Method and equipment for obtaining optimized variable under rank constraint condition

Abstract

The invention provides a method and equipment for obtaining an optimized variable under a rank constraint condition. The method comprises the steps that a target function and constraint conditions thereof which are corresponding to system performance to be optimized during data transmission in a communication system are determined, wherein the target function satisfies a Schur- convex / concave condition and the constraint conditions comprise rank constraint; a matrix and r non-negative real numbers on a Stiefel manifold are obtained; by adopting the matrix and the r non-negative real numbers on the Stiefel manifold, a cost function corresponding to the target function can be enabled to be converged to the optimal local point; r is a rank satisfying the requirement of the optimized variable under the rank constraint condition; the independent variable of the cost function is the matrix and the r non-negative real numbers on the Stiefel manifold; and the optimized variable is obtained according to the matrix and the r non-negative real numbers on the Stiefel manifold, so as to process data to be transmitted according to the optimized variable and realize the system performance to be optimized. By adopting the method and the equipment provided by the embodiment of the invention, the system performance and the application range can be improved.

Description

technical field [0001] The invention relates to signal processing technology, in particular to a method and equipment for obtaining optimization variables under rank constraint conditions. Background technique [0002] Many applications in communication and signal processing can be reduced to a class of optimization problems with rank constraints. For example, in a multiple-input multiple-output (Multiple-Input Multiple-Output, MIMO) communication system, the number of transmitted data streams should be less than or equal to the number of receiving antennas. For such problems with rank constraints, general examples are as follows: [0003] (P1): [0004] s.t.log det(I+QR j )≥b j j = 1, 2, ... (2) [0005] Tr(QP i )≤a i i=1, 2, ... (3) [0006] Q≥0 (4) [0007] rank(Q)≤r(r≤n) (5) [0008] Among them, formula (1) is the objective function to be optimized; formulas (2)-(4) are constraints; formula (5) is an additional rank constraint. α,A,R j , P i , α i is a...

AI Technical Summary

Problems solved by technology

[0010] However, prior art 2 requires that the optimization objective function and constraints are both linear, and the rank constraint is also limited, which limits the types of problems that can be solved in practical applications

Images