Channel Charting for Streaming CSI Data

Channel charting (CC) applies dimensionality reduction to channel state information (CSI) data at the infrastructure basestation side with the goal of extracting pseudo-position information for each user. The self-supervised nature of CC enables predictive tasks that depend on user position without requiring any ground-truth position information. In this work, we focus on the practically relevant streaming CSI data scenario, in which CSI is constantly estimated. To deal with storage limitations, we develop a novel streaming CC architecture that maintains a small core CSI dataset from which the channel charts are learned. Curation of the core CSI dataset is achieved using a min-max-similarity criterion. Numerical validation with measured CSI data demonstrates that our method approaches the accuracy obtained from the complete CSI dataset while using only a fraction of CSI storage and avoiding catastrophic forgetting of old CSI data.

On the Accuracy of Hotelling-Type Asymmetric Tensor Deflation: A Random Tensor Analysis

This work introduces an asymptotic study of Hotelling-type tensor deflation in the presence of noise, in the regime of large tensor dimensions. Specifically, we consider a low-rank asymmetric tensor model of the form $\sum_{i=1}^r \beta_i{\mathcal{A}}_i + {\mathcal{W}}$ where $\beta_i\geq 0$ and the ${\mathcal{A}}_i$'s are unit-norm rank-one tensors such that $\left| \langle {\mathcal{A}}_i, {\mathcal{A}}_j \rangle \right| \in [0, 1]$ for $i\neq j$ and ${\mathcal{W}}$ is an additive noise term. Assuming that the dominant components are successively estimated from the noisy observation and subsequently subtracted, we leverage recent advances in random tensor theory in the regime of asymptotically large tensor dimensions to analytically characterize the estimated singular values and the alignment of estimated and true singular vectors at each step of the deflation procedure. Furthermore, this result can be used to construct estimators of the signal-to-noise ratios $\beta_i$ and the alignments between the estimated and true rank-1 signal components.

Hotelling Deflation on Large Symmetric Spiked Tensors

This paper studies the deflation algorithm when applied to estimate a low-rank symmetric spike contained in a large tensor corrupted by additive Gaussian noise. Specifically, we provide a precise characterization of the large-dimensional performance of deflation in terms of the alignments of the vectors obtained by successive rank-1 approximation and of their estimated weights, assuming non-trivial (fixed) correlations among spike components. Our analysis allows an understanding of the deflation mechanism in the presence of noise and can be exploited for designing more efficient signal estimation methods.

Wireless Channel Charting: Theory, Practice, and Applications

Channel charting is a recently proposed framework that applies dimensionality reduction to channel state information (CSI) in wireless systems with the goal of associating a pseudo-position to each mobile user in a low-dimensional space: the channel chart. Channel charting summarizes the entire CSI dataset in a self-supervised manner, which opens up a range of applications that are tied to user location. In this article, we introduce the theoretical underpinnings of channel charting and present an overview of recent algorithmic developments and experimental results obtained in the field. We furthermore discuss concrete application examples of channel charting to network- and user-related applications, and we provide a perspective on future developments and challenges as well as the role of channel charting in next-generation wireless networks.

On the Accuracy of Hotelling-Type Tensor Deflation: A Random Tensor Analysis

Leveraging on recent advances in random tensor theory, we consider in this paper a rank-$r$ asymmetric spiked tensor model of the form $\sum_{i=1}^r \beta_i A_i + W$ where $\beta_i\geq 0$ and the $A_i$'s are rank-one tensors such that $\langle A_i, A_j \rangle\in [0, 1]$ for $i\neq j$, based on which we provide an asymptotic study of Hotelling-type tensor deflation in the large dimensional regime. Specifically, our analysis characterizes the singular values and alignments at each step of the deflation procedure, for asymptotically large tensor dimensions. This can be used to construct consistent estimators of different quantities involved in the underlying problem, such as the signal-to-noise ratios $\beta_i$ or the alignments between the different signal components $\langle A_i, A_j \rangle$.

Constant Weight Codes with Gabor Dictionaries and Bayesian Decoding for Massive Random Access

This paper considers a general framework for massive random access based on sparse superposition coding. We provide guidelines for the code design and propose the use of constant-weight codes in combination with a dictionary design based on Gabor frames. The decoder applies an extension of approximate message passing (AMP) by iteratively exchanging soft information between an AMP module that accounts for the dictionary structure, and a second inference module that utilizes the structure of the involved constant-weight code. We apply the encoding structure to (i) the unsourced random access setting, where all users employ a common dictionary, and (ii) to the "sourced" random access setting with user-specific dictionaries. When applied to a fading scenario, the communication scheme essentially operates non-coherently, as channel state information is required neither at the transmitter nor at the receiver. We observe that in regimes of practical interest, the proposed scheme compares favorably with state-of-the art schemes, in terms of the (per-user) energy-per-bit requirement, as well as the number of active users that can be simultaneously accommodated in the system. Importantly, this is achieved with a considerably smaller size of the transmitted codewords, potentially yielding lower latency and bandwidth occupancy, as well as lower implementation complexity.

When Random Tensors meet Random Matrices

Relying on random matrix theory (RMT), this paper studies asymmetric order-$d$ spiked tensor models with Gaussian noise. Using the variational definition of the singular vectors and values of (Lim, 2005), we show that the analysis of the considered model boils down to the analysis of an equivalent spiked symmetric block-wise random matrix, that is constructed from contractions of the studied tensor with the singular vectors associated to its best rank-1 approximation. Our approach allows the exact characterization of the almost sure asymptotic singular value and alignments of the corresponding singular vectors with the true spike components, when $\frac{n_i}{\sum_{j=1}^d n_j}\to c_i\in [0, 1]$ with $n_i$'s the tensor dimensions. In contrast to other works that rely mostly on tools from statistical physics to study random tensors, our results rely solely on classical RMT tools such as Stein's lemma. Finally, classical RMT results concerning spiked random matrices are recovered as a particular case.

Triplet-Based Wireless Channel Charting

Channel charting is a data-driven baseband processing technique consisting in applying unsupervised machine learning techniques to channel state information (CSI), with the objective of reducing the dimension of the data and extracting the fundamental parameters governing the distribution of CSI samples observed by a given receiver. In this work, we focus on neural network-based approaches, and propose a new architecture based on triplets of samples. It allows to simultaneously learn a meaningful similarity metric between CSI samples, on the basis of proximity in their respective acquisition times, and to perform the sought dimensionality reduction. The proposed approach is evaluated on a dataset of measured massive MIMO CSI, and is shown to perform well in comparison to the state-of-the-art methods (UMAP, autoencoders and siamese networks). In particular, we show that the obtained chart representation is topologically close to the geographical user position, despite the fact that the charting approach is not supervised by any geographical data.

DNN-based Localization from Channel Estimates: Feature Design and Experimental Results

We consider the use of deep neural networks (DNNs) in the context of channel state information (CSI)-based localization for Massive MIMO cellular systems. We discuss the practical impairments that are likely to be present in practical CSI estimates, and introduce a principled approach to feature design for CSI-based DNN applications based on the objective of making the features invariant to the considered impairments. We demonstrate the efficiency of this approach by applying it to a dataset constituted of geo-tagged CSI measured in an outdoors campus environment, and training a DNN to estimate the position of the UE on the basis of the CSI. We provide an experimental evaluation of several aspects of that learning approach, including localization accuracy, generalization capability, and data aging.

CSI-based Outdoor Localization for Massive MIMO: Experiments with a Learning Approach

We report on experimental results on the use of a learning-based approach to infer the location of a mobile user of a cellular network within a cell, for a 5G-type Massive multiple input, multiple output (MIMO) system. We describe how the sample spatial covariance matrix computed from the CSI can be used as the input to a learning algorithm which attempts to relate it to user location. We discuss several learning approaches, and analyze in depth the application of extreme learning machines, for which theoretical approximate performance benchmarks are available, to the localization problem. We validate the proposed approach using experimental data collected on a Huawei 5G testbed, provide some performance and robustness benchmarks, and discuss practical issues related to the deployment of such a technique in 5G networks.