In Equation 19, D (= [d.sub.cal]), \ is the matrix inversion
operator and r' is the transpose of the vector consisting receivers at spatial positions and Q is the source vector.
It requires [U.sup.2] multiplications and O([U.sup.3]) matrix inversion
It covers approximations and errors in computation, the solution of algebraic and transcendental equations, the solution of simultaneous algebraic equations, the matrix inversion
and eigenvalue problem, empirical laws and curve-fitting, finite differences, interpolations, numerical differentiation and integration, difference equations, the numerical solution of ordinary differential equations, the numerical solution of partial differential equations, linear programming, and a brief review of computers.
However, these methods inevitably involve complicated matrix inversion
due to the large dimensions of massive MIMO systems, resulting in highly burdensome complexity in practice.
Indeed, a problem of the matrix inversion
Though ZF algorithm is simple, the matrix inversion
associated with this algorithm is highly expensive as the number of user antennas increases.
Direct material decomposition via matrix inversion
is a way of calculating the points *1 and *2 in the decomposed image, which is written as follows:
The main advantage of algebraic methods is that they can provide a simple algebraic solution without the computation of matrix inversion
which makes those methods can be applied in a low-cost location system especially for wireless sensor networks (WSNs) [5, 20].
The notion of the need for efficient schemes is the fact that (5) is slow at its initial stage of iterates, and this would increase the computational burdensome of the scheme applied for matrix inversion
It should be noted that (17) does not require any matrix inversion
under the assumption that all users' data is independent from each other and they have a common covariance matrix.
It requires simultaneous equations, a coefficient matrix, matrix inversion
, and matrix multiplication to get the cost allocations.
Other proposed approaches use different strategies to decrease the cost of matrix inversion
. In , a scheme based on the Gauss-Seidel method is used; nevertheless, it remains necessary to compute at least one matrix inversion
, which may result in instability for large matrices.