Finite Resolution Decomposition of a Matrix for Low-Complexity and Energy-Efficient Matrix-Vector Multiplication

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This patent describes a method and system for performing matrix-vector multiplication in a way that significantly reduces computational complexity and energy consumption. The approach approximates the original matrix as a combination of matrices whose elements are positive or negative integer powers of two. This enables all multiplications to be replaced by much simpler bit shifts and additions, allowing fast and efficient processing without requiring high-power, complex hardware. The invention is particularly suited for applications such as wireless MIMO (Multiple-Input Multiple-Output) systems and artificial neural networks, where large-scale matrix operations are frequent and computationally expensive.

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• Wireless communication systems, specifically in the precoding and signal processing of MIMO transmitters and receivers to efficiently generate transmit symbols.
• Machine learning systems, especially artificial neural networks (ANNs), where large matrix-vector multiplications are common in model inference and training.
• Real-time signal processing applications where energy efficiency and low hardware complexity are crucial, such as IoT edge devices and embedded systems.
• Custom hardware design for digital signal processing, such as FPGAs and ASICs implementing efficient matrix-vector operations.
• Mobile devices and base stations operating in 5G or next-generation wireless networks, where massive MIMO and beamforming demand scalable low-power computation.

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• Significantly reduces the computational complexity and energy consumption of large matrix-vector multiplications, enabling real-time processing even in resource-constrained environments.
• Replaces expensive multiplications with simple bit shifts and additions, which are much faster and more energy-efficient to implement in hardware.
• Enables a favorable trade-off between memory usage, computational complexity, and result accuracy by adjusting the number or sparsity of matrix factors.
• Allows existing hardware and software platforms to leverage enhanced efficiency without requiring entirely new architectures, potentially delivering cost savings.
• Maintains or improves signal-to-noise ratio (SNR) and accuracy compared to existing low-complexity methods, making it practical for high-performance communications and machine learning tasks.
• Flexible decomposition methods (sum or product decomposition) allow optimization for different application needs and constraints.

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Patent Abstract

A method for providing transmit symbols to be transmitted by a transmitter to one or more receivers of a wireless MIMO communication system is described. The method includes receiving data to be transmitted to the one or more receivers, and obtaining the transmit symbols to be transmitted by multiplying a data vector including the data to be transmitted by a matrix, like a precoding matrix. The matrix is approximated by a plurality of matrices whose elements are positive or negative integer powers of two so that multiplying the data vector by the matrix includes a series of sub-multiplications, each of the sub-multiplications being realized only by bit shifts and additions.