Multichannel adaptive signal detection in space-time colored compound-gaussian autoregressive processes

Xu, Qi; Ma, Xiaochuan; Yan, Shefeng; Hao, Chengpeng; Shi, Bo

doi:10.1186/1687-6180-2012-69

EURASIP Journal on Advances in Signal Processing

Table 1 Complexity of the CG-PGLRT-SCM detector, CG-PGLRT-NSCM detector, and CG-PGLRT-AML detector for model order P (suppose KN >JP)

From: Multichannel adaptive signal detection in space-time colored compound-gaussian autoregressive processes

Step	Task	Flops	Task	Flops	Task	Flops
S ₁	${\hat{R}}_{x x}$	O(KJ²(N-P))	${\hat{τ}}_{1: K_{NSCM}}$	O(KJ²P²(N-P))	${\hat{τ}}_{1: K_{AML}} (1 : N_{i t})$	O(2J² P ²K(N-P)) +O(N_itKJ(N-P)²)
S ₂	${\hat{R}}_{y y}$	O(KJ ²P²(N-P))	${\overset{⌣}{R}}_{x x}$	O(2KJ²(N-P))	${\bar{R}}_{x x}$	O(2N_itKJ ²(N-P))
S ₃	${\hat{R}}_{y x}$	O(KJ ²P(N-P))	${\overset{⌣}{R}}_{y y}$	O(2KJ ²P²(N-P))	${\bar{R}}_{y y}$	O(2N_itKJ ²P²(N-P))
S ₄	${\hat{A}}_{SCM}^{H}$	O(J³(P³+P²))	${\overset{⌣}{R}}_{y x}$	O(2KJ ²P(N-P))	${\bar{R}}_{y x}$	O(2N_itKJ ²P(N-P))
S ₅	${\hat{Q}}_{SCM}$	O(J³P)	${\hat{A}}_{NSCM}^{H}$	O(J³(P³+P²) -	${\hat{A}}_{AML}^{H}$	O(N_itJ ³(P³ + P ²))
S ₆	${\hat{Q}}_{SCM}^{- 1}$	O(J³)	${\hat{Q}}_{NSCM}$	O(J³P)	${\hat{Q}}_{AML}$	O(N_itJ ³P)
S ₇	$\hat{\tilde{S}}$	O(J ²P(N-P))	${\hat{Q}}_{NSCM}^{- 1}$	O(J³)	${\hat{Q}}_{AML}^{- 1}$	O(N_itJ ³)
S ₈	${\hat{\tilde{X}}}_{0}$	O(J ²P(N-P))	$\overset{⌣}{\tilde{S}}$	O(J ²P(N-P))	$\bar{\tilde{S}}$	O(J ²P(N-P))
S ₉	$ω = {\hat{Q}}_{SCM}^{- 1} \hat{\tilde{S}}$	O(J ²(N-P))	${\overset{⌣}{\tilde{X}}}_{0}$	O(J ²P(N-P))	${\bar{\tilde{X}}}_{0}$	O(J ²P(N-P))
S ₁₀	$ω^{H} \hat{\tilde{S}}$	O(J(N-P)²)	$ω = {\hat{Q}}_{NSCM}^{- 1} \overset{⌣}{\tilde{S}}$	o(j²(n-p))	$ω = {\hat{Q}}_{AML}^{- 1} \bar{\tilde{S}}$	O(J ²(N-P))
S ₁₁	$ω^{H} {\hat{\tilde{X}}}_{0}$	O(J(N-P)²)	$ω^{H} \overset{⌣}{\tilde{S}}$	O(J(N-P)²)	$ω^{H} \bar{\tilde{S}}$	O(J(N-P)²)
S ₁₂	${\hat{\tilde{X}}}_{0}^{H} {\hat{Q}}_{SCM}^{- 1} {\hat{\tilde{X}}}_{0}$	O(J(N - P)(J+N-P))	$ω^{H} {\overset{⌣}{\tilde{X}}}_{0}$	O(J(N-P)²)	$ω^{H} {\bar{\tilde{X}}}_{0}$	O(J(N-P)²)
S ₁₃	-	-	${\overset{⌣}{\tilde{X}}}_{0}^{H} {\hat{Q}}_{NSCM}^{- 1} {\overset{⌣}{\tilde{X}}}_{0}$	O(J(N-P)(J+N - P))	${\bar{\tilde{X}}}_{0}^{H} {\hat{Q}}_{AML}^{- 1} {\bar{\tilde{X}}}_{0}$	O(J(N - P)(J+N-P))
Total		O(KJ ² P ²N) + O(JN²)		O(2KJ ² P ²N) + O(JN²)		O(2N_itKJ ²P²N) + O(N_itKJN²)

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