Require | The received MIMO array data \(\left \{ \mathbf {x}(t) \right \}_{t=1}^{T}\). |
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Ensure | Estimation of {θk,ϕk}, k=1,2,⋯,K. |
Step 1. | \(\hat {\mathbf {R}}_{\mathbf {x}} \leftarrow (1/T){\sum \nolimits }_{t=1}^{T} \mathbf {x}(t)\mathbf {x}^{\mathrm {H}}(t) \); |
Step 2. | Us,W← Perform EVD on \(\hat {\mathbf {R}}_{\mathbf {x}}\) in (6); |
Step 3. | \(\hat {\mathbf {b}} \leftarrow \) Minimize (21) by MODE algorithm; |
Step 4. | \(\left \{\bar {\phi _{i}}\right \}_{i=1}^{K} \leftarrow \) Root polynomial (12) constructed by \(\hat {\mathbf {b}}\); |
Step 5. | \(\left \{\bar {\phi _{i}}\right \}_{i=1}^{K_{1}}, \left \{\bar {\phi _{i}}\right \}_{i=K_{1}+1}^{K} \leftarrow \) Discern uncorrelated and coherent DOA via (25); |
\(\bar {\mathbf {P}}_{\mathbf {D}_{1}\mathbf {D}_{2}} \leftarrow \) Construct oblique projector by (38); | |
Step 6. | \(\{{\bar \theta }_{k}\}_{k=1}^{K_{1}} \leftarrow \) Perform LS fitting to the auto-paired \({\bar {\mathbf {a}}_{u}({\theta }_{k})}\) by (28) and (33); |
Step 7. | \(\bar {\mathbf {Y}}, \bar {\mathbf {U}}_{0}\leftarrow \) Construct virtual MIMO array matrix by (38) and (39), and perform EVD; |
Step 8. | \(\left \{{\bar {\theta }}_{k}\right \}_{k=K_{1}+1}^{K} \leftarrow \) Extract auto-paired \(\bar {\mathbf {a}}_{c}({\theta }_{k})\) by (41) and repeat LS fitting. |