Submatrix Derivation for MIMO Decoding Complexity Reduction
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Solution Overview
Problem
In multiple input and multiple output (MIMO) systems, the existing K-Best search algorithm for decoding is resource-intensive due to the need for frequent matrix inversions as streams are reordered based on Signal-to-Noise-and-Interference ratio (SINR), leading to high computational complexity and resource consumption.
Innovation Solution
An apparatus and method for deriving a submatrix by selecting and rearranging columns and rows of the matrix to calculate an (N-1) × (N-1) submatrix using the Schur complementation method, reducing the need for resource-intensive matrix inversions and identifying the most interfered stream for removal, thereby simplifying the reordering process.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If the K-Best search algorithm is implemented with re-ordering based on SINR, then the decoding performance is improved, but the computational complexity and resource consumption increase significantly
Solution Approach 1:
The channel matrix H is segmented into submatrices during the iterative re-ordering process. Instead of computing the full NxN matrix inverse at each step, the method divides the matrix into smaller blocks (e.g., removing one row and column at a time), processes them separately, and combines results. This segmentation reduces the computational burden from O(N³) to a series of smaller operations.
Solution Approach 2:
The patent performs preliminary calculations by pre-processing the channel matrix H to identify and remove the stream with the lowest SINR before the main decoding process. This preliminary re-ordering step optimizes the matrix structure in advance, making subsequent decoding operations more efficient and reducing the overall computational complexity.
2Productivity
If the number of streams N increases, then the system capacity is improved, but the number of matrix inversions and calculation requirements grow exponentially
Solution Approach 1:
The method segments the large NxN matrix inversion problem into multiple smaller (N-1)×(N-1) submatrix operations performed iteratively. At each iteration, one stream is removed and the corresponding row and column are eliminated, reducing the matrix size step-by-step. This avoids the need to compute the full inverse of increasingly large matrices as N grows.
Solution Approach 2:
Instead of performing complete matrix inversions for all N streams simultaneously, the patent applies partial action by processing streams iteratively, removing one stream at a time based on SINR criteria. This partial processing approach reduces the total computational effort required compared to exhaustive matrix inversion.
3Measurement precision
If complete matrix inversion is performed at each re-ordering step, then the re-ordering accuracy is improved, but the calculation time and resource usage increase
Solution Approach 1:
The complete matrix inversion operation is segmented into iterative steps where only (N-1)×(N-1) submatrices are inverted at each iteration rather than the full NxN matrix. This segmentation maintains re-ordering accuracy by systematically removing streams based on their SINR values while reducing the computational time required for each inversion step.
Data Source
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AI summary
The present invention proposes an apparatus (01) for deriving a submatrix G̃-1.