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In each iteration, the matrix optimization problem is considered in a sequence of 2D subspaces, which leads to one dimensional optimization subproblems.
Proper users' precoders and decoders are designed through a desired signal power maximization model with IA conditions as constraints, which forms a complex matrix optimization problem.
In Equations 17 and 23, the relay matrix optimization problem can be written as begin{array}rcl@ min_{{mathbf{f}}} & & psi_{1}(mathbf{f}) end{array} (24).
According to (20), the sensing matrix optimization problem with the fixed sparse representation matrix Ψ ¯ can be described as argmin Φ Ψ ¯ H Φ H Φ Ψ ¯ − G ~ F 2 (22).
In this section, we address the joint source and relay matrix optimization problem for MIMO multi-relay systems with a linear minimum mean-squared error (MMSE) receiver at the destination node.
and the relay amplifying matrix optimization problem: begin{array}{*{20}l} min_{tilde{mathbf{T}}} & max_{k} quad text{tr}left left[mathbf{I}_{N_{mathrm{b},k}} + tilde{mathbf{T}}^{H}mathbf{G}_{k}^{H}mathbf{G}_{k}tilde{mathbf{T}}right]^{-1}right) end{array} (27a).
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Unfortunately, the use of such techniques often leads to complex matrix optimization problems.
Matrix optimization problems that contain one or more non-convex quadratic matrix constraints are considered.
Subsequently, the applying R-ZF the power and precoding matrix optimization problems are separated and a solution can be found.
Moreover, in similar applications in other fields, there might be large scale similar matrix optimization problems, we believe that the hybrid algorithm will improve MAMA greatly.
The control synthesis conditions for both switching logics are formulated as matrix optimization problems, which are generally non-convex but can be convexified under some simplifying assumptions.
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