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The full column-rank condition of A is related to the full column-rank condition of A(n defined in (10) for an arbitrary receive antenna n.
The first inequality comes from the full column-rank requirement of C◇G and G◇S, while the second one comes from the full column-rank requirement of (S◇C) T. These necessary conditions are useful when one is interested in eliminating system configurations leading to a non-identifiable model.
This concludes the proof of Theorem 3. If there is only one transmit antenna NT, we only need to prove the full column-rank condition of the following matrix [c.f.
To prove the full column-rank condition of [ A ̄ c ( n ) T [ j 0 ], …, A ̄ c ( n ) T [ j V - 1 ] ] T, we can follow similar steps as in Appendices A and B, which lead eventually to the full column-rank condition of a larger matrix Φ g ( 0 ) [ j 0 ] ⋯ Φ g ( N T - 1 ) [ j 0 ] ⋮ ⋱ ⋮ Φ g ( 0 ) [ j V - 1 ] ⋯ Φ g ( N T - 1 ) [ j V - 1 ], (61).
We first prove the full column-rank condition of A ̄ c ( n ) [ j v ] by following the same steps as in Lemma 1 except for (55), where we need to plug in the (O CE-BEM that is based O CE-BEMple blocks as defined in (22).
