Outer Product Matrices for Cross-Correlation Computation
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Solution Overview
Problem
The computation of squares and sums of cross-correlations in CDMA systems is computationally intensive due to the need for explicit cross-correlation calculations between each user and all other users, making it inefficient for practical implementations in signal processing applications.
Innovation Solution
The method involves computing outer product matrices for each code vector, which allows for the direct calculation of squares and sums of cross-correlations without explicit cross-correlation computation, eliminating the need for squaring units and simplifying updates in multi-user systems.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional cross-correlation computation methods are used, then accurate cross-correlation metrics are obtained, but computational complexity increases quadratically with the number of users
Solution Approach 1:
The patent pre-computes and stores outer product matrices for each user's spreading code before the actual cross-correlation calculation is needed. These outer product matrices are computed once and reused for all cross-correlation calculations involving that user, eliminating the need to re-compute them for each user pair. This preliminary action reduces the computational complexity from quadratic to linear with respect to the number of users.
Solution Approach 2:
The patent introduces outer product matrices as an intermediary structure between the spreading codes and the cross-correlation metrics. Instead of directly computing cross-correlations between all user pairs, the system first transforms the spreading codes into outer product matrices, then uses these matrices to efficiently compute the cross-correlation metrics. This intermediary representation enables more efficient computation while maintaining accuracy.
2Loss of information
If explicit cross-correlation calculations are performed between each user and all other users, then complete cross-correlation information is obtained, but computation time increases significantly
Solution Approach 1:
The system pre-computes outer product matrices for all users before the actual signal processing operation. These matrices are stored and reused, so when cross-correlation metrics are needed, they can be computed quickly by combining the pre-computed matrices with the current signal data, rather than performing complete cross-correlation calculations from scratch.
Solution Approach 2:
The patent segments the cross-correlation computation into independent outer product matrix calculations for each user, which can be performed separately and in parallel. This segmentation allows the computation to be divided into manageable pieces that can be processed independently, reducing the overall computation time while maintaining complete cross-correlation information.
3Measurement precision
If squaring operations are performed on cross-correlations to compute sum of squares, then accurate SSXC metrics are obtained, but computational intensity increases due to bitwise multiplication
Solution Approach 1:
The patent pre-computes the outer product matrices which include the squared terms needed for sum of squares calculations. By having these squared values pre-computed and stored in the outer product matrices, the system avoids performing intensive bitwise squaring operations at the time when sum of squares metrics are actually needed, thereby reducing computational intensity while maintaining accuracy.
Data Source
AI summary
The subject matter described herein includes a method for simplified computation of metrics of cross-correlations of binary codes and for using the metrics for signal processing applications. The method includes computing an outer product matrix based on a first code vector. The method further includes computing an outer product matrix based on at least one second code vector. The method further includes computing a metric of cross-correlations between the first code and the at least one second code vector using the outer product matrices. The method further includes using the metric to perform a signal processing operation.