Comparative Analytical Study of SCMA Detection Methods for PA Nonlinearity Mitigation

Non-orthogonal multiple access (NOMA) has emerged as a promising technology that allows for multiplexing several users over limited time-frequency resources. Among existing NOMA methods, sparse code multiple access (SCMA) is especially attractive; not only for its coding gain using suitable codebook design methodologies, but also for the guarantee of optimal detection using message passing algorithm (MPA). Despite SCMA’s benefits, the bit error rate (BER) performance of SCMA systems is known to degrade due to nonlinear power amplifiers at the transmitter. To mitigate this degradation, two types of detectors have recently emerged, namely, the Bussgang-based approaches and the reproducing kernel Hilbert space (RKHS)-based approaches. This paper presents analytical results on the error-floor of the Bussgang-based MPA, and compares it with a universally optimal RKHS-based MPA using random Fourier features (RFF). Although the Bussgang-based MPA is computationally simpler, it attains a higher BER floor compared to its RKHS-based counterpart. This error floor and the BER’s performance gap are quantified analytically and validated via computer simulations.

A random matrix analysis of random Fourier features: beyond the Gaussian kernel, a precise phase transition, and the corresponding double descent*

This article characterizes the exact asymptotics of random Fourier feature (RFF) regression, in the realistic setting where the number of data samples n, their dimension p, and the dimension of feature space N are all large and comparable. In this regime, the random RFF Gram matrix no longer converges to the well-known limiting Gaussian kernel matrix (as it does when N → ∞ alone), but it still has a tractable behavior that is captured by our analysis. This analysis also provides accurate estimates of training and test regression errors for large n, p, N. Based on these estimates, a precise characterization of two qualitatively different phases of learning, including the phase transition between them, is provided; and the corresponding double descent test error curve is derived from this phase transition behavior. These results do not depend on strong assumptions on the data distribution, and they perfectly match empirical results on real-world data sets.

Random Fourier Features-Based Deep Learning Improvement with Class Activation Interpretability for Nerve Structure Segmentation

Peripheral nerve blocking (PNB) is a standard procedure to support regional anesthesia. Still, correct localization of the nerve’s structure is needed to avoid adverse effects; thereby, ultrasound images are used as an aid approach. In addition, image-based automatic nerve segmentation from deep learning methods has been proposed to mitigate attenuation and speckle noise ultrasonography issues. Notwithstanding, complex architectures highlight the region of interest lacking suitable data interpretability concerning the learned features from raw instances. Here, a kernel-based deep learning enhancement is introduced for nerve structure segmentation. In a nutshell, a random Fourier features-based approach was utilized to complement three well-known semantic segmentation architectures, e.g., fully convolutional network, U-net, and ResUnet. Moreover, two ultrasound image datasets for PNB were tested. Obtained results show that our kernel-based approach provides a better generalization capability from image segmentation-based assessments on different nerve structures. Further, for data interpretability, a semantic segmentation extension of the GradCam++ for class-activation mapping was used to reveal relevant learned features separating between nerve and background. Thus, our proposal favors both straightforward (shallow) and complex architectures (deeper neural networks).

Wind field reconstruction with adaptive random Fourier features

We investigate the use of spatial interpolation methods for reconstructing the horizontal near-surface wind field given a sparse set of measurements. In particular, random Fourier features is compared with a set of benchmark methods including kriging and inverse distance weighting. Random Fourier features is a linear model β ( x ) = ∑ k = 1 K β k e i ω k x approximating the velocity field, with randomly sampled frequencies ω k and amplitudes β k trained to minimize a loss function. We include a physically motivated divergence penalty | ∇ ⋅ β ( x ) | 2 , as well as a penalty on the Sobolev norm of β . We derive a bound on the generalization error and a sampling density that minimizes the bound. We then devise an adaptive Metropolis–Hastings algorithm for sampling the frequencies of the optimal distribution. In our experiments, our random Fourier features model outperforms the benchmark models.