MIMO OFDM Decoder Complexity Reduction via QR Decomposition
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Solution Overview
Problem
High computational complexity of maximum-likelihood (ML) MIMO OFDM decoders hinders their practical application in real-time communication systems, despite offering the best performance in bit error rate (BER) terms, due to exponential complexity in square modulation systems.
Innovation Solution
The Euclidean distance expression is transformed using QR decomposition into a simpler form by decomposing the channel matrix into a product of sparse and unitary matrices, reducing the search space from M^2 to 2M constellation points through orthogonal decomposition and Gray coding, thereby reducing computational complexity without performance degradation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If maximum-likelihood (ML) MIMO OFDM decoding is implemented to achieve best BER performance, then decoding performance is improved, but computational complexity increases exponentially
Solution Approach 1:
The patent segments the exhaustive search space of M2 constellation points by exploiting the independent in-phase and quadrature components of QAM modulation. This divides the search into separate dimensional searches, reducing complexity from exponential M2 to linear 2M operations while maintaining ML decoding performance.
Solution Approach 2:
The patent transforms the two-dimensional constellation search problem into separate one-dimensional searches along the in-phase and quadrature dimensions. By treating each dimension independently and searching along axes rather than across the full 2D space, the computational complexity is reduced from exponential to linear while preserving the maximum-likelihood detection performance.
2Measurement precision
If exhaustive search over all constellation points is performed to achieve optimal ML decoding, then decoding accuracy is improved, but processing time increases
Solution Approach 1:
The patent segments the exhaustive search by exploiting dimensional independence in QAM modulation. Instead of searching all M2 constellation points, it separates the search into independent in-phase and quadrature component searches, reducing the number of operations from M2 to 2M while maintaining optimal decoding accuracy.
Solution Approach 2:
The patent performs preliminary decomposition of the received signal into in-phase and quadrature components before the actual constellation search. This preliminary separation enables independent dimensional searches, significantly reducing processing time while preserving decoding accuracy by maintaining the maximum-likelihood detection principle.
3Productivity
If MIMO system uses higher order square modulation to increase throughput, then spectral efficiency is improved, but decoder complexity increases exponentially
Solution Approach 1:
The patent segments the constellation search space by exploiting the independent in-phase and quadrature dimensions of square QAM modulation. This segmentation reduces the decoder complexity from exponential M2 operations to linear 2M operations, enabling higher order modulations (64-QAM, 256-QAM) to be used in MIMO systems without prohibitively complex decoders, thus maintaining high spectral efficiency.
Solution Approach 2:
The patent transforms the complex two-dimensional constellation search into separate one-dimensional searches along the in-phase and quadrature axes. This dimensional transformation reduces decoder complexity from exponential to linear, making it feasible to implement high-order square modulations in practical MIMO systems while maintaining the spectral efficiency benefits.
Data Source
AI summary
A method and a system for reducing computational complexity in a maximum-likelihood MIMO decoder, while maintaining its high performance. A factorization operation is applied on the channel Matrix H. The decomposition creates two matrixes: an upper triangular with only real-numbers on the diagonal and a unitary matrix. The decomposition simplifies the representation of the distance calculation needed for constellation points search. An exhaustive search for all the points in the constellation for two spatial streams t(1), t(2) is performed, searching all possible transmit points of (t2), wherein each point generates a SISO slicing problem in terms of transmit points of (t1); Then, decomposing x,y components of t(1), thus turning a two-dimensional problem into two one-dimensional problems. Finally searching the remaining points of t(1) and using Gray coding in the constellation points arrangement and the symmetry deriving from it to further reduce the number of constellation points that have to be searched.