Reduced Complexity GPR for DS-CDMA Signal Recovery
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Solution Overview
Problem
The complexity of Gaussian process regression (GPR) in DS-CDMA systems is high, requiring O(n^3) computation and O(n^2) storage, making it unsuitable for practical implementation in communication devices due to the need for extensive computational resources and training effort.
Innovation Solution
The method employs fast Fourier transform (FFT), the law of log determinant, and stochastic gradient descent (SGD) to reduce the complexity of GPR, calculating partial derivatives and updating hyper-parameters to converge the negative marginal log likelihood, thereby reducing computational complexity to O(n log n) and storage complexity to O(n), facilitating efficient multi-user detection.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If Gaussian process regression (GPR) is used for multi-user detection in DS-CDMA systems, then signal recovery accuracy is improved, but computational complexity increases to O(n^3) and storage requirements increase to O(n^2)
Solution Approach 1:
The patent segments the large-scale GPR computation into multiple smaller sub-problems by dividing the training data into batches and processing them sequentially. This reduces the memory footprint from O(n^2) to O(b^2) where b is batch size, and enables parallel processing of different batches to reduce overall computational complexity.
Solution Approach 2:
The patent transforms the computational problem from the time domain to the frequency domain using Fast Fourier Transform (FFT). This dimensional transformation reduces the computational complexity of convolution operations from O(n^2) to O(n log n), directly addressing the computational burden of standard GPR implementation.
2Measurement precision
If Gaussian process regression (GPR) is used for multi-user detection in DS-CDMA systems, then signal recovery accuracy is improved, but storage requirements increase to O(n^2)
Solution Approach 1:
The patent segments the training data into smaller batches that can be processed independently. This segmentation reduces the storage requirement from storing the full n×n covariance matrix to storing only b×b covariance matrices where b is the batch size, achieving O(b^2) storage complexity instead of O(n^2).
Solution Approach 2:
The patent discards the full training dataset after processing each batch, keeping only the necessary model parameters and batch-specific computations in memory. This approach recovers storage space by eliminating the need to store the complete n×n covariance matrix, reducing storage complexity to O(b^2) while maintaining the ability to process all data through multiple batches.
3Measurement precision
If standard GPR implementation is used, then accurate signal estimation is achieved, but training time and computational resources are excessively high for practical communication devices
Solution Approach 1:
The patent performs preliminary actions by pre-processing the training data into batches and pre-computing the covariance matrices for each batch before the main GPR training process. This preliminary segmentation enables more efficient parallel processing and reduces the computational burden during the actual training phase, improving overall training efficiency.
Solution Approach 2:
The patent applies Fast Fourier Transform to transform the computational problem into the frequency domain, where convolution operations become simple multiplications. This dimensional change reduces the training computational complexity from O(n^3) to O(n log n), making the training process feasible for practical communication devices with limited computational resources.
Data Source
AI summary
Disclosed is a method for recovering an original signal in a DS-CDMA system based on complexity reduction. In such a method, first, a partial derivative for rMLL is calculated by using a partial derivative generated by applying fast Fourier transform (FFT) to a reduced negative marginal log likelihood (rMLL) obtained by applying a law of log determinant to a Gaussian process regression (GPR) scheme used for the multi-user detection and thereafter, integrating stochastic gradient descent (SGD). Thereafter, the rMLL is calculated by using the partial derivative for the rMLL and a hyper-parameter is updated to a convergence point until an error gap is converged by repeated calculation of the rMLL. Next, a kernel function used for estimating a matched filter is calculated by using the hyper-parameter estimated through the convergence and the original signal for each of multi-users is recovered by using the kernel function.