Multi-Antenna Symbol Transmission Using Butson Hadamard Codes
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Solution Overview
Problem
The construction of orthogonal cover codes for long training fields (LTFs) in advanced antenna systems, such as those supporting up to 16 space-time streams, becomes impractical with existing methods, particularly for the IEEE 802.11 standard enhancements like EHT, due to the impracticality of exhaustive computer searches for P matrices as the dimension increases.
Innovation Solution
The use of Butson-type Hadamard matrices or their sub-matrices with a minimum number of non-real elements, specifically ±{1, j}, is proposed for transmitting symbols from multiple antennas, where the number of rows or columns of the matrix is at least the number of antennas, and the matrix supports up to 10 or 14 space-time streams.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If exhaustive computer search is used to construct P matrices for MIMO operation, then complete orthogonal cover codes can be obtained, but the method becomes impractical as matrix dimension increases
Solution Approach 1:
The patent segments the construction process by using structured Hadamard matrices with specific patterns (real and imaginary components) rather than exhaustive search. The P matrices are constructed by combining real Hadamard matrices with imaginary unit j, creating a systematic approach that divides the problem into manageable components (real parts and imaginary parts) that can be generated through defined operations rather than complete enumeration.
Solution Approach 2:
The patent changes the parameter space by utilizing Hadamard matrices of Butson-type H(4, n) where entries are powers of the fourth root of unity (±1, ±j). This parameter transformation allows the construction of orthogonal cover codes for up to 16 space-time streams by systematically varying the matrix dimension parameter n while maintaining the orthogonal property through the Hadamard structure, avoiding exhaustive search.
2Adaptability or versatility
If Hadamard matrices with more non-real elements are used, then higher dimensional MIMO support is achieved, but computational complexity increases
Solution Approach 1:
The patent applies local quality by using Hadamard matrices where only specific positions contain non-real elements (imaginary unit j). The matrices are structured so that real and imaginary components are distributed in specific patterns, allowing selective multiplication operations. This localized approach to non-real elements enables support for higher MIMO dimensions while controlling computational complexity by minimizing the number of complex multiplications required.
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 6, and the matrix comprises or is a sub-matrix of a Butson-type Hadamard matrix that includes only a minimum number of non-real elements.