I have this equation
$$r^{(c,b)}[i]=\sum_{m=1}^M\sum_{n=0}^{N-1}\mathbf{h}_m^{(c,b)H}\mathbf{W}_m[n]\mathbf{s}_m[n]g\left(\left[i-n\right]T_s-\psi_{c,m}\right)$$
where $\mathbf{h}_m^{(c,b)}\in\mathbb{C}^L$, $\mathbf{W}_m[n]\in\mathbb{C}^{L\times L}$, $\mathbf{s}_m[n]=\left[s_m^{(1)}[n]\cdots s_m^{(L)}[n]\right]^T$, and where $\left\{s_m^{(l)}[n]\right\}_{l=1}^L$ and $g(.)$ are scalars. $(.)^H$ is the Hermitian operator. I want to write
$$\mathbf{r}^{(c,b)}=\left[r^{(c,b)}[0]\cdots r^{(c,b)}[N-1]\right]^T$$
in compact form.
My attempt:
Let
$$\mathbf{G}_{c,m}[i]=\left[g\left(iT_s-\psi_{c,m}\right)\mathbf{I}_L\cdots g\left(\left[i-N+1\right]T_s-\psi_{c,m}\right)\mathbf{I}_L\right]$$,
$$\mathbf{W}_m=\text{blockdiag}\left(\mathbf{W}_m[0],\cdots,\mathbf{W}_m[N-1]\right)$$
and
$$\mathbf{s}_m=\left[\mathbf{s}_m[0]^T\cdots \mathbf{s}_m[N-1]^T\right]^T$$
where $\mathbf{I}_L$ is $L\times L$ identity matrix, and $\text{blockdiag}(.)$ is block diagonal operation.
Then we can write $r^{(c,b)}[i]$ as
$$r^{(c,b)}[i]=\sum_{m=1}^M\mathbf{h}_m^{(c,b)H}\mathbf{G}_{c,m}[i]\mathbf{W}_m\mathbf{s}_m$$
However, I get stuck here. How to proceed to write $\mathbf{r}^{(c,b)}$ in compact form?