Table 1 The summary of PDA detector

1) Initialization: p(x _k |y ⁱ)=1/M,k=1,⋯,N _t N _m .

2) Decorrelated model: Calculate \(\tilde {\mathbf {y}}^{i}\) according to (6)

3) For k=1:N _t N _m

 ∙ Data association: Compute \(E(\mathbf {v}^{i}_{k})\), \(V(\mathbf {v}^{i}_{k})\) and \(U(\mathbf {v}^{i}_{k})\) from (10), (11) and (12).

 ∙ Probability update: Calculate APPs p(x _k |y ⁱ) according to (20).

4) Convergence testing: If the APPs converge, go to 5). Otherwise, go back to 3).

5) LLR updating: Update LLR \(\mathbf {\Lambda }^{i}_{k}\) according to (21).

6) Detection: Detect x _k according to (23).