Table 2 Complexity of the GLRT-LQ detector with SCM, NSCM, and AML estimators (at least K ≥ JN)

S ₁

${\widehat{\text{R}}}_{\text{SCM}}$

O(KJ² N ²)

${\widehat{\text{R}}}_{\text{NSCM}}$

O(2KJ² N ²)

${\widehat{\text{R}}}_{\text{AML}}$

O(N _it KJ ³ N ³)

S ₂

${\widehat{\text{R}}}_{\text{SCM}}^{-1}$

O(J ³ N ³)

${\widehat{\text{R}}}_{\text{NSCM}}^{-1}$

O(J³ N ³)

${\widehat{\text{R}}}_{\text{AML}}^{-1}$

O(J ³N³)

S ₃

${\omega }_{\text{SCM}}={\widehat{\text{R}}}_{\text{SCM}}^{-1}\mathbf{\text{s}}$

O(J²N²)

${\omega }_{\text{NSCM}}={\widehat{\text{R}}}_{\text{NSCM}}^{-1}\mathbf{\text{s}}$

O(J² N ²)

${\omega }_{\text{AML}}={\widehat{\text{R}}}_{\text{AML}}^{-1}\mathbf{\text{s}}$

O(J² N ²)

S ₄

${\omega }_{\text{SCM}}^H\mathbf{\text{s}}$

O(JN)

${\omega }_{\text{NSCM}}^H\mathbf{\text{s}}$

O(JN)

${\omega }_{\text{AML}}^H\mathbf{\text{s}}$

O(JN)

S ₅

${\omega }_{\text{SCM}}^H{\mathbf{\text{x}}}_{\text{0}}$

O(JN)

${\omega }_{\text{NSCM}}^H{\mathbf{\text{x}}}_{\text{0}}$

O(JN)

${\omega }_{\text{AML}}^H{\mathbf{\text{x}}}_{\text{0}}$

O(JN)

S ₆

${\text{x}}_0^H{\widehat{\text{R}}}_{\text{SCM}}^{-1}{\text{x}}_0$

O(JN(JN+1))

${\text{x}}_0^H{\widehat{\text{R}}}_{\text{NSCM}}^{-1}{\text{x}}_0$

O(JN(JN+1))

${\text{x}}_0^H{\widehat{\text{R}}}_{\text{AML}}^{-1}{\text{x}}_0$

O(JN(JN+1))

Total

O(KJ²N²)≥O(J³N³)

O(2KJ ² N ²)≥O(2J ³ N ³)

O(N _it KJ ³ N ³)≥O(N _it J ⁴ N ⁴)