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Christoph Studer

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Published work

55 published item(s)

preprint2026arXiv

GazeVLM: Active Vision via Internal Attention Control for Multimodal Reasoning

Human visual reasoning is governed by active vision, a process where metacognitive control drives top-down goal-directed attention, dynamically routing foveal focus toward task-relevant details while maintaining peripheral awareness of the global scene. In contrast, modern Vision-Language Models (VLMs) process visual information passively, relying on the static accumulation of massive token contexts that dilute spatial reasoning and induce linguistic hallucinations. Here we propose the following paradigm shift: GazeVLM, a multimodal architecture that internalizes this metacognitive oversight over its deployment of attention resources directly into the reasoning loop. By empowering the VLM to autonomously generate gaze tokens ($\texttt{<LOOK>}$), GazeVLM establishes a top-down control mechanism over its own causal attention mask. The model dynamically dictates its focal intent, triggering a continuous suppression bias that dampens irrelevant visual features, implementing spatial selective attention and simulating foveal fixation. Once local reasoning concludes, the bias lifts, seamlessly restoring the global view. This architecture enables the model to fluidly transition between global spatial awareness and localized focal reasoning without relying on external agentic contraptions like cropping tools, or inflating the context window with additional visual tokens derived from localized visual patches. Trained with a bespoke Group Relative Policy Optimization (GRPO) procedure that rewards valid grounding, our 4B-parameter GazeVLM delivers strong high-resolution multimodal reasoning performance, surpassing state-of-the-art VLMs in its parameter class by nearly 4% and agentic multimodal pipelines built around thinking with images by more than 5% on HRBench-4k and HRBench-8k.

preprint2026arXiv

Learning Sparsifying Transforms for mmWave Communication via $\ell^4$-Norm Maximization

The high directionality of wave propagation at millimeter-wave (mmWave) carrier frequencies results in only a small number of significant transmission paths between user equipments and the basestation (BS). This sparse nature of wave propagation is revealed in the beamspace domain, which is traditionally obtained by taking the spatial discrete Fourier transform (DFT) across a uniform linear antenna array at the BS, where each DFT output is associated with a distinct beam. In recent years, beamspace processing has emerged as a promising technique to reduce baseband complexity and power consumption in all-digital massive multiuser (MU) multiple-input multiple-output (MIMO) systems operating at mmWave frequencies. However, it remains unclear whether the DFT is the optimal sparsifying transform for finite-dimensional antenna arrays. In this paper, we extend the framework of Zhai et al. for complete dictionary learning via $\ell^4$-norm maximization to the complex case in order to learn new sparsifying transforms. We provide a theoretical foundation for $\ell^4$-norm maximization and propose two suitable learning algorithms. We then utilize these algorithms (i) to assess the optimality of the DFT for sparsifying channel vectors theoretically and via simulations and (ii) to learn improved sparsifying transforms for real-world and synthetically generated channel vectors.

preprint2026arXiv

On the Complexity of Electromagnetic Far-Field Modeling

Modern wireless systems are envisioned to employ antenna architectures that not only transmit and receive electromagnetic (EM) waves, but also intentionally reflect and possibly transform incident EM waves. In this paper, we propose a mathematically rigorous framework grounded in Maxwell's equations for analyzing the complexity of EM far-field modeling of general antenna architectures. We show that-under physically meaningful assumptions-such antenna architectures exhibit limited complexity, i.e., can be modeled by finite-rank operators using finitely many parameters. Furthermore, we construct a sequence of finite-rank operators whose approximation error decays super-exponentially once the operator rank exceeds an effective bandwidth associated with the antenna architecture and the analysis frequency. These results constitute a fundamental prerequisite for the efficient and accurate modeling of general antenna architectures on digital computing platforms.

preprint2024arXiv

LoFi User Scheduling for Multiuser MIMO Wireless Systems

We propose new low-fidelity (LoFi) user equipment (UE) scheduling algorithms for multiuser multiple-input multiple-output (MIMO) wireless communication systems. The proposed methods rely on an efficient guess-and-check procedure that, given an objective function, performs paired comparisons between random subsets of UEs that should be scheduled in certain time slots. The proposed LoFi scheduling methods are computationally efficient, highly parallelizable, and gradient-free, which enables the use of almost arbitrary, non-differentiable objective functions. System simulations in a millimeter-wave (mmWave) multiuser MIMO scenario demonstrate that the proposed LoFi schedulers outperform a range of state-of-the-art user scheduling algorithms in terms of bit error-rate and/or computational complexity.

preprint2022arXiv

An Optimization-Based User Scheduling Framework for mmWave Massive MU-MIMO Systems

We propose a novel user equipment (UE) scheduling framework for millimeter-wave (mmWave) massive multiuser (MU) multiple-input multiple-output (MIMO) wireless systems. Our framework determines (sub)sets of UEs that should transmit simultaneously in a given time slot by approximately solving a nonconvex optimization problem using forward-backward splitting. Our UE scheduling framework is flexible in the sense that it (i) supports a variety of cost functions, including post-equalization mean square error and sum rate, and (ii) enables precise control over the minimum and maximum number of resources the UEs should occupy. We demonstrate the efficacy of our framework using realistic mmWave channel vectors generated with a commercial ray-tracer. We show that our UE scheduler outperforms a range of existing scheduling methods and closely approaches the performance of an exhaustive search.

preprint2022arXiv

Beam Alignment for the Cell-Free mmWave Massive MU-MIMO Uplink

Millimeter-wave (mmWave) cell-free massive multi-user (MU) multiple-input multiple-output (MIMO) systems combine the large bandwidths available at mmWave frequencies with the improved coverage of cell-free systems. However, to combat the high path loss at mmWave frequencies, user equipments (UEs) must form beams in meaningful directions, i.e., to a nearby access point (AP). At the same time, multiple UEs should avoid transmitting to the same AP to reduce MU interference. We propose an interference-aware method for beam alignment (BA) in the cell-free mmWave massive MU-MIMO uplink. In the considered scenario, the APs perform full digital receive beamforming while the UEs perform analog transmit beamforming. We evaluate our method using realistic mmWave channels from a commercial ray-tracer, showing the superiority of the proposed method over omnidirectional transmission as well as over methods that do not take MU interference into account.

preprint2022arXiv

Mitigating Smart Jammers in MU-MIMO via Joint Channel Estimation and Data Detection

Wireless systems must be resilient to jamming attacks. Existing mitigation methods require knowledge of the jammer's transmit characteristics. However, this knowledge may be difficult to acquire, especially for smart jammers that attack only specific instants during transmission in order to evade mitigation. We propose a novel method that mitigates attacks by smart jammers on massive multi-user multiple-input multiple-output (MU-MIMO) basestations (BSs). Our approach builds on recent progress in joint channel estimation and data detection (JED) and exploits the fact that a jammer cannot change its subspace within a coherence interval. Our method, called MAED (short for MitigAtion, Estimation, and Detection), uses a novel problem formulation that combines jammer estimation and mitigation, channel estimation, and data detection, instead of separating these tasks. We solve the problem approximately with an efficient iterative algorithm. Our results show that MAED effectively mitigates a wide range of smart jamming attacks without having any a priori knowledge about the attack type.

preprint2021arXiv

Blind SNR Estimation and Nonparametric Channel Denoising in Multi-Antenna mmWave Systems

We propose blind estimators for the average noise power, receive signal power, signal-to-noise ratio (SNR), and mean-square error (MSE), suitable for multi-antenna millimeter wave (mmWave) wireless systems. The proposed estimators can be computed at low complexity and solely rely on beamspace sparsity, i.e., the fact that only a small number of dominant propagation paths exist in typical mmWave channels. Our estimators can be used (i) to quickly track some of the key quantities in multi-antenna mmWave systems while avoiding additional pilot overhead and (ii) to design efficient nonparametric algorithms that require such quantities. We provide a theoretical analysis of the proposed estimators, and we demonstrate their efficacy via synthetic experiments and using a nonparametric channel-vector denoising task with realistic multi-antenna mmWave channels.

preprint2020arXiv

Adversarially robust transfer learning

Transfer learning, in which a network is trained on one task and re-purposed on another, is often used to produce neural network classifiers when data is scarce or full-scale training is too costly. When the goal is to produce a model that is not only accurate but also adversarially robust, data scarcity and computational limitations become even more cumbersome. We consider robust transfer learning, in which we transfer not only performance but also robustness from a source model to a target domain. We start by observing that robust networks contain robust feature extractors. By training classifiers on top of these feature extractors, we produce new models that inherit the robustness of their parent networks. We then consider the case of fine tuning a network by re-training end-to-end in the target domain. When using lifelong learning strategies, this process preserves the robustness of the source network while achieving high accuracy. By using such strategies, it is possible to produce accurate and robust models with little data, and without the cost of adversarial training. Additionally, we can improve the generalization of adversarially trained models, while maintaining their robustness.

preprint2020arXiv

Algorithm and VLSI Design for 1-bit Data Detection in Massive MIMO-OFDM

The use of low-resolution data converters in the radio-frequency (RF) chains of all-digital massive multiple-input multiple-output (MIMO) basestations promises significant reductions in power consumption, hardware costs, and interconnect bandwidth. We propose a quantization-aware data-detection algorithm which mitigates the performance loss of 1-bit quantized massive MIMO orthogonal frequency-division multiplexing (OFDM) systems. Since the system performance heavily depends on the quality of channel estimates, we also develop a nonlinear 1-bit channel estimation algorithm that builds upon the proposed data detection algorithm. We show that the proposed algorithms significantly outperform linear data detectors and channel estimators in terms of bit error rate. For the proposed nonlinear data detection algorithm, we develop a very large scale integration (VLSI) architecture and present implementation results on a Xilinx Virtex-7 field programmable gate array (FPGA). Our implementation results are, to the best of our knowledge, the first for 1-bit massive MU-MIMO-OFDM systems and demonstrate comparable hardware efficiency with respect to state-of-the-art linear data detectors designed for systems with high-resolution data converters, while achieving lower bit error rate.

preprint2020arXiv

Analog vs. Digital Spatial Transforms: A Throughput, Power, and Area Comparison

Spatial linear transforms that process multiple parallel analog signals to simplify downstream signal processing find widespread use in multi-antenna communication systems, machine learning inference, data compression, audio and ultrasound applications, among many others. In the past, a wide range of mixed-signal as well as digital spatial transform circuits have been proposed---it is, however, a longstanding question whether analog or digital transforms are superior in terms of throughput, power, and area. In this paper, we focus on Hadamard transforms and perform a systematic comparison of state-of-the-art analog and digital circuits implementing spatial transforms in the same 65\,nm CMOS technology. We analyze the trade-offs between throughput, power, and area, and we identify regimes in which mixed-signal or digital Hadamard transforms are preferable. Our comparison reveals that (i) there is no clear winner and (ii) analog-to-digital conversion is often dominating area and energy efficiency---and not the spatial transform.

preprint2020arXiv

Are adversarial examples inevitable?

A wide range of defenses have been proposed to harden neural networks against adversarial attacks. However, a pattern has emerged in which the majority of adversarial defenses are quickly broken by new attacks. Given the lack of success at generating robust defenses, we are led to ask a fundamental question: Are adversarial attacks inevitable? This paper analyzes adversarial examples from a theoretical perspective, and identifies fundamental bounds on the susceptibility of a classifier to adversarial attacks. We show that, for certain classes of problems, adversarial examples are inescapable. Using experiments, we explore the implications of theoretical guarantees for real-world problems and discuss how factors such as dimensionality and image complexity limit a classifier's robustness against adversarial examples.

preprint2020arXiv

Beamspace Channel Estimation for Massive MIMO mmWave Systems: Algorithm and VLSI Design

Millimeter-wave (mmWave) communication in combination with massive multiuser multiple-input multiple-output (MU-MIMO) enables high-bandwidth data transmission to multiple users in the same time-frequency resource. The strong path loss of wave propagation at such high frequencies necessitates accurate channel state information to ensure reliable data transmission. We propose a novel channel estimation algorithm called BEAmspace CHannel EStimation (BEACHES), which leverages the fact that wave propagation at mmWave frequencies is predominantly directional. BEACHES adaptively denoises the channel vectors in the beamspace domain using an adaptive shrinkage procedure that relies on Stein's unbiased risk estimator (SURE). Simulation results for line-of-sight (LoS) and non-LoS mmWave channels reveal that BEACHES performs on par with state-of-the-art channel estimation methods while requiring orders-of-magnitude lower complexity. To demonstrate the effectiveness of BEACHES in practice, we develop a very large-scale integration (VLSI) architecture and provide field-programmable gate array (FPGA) implementation results. Our results show that adaptive channel denoising can be performed at high throughput and in a hardware-friendly manner for massive MU-MIMO mmWave systems with hundreds of antennas.

preprint2020arXiv

Finite-Alphabet MMSE Equalization for All-Digital Massive MU-MIMO mmWave Communication

We propose finite-alphabet equalization, a new paradigm that restricts the entries of the spatial equalization matrix to low-resolution numbers, enabling high-throughput, low-power, and low-cost hardware equalizers. To minimize the performance loss of this paradigm, we introduce FAME, short for finite-alphabet minimum mean-square error (MMSE) equalization, which is able to significantly outperform a naive quantization of the linear MMSE matrix. We develop efficient algorithms to approximately solve the NP-hard FAME problem and showcase that near-optimal performance can be achieved with equalization coefficients quantized to only 1-3 bits for massive multi-user multiple-input multiple-output (MU-MIMO) millimeter-wave (mmWave) systems. We provide very-large scale integration (VLSI) results that demonstrate a reduction in equalization power and area by at least a factor of 3.9x and 5.8x, respectively.

preprint2020arXiv

Finite-Alphabet Wiener Filter Precoding for mmWave Massive MU-MIMO Systems

Power consumption of multi-user (MU) precoding is a major concern in all-digital massive MU multiple-input multiple-output (MIMO) base-stations with hundreds of antenna elements operating at millimeter-wave (mmWave) frequencies. We propose to replace part of the linear Wiener filter (WF) precoding matrix by a finite-alphabet WF precoding (FAWP) matrix, which enables the use of low-precision hardware that consumes low power and area. To minimize the performance loss of our approach, we present methods that efficiently compute FAWP matrices that best mimic the WF precoder. Our results show that FAWP matrices approach infinite-precision error-rate and error-vector magnitude performance with only 3-bit precoding weights, even when operating in realistic mmWave channels. Hence, FAWP is a promising approach to substantially reduce power consumption and silicon area in all-digital mmWave massive MU-MIMO systems.

preprint2020arXiv

Headless Horseman: Adversarial Attacks on Transfer Learning Models

Transfer learning facilitates the training of task-specific classifiers using pre-trained models as feature extractors. We present a family of transferable adversarial attacks against such classifiers, generated without access to the classification head; we call these \emph{headless attacks}. We first demonstrate successful transfer attacks against a victim network using \textit{only} its feature extractor. This motivates the introduction of a label-blind adversarial attack. This transfer attack method does not require any information about the class-label space of the victim. Our attack lowers the accuracy of a ResNet18 trained on CIFAR10 by over 40\%.

preprint2020arXiv

High-Bandwidth Spatial Equalization for mmWave Massive MU-MIMO with Processing-In-Memory

All-digital basestation (BS) architectures enable superior spectral efficiency compared to hybrid solutions in massive multi-user MIMO systems. However, supporting large bandwidths with all-digital architectures at mmWave frequencies is challenging as traditional baseband processing would result in excessively high power consumption and large silicon area. The recently-proposed concept of finite-alphabet equalization is able to address both of these issues by using equalization matrices that contain low-resolution entries to lower the power and complexity of high-throughput matrix-vector products in hardware. In this paper, we explore two different finite-alphabet equalization hardware implementations that tightly integrate the memory and processing elements: (i) a parallel array of multiply-accumulate (MAC) units and (ii) a bit-serial processing-in-memory (PIM) architecture. Our all-digital VLSI implementation results in 28nm CMOS show that the bit-serial PIM architecture reduces the area and power consumption up to a factor of 2x and 3x, respectively, when compared to a parallel MAC array that operates at the same throughput.

preprint2020arXiv

Identifying Unused RF Channels Using Least Matching Pursuit

Cognitive radio aims at identifying unused radio-frequency (RF) bands with the goal of re-using them opportunistically for other services. While compressive sensing (CS) has been used to identify strong signals (or interferers) in the RF spectrum from sub-Nyquist measurements, identifying unused frequencies from CS measurements appears to be uncharted territory. In this paper, we propose a novel method for identifying unused RF bands using an algorithm we call least matching pursuit (LMP). We present a sufficient condition for which LMP is guaranteed to identify unused frequency bands and develop an improved algorithm that is inspired by our theoretical result. We perform simulations for a CS-based RF whitespace detection task in order to demonstrate that LMP is able to outperform black-box approaches that build on deep neural networks.

preprint2020arXiv

MSE-Optimal Neural Network Initialization via Layer Fusion

Deep neural networks achieve state-of-the-art performance for a range of classification and inference tasks. However, the use of stochastic gradient descent combined with the nonconvexity of the underlying optimization problems renders parameter learning susceptible to initialization. To address this issue, a variety of methods that rely on random parameter initialization or knowledge distillation have been proposed in the past. In this paper, we propose FuseInit, a novel method to initialize shallower networks by fusing neighboring layers of deeper networks that are trained with random initialization. We develop theoretical results and efficient algorithms for mean-square error (MSE)-optimal fusion of neighboring dense-dense, convolutional-dense, and convolutional-convolutional layers. We show experiments for a range of classification and regression datasets, which suggest that deeper neural networks are less sensitive to initialization and shallower networks can perform better (sometimes as well as their deeper counterparts) if initialized with FuseInit.

preprint2020arXiv

Soft-Output Finite Alphabet Equalization for mmWAVE Massive MIMO

Next-generation wireless systems are expected to combine millimeter-wave (mmWave) and massive multi-user multiple-input multiple-output (MU-MIMO) technologies to deliver high data-rates. These technologies require the basestations (BSs) to process high-dimensional data at extreme rates, which results in high power dissipation and system costs. Finite-alphabet equalization has been proposed recently to reduce the power consumption and silicon area of uplink spatial equalization circuitry at the BS by coarsely quantizing the equalization matrix. In this work, we improve upon finite-alphabet equalization by performing unbiased estimation and soft-output computation for coded systems. By simulating a massive MU-MIMO system that uses orthogonal frequency-division multiplexing and per-user convolutional coding, we show that soft-output finite-alphabet equalization delivers competitive error-rate performance using only 1 to 3 bits per entry of the equalization matrix, even for challenging mmWave channels.

preprint2020arXiv

Sparse Beamspace Equalization for Massive MU-MIMO mmWave Systems

We propose equalization-based data detection algorithms for all-digital millimeter-wave (mmWave) massive multiuser multiple-input multiple-out (MU-MIMO) systems that exploit sparsity in the beamspace domain to reduce complexity. We provide a condition on the number of users, basestation antennas, and channel sparsity for which beamspace equalization can be less complex than conventional antenna-domain processing. We evaluate the performance-complexity trade-offs of existing and new beamspace equalization algorithms using simulations with realistic mmWave channel models. Our results reveal that one of our proposed beamspace equalization algorithms achieves up to 8x complexity reduction under line-of-sight conditions, assuming a sufficiently large number of transmissions within the channel coherence interval.

preprint2020arXiv

Sparsity-Adaptive Beamspace Channel Estimation for 1-Bit mmWave Massive MIMO Systems

We propose sparsity-adaptive beamspace channel estimation algorithms that improve accuracy for 1-bit data converters in all-digital millimeter-wave (mmWave) massive multiple-input multiple-output (MIMO) basestations. Our algorithms include a tuning stage based on Stein's unbiased risk estimate (SURE) that automatically selects optimal denoising parameters depending on the instantaneous channel conditions. Simulation results with line-of-sight (LoS) and non-LoS mmWave massive MIMO channel models show that our algorithms improve channel estimation accuracy with 1-bit measurements in a computationally-efficient manner.

preprint2020arXiv

WrapNet: Neural Net Inference with Ultra-Low-Resolution Arithmetic

Low-resolution neural networks represent both weights and activations with few bits, drastically reducing the multiplication complexity. Nonetheless, these products are accumulated using high-resolution (typically 32-bit) additions, an operation that dominates the arithmetic complexity of inference when using extreme quantization (e.g., binary weights). To further optimize inference, we propose a method that adapts neural networks to use low-resolution (8-bit) additions in the accumulators, achieving classification accuracy comparable to their 32-bit counterparts. We achieve resilience to low-resolution accumulation by inserting a cyclic activation layer, as well as an overflow penalty regularizer. We demonstrate the efficacy of our approach on both software and hardware platforms.

preprint2016arXiv

A Field Guide to Forward-Backward Splitting with a FASTA Implementation

Non-differentiable and constrained optimization play a key role in machine learning, signal and image processing, communications, and beyond. For high-dimensional minimization problems involving large datasets or many unknowns, the forward-backward splitting method provides a simple, practical solver. Despite its apparently simplicity, the performance of the forward-backward splitting is highly sensitive to implementation details. This article is an introductory review of forward-backward splitting with a special emphasis on practical implementation concerns. Issues like stepsize selection, acceleration, stopping conditions, and initialization are considered. Numerical experiments are used to compare the effectiveness of different approaches. Many variations of forward-backward splitting are implemented in the solver FASTA (short for Fast Adaptive Shrinkage/Thresholding Algorithm). FASTA provides a simple interface for applying forward-backward splitting to a broad range of problems.

preprint2016arXiv

An Empirical Study of ADMM for Nonconvex Problems

The alternating direction method of multipliers (ADMM) is a common optimization tool for solving constrained and non-differentiable problems. We provide an empirical study of the practical performance of ADMM on several nonconvex applications, including l0 regularized linear regression, l0 regularized image denoising, phase retrieval, and eigenvector computation. Our experiments suggest that ADMM performs well on a broad class of non-convex problems. Moreover, recently proposed adaptive ADMM methods, which automatically tune penalty parameters as the method runs, can improve algorithm efficiency and solution quality compared to ADMM with a non-tuned penalty.

preprint2016arXiv

Biconvex Relaxation for Semidefinite Programming in Computer Vision

Semidefinite programming is an indispensable tool in computer vision, but general-purpose solvers for semidefinite programs are often too slow and memory intensive for large-scale problems. We propose a general framework to approximately solve large-scale semidefinite problems (SDPs) at low complexity. Our approach, referred to as biconvex relaxation (BCR), transforms a general SDP into a specific biconvex optimization problem, which can then be solved in the original, low-dimensional variable space at low complexity. The resulting biconvex problem is solved using an efficient alternating minimization (AM) procedure. Since AM has the potential to get stuck in local minima, we propose a general initialization scheme that enables BCR to start close to a global optimum - this is key for our algorithm to quickly converge to optimal or near-optimal solutions. We showcase the efficacy of our approach on three applications in computer vision, namely segmentation, co-segmentation, and manifold metric learning. BCR achieves solution quality comparable to state-of-the-art SDP methods with speedups between 4X and 35X. At the same time, BCR handles a more general set of SDPs than previous approaches, which are more specialized.

preprint2016arXiv

Data Detection in Large Multi-Antenna Wireless Systems via Approximate Semidefinite Relaxation

Practical data detectors for future wireless systems with hundreds of antennas at the base station must achieve high throughput and low error rate at low complexity. Since the complexity of maximum-likelihood (ML) data detection is prohibitive for such large wireless systems, approximate methods are necessary. In this paper, we propose a novel data detection algorithm referred to as Triangular Approximate SEmidefinite Relaxation (TASER), which is suitable for two application scenarios: (i) coherent data detection in large multi-user multiple-input multiple-output (MU-MIMO) wireless systems and (ii) joint channel estimation and data detection in large single-input multiple-output (SIMO) wireless systems. For both scenarios, we show that TASER achieves near-ML error-rate performance at low complexity by relaxing the associated ML-detection problems into a semidefinite program, which we solve approximately using a preconditioned forward-backward splitting procedure. Since the resulting problem is non-convex, we provide convergence guarantees for our algorithm. To demonstrate the efficacy of TASER in practice, we design a systolic architecture that enables our algorithm to achieve high throughput at low hardware complexity, and we develop reference field-programmable gate array (FPGA) and application-specific integrated circuit (ASIC) designs for various antenna configurations.

preprint2016arXiv

Estimating Sparse Signals with Smooth Support via Convex Programming and Block Sparsity

Conventional algorithms for sparse signal recovery and sparse representation rely on $l_1$-norm regularized variational methods. However, when applied to the reconstruction of $\textit{sparse images}$, i.e., images where only a few pixels are non-zero, simple $l_1$-norm-based methods ignore potential correlations in the support between adjacent pixels. In a number of applications, one is interested in images that are not only sparse, but also have a support with smooth (or contiguous) boundaries. Existing algorithms that take into account such a support structure mostly rely on non-convex methods and---as a consequence---do not scale well to high-dimensional problems and/or do not converge to global optima. In this paper, we explore the use of new block $l_1$-norm regularizers, which enforce image sparsity while simultaneously promoting smooth support structure. By exploiting the convexity of our regularizers, we develop new computationally-efficient recovery algorithms that guarantee global optimality. We demonstrate the efficacy of our regularizers on a variety of imaging tasks including compressive image recovery, image restoration, and robust PCA.

preprint2016arXiv

High-Throughput Data Detection for Massive MU-MIMO-OFDM using Coordinate Descent

Data detection in massive multi-user (MU) multiple-input multiple-output (MIMO) wireless systems is among the most critical tasks due to the excessively high implementation complexity. In this paper, we propose a novel, equalization-based soft-output data-detection algorithm and corresponding reference FPGA designs for wideband massive MU-MIMO systems that use orthogonal frequency-division multiplexing (OFDM). Our data-detection algorithm performs approximate minimum mean-square error (MMSE) or box-constrained equalization using coordinate descent. We deploy a variety of algorithm-level optimizations that enable near-optimal error-rate performance at low implementation complexity, even for systems with hundreds of base-station (BS) antennas and thousands of subcarriers. We design a parallel VLSI architecture that uses pipeline interleaving and can be parametrized at design time to support various antenna configurations. We develop reference FPGA designs for massive MU-MIMO-OFDM systems and provide an extensive comparison to existing designs in terms of implementation complexity, throughput, and error-rate performance. For a 128 BS antenna, 8 user massive MU-MIMO-OFDM system, our FPGA design outperforms the next-best implementation by more than 2.6x in terms of throughput per FPGA look-up tables.

preprint2016arXiv

Quantized Massive MU-MIMO-OFDM Uplink

Coarse quantization at the base station (BS) of a massive multi-user (MU) multiple-input multiple-output (MIMO) wireless system promises significant power and cost savings. Coarse quantization also enables significant reductions of the raw analog-to-digital converter (ADC) data that must be transferred from a spatially-separated antenna array to the baseband processing unit. The theoretical limits as well as practical transceiver algorithms for such quantized MU-MIMO systems operating over frequency-flat, narrowband channels have been studied extensively. However, the practically relevant scenario where such communication systems operate over frequency-selective, wideband channels is less well understood. This paper investigates the uplink performance of a quantized massive MU-MIMO system that deploys orthogonal frequency-division multiplexing (OFDM) for wideband communication. We propose new algorithms for quantized maximum a-posteriori (MAP) channel estimation and data detection, and we study the associated performance/quantization trade-offs. Our results demonstrate that coarse quantization (e.g., four to six bits, depending on the ratio between the number of BS antennas and the number of users) in massive MU-MIMO-OFDM systems entails virtually no performance loss compared to the infinite-precision case at no additional cost in terms of baseband processing complexity.

preprint2015arXiv

Democratic Representations

Minimization of the $\ell_{\infty}$ (or maximum) norm subject to a constraint that imposes consistency to an underdetermined system of linear equations finds use in a large number of practical applications, including vector quantization, approximate nearest neighbor search, peak-to-average power ratio (or "crest factor") reduction in communication systems, and peak force minimization in robotics and control. This paper analyzes the fundamental properties of signal representations obtained by solving such a convex optimization problem. We develop bounds on the maximum magnitude of such representations using the uncertainty principle (UP) introduced by Lyubarskii and Vershynin, and study the efficacy of $\ell_{\infty}$-norm-based dynamic range reduction. Our analysis shows that matrices satisfying the UP, such as randomly subsampled Fourier or i.i.d. Gaussian matrices, enable the computation of what we call democratic representations, whose entries all have small and similar magnitude, as well as low dynamic range. To compute democratic representations at low computational complexity, we present two new, efficient convex optimization algorithms. We finally demonstrate the efficacy of democratic representations for dynamic range reduction in a DVB-T2-based broadcast system.

preprint2015arXiv

Linear Large-Scale MIMO Data Detection for 5G Multi-Carrier Waveform Candidates

Fifth generation (5G) wireless systems are expected to combine emerging transmission technologies, such as large-scale multiple-input multiple-output (MIMO) and non-orthogonal multi-carrier waveforms, to improve the spectral efficiency and to reduce out-of-band (OOB) emissions. This paper investigates the efficacy of two promising multi-carrier waveforms that reduce OOB emissions in combination with large-scale MIMO, namely filter bank multi-carrier (FBMC) and generalized frequency division multiplexing (GFDM). We develop novel, low-complexity data detection algorithms for both of these waveforms. We investigate the associated performance/complexity trade-offs in the context of large-scale MIMO, and we study the peak-to-average power ratio (PAPR). Our results show that reducing the OOB emissions with FBMC and GFDM leads to higher computational complexity and PAPR compared to that of orthogonal frequency-division multiplexing (OFDM) and single-carrier frequency division multiple access (SC-FDMA).

preprint2015arXiv

One-Bit Massive MIMO: Channel Estimation and High-Order Modulations

We investigate the information-theoretic throughout achievable on a fading communication link when the receiver is equipped with one-bit analog-to-digital converters (ADCs). The analysis is conducted for the setting where neither the transmitter nor the receiver have a priori information on the realization of the fading channels. This means that channel-state information needs to be acquired at the receiver on the basis of the one-bit quantized channel outputs. We show that least-squares (LS) channel estimation combined with joint pilot and data processing is capacity achieving in the single-user, single-receive-antenna case. We also investigate the achievable uplink throughput in a massive multiple-input multiple-output system where each element of the antenna array at the receiver base-station feeds a one-bit ADC. We show that LS channel estimation and maximum-ratio combining are sufficient to support both multiuser operation and the use of high-order constellations. This holds in spite of the severe nonlinearity introduced by the one-bit ADCs.

preprint2015arXiv

Optimal Large-MIMO Data Detection with Transmit Impairments

Real-world transceiver designs for multiple-input multiple-output (MIMO) wireless communication systems are affected by a number of hardware impairments that already appear at the transmit side, such as amplifier non-linearities, quantization artifacts, and phase noise. While such transmit-side impairments are routinely ignored in the data-detection literature, they often limit reliable communication in practical systems. In this paper, we present a novel data-detection algorithm, referred to as large-MIMO approximate message passing with transmit impairments (short LAMA-I), which takes into account a broad range of transmit-side impairments in wireless systems with a large number of transmit and receive antennas. We provide conditions in the large-system limit for which LAMA-I achieves the error-rate performance of the individually-optimal (IO) data detector. We furthermore demonstrate that LAMA-I achieves near-IO performance at low computational complexity in realistic, finite dimensional large-MIMO systems.

preprint2015arXiv

Optimality of Large MIMO Detection via Approximate Message Passing

Optimal data detection in multiple-input multiple-output (MIMO) communication systems with a large number of antennas at both ends of the wireless link entails prohibitive computational complexity. In order to reduce the computational complexity, a variety of sub-optimal detection algorithms have been proposed in the literature. In this paper, we analyze the optimality of a novel data-detection method for large MIMO systems that relies on approximate message passing (AMP). We show that our algorithm, referred to as individually-optimal (IO) large-MIMO AMP (short IO-LAMA), is able to perform IO data detection given certain conditions on the MIMO system and the constellation set (e.g., QAM or PSK) are met.

preprint2015arXiv

Recovery of Signals with Low Density

Sparse signals (i.e., vectors with a small number of non-zero entries) build the foundation of most kernel (or nullspace) results, uncertainty relations, and recovery guarantees in the sparse signal processing and compressive sensing literature. In this paper, we introduce a novel signal-density measure that extends the common notion of sparsity to non-sparse signals whose entries' magnitudes decay rapidly. By taking into account such magnitude information, we derive a more general and less restrictive kernel result and uncertainty relation. Furthermore, we demonstrate the effectiveness of the proposed signal-density measure by showing that orthogonal matching pursuit (OMP) provably recovers low-density signals with up to 2$\times$ more non-zero coefficients compared to that guaranteed by standard results for sparse signals.

preprint2015arXiv

SPRITE: A Response Model For Multiple Choice Testing

Item response theory (IRT) models for categorical response data are widely used in the analysis of educational data, computerized adaptive testing, and psychological surveys. However, most IRT models rely on both the assumption that categories are strictly ordered and the assumption that this ordering is known a priori. These assumptions are impractical in many real-world scenarios, such as multiple-choice exams where the levels of incorrectness for the distractor categories are often unknown. While a number of results exist on IRT models for unordered categorical data, they tend to have restrictive modeling assumptions that lead to poor data fitting performance in practice. Furthermore, existing unordered categorical models have parameters that are difficult to interpret. In this work, we propose a novel methodology for unordered categorical IRT that we call SPRITE (short for stochastic polytomous response item model) that: (i) analyzes both ordered and unordered categories, (ii) offers interpretable outputs, and (iii) provides improved data fitting compared to existing models. We compare SPRITE to existing item response models and demonstrate its efficacy on both synthetic and real-world educational datasets.

preprint2015arXiv

Video Compressive Sensing for Spatial Multiplexing Cameras using Motion-Flow Models

Spatial multiplexing cameras (SMCs) acquire a (typically static) scene through a series of coded projections using a spatial light modulator (e.g., a digital micro-mirror device) and a few optical sensors. This approach finds use in imaging applications where full-frame sensors are either too expensive (e.g., for short-wave infrared wavelengths) or unavailable. Existing SMC systems reconstruct static scenes using techniques from compressive sensing (CS). For videos, however, existing acquisition and recovery methods deliver poor quality. In this paper, we propose the CS multi-scale video (CS-MUVI) sensing and recovery framework for high-quality video acquisition and recovery using SMCs. Our framework features novel sensing matrices that enable the efficient computation of a low-resolution video preview, while enabling high-resolution video recovery using convex optimization. To further improve the quality of the reconstructed videos, we extract optical-flow estimates from the low-resolution previews and impose them as constraints in the recovery procedure. We demonstrate the efficacy of our CS-MUVI framework for a host of synthetic and real measured SMC video data, and we show that high-quality videos can be recovered at roughly $60\times$ compression.

preprint2014arXiv

Conjugate Gradient-based Soft-Output Detection and Precoding in Massive MIMO Systems

Massive multiple-input multiple-output (MIMO) promises improved spectral efficiency, coverage, and range, compared to conventional (small-scale) MIMO wireless systems. Unfortunately, these benefits come at the cost of significantly increased computational complexity, especially for systems with realistic antenna configurations. To reduce the complexity of data detection (in the uplink) and precoding (in the downlink) in massive MIMO systems, we propose to use conjugate gradient (CG) methods. While precoding using CG is rather straightforward, soft-output minimum mean-square error (MMSE) detection requires the computation of the post-equalization signal-to-interference-and-noise-ratio (SINR). To enable CG for soft-output detection, we propose a novel way of computing the SINR directly within the CG algorithm at low complexity. We investigate the performance/complexity trade-offs associated with CG-based soft-output detection and precoding, and we compare it to exact and approximate methods. Our results reveal that the proposed method outperforms existing algorithms for massive MIMO systems with realistic antenna configurations.

preprint2014arXiv

Large-Scale MIMO Detection for 3GPP LTE: Algorithms and FPGA Implementations

Large-scale (or massive) multiple-input multiple-output (MIMO) is expected to be one of the key technologies in next-generation multi-user cellular systems, based on the upcoming 3GPP LTE Release 12 standard, for example. In this work, we propose - to the best of our knowledge - the first VLSI design enabling high-throughput data detection in single-carrier frequency-division multiple access (SC-FDMA)-based large-scale MIMO systems. We propose a new approximate matrix inversion algorithm relying on a Neumann series expansion, which substantially reduces the complexity of linear data detection. We analyze the associated error, and we compare its performance and complexity to those of an exact linear detector. We present corresponding VLSI architectures, which perform exact and approximate soft-output detection for large-scale MIMO systems with various antenna/user configurations. Reference implementation results for a Xilinx Virtex-7 XC7VX980T FPGA show that our designs are able to achieve more than 600 Mb/s for a 128 antenna, 8 user 3GPP LTE-based large-scale MIMO system. We finally provide a performance/complexity trade-off comparison using the presented FPGA designs, which reveals that the detector circuit of choice is determined by the ratio between BS antennas and users, as well as the desired error-rate performance.

preprint2014arXiv

Quantized Matrix Completion for Personalized Learning

The recently proposed SPARse Factor Analysis (SPARFA) framework for personalized learning performs factor analysis on ordinal or binary-valued (e.g., correct/incorrect) graded learner responses to questions. The underlying factors are termed "concepts" (or knowledge components) and are used for learning analytics (LA), the estimation of learner concept-knowledge profiles, and for content analytics (CA), the estimation of question-concept associations and question difficulties. While SPARFA is a powerful tool for LA and CA, it requires a number of algorithm parameters (including the number of concepts), which are difficult to determine in practice. In this paper, we propose SPARFA-Lite, a convex optimization-based method for LA that builds on matrix completion, which only requires a single algorithm parameter and enables us to automatically identify the required number of concepts. Using a variety of educational datasets, we demonstrate that SPARFALite (i) achieves comparable performance in predicting unobserved learner responses to existing methods, including item response theory (IRT) and SPARFA, and (ii) is computationally more efficient.

preprint2014arXiv

Tag-Aware Ordinal Sparse Factor Analysis for Learning and Content Analytics

Machine learning offers novel ways and means to design personalized learning systems wherein each student's educational experience is customized in real time depending on their background, learning goals, and performance to date. SPARse Factor Analysis (SPARFA) is a novel framework for machine learning-based learning analytics, which estimates a learner's knowledge of the concepts underlying a domain, and content analytics, which estimates the relationships among a collection of questions and those concepts. SPARFA jointly learns the associations among the questions and the concepts, learner concept knowledge profiles, and the underlying question difficulties, solely based on the correct/incorrect graded responses of a population of learners to a collection of questions. In this paper, we extend the SPARFA framework significantly to enable: (i) the analysis of graded responses on an ordinal scale (partial credit) rather than a binary scale (correct/incorrect); (ii) the exploitation of tags/labels for questions that partially describe the question{concept associations. The resulting Ordinal SPARFA-Tag framework greatly enhances the interpretability of the estimated concepts. We demonstrate using real educational data that Ordinal SPARFA-Tag outperforms both SPARFA and existing collaborative filtering techniques in predicting missing learner responses.

preprint2013arXiv

Joint Topic Modeling and Factor Analysis of Textual Information and Graded Response Data

Modern machine learning methods are critical to the development of large-scale personalized learning systems that cater directly to the needs of individual learners. The recently developed SPARse Factor Analysis (SPARFA) framework provides a new statistical model and algorithms for machine learning-based learning analytics, which estimate a learner's knowledge of the latent concepts underlying a domain, and content analytics, which estimate the relationships among a collection of questions and the latent concepts. SPARFA estimates these quantities given only the binary-valued graded responses to a collection of questions. In order to better interpret the estimated latent concepts, SPARFA relies on a post-processing step that utilizes user-defined tags (e.g., topics or keywords) available for each question. In this paper, we relax the need for user-defined tags by extending SPARFA to jointly process both graded learner responses and the text of each question and its associated answer(s) or other feedback. Our purely data-driven approach (i) enhances the interpretability of the estimated latent concepts without the need of explicitly generating a set of tags or performing a post-processing step, (ii) improves the prediction performance of SPARFA, and (iii) scales to large test/assessments where human annotation would prove burdensome. We demonstrate the efficacy of the proposed approach on two real educational datasets.

preprint2013arXiv

Maximin Analysis of Message Passing Algorithms for Recovering Block Sparse Signals

We consider the problem of recovering a block (or group) sparse signal from an underdetermined set of random linear measurements, which appear in compressed sensing applications such as radar and imaging. Recent results of Donoho, Johnstone, and Montanari have shown that approximate message passing (AMP) in combination with Stein's shrinkage outperforms group LASSO for large block sizes. In this paper, we prove that, for a fixed block size and in the strong undersampling regime (i.e., having very few measurements compared to the ambient dimension), AMP cannot improve upon group LASSO, thereby complementing the results of Donoho et al.

preprint2013arXiv

Sparse Factor Analysis for Learning and Content Analytics

We develop a new model and algorithms for machine learning-based learning analytics, which estimate a learner's knowledge of the concepts underlying a domain, and content analytics, which estimate the relationships among a collection of questions and those concepts. Our model represents the probability that a learner provides the correct response to a question in terms of three factors: their understanding of a set of underlying concepts, the concepts involved in each question, and each question's intrinsic difficulty. We estimate these factors given the graded responses to a collection of questions. The underlying estimation problem is ill-posed in general, especially when only a subset of the questions are answered. The key observation that enables a well-posed solution is the fact that typical educational domains of interest involve only a small number of key concepts. Leveraging this observation, we develop both a bi-convex maximum-likelihood and a Bayesian solution to the resulting SPARse Factor Analysis (SPARFA) problem. We also incorporate user-defined tags on questions to facilitate the interpretability of the estimated factors. Experiments with synthetic and real-world data demonstrate the efficacy of our approach. Finally, we make a connection between SPARFA and noisy, binary-valued (1-bit) dictionary learning that is of independent interest.

preprint2013arXiv

Stable Restoration and Separation of Approximately Sparse Signals

This paper develops new theory and algorithms to recover signals that are approximately sparse in some general dictionary (i.e., a basis, frame, or over-/incomplete matrix) but corrupted by a combination of interference having a sparse representation in a second general dictionary and measurement noise. The algorithms and analytical recovery conditions consider varying degrees of signal and interference support-set knowledge. Particular applications covered by the proposed framework include the restoration of signals impaired by impulse noise, narrowband interference, or saturation/clipping, as well as image in-painting, super-resolution, and signal separation. Two application examples for audio and image restoration demonstrate the efficacy of the approach.

preprint2013arXiv

Time-varying Learning and Content Analytics via Sparse Factor Analysis

We propose SPARFA-Trace, a new machine learning-based framework for time-varying learning and content analytics for education applications. We develop a novel message passing-based, blind, approximate Kalman filter for sparse factor analysis (SPARFA), that jointly (i) traces learner concept knowledge over time, (ii) analyzes learner concept knowledge state transitions (induced by interacting with learning resources, such as textbook sections, lecture videos, etc, or the forgetting effect), and (iii) estimates the content organization and intrinsic difficulty of the assessment questions. These quantities are estimated solely from binary-valued (correct/incorrect) graded learner response data and a summary of the specific actions each learner performs (e.g., answering a question or studying a learning resource) at each time instance. Experimental results on two online course datasets demonstrate that SPARFA-Trace is capable of tracing each learner's concept knowledge evolution over time, as well as analyzing the quality and content organization of learning resources, the question-concept associations, and the question intrinsic difficulties. Moreover, we show that SPARFA-Trace achieves comparable or better performance in predicting unobserved learner responses than existing collaborative filtering and knowledge tracing approaches for personalized education.

preprint2012arXiv

Data Mapping for Unreliable Memories

Future digital signal processing (DSP) systems must provide robustness on algorithm and application level to the presence of reliability issues that come along with corresponding implementations in modern semiconductor process technologies. In this paper, we address this issue by investigating the impact of unreliable memories on general DSP systems. In particular, we propose a novel framework to characterize the effects of unreliable memories, which enables us to devise novel methods to mitigate the associated performance loss. We propose to deploy specifically designed data representations, which have the capability of substantially improving the system reliability compared to that realized by conventional data representations used in digital integrated circuits, such as 2s complement or sign-magnitude number formats. To demonstrate the efficacy of the proposed framework, we analyze the impact of unreliable memories on coded communication systems, and we show that the deployment of optimized data representations substantially improves the error-rate performance of such systems.

preprint2012arXiv

PAR-Aware Large-Scale Multi-User MIMO-OFDM Downlink

We investigate an orthogonal frequency-division multiplexing (OFDM)-based downlink transmission scheme for large-scale multi-user (MU) multiple-input multiple-output (MIMO) wireless systems. The use of OFDM causes a high peak-to-average (power) ratio (PAR), which necessitates expensive and power-inefficient radio-frequency (RF) components at the base station. In this paper, we present a novel downlink transmission scheme, which exploits the massive degrees-of-freedom available in large-scale MU-MIMO-OFDM systems to achieve low PAR. Specifically, we propose to jointly perform MU precoding, OFDM modulation, and PAR reduction by solving a convex optimization problem. We develop a corresponding fast iterative truncation algorithm (FITRA) and show numerical results to demonstrate tremendous PAR-reduction capabilities. The significantly reduced linearity requirements eventually enable the use of low-cost RF components for the large-scale MU-MIMO-OFDM downlink.

preprint2012arXiv

Probabilistic Recovery Guarantees for Sparsely Corrupted Signals

We consider the recovery of sparse signals subject to sparse interference, as introduced in Studer et al., IEEE Trans. IT, 2012. We present novel probabilistic recovery guarantees for this framework, covering varying degrees of knowledge of the signal and interference support, which are relevant for a large number of practical applications. Our results assume that the sparsifying dictionaries are characterized by coherence parameters and we require randomness only in the signal and/or interference. The obtained recovery guarantees show that one can recover sparsely corrupted signals with overwhelming probability, even if the sparsity of both the signal and interference scale (near) linearly with the number of measurements.

preprint2012arXiv

Sparse Signal Separation in Redundant Dictionaries

We formulate a unified framework for the separation of signals that are sparse in "morphologically" different redundant dictionaries. This formulation incorporates the so-called "analysis" and "synthesis" approaches as special cases and contains novel hybrid setups. We find corresponding coherence-based recovery guarantees for an l1-norm based separation algorithm. Our results recover those reported in Studer and Baraniuk, ACHA, submitted, for the synthesis setting, provide new recovery guarantees for the analysis setting, and form a basis for comparing performance in the analysis and synthesis settings. As an aside our findings complement the D-RIP recovery results reported in Candès et al., ACHA, 2011, for the "analysis" signal recovery problem: minimize_x ||Ψx||_1 subject to ||y - Ax||_2 \leq ε, by delivering corresponding coherence-based recovery results.

preprint2011arXiv

Recovery of Sparsely Corrupted Signals

We investigate the recovery of signals exhibiting a sparse representation in a general (i.e., possibly redundant or incomplete) dictionary that are corrupted by additive noise admitting a sparse representation in another general dictionary. This setup covers a wide range of applications, such as image inpainting, super-resolution, signal separation, and recovery of signals that are impaired by, e.g., clipping, impulse noise, or narrowband interference. We present deterministic recovery guarantees based on a novel uncertainty relation for pairs of general dictionaries and we provide corresponding practicable recovery algorithms. The recovery guarantees we find depend on the signal and noise sparsity levels, on the coherence parameters of the involved dictionaries, and on the amount of prior knowledge about the signal and noise support sets.

preprint2010arXiv

MIMO Transmission with Residual Transmit-RF Impairments

Physical transceiver implementations for multiple-input multiple-output (MIMO) wireless communication systems suffer from transmit-RF (Tx-RF) impairments. In this paper, we study the effect on channel capacity and error-rate performance of residual Tx-RF impairments that defy proper compensation. In particular, we demonstrate that such residual distortions severely degrade the performance of (near-)optimum MIMO detection algorithms. To mitigate this performance loss, we propose an efficient algorithm, which is based on an i.i.d. Gaussian model for the distortion caused by these impairments. In order to validate this model, we provide measurement results based on a 4-stream Tx-RF chain implementation for MIMO orthogonal frequency-division multiplexing (OFDM).

preprint2009arXiv

Tail Behavior of Sphere-Decoding Complexity in Random Lattices

We analyze the (computational) complexity distribution of sphere-decoding (SD) for random infinite lattices. In particular, we show that under fairly general assumptions on the statistics of the lattice basis matrix, the tail behavior of the SD complexity distribution is solely determined by the inverse volume of a fundamental region of the underlying lattice. Particularizing this result to NxM, N>=M, i.i.d. Gaussian lattice basis matrices, we find that the corresponding complexity distribution is of Pareto-type with tail exponent given by N-M+1. We furthermore show that this tail exponent is not improved by lattice-reduction, which includes layer-sorting as a special case.