Algorithm 1. The Algorithm of MF-SIC-SAC in 4-SSB domain.
Initialization of MMSE filter:
1	$w_n= {\left({\overline{H}}_n{\overline{H}}_n^H + {\sigma }^{2}I\right)}^{-1}{\left(H\right)}_n, n= 1,\dots ,N_T$
2	for $n=1$ to $N_T$ do
3	${\tilde{d}}_n= w_n^H{d}_n$
4	If ${\tilde{d}}_n\in$ Shadow Area
5	${\tilde{z}}_n= {\left[ c_1, c_2, \dots , c_M\right]}^T$
6	for $m=1$ to $M$ do
7	for $j= n$ to $N_T$ do
8	${\widehat{d}}_{j,m}= {\check{d}}_n - {\left(H\right)}_n {\left({\widehat{z}}_n\right)}_m$
9	$-{{\displaystyle \sum }}_{p= n+1}^{j-1}{\left(H\right)}_p{b}_{p,m}$
10	$b_{j,m}= Q\left(w_j^H{\widehat{d}}_{j,m}\right)$
11	end for
12	end for
13	$b_m= {\left[b_{1,m},\dots ,b_{N_{T,},m}\right]}^T$
14	$m_{opt }=\arg \min { }_{1\le m\le M}$ $\Vert d_{i,SSB,n}-H{b}_m{\Vert }^2$
15	${\widehat{d}}_n= {\left({\widehat{z}}_n\right)}_{m_{opt}}$
16	else
17	${\widehat{d}}_n= Q\left({\tilde{d}}_n\right)$
18	end if
19	${\stackrel{\mathbf{ˇ}}{\mathit{d}}}_{\mathit{i}\mathbf{,}\mathit{S}\mathit{S}\mathit{B}\mathbf{,}\mathit{n}}= {\mathit{d}}_{\mathit{i}\mathbf{,}\mathit{S}\mathit{S}\mathit{B}\mathbf{,}\mathit{n}} - {{\displaystyle \mathbf{\sum }}}_{\mathit{k}=\mathit{1}}^{\mathit{n}-\mathit{1}}{\left(H\right)}_{\mathit{k}}{\widehat{\mathit{d}}}_{\mathit{k}}$
20	end for