A new approach for inversion of large random matrices in massive MIMO systems

Area of Science:

• Electrical Engineering
• Applied Mathematics
• Signal Processing

Background:

• Massive Multiple-Input Multiple-Output (MIMO) systems require efficient inversion of large random matrices.
• Existing methods may struggle with the scale and complexity of matrices in modern MIMO systems.

Purpose of the Study:

• To introduce a novel, computationally efficient approach for inverting large random matrices.
• To provide a method applicable to all types of linear systems (determined, over-determined, under-determined).

Main Methods:

• The approach defines inverse vectors for each column of the principal matrix.
• Each inverse vector must satisfy null-space and normalization constraints.
• The problem is decomposed and distributed across columns, akin to network nodes or swarming particles.

Main Results:

• The method successfully decomposes the matrix inversion problem, reducing computational load.
• It offers a unified solution for determined, over-determined, and under-determined linear systems, bypassing generalized inverse formation.
• The approach is independent of matrix size, structure, or sparsity, making it ideal for large random matrices in massive MIMO.

Conclusions:

• This novel inverse vector approach provides an efficient and versatile method for large random matrix inversion.
• It enhances computational feasibility in massive MIMO systems and offers flexibility in finding exact or approximate inverses.