QR Decomposition Detection for Overlapped Multiplexing
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Solution Overview
Problem
In overlapped multiplexing systems, traditional decoding methods like Viterbi, MAP, and Log-MAP face high complexity and require large storage capacity, making engineering implementation difficult, especially when the number of overlapped multiplexing is large.
Innovation Solution
A QR decomposition-based detection method is applied, which involves decomposing the multiplexing waveform matrix into a unitary and upper triangular matrix, performing matrix multiplication, and layer-by-layer detection using a quantized decision factor to decode the receive sequence.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional decoding methods (Viterbi, MAP, Log-MAP) are used in overlapped multiplexing systems, then decoding accuracy can be maintained, but decoding complexity increases exponentially and large storage capacity is required
Solution Approach 1:
The patent segments the decoding process into two distinct stages: first performing QR decomposition on the multiplexing waveform matrix to obtain a triangular matrix, then using this triangular matrix for simplified layer-by-layer detection. This segmentation transforms the original complex single-stage decoding into a two-stage process where the first stage (QR decomposition) is performed once and reused, significantly reducing the exponential complexity of traditional methods while maintaining decoding accuracy.
2Reliability
If traditional decoding methods are used with large quantity K of overlapped multiplexing, then complete signal detection is achieved, but storage capacity requirements become prohibitively large
Solution Approach 1:
The patent performs preliminary QR decomposition on the multiplexing waveform matrix before the actual detection process. The resulting triangular matrix is stored and reused for all subsequent detections, regardless of the quantity K of overlapped multiplexing. This preliminary action eliminates the need to store large quantities of data for each detection operation, reducing storage capacity requirements while ensuring complete signal detection.
3Measurement precision
If traditional decoding methods are implemented, then accurate signal recovery is possible, but implementation difficulty in actual engineering increases
Solution Approach 1:
The patent changes the mathematical parameters by transforming the multiplexing waveform matrix into a triangular matrix through QR decomposition. This parameter transformation simplifies the detection equations from complex matrix inversions to simpler triangular system solutions, making the implementation more straightforward and easier to manufacture in actual engineering while preserving signal recovery accuracy.
Data Source
AI summary
Provided are a QR decomposition-based detection method and apparatus based on overlapped multiplexing. The QR decomposition-based detection method includes: step S1: obtaining a receive sequence, where the receive sequence is a sequence obtained by encoding and modulating an input signal based on a multiplexing waveform matrix and transmitting the signal through a Gaussian channel; and step S2: detecting the receive sequence by using a QR decomposition algorithm, where step S2 includes: decomposing a foreknown multiplexing waveform matrix into a unitary matrix and an upper triangular matrix; performing matrix multiplication processing on the receive sequence based on the unitary matrix, to obtain a data sequence; and performing layer-by-layer detection on the data sequence based on the data sequence, the upper triangular matrix, and a quantized decision factor.