Algorithm 1 Uplink channel estimation with UTAMP-SBL.

Input: The received signal $\mathbf{y}$ and the matrix $\mathsf{\Phi }$. Output: The estimated sparse channel ${\hat{\mathbf{h}}}^{\omega }$. 1:Initialization: SVD $\mathsf{\Phi }=\mathbf{U}\mathsf{\Sigma }\mathbf{V}$, $\mathbf{r}={\mathbf{U}}^{\mathsf{H}}\mathbf{y}$, $v_{h^{\omega }}=1$, ${\hat{\mathbf{h}}}^{\omega }=\mathbf{0}$, $\mathbf{s}=\mathbf{0}$, $\hat{\sigma }=1$, $\hat{\gamma }=\mathbf{1}$, $\widehat{ϵ}=0.001$ 2:repeat 3: Calculate the mean $\mathit{\mu }$ and variance ${\mathit{\tau }}_{\mu }$ as (16). 4: Calculate the mean $\hat{\mathbf{z}}$ and variance ${\mathbf{v}}_z$ as (14). 5: Update the noise variance $\hat{\sigma }$ as (18). 6: Calculate the mean $\mathbf{s}$ and variance ${\mathit{\tau }}_s$ as (17). 7: Calculate the mean $\mathit{\pi }$ and variance ${\tau }_{\pi }$ as (16). 8: Calculate the mean ${\hat{\mathbf{h}}}^{\omega }$ and variance $v_{h^{\omega }}$ as (15). 9: Calculate the variance $\hat{\gamma }$ according to (21). 10: Update the parameter $\widehat{ϵ}$ according to (22). 11:until halt