Cauchy-Schwarz Regularizers

We introduce a novel class of regularization functions, called Cauchy-Schwarz (CS) regularizers, which can be designed to induce a wide range of properties in solution vectors of optimization problems. To demonstrate the versatility of CS regularizers, we derive regularization functions that promote discrete-valued vectors, eigenvectors of a given matrix, and orthogonal matrices. The resulting CS regularizers are simple, differentiable, and can be free of spurious stationary points, making them suitable for gradient-based solvers and large-scale optimization problems. In addition, CS regularizers automatically adapt to the appropriate scale, which is, for example, beneficial when discretizing the weights of neural networks. To demonstrate the efficacy of CS regularizers, we provide results for solving underdetermined systems of linear equations and weight quantization in neural networks. Furthermore, we discuss specializations, variations, and generalizations, which lead to an even broader class of new and possibly more powerful regularizers.

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.

Channel Charting in Real-World Coordinates

Channel charting is an emerging self-supervised method that maps channel state information (CSI) to a low-dimensional latent space, which represents pseudo-positions of user equipments (UEs). While this latent space preserves local geometry, i.e., nearby UEs are nearby in latent space, the pseudo-positions are in arbitrary coordinates and global geometry is not preserved. In order to enable channel charting in real-world coordinates, we propose a novel bilateration loss for multipoint wireless systems in which only the access point (AP) locations are known--no geometrical models or ground-truth UE position information is required. The idea behind this bilateration loss is to compare the received power at pairs of APs in order to determine whether a UE should be placed closer to one AP or the other in latent space. We demonstrate the efficacy of our method using channel vectors from a commercial ray-tracer.

Alternating Projections Method for Joint Precoding and Peak-to-Average-Power Ratio Reduction

Orthogonal frequency-division multiplexing (OFDM) time-domain signals exhibit high peak-to-average (power) ratio (PAR), which requires linear radio-frequency chains to avoid an increase in error-vector magnitude (EVM) and out-of-band (OOB) emissions. In this paper, we propose a novel joint PAR reduction and precoding algorithm that relaxes these linearity requirements in massive multiuser (MU) multiple-input multiple-output (MIMO) wireless systems. Concretely, we develop a novel alternating projections method, which limits the PAR and transmit power increase while simultaneously suppressing MU interference. We provide a theoretical foundation of our algorithm and provide simulation results for a massive MU-MIMO-OFDM scenario. Our results demonstrate significant PAR reduction while limiting the transmit power, without causing EVM or OOB emissions.

Feature Learning for Neural-Network-Based Positioning with Channel State Information

Recent channel state information (CSI)-based positioning pipelines rely on deep neural networks (DNNs) in order to learn a mapping from estimated CSI to position. Since real-world communication transceivers suffer from hardware impairments, CSI-based positioning systems typically rely on features that are designed by hand. In this paper, we propose a CSI-based positioning pipeline that directly takes raw CSI measurements and learns features using a structured DNN in order to generate probability maps describing the likelihood of the transmitter being at pre-defined grid points. To further improve the positioning accuracy of moving user equipments, we propose to fuse a time-series of learned CSI features or a time-series of probability maps. To demonstrate the efficacy of our methods, we perform experiments with real-world indoor line-of-sight (LoS) and non-LoS channel measurements. We show that CSI feature learning and time-series fusion can reduce the mean distance error by up to 2.5$\boldsymbol\times$ compared to the state-of-the-art.

Hardware-Aware Beamspace Precoding for All-Digital mmWave Massive MU-MIMO

Massive multi-user multiple-input multiple-output (MU-MIMO) wireless systems operating at millimeter-wave (mmWave) frequencies enable simultaneous wideband data transmission to a large number of users. In order to reduce the complexity of MU precoding in all-digital basestation architectures, we propose a two-stage precoding architecture that first performs precoding using a sparse matrix in the beamspace domain, followed by an inverse fast Fourier transform that converts the result to the antenna domain. The sparse precoding matrix requires a small number of multipliers and enables regular hardware architectures, which allows the design of hardware-efficient all-digital precoders. Simulation results demonstrate that our methods approach the error-rate of conventional Wiener filter precoding with more than 2x reduced complexity.

$\ell^p\!-\!\ell^q$-Norm Minimization for Joint Precoding and Peak-to-Average-Power Ratio Reduction

Wireless communication systems that rely on orthogonal frequency-division multiplexing (OFDM) suffer from a high peak-to-average (power) ratio (PAR), which necessitates power-inefficient radio-frequency (RF) chains to avoid an increase in error-vector magnitude (EVM) and out-of-band (OOB) emissions. The situation is further aggravated in massive multiuser (MU) multiple-input multiple-output (MIMO) systems that would require hundreds of linear RF chains. In this paper, we present a novel approach to joint precoding and PAR reduction that builds upon a novel $\ell^p\!-\!\ell^q$-norm formulation, which is able to find minimum PAR solutions while suppressing MU interference. We provide a theoretical underpinning of our approach and provide simulation results for a massive MU-MIMO-OFDM system that demonstrate significant reductions in PAR at low complexity, without causing an increase in EVM or OOB emissions.

Optimality of the Discrete Fourier Transform for Beamspace Massive MU-MIMO Communication

Beamspace processing is an emerging technique to reduce baseband complexity in massive multiuser (MU) multiple-input multiple-output (MIMO) communication systems operating at millimeter-wave (mmWave) and terahertz frequencies. The high directionality of wave propagation at such high frequencies ensures that only a small number of transmission paths exist between user equipments and basestation (BS). In order to resolve the sparse nature of wave propagation, beamspace processing traditionally computes a spatial discrete Fourier transform (DFT) across a uniform linear antenna array at the BS where each DFT output is associated with a specific beam. In this paper, we study optimality conditions of the DFT for sparsity-based beamspace processing with idealistic mmWave channel models and realistic channels. To this end, we propose two algorithms that learn unitary beamspace transforms using an $\ell^4$-norm-based sparsity measure, and we investigate their optimality theoretically and via simulations.