Table 1 Layered single-dimensional search-based sparse-aware multiuser detection

Step 1:

Use ZF/MMSE detectors to achieve \(\hat{\mathbf{x }}\)

Step 2:

Reconstruct a sparse system via \(\hat{\mathbf{y }}={\mathbf{y }}-\mathbf{H }\hat{\mathbf{x }}\)

Step 3:

Apply QR decomposition, i.e., \(\tilde{\mathbf{y }}=\mathbf{Q }^T\hat{\mathbf{y }}\)

Step 4:

Initializations: \(\lambda\)

Step 5:

for \(i=2^{n}-1, (2^{n}-1)-1,\dots ,1\) do

   for \(k=2K, 2K-1,\dots ,1\) do

   1. Compute \({\bar{v}}_k^i\) via (17)

   2. Map \({\bar{v}}_k^i\) into \({{\mathcal{A}}}_i\) via (19)

   end for

   3. Update the sparse system via \(\hat{\mathbf{y }}=\bar{{\mathbf{y}}}-\bar{{\mathbf{H}}}(\hat{\mathbf{x }}+\hat{\mathbf{v }}_i)\)

end for

Step 6:

Attain the detected symbol error vector \(\hat{{\mathbf{e }}}=\sum _{i=1}^{2^{n}-1}\hat{{\mathbf{v }}}_i\)

Step 7:

Refine the detected vector through \(\hat{\mathbf{x }}={\hat{\mathbf{x }}}+\hat{\mathbf{e }}\)