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Table 1 The proposed buffer-aided cooperative DSTC scheme

From: Buffer-aided distributed space-time coding schemes and algorithms for cooperative DS-CDMA systems

% List all possible relay pairs

% Select the combination with the highest SINR

\(\phantom {\dot {i}\!}\mathrm {SINR_{p,q}=max \{ \text {SINR}_{sr_{m,n}},\text {SINR}_{r_{m,n}d} \}}\)

%Source-relay link

if \(\phantom {\dot {i}\!}\mathrm {SINR_{p,q}} \in [\mathrm {SINR_{sr_{m,n}}}], m,n \in [1,L]\)

if the buffers entries are not full

\(\phantom {\dot {i}\!}\mathbf {y}_{sr_{l}}(2i-1)=\sum \limits _{k=1}^{K} \mathbf {h}_{s_{k}r_{l}} b_{k}(2i-1)+\mathbf {n}_{sr_{l}}(2i-1),l\in [p,q],\)

\(\phantom {\dot {i}\!}\mathbf {y}_{sr_{l}}(2i)=\sum \limits _{k=1}^{K} \mathbf {h}_{s_{k}r_{l}} b_{k}(2i)+\mathbf {n}_{sr_{l}}(2i),l\in [p,q].\)

%Apply the detectors at relay n and relay q to obtain

\(\phantom {\dot {i}\!}\hat {b}_{r_{l}d,k}(2i-1)\) and \(\hat {b}_{r_{l}d,k}(2i)\) and store them

in the corresponding buffer entries (l∈[p,q])

break

else %choose the second highest SINR

\(\phantom {\dot {i}\!}\mathrm {SINR^{pre}_{p,q}}=\mathrm {SINR_{p,q}}\)

\(\phantom {\dot {i}\!}\mathrm {SINR_{p,q}} \in \text {max} \{\mathrm {SINR_{sr_{m,n}}}, \text {SINR}_{\mathrm {r_{m,n}d}} \} \setminus \mathrm {SINR^{pre}_{p,q}}\)

end

else %Relay-destination link

\(\phantom {\dot {i}\!}\mathrm {SINR_{p,q}} \in [\mathrm {SINR_{r_{m,n}d}}], m,n \in [1,L]\)

if the buffers entries are not empty

\(\phantom {\dot {i}\!}\mathbf {y}_{r_{p,q}d,k}(2i-1)= \mathbf {h}_{r_{p}d}^{k} \hat {b}_{r_{p}d,k}(2i-1)+\mathbf {h}_{r_{q}d}^{k} \hat {b}_{r_{q}d,k}(2i)+\mathbf {n}(2i-1),\)

\(\phantom {\dot {i}\!}\mathbf {y}_{r_{p,q}d,k}(2i)=\mathbf {h}_{r_{q}d}^{k} \hat {b}^{*}_{r_{p}d,k}(2i-1)-\mathbf {h}_{r_{p}d}^{k} \hat {b}^{*}_{r_{q}d,k}(2i)+\mathbf {n}(2i).\)

%Apply the detectors/ML at the destination for detection

break

else%choose the second highest SINR

\(\mathrm {SINR^{pre}_{p,q}}=\mathrm {SINR_{p,q}}\)

\(\phantom {\dot {i}\!}\mathrm {SINR_{p,q}} \in \text {max} \{ \mathrm {SINR_{sr_{m,n}}}, \mathrm {SINR_{r_{m,n}d}}\} \setminus \mathrm { SINR^{pre}_{p,q}}\)

end

end

%Re-calculated the SINR for different link combinations and

repeat the above process