}\right)\end{array}\right]$ Output: $\widehat{\theta }$: the DOA estimation result of the direct path. Process: 1: Calculate the distribution of the DOA estimation Θ in (14) by using the histogram method. 2: Select the K intervals with the most members to form the candidate bearing collection C = {ϕ1, ϕ2, …, ϕK} 3: Calculate the 0-norm value $l^0$, mean value of the DOA and power $\left(\overline{\theta }, \overline{p}\right)$ and standard deviation $\left({\sigma }_{\theta }, {\sigma }_p\right)$ of each category ϕ in set C. 4: Obtain the statistic characteristic set of each category $s\left(\varphi \right)=\left\{{(l^0,\overline{\theta }, \overline{p},{ \mathsf{\sigma }}_{\theta },{\mathsf{\sigma }}_p)}_1, {(l^0,\overline{\theta }, \overline{p},{ \mathsf{\sigma }}_{\theta },{\mathsf{\sigma }}_p)}_2, \cdots , {(l^0,\overline{\theta }, \overline{p},{ \mathsf{\sigma }}_{\theta },{\mathsf{\sigma }}_p)}_K\right\}$ 5: Calculate the index of one or several categories with the largest $l^0$ as the output of classifier h1 $h_1\left({\varphi }^{\prime }\right)=\underset{i}{\mathrm{argmax}}[{(l^0)}_i]$ 6: Calculate the category index with the minimum ${\sigma }_{\theta }$ as the output of classifier h2 $h_2\left({\varphi }^{\prime }\right)=\underset{i}{\arg min}\left[ {({\sigma }_{\theta })}_i\right]$ 7: Calculate the category index with the minimum ${\sigma }_p$ as the output of classifier h3 $h_3\left({\varphi }^{\prime }\right)=\underset{i}{\mathrm{argmin}}\left[ {({\sigma }_p)}_i\right]$ 8: Calculate the DOA estimation result $\widehat{\theta }$ of the direct path from the joint classifier H by using an absolute majority voting method $\widehat{\theta }=\{\begin{array}{l}{\overline{\theta }}_j, \mathrm{if} {\displaystyle \sum _{i=1}^3}{h}_i^j>0.5{\displaystyle \sum _{t=1}^K}{\displaystyle \sum _{i=1}^3}{h}_i^t\\ \text{no direct path}, \mathrm{others} \end{array}$ 9: The direct-path recognition processing is done.