Multi-antenna techniques for interference mitigation in GNSS signal acquisition

EURASIP Journal on Advances in Signal Processing

Table 2 Computational complexity of acquisition algorithms

Algorithm	Test statistic	Operation	Cost
GLRT	${\hat{r}}_{xd}$	Matrix × Vector	$O (NKL)$
	${\hat{R}}_{xx}$	Matrix × Matrix	$O (N^{2} K)$
	${\hat{R}}_{xx}^{- 1}$	Matrix inversion	$O (N^{3})$
	$T (X) = {\hat{r}}_{xd}^{H} {\hat{R}}_{dd}^{- 1} {\hat{R}}_{xx}^{- 1} {\hat{r}}_{xd}$	Matrix-vector	$O (N^{2} L + NL)$
TRB	${\hat{r}}_{xd}$	Matrix × Vector	$O (NKL)$
	${\hat{R}}_{xx}$	Matrix × Matrix	$O (N^{2} K)$
	${\hat{R}}_{xx}^{- 1}$	Matrix inversion	$O (N^{3})$
	$\hat{w} = {\hat{R}}_{xx}^{- 1} {\hat{r}}_{xd}$	Matrix × Vector	$O (N^{2} L)$
	$y = {\hat{w}}^{H} X$	Vector × Matrix	$O (NKL)$
	$R_{yd} = \frac{1}{K} y d^{H}$	Vector × Vector	$O (KL)$
	$R_{yy} = w^{H} {\hat{R}}_{xx} w$	Vector × Matrix	$O (N^{2} L + NL)$
	$T (y) = \frac{{\hat{R}}_{yd}^{H} {\hat{R}}_{yd}}{{\hat{R}}_{yy}}$	Scalar	$O (2 L)$
MVDR	${\hat{R}}_{xx}$	Matrix × Matrix	$O (N^{2} K)$
	${\hat{R}}_{xx}^{- 1}$	Matrix inversion	$O (N^{3})$
	$\hat{w} = \frac{{\hat{R}}_{xx}^{- 1} h_{0}}{h_{0}^{H} {\hat{R}}_{xx}^{- 1} h_{0}}$	Matrix × Vector	$O (2 N^{2} + 3 N)$
	$y = {\hat{w}}^{H} X$	Vector × Matrix	$O (NK)$
	$R_{yd} = \frac{1}{K} y d^{H}$	Vector × Vector	$O (KL)$
	$R_{yy} = w^{H} {\hat{R}}_{xx} w$	Vector × Matrix	$O (N^{2} + N)$
	$T (y) = \frac{{\hat{R}}_{yd}^{H} {\hat{R}}_{yd}}{{\hat{R}}_{yy}}$	Scalar	$O (2 L)$