Hadamard Matrix Construction for 16 Space-Time Streams
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Solution Overview
Problem
The construction of real-valued P matrices for more than 8 space-time streams becomes impractical due to the complexity of exhaustive computer searches, necessitating a more efficient method for generating matrices that provide orthogonal cover codes for advanced antenna systems supporting up to 16 space-time streams.
Innovation Solution
The use of maximum excess real Hadamard matrices, which are sub-matrices of real Hadamard matrices with specific properties, is proposed to reduce computational complexity and memory requirements by selecting columns or rows for symbol transmission, allowing for efficient support of at least 9 space-time streams up to 16 streams.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If exhaustive computer search is used to construct real-valued P matrices for more than 8 space-time streams, then complete matrix construction is achieved, but computational complexity becomes impractical
Solution Approach 1:
The patent segments the problem of constructing P matrices for more than 8 space-time streams by dividing it into smaller sub-problems that can be solved using structured Hadamard matrix construction methods. Instead of performing exhaustive search over the entire space, the method breaks down the matrix construction into systematic steps based on Hadamard matrix properties, thereby reducing computational complexity while maintaining completeness.
2Adaptability or versatility
If matrix dimension increases to support more space-time streams, then system capacity is improved, but memory requirements increase
Solution Approach 1:
The patent changes the parameter of matrix construction from exhaustive search to structured Hadamard matrix generation. By using the mathematical properties of Hadamard matrices and systematic construction algorithms, the method reduces memory requirements while supporting increased matrix dimensions for more space-time streams. The structured approach requires storing only the construction rules rather than enumerating all possible matrices.
Data Source
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AI summary
Methods and apparatus are provided for transmitting a symbol from a plurality of antennas. In one example, a method comprises transmitting simultaneously, from each antenna, the symbol multiplied by a respective element of a selected column of a matrix. The number of rows of the matrix is at least the number of antennas, the number of columns of the matrix is at least 9, and the matrix comprises or is a sub-matrix of a real Hadamard matrix of maximum excess.