Geometric Deep Learning for Low-Complexity Lattice Reduction
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Solution Overview
Problem
Lattice reduction is NP-hard and unfeasible to solve directly, leading to challenges in harnessing the full potential of MIMO systems due to increased computational complexity and non-orthogonality of MIMO channels, which affects the performance of MIMO detectors.
Innovation Solution
A neural lattice reduction process is implemented, iteratively reducing lattices through a recursion process, providing a computationally efficient MIMO demapping process that leverages the structure of real-world channels and can be parallelized across multiple lattices, reducing runtime compared to traditional LLL algorithms.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If traditional lattice reduction algorithms (LLL) are used to solve the Closest Vector Problem and Shortest Vector Problem in MIMO systems, then the problems can be solved when bases are orthogonal or nearly-orthogonal, but the computational complexity increases exponentially with the number of antennas and the detector complexity increases due to non-orthogonality of MIMO channels
Solution Approach 1:
The patent transforms the lattice reduction problem from the original basis representation to a Gram matrix representation, changing the parameter space in which the problem is solved. This transformation enables the application of neural network-based methods that operate on the Gram matrix, fundamentally altering how the reduction is performed and reducing computational complexity while maintaining accuracy
Solution Approach 2:
The patent replaces traditional algorithmic mechanical processes (LLL algorithm iterations) with a neural network-based system. The neural lattice reduction model learns optimal reduction strategies through training, substituting the step-by-step mechanical algorithmic approach with a learned model that can directly predict reduction operations, thereby reducing detector complexity
2Reliability
If exact lattice reduction is performed to achieve optimal MIMO detection performance, then the Closest Vector Problem and Shortest Vector Problem can be solved, but the problem becomes NP-hard and unfeasible to solve directly
Solution Approach 1:
The patent applies partial action by using the neural lattice reduction model to perform reduction operations that are sufficient for practical MIMO detection performance without achieving complete exact reduction. The model learns to perform the necessary reduction steps to achieve good detection performance while avoiding the computationally expensive path to exact reduction, thus improving computational efficiency
Solution Approach 2:
The patent employs approximate reduction techniques through the neural network model that provide sufficient performance for practical applications without the computational burden of exact reduction. The model generates reduction operations that are 'good enough' for real-time MIMO detection, sacrificing the theoretical optimality of exact reduction for practical computational efficiency
3Productivity
If the number of antennas in MIMO systems is increased to improve data carrying capacity, then spectral efficiency improves, but the computational complexity of the detector increases exponentially
Solution Approach 1:
The patent changes the dimensionality of the problem representation by transforming from operating directly on the basis matrices to operating on Gram matrices. This dimensional transformation allows the neural network to process the lattice reduction problem in a different space where the computational complexity does not scale exponentially with the number of antennas, enabling high-dimensional MIMO systems to be handled efficiently
Data Source
AI summary
Certain aspects of the present disclosure provide techniques for wireless communications by an apparatus. Certain techniques include receiving signals corresponding to a MIMO channel matrix; generating a first gram matrix from a basis for a first lattice corresponding to a first signal of the received signals; providing the first gram matrix to a neural lattice reduction model comprising an equivariant neural network configured to generate a current extended Gauss move; generating, with the neural lattice reduction model, a current partial changed basis based on the current extended Gauss move and the basis; executing one or more additional iterations of the neural lattice reduction model; and demapping the MIMO channel matrix based on combining the current partial changed basis and each of the additional partial changed basis generated by each of the one or more additional iterations of the neural lattice reduction model.