Systolic Array Permutation for QR Decomposition Overflow
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
In multiple input multiple output (MIMO) systems, the existing methods for QR decomposition and MMSE calculations face issues with overflow and loss of precision due to small input values, leading to inaccuracies in symbol estimation, which requires additional hardware to handle larger bit numbers.
Innovation Solution
The proposed solution involves selectively rearranging elements of the input matrix to prevent division operations from being dominated by small input symbols, using permutations to ensure that larger elements are processed first, thereby avoiding overflow and reducing hardware requirements.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If QR decomposition and MMSE calculations are performed using existing methods in MIMO systems, then symbol detection can be achieved, but overflow and loss of precision occur due to small input values, requiring additional hardware to handle larger bit numbers
Solution Approach 1:
The patent applies preliminary action by reordering columns of the channel matrix before processing to ensure that larger elements are processed first in the QR decomposition algorithm. This preprocessing step prevents small input values from causing overflow in subsequent division operations, thereby maintaining precision without requiring additional hardware bits.
Solution Approach 2:
The patent changes the parameter ordering of matrix elements rather than changing the values themselves. By permuting columns based on element magnitudes and processing larger elements first, the system maintains numerical stability and prevents overflow conditions that would otherwise require wider data paths and more complex hardware.
2Reliability
If column reordering is performed based on first values in columns, then overflow is prevented in division operations, but additional preprocessing circuitry is required
Solution Approach 1:
The patent applies local quality by implementing reordering only at specific critical points in the algorithm - specifically reordering columns based on the first (pivot) elements before QR decomposition. This localized approach addresses overflow risks at division operations without requiring comprehensive reordering of all matrix elements, thus limiting preprocessing complexity to only where necessary.
3Measurement precision
If all possible symbol combinations are evaluated for maximum-likelihood detection, then detection accuracy is maximized, but the computational complexity becomes infeasible for higher order modulation and large number of antennas
Solution Approach 1:
The patent segments the detection problem into two parts: first performing QR decomposition to transform the system into a simpler form with reduced interference, then performing detection on the transformed system. This segmentation avoids evaluating all possible symbol combinations by exploiting the triangular structure of the R matrix from QR decomposition, reducing complexity from exponential to polynomial while maintaining detection accuracy.
Data Source
AI summary
In one embodiment, a circuit for matrix decomposition is provided. The circuit includes an input circuit for receiving a first matrix. A permutation circuit is coupled to the input circuit and configured to interchange columns of the first matrix according to a selected permutation to produce a second matrix. A systolic array is coupled to the permutation circuit and configured to perform QR decomposition of the second matrix to produce a third matrix and a fourth matrix. A reverse permutation circuit is coupled to the systolic array and configured to interchange rows of the third matrix according to an inverse of the selected permutation to produce a first factor matrix and interchange rows of the fourth matrix according to the inverse of the selected permutation to produce a second factor matrix.