Unitary Matrix Codebook via Eigen-Coordinate Transformation
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Solution Overview
Problem
Existing unitary matrix codebooks constructed using the Hochwald method are constrained by equal energy distribution among elements within and across codewords, limiting their distribution in the Grassmannian manifold and thus their performance.
Innovation Solution
An eigen-coordinate transformation method is applied to relax the fixed-energy-distribution constraint, allowing for a more optimal distribution of codewords by transforming the first codeword into eigen-coordinates, applying the Hochwald construction, and then transforming back into Euclidean coordinates, with additional parameterization using eigen vectors and a Householder structure.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If the Hochwald construction method is used to generate codebooks, then the computational complexity is reduced and storage is facilitated, but the energy distribution among elements within and across codewords is constrained to be equal, limiting the codebook distribution in the Grassmannian manifold
Solution Approach 1:
The patent applies parameter changes by transforming the codebook generation process into eigen-coordinate space, where the energy distribution constraints are relaxed. By changing the coordinate system from Euclidean to eigen-coordinates and back, the method maintains the computational efficiency of the Hochwald construction while achieving superior codebook distribution properties that maximize the minimum Chordal distance.
2Reliability
If random computation and distribution of codewords within the Grassmannian manifold is used, then the minimum Chordal distance is maximized, but the computational burden becomes impractical for systems with large amounts of transmit antennas and spatial streams
Solution Approach 1:
The patent introduces an intermediary transformation step that converts the codebook generation problem from a complex random search in the Grassmannian manifold to a simpler process in eigen-coordinate space. The transformation matrices V and VH act as intermediaries that preserve the optimal distribution properties while enabling systematic construction through the Hochwald method, thus reducing computational burden.
3Ease of manufacture
If the fixed-energy-distribution constraint is enforced in the Hochwald construction, then the codebook can be systematically constructed, but the distribution of codewords in the Grassmannian manifold can be improved upon
Solution Approach 1:
The patent resolves the contradiction by moving the codebook construction to a different dimensional space - eigen-coordinate space. In this transformed domain, the energy distribution constraints are relaxed, allowing for superior codebook distribution. The transformation back to Euclidean coordinates preserves the systematic construction capability while achieving improved distribution properties that maximize the minimum Chordal distance.
Data Source
AI summary
A method of deriving a codebook including deriving a first codeword Pl in Euclidean coordinates, transforming the first codeword into eigen-coordinates, applying a Hochwald construction to the first codeword in eigen-coordinates to derive a plurality of codewords in eigen-coordinates and transforming the plurality of codewords in eigen-coordinates into a plurality of codewords in Euclidean coordinates to form the codebook.