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Learning at the Speed of Wireless: Online Real-Time Learning for AI-Enabled MIMO in NextG
Mar 05, 2024
Integration of artificial intelligence (AI) and machine learning (ML) into the air interface has been envisioned as a key technology for next-generation (NextG) cellular networks. At the air interface, multiple-input multiple-output (MIMO) and its variants such as multi-user MIMO (MU-MIMO) and massive/full-dimension MIMO have been key enablers across successive generations of cellular networks with evolving complexity and design challenges. Initiating active investigation into leveraging AI/ML tools to address these challenges for MIMO becomes a critical step towards an AI-enabled NextG air interface. At the NextG air interface, the underlying wireless environment will be extremely dynamic with operation adaptations performed on a sub-millisecond basis by MIMO operations such as MU-MIMO scheduling and rank/link adaptation. Given the enormously large number of operation adaptation possibilities, we contend that online real-time AI/ML-based approaches constitute a promising paradigm. To this end, we outline the inherent challenges and offer insights into the design of such online real-time AI/ML-based solutions for MIMO operations. An online real-time AI/ML-based method for MIMO-OFDM channel estimation is then presented, serving as a potential roadmap for developing similar techniques across various MIMO operations in NextG.
Operator SVD with Neural Networks via Nested Low-Rank Approximation
Feb 06, 2024Computing eigenvalue decomposition (EVD) of a given linear operator, or finding its leading eigenvalues and eigenfunctions, is a fundamental task in many machine learning and scientific computing problems. For high-dimensional eigenvalue problems, training neural networks to parameterize the eigenfunctions is considered as a promising alternative to the classical numerical linear algebra techniques. This paper proposes a new optimization framework based on the low-rank approximation characterization of a truncated singular value decomposition, accompanied by new techniques called nesting for learning the top-$L$ singular values and singular functions in the correct order. The proposed method promotes the desired orthogonality in the learned functions implicitly and efficiently via an unconstrained optimization formulation, which is easy to solve with off-the-shelf gradient-based optimization algorithms. We demonstrate the effectiveness of the proposed optimization framework for use cases in computational physics and machine learning.
2D-RC: Two-Dimensional Neural Network Approach for OTFS Symbol Detection
Nov 14, 2023Orthogonal time frequency space (OTFS) is a promising modulation scheme for wireless communication in high-mobility scenarios. Recently, a reservoir computing (RC) based approach has been introduced for online subframe-based symbol detection in the OTFS system, where only a limited number of over-the-air (OTA) pilot symbols are utilized for training. However, this approach does not leverage the domain knowledge specific to the OTFS system. This paper introduces a novel two-dimensional RC (2D-RC) method that incorporates the structural knowledge of the OTFS system into the design for online symbol detection on a subframe basis. Specifically, as the channel response acts as a two-dimensional (2D) operation over the transmitted information symbols in the delay-Doppler (DD) domain, the 2D-RC is designed to have a 2D structure to equalize the channel. With the introduced architecture, the 2D-RC can benefit from the predictable channel representation in the DD domain. Moreover, unlike the previous work that requires multiple RCs to learn the channel feature, the 2D-RC only requires a single neural network for detection. Experimental results demonstrate the effectiveness of the 2D-RC approach across different OTFS system variants and modulation orders.
Towards Explainable Machine Learning: The Effectiveness of Reservoir Computing in Wireless Receive Processing
Oct 08, 2023Deep learning has seen a rapid adoption in a variety of wireless communications applications, including at the physical layer. While it has delivered impressive performance in tasks such as channel equalization and receive processing/symbol detection, it leaves much to be desired when it comes to explaining this superior performance. In this work, we investigate the specific task of channel equalization by applying a popular learning-based technique known as Reservoir Computing (RC), which has shown superior performance compared to conventional methods and other learning-based approaches. Specifically, we apply the echo state network (ESN) as a channel equalizer and provide a first principles-based signal processing understanding of its operation. With this groundwork, we incorporate the available domain knowledge in the form of the statistics of the wireless channel directly into the weights of the ESN model. This paves the way for optimized initialization of the ESN model weights, which are traditionally untrained and randomly initialized. Finally, we show the improvement in receive processing/symbol detection performance with this optimized initialization through simulations. This is a first step towards explainable machine learning (XML) and assigning practical model interpretability that can be utilized together with the available domain knowledge to improve performance and enhance detection reliability.
A Geometric Framework for Neural Feature Learning
Sep 18, 2023We present a novel framework for learning system design based on neural feature extractors by exploiting geometric structures in feature spaces. First, we introduce the feature geometry, which unifies statistical dependence and features in the same functional space with geometric structures. By applying the feature geometry, we formulate each learning problem as solving the optimal feature approximation of the dependence component specified by the learning setting. We propose a nesting technique for designing learning algorithms to learn the optimal features from data samples, which can be applied to off-the-shelf network architectures and optimizers. To demonstrate the application of the nesting technique, we further discuss multivariate learning problems, including conditioned inference and multimodal learning, where we present the optimal features and reveal their connections to classical approaches.
Universal Approximation of Linear Time-Invariant (LTI) Systems through RNNs: Power of Randomness in Reservoir Computing
Aug 04, 2023Recurrent neural networks (RNNs) are known to be universal approximators of dynamic systems under fairly mild and general assumptions, making them good tools to process temporal information. However, RNNs usually suffer from the issues of vanishing and exploding gradients in the standard RNN training. Reservoir computing (RC), a special RNN where the recurrent weights are randomized and left untrained, has been introduced to overcome these issues and has demonstrated superior empirical performance in fields as diverse as natural language processing and wireless communications especially in scenarios where training samples are extremely limited. On the contrary, the theoretical grounding to support this observed performance has not been fully developed at the same pace. In this work, we show that RNNs can provide universal approximation of linear time-invariant (LTI) systems. Specifically, we show that RC can universally approximate a general LTI system. We present a clear signal processing interpretation of RC and utilize this understanding in the problem of simulating a generic LTI system through RC. Under this setup, we analytically characterize the optimal probability distribution function for generating the recurrent weights of the underlying RNN of the RC. We provide extensive numerical evaluations to validate the optimality of the derived optimum distribution of the recurrent weights of the RC for the LTI system simulation problem. Our work results in clear signal processing-based model interpretability of RC and provides theoretical explanation for the power of randomness in setting instead of training RC's recurrent weights. It further provides a complete optimum analytical characterization for the untrained recurrent weights, marking an important step towards explainable machine learning (XML) which is extremely important for applications where training samples are limited.
Learning to Estimate: A Real-Time Online Learning Framework for MIMO-OFDM Channel Estimation
May 22, 2023
In this paper we introduce StructNet-CE, a novel real-time online learning framework for MIMO-OFDM channel estimation, which only utilizes over-the-air (OTA) pilot symbols for online training and converges within one OFDM subframe. The design of StructNet-CE leverages the structure information in the MIMO-OFDM system, including the repetitive structure of modulation constellation and the invariant property of symbol classification to inter-stream interference. The embedded structure information enables StructNet-CE to conduct channel estimation with a binary classification task and accurately learn channel coefficients with as few as two pilot OFDM symbols. Experiments show that the channel estimation performance is significantly improved with the incorporation of structure knowledge. StructNet-CE is compatible and readily applicable to current and future wireless networks, demonstrating the effectiveness and importance of combining machine learning techniques with domain knowledge for wireless communication systems.
Interference-Aware Constellation Design for Z-Interference Channels with Imperfect CSI
Mar 15, 2023
A deep autoencoder (DAE)-based end-to-end communication over the two-user Z-interference channel (ZIC) with finite-alphabet inputs is designed in this paper. The design is for imperfect channel state information (CSI) where both estimation and quantization errors exist. The proposed structure jointly optimizes the encoders and decoders to generate interferenceaware constellations that adapt their shape to the interference intensity in order to minimize the bit error rate. A normalization layer is designed to guarantee an average power constraint in the DAE while allowing the architecture to generate constellations with nonuniform shapes. This brings further shaping gain compared to standard uniform constellations such as quadrature amplitude modulation. The performance of the DAE-ZIC is compared with two conventional methods, i.e., standard and rotated constellations. The proposed structure significantly enhances the performance of the ZIC. Simulation results confirm bit error rate reduction in all interference regimes (weak, moderate, and strong). At a signal-to-noise ratio of 20dB, the improvements reach about two orders of magnitude when only quantization error exists, indicating that the DAE-ZIC is highly robust to the interference compared to the conventional methods.
Kernel Subspace and Feature Extraction
Jan 04, 2023We study kernel methods in machine learning from the perspective of feature subspace. We establish a one-to-one correspondence between feature subspaces and kernels and propose an information-theoretic measure for kernels. In particular, we construct a kernel from Hirschfeld--Gebelein--R\'{e}nyi maximal correlation functions, coined the maximal correlation kernel, and demonstrate its information-theoretic optimality. We use the support vector machine (SVM) as an example to illustrate a connection between kernel methods and feature extraction approaches. We show that the kernel SVM on maximal correlation kernel achieves minimum prediction error. Finally, we interpret the Fisher kernel as a special maximal correlation kernel and establish its optimality.
An Information-Theoretic Approach to Transferability in Task Transfer Learning
Dec 20, 2022
Task transfer learning is a popular technique in image processing applications that uses pre-trained models to reduce the supervision cost of related tasks. An important question is to determine task transferability, i.e. given a common input domain, estimating to what extent representations learned from a source task can help in learning a target task. Typically, transferability is either measured experimentally or inferred through task relatedness, which is often defined without a clear operational meaning. In this paper, we present a novel metric, H-score, an easily-computable evaluation function that estimates the performance of transferred representations from one task to another in classification problems using statistical and information theoretic principles. Experiments on real image data show that our metric is not only consistent with the empirical transferability measurement, but also useful to practitioners in applications such as source model selection and task transfer curriculum learning.