Division-Free Householder Matrix for MIMO QR Decomposition
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Solution Overview
Problem
Current QR decomposition techniques for MIMO receivers are impractical in real-time due to high hardware complexity and computation latency, especially in high-dimensional systems, as they require numerous division operations.
Innovation Solution
A method that determines a Householder matrix without performing division operations, allowing for the decomposition of a complex channel matrix into an orthogonal and upper triangular matrix with a predetermined number of zeros in the upper triangle, reducing computational complexity.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional QR decomposition techniques (Gram-Schmidt, Householder transformation, Givens rotation) are used, then accurate decomposition of complex channel matrix is achieved, but hardware complexity and computation latency increase significantly due to numerous multiplication, division and square-root operations
Solution Approach 1:
The patent extracts and eliminates the division operations from the Householder transformation algorithm, keeping only the multiplication and subtraction operations that are less computationally intensive and easier to implement in hardware
Solution Approach 2:
The patent modifies the Householder transformation by changing the computational parameters - specifically by avoiding square-root operations and division operations that require complex hardware, thereby simplifying the implementation while maintaining decomposition accuracy
2Measurement precision
If modified sequence of Givens rotations algorithm is used, then QR decomposition is achieved, but a large number of rotation and division operations are still required for high-dimensional MIMO systems
Solution Approach 1:
The patent removes division operations from the decomposition process entirely, which directly improves productivity by reducing the number of computationally intensive operations that limit real-time processing capability in high-dimensional systems
3Reliability
If QR decomposition is performed to enable various MIMO detection algorithms, then detection performance is improved, but computation latency increases due to the complexity of the decomposition process
Solution Approach 1:
By extracting and removing the computationally expensive division and square-root operations from the Householder transformation, the patent significantly reduces computation latency while preserving the essential functionality needed for accurate MIMO detection
Solution Approach 2:
The patent changes the computational parameters of the decomposition algorithm to eliminate operations that contribute most to computation latency, thereby enabling faster real-time processing without sacrificing detection performance
Data Source
AI summary
Method and system for decomposing a complex channel matrix at MIMO receiver is disclosed. The method comprises determining a real channel matrix from the complex channel matrix, wherein the number of rows and columns of the real channel matrix depends on a number of transmitting chains and a number of receiving chains. Thereafter, the below mentioned steps repeated predetermined number of times: A pre-Householder vector is determined based on the real channel matrix. A Householder vector is determined based on the pre-Householder vector. Thereafter a Householder matrix is determined based on the Householder vector and a transpose of the Householder vector without performing division operation. Finally, an orthogonal matrix and an upper triangular matrix are determined based on the Householder matrix, wherein the upper triangular matrix comprises a predetermined number of zeros in an upper triangle.