Table 1 Notation used in the paper
From: User grouping and resource allocation in multiuser MIMO systems under SWIPT
\(\mathcal {A}\) | Set |
\(\mathcal {A}=\{a_{1},a_{2},\dots \}\) | Set \(\mathcal {A}\) containing the elements {a1,a2,… } |
\(|\mathcal {A}|\) | Number of elements in set \(\mathcal {A}\) |
\(a \in \mathcal {A}\) | a belongs to set \(\mathcal {A}\) |
\(\mathcal {A} \setminus a\) | Set resulting from subtracting a from set \(\mathcal {A}\) |
∅ | Empty set |
\(\mathcal {A} \subseteq \mathcal {B}\) | Set \(\mathcal {A}\) is included in or equal to set \(\mathcal {B}\) |
\(\mathcal {A}\cap \mathcal {B}, \mathcal {A}\cup \mathcal {B}\) | Intersection of sets \(\mathcal {A}\) and \(\mathcal {B}\), union of sets \(\mathcal {A}\) and \(\mathcal {B}\) |
a,A | Vector a, matrix A |
aT,AT | Transpose of vector a, matrix A |
aH,AH | Hermitian (transpose conjugated) of vector a, matrix A |
Tr(A), det(A) | Trace of matrix A, determinant of matrix A |
A≽0 | Matrix A is positive semidefinite |
||a|| | Norm-2 of vector a |
\(\mathbb {C}^{m\times n}\) | Set of complex matrices of size m×n |
I n | Identity matrix of size n×n |
\(\mathbb {E}[\cdot ]\) | Expectation |
\(=, \triangleq,\neq \) | Equal, equal by definition, different |
>,≥,<,≤ | Higher, higher or equal, lower, lower or equal |
log(·), exp(·)=e(·) | Logarithm, exponential |
n! | Factorial of n |
\(\sum \) | Summation |
min, max | Minimum, maximum |
\((x)^{b}_{a}\) | \((x)^{b}_{a} = \min \{\max \{a,x\},b\}\) |
a b | a to b |
∀ | For all |
\(\mathop {\text {maximize}}_{x_{1},x_{2},\dots }\) | Maximization with respect to variables x1,x2,… |
\(\mathop {\text {minimize}}_{x_{1},x_{2},\dots }\) | Minimization with respect to variables x1,x2,… |
x ⋆ | Optimum value of x |
f−1(·) | Inverse function |
x←y | x is updated with y |