Table 2 Summary of the symbol-level turbo combining algorithm

Initialize ${\bar{\mathbf{\xi }}}_{t,j}^{\left(0\right)}\left(s\right)$with 0.

1.

Combining at round k

1.1. At each iteration,

   1.1.1 Compute the forward and backward filters using (14) and (15).

   1.1.2 Compute the MMSE estimate on x _f using (13).

   1.1.3 Update ${\bar{\mathbf{\xi }}}_{t,j}^{\left(k\right)}\left(s\right)$according to (31).

   1.1.4 Compute extrinsic LLRs ${\varphi }_{t,j,m}^{\left(e\right)}$using (30).

1.3. end 1.1.