Envelope correlations (1/5) It is useful to define transfer function's envelope-correlations.Considering the module of the generic transfer function M(z)I in a e-kind domain z,the domain span△z and the average valueM,over△z we have:: "z-wise"correlation (envelope correlation) w(e-MlM(e+o-l] R(8)=4 R(0)=1,-1<R(⊙)s1 Jw(a-l了t {R(}=0 Especially frequency and space correlations are useful.The last one is fundamental for diversity techniques and MIMO. Envelope correlations (1/5) It is useful to define transfer function’s envelope-correlations. Considering the module of the generic transfer function |M(z)| in a e-kind domain z, the domain span Δz and the average value over Δz we have: “z-wise” correlation (envelope correlation) R z (δ ) = M (z) − M Δz ⎡ ⎣ ⎤ ⎦ M (z +δ ) − M Δz ⎡ ⎣ ⎤ ⎦ dz Δz ∫ M (z) − M Δz ⎡ ⎣ ⎤ ⎦ 2 dz Δz ∫ ; R z (0) = 1, −1< R z (δ ) ≤1 z M Δ Especially frequency and space correlations are useful. The last one is fundamental for diversity techniques and MIMO. lim δ→∞ R z { (δ )} = 0