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Table 1 The definitions of the symbols used in the paper

From: Robust widely linear beamforming using estimation of extended covariance matrix and steering vector

Symbols Definitions
(·) Conjugate operator
(·)T Transpose operator
(·)H Hermitian transpose operator
(·)−1 Matrix inversion operator
〈·〉 Time-averaging operation
E[·] Expectation operator
IN N×N identity matrix
diag{·} Diagonalization operator
|·| Absolute value operator
· Euclidean norm
Set intersection
eigmax(·) Maximum eigenvalue of a matrix
N Number of array antennas
M Number of narrowband signals
k Time index of snapshots
x Array observation vector
a Steering vector
s Complex waveform
v Whole interference-plus-noise vector
γ Noncircularity coefficient
σ2 Time-averaged power
|γ| Noncircularity rate
ϕ Noncircularity phase
R Covariance matrix
C Pseudo covariance matrix
\(\breve {\mathbf {x}}\) Extended observation vector
\(\breve {\mathbf {v}}\) Extended interference-plus-noise vector
\(\mathbf {R}_{\breve {x}}\) Extended covariance matrix
s Orthogonal decomposition of s
\(\breve {\mathbf {a}}\) Extended steering vector
\(\breve {\mathbf {v}}_{\gamma }\) Global noise vector
y WLB output
\(\breve {\mathbf {w}}\) WLB weight vector
SINR Output signal-to-interference-plus-noise ratio
K Number of observed snapshots
\(\bar {\delta }\) Minimum eigenvalue of \(\mathbf {R}_{\hat {\breve {x}}}\)
θ Signal direction
Θ Signal angular sector
αi Eigenvalue of \(\mathbf {R}_{\hat {x}}\)
gi Eigenvector of \(\mathbf {R}_{\hat {x}}\)
G Subspace projection matrix
Γ Diagonal matrix
β Adaptive uncertainty level
η Lagrange multiplier
ϱ Threshold constant
λi Eigenvalue of \(\mathbf {R}_{\hat {\breve {x}}}\)
qi Eigenvector of \(\mathbf {R}_{\hat {\breve {x}}}\)
Q Matrix containing eigenvectors
Λ Diagonal matrix containing eigenvalues
f Projection value
Q Number of principal eigenvectors
F Extended subspace projection matrix
ε A predefined constant
Π Extended subspace
π Subspace coefficient vector
p(θ) Spatial power spectrum
μl Eigenvalue of \(\breve {\mathbf {R}}_{s}\)
ul Eigenvector of \(\breve {\mathbf {R}}_{s}\)
U Matrix containing eigenvectors
U Number of principal eigenvectors
ζ A predefined constant
Ω Diagonal matrix containing eigenvalues