Pipelined MIMO LMMSE Receiver Using Small-Matrix Inversion
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Solution Overview
Problem
MIMO receivers face high complexity due to the need to invert large correlation matrices, which is impractical for portable wireless devices, especially with increasing numbers of antennas, leading to inefficiencies in hardware implementation and stability issues with existing algorithms.
Innovation Solution
The solution involves inverting smaller sub-matrices instead of the overall NF×NF matrix, using Hermitian optimization and tree pruning to reduce the complexity of FFT designs, and combining Fourier transformed sub-matrix elements with a Fourier transformed channel matrix to simplify calculations and parallelize processing.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If the conventional LMMSE equalizer inverts the large NF×NF correlation matrix, then the equalization performance is maintained, but the hardware complexity increases dramatically to O((NF)³)
Solution Approach 1:
The patent divides the large NF×NF correlation matrix into multiple smaller N×N submatrices through block partitioning. This segmentation allows the system to invert smaller matrices individually rather than one large matrix, reducing the computational complexity from O((NF)³) to O(N³×(NF/N)) = O(N²F), making the implementation feasible for portable devices with multiple antennas.
2Reliability
If the number of antennas N is increased to improve signal quality and capacity, then the communication performance is enhanced, but the receiver complexity increases dramatically
Solution Approach 1:
By partitioning the correlation matrix into N×N submatrices based on the antenna configuration, the patent enables scalable implementation. When N increases, the system processes multiple smaller submatrices rather than one exponentially larger matrix, allowing the complexity to grow linearly with the number of antennas rather than cubically.
Solution Approach 2:
The patent transforms the problem from inverting a correlation matrix of size NF×NF to inverting submatrices of size N×N. This parameter transformation changes the complexity relationship from cubic in terms of total dimension (NF)³ to cubic in terms of antenna dimension N³, which is much more manageable for portable devices.
3Device complexity
If the FFT-based equalizer is used to reduce matrix inversion complexity, then the computational load is reduced, but the stability problems arise due to convergence dependence on step size selection
Solution Approach 1:
The patent combines the stability of direct matrix inversion methods with the complexity reduction of FFT-based approaches by segmenting the large matrix into smaller submatrices. This allows the use of stable inversion algorithms on each small submatrix while maintaining the overall computational efficiency, avoiding the stability issues that arise in adaptive algorithms.
Data Source
AI summary
Disclosed is a LMMSE receiver that restores orthogonality of spreading codes in the downlink channel for a spread spectrum signal received over N receive antennas. The FFT-based chip equalizer tap solver reduces the direct matrix inverse of the prior art to the inverse of some submatrices of size N×N with the dimension of the receive antennas, and most efficiently reduces matrix inverses to no larger than 2×2. Complexity is further reduced over a conventional Fast Fourier Transform approach by Hermitian optimization to the inverse of submatrices and tree pruning. For a receiver with N=4 or N=2 with double oversampling, the resulting 4×4 matrices are partitioned into 2×2 block sub-matrices, inverted, and rebuilt into a 4×4 matrix. Common computations are found and repeated computations are eliminated to improve efficiency. Generic design architecture is derived from the special design blocks to eliminate redundancies in complex operations. Optimally, the architecture is parallel and pipelined.