Algorithm 1 The proposed fully iterative hybrid space-frequency multi-user algorithm for broadband mmWave mMIMO systems
1:	for$i=1,\dots ,i_{max}$do
2:		Compute${\overline{W}}_{fd,k}^{(i)}$ accordingly to (20)
3:		${\overline{W}}_{res,k,0}^{(i)}={\overline{W}}_{fd,k}^{(i)}{\tilde{R}}_k^{(i-1)}$
4:		$W_{a,0}^{(i)}$= Empty Matrix
5:		for$r=1,\dots ,N_{rx}^{RF}$do
6:			${\Pi }_{k,r}={\overline{W}}_{res,k,r-1}^{(i)}{A}_{rx}$; ${\Gamma }_{k,r}={({\tilde{R}}_k^{(i-1)})}^{1/2}{A}_{rx}$
7:			$n_{opt,r}=\arg {\max }_{l=1,\dots ,N_{CB}}{\displaystyle \sum _{k=1}^S\frac{{\left[{\Pi }_{k,r}^H{\Pi }_{k,r}\right]}_{l,l}}{{\left[{\Gamma }_{k,r}^H{\Gamma }_{k,r}\right]}_{l,l}^{}}}$
8:			$W_{a,r}^{(i)}=[W_{a,r-1}^{(i)}|A_{rx}^{(n_{opt,r})}]$
9:			$W_{a,r}^{(i)}=[W_{a,r-1}^{(i)}|A_{rx}^{(n_{opt,r})}]$
10:			$W_{d,k,r}^{(i)}=W_{d,k}^{(i)}[W_{a,r}^{(i)}]$
11:			${\overline{W}}_{res,k,r}^{(i)}=({\overline{W}}_{fd,k}^{(i)}-W_{ad,k,r}^{(i)}){\tilde{R}}_k^{(i-1)}$
12:		end for
13:		$B_{d,k}^{(i)}=\left(W_{d,k}^{(i)}{(W_a^{(i)})}^H{H}_k-I_U\right){\left({\Psi }^{(i-1)}\right)}^H$
14:		${\tilde{c}}_k^{(i)}=W_{d,k}^{(i)}{(W_a^{(i)})}^H{y}_k-B_{d,k}^{(i)}{\widehat{c}}_k^{(i-1)}$
15:		Compute${\widehat{c}}_k^{(i)}$and${\Psi }^{(i)}$
16:	end for