Integer QAM Rotation Matrices for Full-Diversity Joint Decoding
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Solution Overview
Problem
Current wireless communication systems, particularly those using QAM signals, face challenges in achieving optimal diversity and coding gain due to complex spreading rotation matrices, which also increase decoding complexity, and lack efficient methods for designing integer rotation matrices to achieve higher diversity orders like 3 or 4 for 4-QAM signals.
Innovation Solution
The development of 2×2, 3×3, and 4×4 integer spreading rotation matrices that simplify the modulation scheme by using linear transformations over independent channels, allowing for higher order diversity through joint decoding and cooperative relaying, specifically in decode-remodulate-forward (D-ReM-F) schemes.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If rotated DFT spreading matrices are used to achieve full diversity, then diversity gain is improved, but decoding complexity increases and coding gain is not maximized
Solution Approach 1:
The patent changes the fundamental parameters of the spreading matrix from complex-valued rotated DFT matrices to integer-valued matrices. This parameter change simplifies the decoding operations while maintaining the diversity gain property, directly resolving the contradiction between reliability and device complexity.
Solution Approach 2:
The patent employs simple integer matrices that are computationally inexpensive to process, replacing the more complex rotated DFT matrices. These integer matrices achieve the same diversity goal with significantly lower computational cost, addressing both the complexity and coding gain issues.
2Reliability
If dual-carrier modulation with rotated DFT matrices is used for 4-QAM signals, then diversity 2 is achieved, but coding gain is not maximized
Solution Approach 1:
The patent modifies the spreading matrix parameters from rotated DFT structure to integer matrix structure, which enables better optimization of coding gain while preserving the diversity order. The integer matrices allow for more flexible signal space rotation that maximizes the minimum distance between constellation points.
Solution Approach 2:
The patent combines multiple integer spreading matrices of different sizes (2×2, 3×3, 4×4) to create a composite solution that can achieve different diversity orders (2, 3, or 4) depending on the specific channel conditions and signal requirements, optimizing coding gain across various scenarios.
3Power
If decode-forward mode is used in cooperative relaying, then higher gain is achieved when S-R channel quality is good, but decoding errors may occur and switch to non-cooperative mode
Solution Approach 1:
The patent applies spread-rotation coding at the source before transmission to the relay. This pre-processing provides inherent error protection that cushions against decoding errors at the relay, allowing the decode-forward mode to operate more reliably and maintain cooperative diversity even in less ideal channel conditions.
Solution Approach 2:
The patent implements a mechanism where the relay node can switch between decode-forward and amplify-forward modes based on channel conditions and decoding success. The spread-rotation coding provides a foundation that makes the DF mode more robust, and the feedback from decoding performance enables adaptive mode selection to maintain reliability.
Data Source
AI summary
Diversity techniques are commonly used in wireless communications to combat multipath fading. Recent interests in ultra-wideband technology focus on multi-band OFDM systems that can explore the high diversity due to the independent frequency bands. To achieve full diversity with high data rate, a system, apparatus and method that uses coded modulation with spreading rotation of transmitted signals. A 2×2 integer rotation matrix for QAM signals, 3×3 and 4×4 integer rotation matrices for QAM signals are provided. Compared with the non-regular QAM shape for real rotation matrices, each of these integer rotation matrices makes the regular QAM shape after rotation.