arXiv subjects

Ralf R. Müller

Publications and source records attributed to Ralf R. Müller.

At least 19 recordsLinked to original sources

arXiv2026

On the Asymptotic of Coupled Spherical Integrals: An Operator-Valued Extension of the Free Fourier Transform

In this paper the asymptotic exponent of coupled Harish-Chandra-Itzykson-Zuber (HCIZ) integrals is studied. We consider $L$ rank-one HCIZ integrals which are coupled through additive exponent terms, with $L>1$ finite. We show that the normalized asymptotic concentration exponent in the rank-one case is, under some constraints, characterized by the operator-valued R-transform. In this way the coupled HCIZ integral provides the operator-valued free analog of the classical Laplace transform. The result can be used to recover the asymptotics of rank-one non-self-adjoint spherical integrals, if the constant matrix is R-diagonal in the sense of free probability. Furthermore, we show that $L$ coupled HCIZ integrals of rank $M(N)=O\left(N^{1/2-ε}\right)$ can be factorized into $M(N)$ rank-one $L$-fold coupled spherical integrals, and characterize the operator-valued R-transform for R-cyclic matrices on the algebra of real, diagonal $L\times L$ matrices. The treatment of coupled spin glasses with correlated disorder is enabled by our asymptotic exponent.

math.PR↗

arXiv2026

The Confusion is Real: GRAPHIC -- A Network Science Approach to Confusion Matrices in Deep Learning

Explainable artificial intelligence has emerged as a promising field of research to address reliability concerns in artificial intelligence. Despite significant progress in explainable artificial intelligence, few methods provide a systematic way to visualize and understand how classes are confused and how their relationships evolve as training progresses. In this work, we present GRAPHIC, an architecture-agnostic approach that analyzes neural networks on a class level. It leverages confusion matrices derived from intermediate layers using linear classifiers. We interpret these as adjacency matrices of directed graphs, allowing tools from network science to visualize and quantify learning dynamics across training epochs and intermediate layers. GRAPHIC provides insights into linear class separability, dataset issues, and architectural behavior, revealing, for example, similarities between flatfish and man and labeling ambiguities validated in a human study. In summary, by uncovering real confusions, GRAPHIC offers new perspectives on how neural networks learn. The code is available at https://github.com/Johanna-S-Froehlich/GRAPHIC.

cs.LG↗

arXiv2026

Geometric Analysis of Blind User Identification for Massive MIMO Networks

Applying Nearest Convex Hull Classification (NCHC) to blind user identification in a massive Multiple Input Multiple Output (MIMO) communications system is proposed. The method is blind in the way that the Base Station (BS) only requires a training sequence containing unknown data symbols obtained from the user without further knowledge on the channel, modulation, coding or even noise power. We evaluate the algorithm under the assumption of gaussian transmit signals using the non-rigorous replica method. To facilitate the computations the existence of an Operator Valued Free Fourier Transform is postulated, which is verified by Monte Carlo simulation. The replica computations are conducted in the large but finite system by applying saddle-point integration with inverse temperature $β$ as the large parameter. The classifier accuracy is estimated by gaussian approximation through moment-matching.

eess.SP↗

arXiv2025

Coding for Computation: Efficient Compression of Neural Networks for Reconfigurable Hardware

As state of the art neural networks (NNs) continue to grow in size, their resource-efficient implementation becomes ever more important. In this paper, we introduce a compression scheme that reduces the number of computations required for NN inference on reconfigurable hardware such as FPGAs. This is achieved by combining pruning via regularized training, weight sharing and linear computation coding (LCC). Contrary to common NN compression techniques, where the objective is to reduce the memory used for storing the weights of the NNs, our approach is optimized to reduce the number of additions required for inference in a hardware-friendly manner. The proposed scheme achieves competitive performance for simple multilayer perceptrons, as well as for large scale deep NNs such as ResNet-34.

cs.LG↗

arXiv2024

Multi-Antenna Towards Inband Shift Keying

We propose a new continuous phase frequency shift keying that is particularly suited for multi-antenna communications when the link budget is critical and beam alignment is problematic. It combines the constant envelope of frequency modulation with low-rate repetition coding in order to compensate for the absence of transmit beamforming. Although it is a frequency modulation, its transmit signal shows close to rectangular spectral shape. Similar to GSM's Gaussian minimum shift keying, it can be well approximated by linear modulation, when combined with differential precoding. This allows for easy coherent demodulation by means of a windowed fast Fourier transform.

cs.IT↗

arXiv2024

A New Radio to Overcome Critical Link Budgets

We propose Multi-Antenna (MA) Towards Inband Shift Keying (TISK): a new multi-carrier radio concept to cope with critical link budgets. In contrast to common proposals that rely on analog beamforming at both transmitter and receiver, MA-TISK does not require beam alignment. The transmitted signals have all constant envelope in continuous time, which allows for efficient, low-cost power amplification and up-conversion. The concept is compatible with any linear PSK-modulation as well as pulse position modulation. Each sub-carrier is sent over a separate antenna that is equipped with a voltage-controlled oscillator. The phases of these oscillators are controlled by digital baseband. Temporal signal combining makes up for the lack of beamforming gain at the transmitter. A common message may be broadcast to many receivers, simultaneously. Demodulation can be efficiently implemented by means of fast Fourier transform. MA-TISK does not suffer from spectral re-growth issues plaguing other constant envelope modulations like GMSK. Almost rectangular signal spectra similar to those for linear modulation with root-raised-cosine pulse shaping are possible. For the 100 MHz-wide spectral mask of 5G downlink, QPSK-modulation allows for 160 MBit/s with 5.74 MHz subcarrier spacing when using 16 transmit antennas. The wide carrier spacing makes the signals insensitive to Doppler effects. There is no loss in link budget gain compared to spatial beamforming at the transmitter.

cs.IT↗

arXiv2024

Graph-based Algorithms for Linear Computation Coding

We revisit existing linear computation coding (LCC) algorithms, and introduce a new framework that measures the computational cost of computing multidimensional linear functions, not only in terms of the number of additions, but also with respect to their suitability for parallel processing. Utilizing directed acyclic graphs, which correspond to signal flow graphs in hardware, we propose a novel LCC algorithm that controls the trade-off between the total number of operations and their parallel executability. Numerical evaluations show that the proposed algorithm, constrained to a fully parallel structure, outperforms existing schemes.

cs.IT↗

arXiv2023

Linear Computation Coding: Exponential Search and Reduced-State Algorithms

Linear computation coding is concerned with the compression of multidimensional linear functions, i.e. with reducing the computational effort of multiplying an arbitrary vector to an arbitrary, but known, constant matrix. This paper advances over the state-of-the art, that is based on a discrete matching pursuit (DMP) algorithm, by a step-wise optimal search. Offering significant performance gains over DMP, it is however computationally infeasible for large matrices and high accuracy. Therefore, a reduced-state algorithm is introduced that offers performance superior to DMP, while still being computationally feasible even for large matrices. Depending on the matrix size, the performance gain over DMP is on the order of at least 10%.

cs.IT↗

arXiv2022

Statistical-CSI-Based Antenna Selection and Precoding in Uplink MIMO

Classical antenna selection schemes require instantaneous channel state information (CSI). This leads to high signaling overhead in the system. This work proposes a novel joint receive antenna selection and precoding scheme for multiuser multiple-input multiple-output uplink transmission that relies only on the long-term statistics of the CSI. The proposed scheme designs the switching network and the uplink precoders, such that the expected throughput of the system in the long term is maximized. Invoking results from the random matrix theory, we derive a closed-form expression for the expected throughput of the system. We then develop a tractable iterative algorithm to tackle the throughput maximization problem, capitalizing on the alternating optimization and majorization-maximization (MM) techniques. Numerical results substantiate the efficiency of the proposed approach and its superior performance as compared with the baseline.

eess.SP↗

arXiv2022

Joint Receive Antenna Selection and Beamforming in RIS-Aided MIMO Systems

This work studies a low-complexity design for reconfigurable intelligent surface (RIS)-aided multiuser multiple-input multiple-output systems. The base station (BS) applies receive antenna selection to connect a subset of its antennas to the available radio frequency chains. For this setting, the BS switching network, uplink precoders, and RIS phase-shifts are jointly designed, such that the uplink sum-rate is maximized. The principle design problem reduces to an NP-hard mixed-integer optimization. We hence invoke the weighted minimum mean squared error technique and the penalty dual decomposition method to develop a tractable iterative algorithm that approximates the optimal design effectively. Our numerical investigations verify the efficiency of the proposed algorithm and its superior performance as compared with the benchmark.

eess.SP↗

arXiv2022

A High-Level Comparison of Recent Technologies for Massive MIMO Architectures

Since the introduction of massive MIMO (mMIMO), the design of a transceiver with feasible complexity has been a challenging problem. Initially, it was believed that the main issue in this respect is the overall RF-cost. However, as mMIMO is becoming more and more a key technology for future wireless networks, it is realized, that the RF-cost is only one of many implementational challenges and design trade-offs. In this paper, we present, analyze and compare various novel mMIMO architectures, considering recent emerging technologies such as intelligent surface-assisted and Rotman lens based architectures. These are compared to the conventional fully digital (FD) and hybrid analog-digital beamforming (HADB) approaches. To enable a fair comparison, we account for various hardware imperfections and losses and utilize a novel, universal algorithm for signal precoding. Based on our thorough investigations, we draw a generic efficiency to quality trade-off for various mMIMO architectures. We find that in a typical cellular communication setting the reflect/transmit array based architectures sketch the best overall trade-off. Further, we show that in a qualitative ranking the power efficiency of the considered architectures is independent of the frequency range.

cs.IT↗

arXiv2022

Analysis of Sparse Recovery Algorithms via the Replica Method

This manuscript goes through the fundamental connections between statistical mechanics and estimation theory by focusing on the particular problem of compressive sensing. We first show that the asymptotic analysis of a sparse recovery algorithm is mathematically equivalent to the problem of calculating the free energy of a spin glass in the thermodynamic limit. We then use the replica method from statistical mechanics to evaluate the performance in the asymptotic regime. The asymptotic results have several applications in communications and signal processing. We briefly go through two instances of these applications: Characterization of joint sparse recovery algorithms used in distributed compressive sensing, and tuning of receivers employed for detection of spatially modulated signals.

cs.IT↗

arXiv2022

Matching Pursuit Based Scheduling for Over-the-Air Federated Learning

This paper develops a class of low-complexity device scheduling algorithms for over-the-air federated learning via the method of matching pursuit. The proposed scheme tracks closely the close-to-optimal performance achieved by difference-of-convex programming, and outperforms significantly the well-known benchmark algorithms based on convex relaxation. Compared to the state-of-the-art, the proposed scheme poses a drastically lower computational load on the system: For $K$ devices and $N$ antennas at the parameter server, the benchmark complexity scales with $\left(N^2+K\right)^3 + N^6$ while the complexity of the proposed scheme scales with $K^p N^q$ for some $0 < p,q \leq 2$. The efficiency of the proposed scheme is confirmed via numerical experiments on the CIFAR-10 dataset.

cs.IT↗

arXiv2022

On the Ergodic Mutual Information of Keyhole MIMO Channels With Finite-Alphabet Inputs

This letter studies the ergodic mutual information (EMI) of keyhole multiple-input multiple-output channels having finite-alphabet input signals. The EMI is first investigated for single-stream transmission considering both cases with and without the channel state information at the transmitter. Then, the derived results are extended to the scenario of multi-stream transmission. Asymptotic analyses are performed in the regime of high signal-to-noise ratio (SNR). The high-SNR EMI is shown to converge to a constant with its rate of convergence determined by the diversity order. On this basis, the influence of the keyhole effect on the EMI is discussed. The analytical results are validated by numerical simulations.

cs.IT↗

arXiv2022

Bayesian Inference with Nonlinear Generative Models: Comments on Secure Learning

Unlike the classical linear model, nonlinear generative models have been addressed sparsely in the literature of statistical learning. This work aims to bringing attention to these models and their secrecy potential. To this end, we invoke the replica method to derive the asymptotic normalized cross entropy in an inverse probability problem whose generative model is described by a Gaussian random field with a generic covariance function. Our derivations further demonstrate the asymptotic statistical decoupling of the Bayesian estimator and specify the decoupled setting for a given nonlinear model. The replica solution depicts that strictly nonlinear models establish an all-or-nothing phase transition: There exists a critical load at which the optimal Bayesian inference changes from perfect to an uncorrelated learning. Based on this finding, we design a new secure coding scheme which achieves the secrecy capacity of the wiretap channel. This interesting result implies that strictly nonlinear generative models are perfectly secured without any secure coding. We justify this latter statement through the analysis of an illustrative model for perfectly secure and reliable inference.

cs.IT↗

arXiv2022

How Should IRSs Scale to Harden Multi-Antenna Channels?

This work extends the concept of channel hardening to multi-antenna systems that are aided by intelligent reflecting surfaces (IRSs). For fading links between a multi-antenna transmitter and a single-antenna receiver, we derive an accurate approximation for the distribution of the input-output mutual information when the number of reflecting elements grows large. The asymptotic results demonstrate that by increasing the number of elements on the IRS, the end-to-end channel hardens as long as the physical dimensions of the IRS grow as well. The growth rate however need not to be of a specific order and can be significantly sub-linear. The validity of the analytical result is confirmed by numerical experiments.

cs.IT↗

arXiv2022

Secure Coding via Gaussian Random Fields

Inverse probability problems whose generative models are given by strictly nonlinear Gaussian random fields show the all-or-nothing behavior: There exists a critical rate at which Bayesian inference exhibits a phase transition. Below this rate, the optimal Bayesian estimator recovers the data perfectly, and above it the recovered data becomes uncorrelated. This study uses the replica method from the theory of spin glasses to show that this critical rate is the channel capacity. This interesting finding has a particular application to the problem of secure transmission: A strictly nonlinear Gaussian random field along with random binning can be used to securely encode a confidential message in a wiretap channel. Our large-system characterization demonstrates that this secure coding scheme asymptotically achieves the secrecy capacity of the Gaussian wiretap channel.

cs.IT↗

arXiv2022

Channel Hardening of IRS-Aided Multi-Antenna Systems: How Should IRSs Scale?

Unlike active array antennas, intelligent reflecting surfaces (IRSs) are efficiently implemented at large dimensions. This allows for traceable realizations of large-scale IRS-aided MIMO systems in which not necessarily the array antennas, but the passive IRSs are large. It is widely believed that large IRS-aided MIMO settings maintain the fundamental features of massive MIMO systems, and hence they are the implementationally feasible technology for establishing the performance of large-scale MIMO settings. This work gives a rigorous proof to this belief. We show that using a large passive IRS, the end-to-end MIMO channel between the transmitter and the receiver always hardens, even if the IRS elements are strongly correlated. For the fading direct and reflection links between the transmitter and the receiver, our derivations demonstrate that as the number of IRS elements grows large, the capacity of end-to-end channel converges in distribution to a real-valued Gaussian random variable whose variance goes to zero. The order of this drop depends on how the physical dimensions of the IRS grow. We derive this order explicitly. Numerical experiments depict that the analytical asymptotic distribution almost perfectly matches the histogram of the capacity, even in practical scenarios. As a sample application of the results, we use the asymptotic characterization to study the dimensional trade-off between the transmitter and the IRS. The result is intuitive: For a given target performance, the larger the IRS is, the less transmit antennas are required to achieve the target. For an arbitrary ergodic and outage performance, we characterize this trade-off analytically. Our investigations demonstrate that using a practical IRS size, the target performance can be achieved with significantly small end-to-end MIMO dimensions.

cs.IT↗