Equivariant network architectures are a well-established tool for predicting invariant or equivariant quantities. However, almost all learning problems considered in this context feature a global symmetry, i.e. each point of the underlying space is transformed with the same group element, as opposed to a local *gauge* symmetry, where each point is transformed with a different group element, exponentially enlarging the size of the symmetry group. We use gauge equivariant networks to predict topological invariants (Chern numbers) of multiband topological insulators for the first time. The gauge symmetry of the network guarantees that the predicted quantity is a topological invariant. A major technical challenge is that the relevant gauge equivariant networks are plagued by instabilities in their training, severely limiting their usefulness. In particular, for larger gauge groups the instabilities make training impossible. We resolve this problem by introducing a novel gauge equivariant normalization layer which stabilizes the training. Furthermore, we prove a universal approximation theorem for our model. We train on samples with trivial Chern number only but show that our model generalizes to samples with non-trivial Chern number and provide various ablations of our setup.

In this paper we develop a geometric framework for equivariant manifold neural ordinary differential equations (NODEs), and use it to analyse their modelling capabilities for symmetric data. First, we consider the action of a Lie group $G$ on a smooth manifold $M$ and establish the equivalence between equivariance of vector fields, symmetries of the corresponding Cauchy problems, and equivariance of the associated NODEs. We also propose a novel formulation of the equivariant NODEs in terms of the differential invariants of the action of $G$ on $M$, based on Lie theory for symmetries of differential equations, which provides an efficient parameterisation of the space of equivariant vector fields in a way that is agnostic to both the manifold $M$ and the symmetry group $G$. Second, we construct augmented manifold NODEs through embeddings into equivariant flows, and show that they are universal approximators of equivariant diffeomorphisms on any connected $M$. Furthermore, we show that the augmented NODEs can be incorporated in the geometric framework and parametrised using higher order differential invariants. Finally, we consider the induced action of $G$ on different fields on $M$ and show how it generalises previous work, e.g., continuous normalizing flows, to equivariant models in any geometry.

High-resolution wide-angle fisheye images are becoming more and more important for robotics applications such as autonomous driving. However, using ordinary convolutional neural networks or vision transformers on this data is problematic due to projection and distortion losses introduced when projecting to a rectangular grid on the plane. We introduce the HEAL-SWIN transformer, which combines the highly uniform Hierarchi-cal Equal Area iso-Latitude Pixelation (HEALPix) grid used in astrophysics and cosmology with the Hierarchical Shifted-Window (SWIN) transformer to yield an efficient and flexible model capable of training on high-resolution, distortion-free spherical data. In HEAL-SWIN, the nested structure of the HEALPix grid is used to perform the patching and windowing operations of the SWIN transformer, enabling the network to process spherical representations with minimal computational overhead. We demonstrate the superior performance of our model on both synthetic and real automotive datasets, as well as a selection of other image datasets, for semantic segmentation, depth regression and classification tasks. Our code is publicly available11https://github.com/JanEGerken/HEAL-SWIN.

We analyze the role of rotational equivariance in convolutional neural networks (CNNs) applied to spherical images. We compare the performance of the group equivariant networks known as S2CNNs and standard non-equivariant CNNs trained with an increasing amount of data augmentation. The chosen architectures can be considered baseline references for the respective design paradigms. Our models are trained and evaluated on single or multiple items from the MNIST- or FashionMNIST dataset projected onto the sphere. For the task of image classification, which is inherently rotationally invariant, we find that by considerably increasing the amount of data augmentation and the size of the networks, it is possible for the standard CNNs to reach at least the same performance as the equivariant network. In contrast, for the inherently equivariant task of semantic segmentation, the non-equivariant networks are consistently outperformed by the equivariant networks with significantly fewer parameters. We also analyze and compare the inference latency and training times of the different networks, enabling detailed tradeoff considerations between equivariant architectures and data augmentation for practical problems.

The capacity of the MIMO channel taking into account both a limitation on total consumed power, and per-antenna radiated power constraints is considered. The total consumed power takes into account the traditionally used sum radiated power, and also the power dissipation in the amplifiers. For a fixed channel with full CSI at both the transmitter and the receiver, maximization of the mutual information is formulated as an optimization problem. Lower and upper bounds on the capacity are provided by numerical algorithms based on partitioning of the feasible region. Both bounds are shown to converge and give the exact capacity when number of regions increases. The bounds are also used to construct a monotonic optimization algorithm based on the branch-and-bound approach. An efficient suboptimal algorithm based on successive convex approximation performing close to the capacity is also presented. Numerical results show that the performance of the solution obtained from the suboptimal algorithm is close to that of the global optimal solution. Simulation results also show that in the low SNR regime, antenna selection provides performance that is close to the optimal scheme while at high SNR, uniform power allocation performs close to the optimal scheme.

In this paper we deal with spoofing detection in GNSS receivers. We derive the optimal genie detector when the true positions are perfectly known, and the observation errors are Gaussian, as a benchmark for other detectors. The system model considers three dimensional positions, and includes correlated errors. In addition, we propose several detectors that do not need any position knowledge, that outperform recently proposed detectors in many interesting cases.

For both maximum ratio transmission (MRT) and zero forcing (ZF) precoding schemes and given any specific rate requirement the optimal transmit power, number of antennas to be used, number of users to be served and number of pilots spent on channel training are found with the objective to minimize the total consumed power at the base station. The optimization problem is solved by finding closed form expressions of the optimal transmit power and then search over the remaining discrete variables. The analysis consists of two parts, the first part investigates the situation when only power consumed in the RF amplifiers is considered. The second part includes both the power consumed in the RF amplifiers and in other transceiver circuits. In the former case having all antennas active while reducing the transmit power is optimal. Adaptive scheme to switch off some of the antennas at the base stations is found to be optimal in the latter case.

Measurements for outdoor multiple‐input–multiple‐output (MIMO) capacity assessment are generally technically complicated, time consuming and expensive activities and few results are therefore published in the literature. Terrestrial Trunked Radio (TETRA) systems suffer from poor capacity and could be significantly improved by MIMO technology. However, performing outdoor channel measurements in relevant environments is very difficult because of interference problems with operating systems. In this study, the authors propose an estimation of the MIMO capacity for TETRA systems, based on outdoor MIMO measurements carried out at 300 MHz.

We investigate multiple-input single-output channel capacity taking dissipation in the power amplifiers into account. We consider the case of a fixed channel with full channel state information (CSI) at both the transmitter and receiver. The capacity expression is given on closed form, and we show that the optimal solution is antenna selection. An algorithm for finding minimum consumed power for any given mutual information is further developed, and we show that the power-mutual information pair is capacity-achieving. We also investigate the ergodic Rayleigh fading channel with full CSI at the receiver and no instantaneous CSI at the transmitter. We devise a numerical approach which finds the global optimum given a quantization of the space of possible allocated powers. We further show that down to the simulation precision, the ergodic Rayleigh fading solution again is antenna selection. It is shown that the allocation algorithms have low computational complexity and give significant rate and total consumed power gains in comparison to previous state of the art.

The fundamental problem of our interest is soft MIMO detection for the case of block fading, i.e., when the transmitted codeword spans over several independent channel realizations. We develop methods that adaptively allocate computational resources to the detection problems of each channel realization, under a total per-codeword complexity constraint. The new results consist of a new algorithm, a new performance measure, and a thorough complexity discussion.

We derive a Gaussian approximation of the LLR distribution conditioned on the transmitted signal and the channel matrix for the soft-output via partial marginalization MIMO detector. This detector performs exact ML as a special case. Our main results consist of discussing the operational meaning of this approximation and a proof that, in the limit of high SNR, the LLR distribution of interest converges in probability towards a Gaussian distribution.

A recently proposed method for transmission of correlated sources under noise-free conditions, power series quantization (PSQ), uses a separate linear or nonlinear predictor for each quantizer region, and has shown to increase performance compared to several common quantization schemes for sources with memory. In this paper, it is shown how to apply PSQ for transmission of a source with memory over a noisy channel. A channel-optimized PSQ (COPSQ) encoder and codebook optimization algorithms are derived. The suggested scheme is shown to increase performance compared with previous state-of-the- art methods.

We propose a framework for multiple description coding (MDC) of sources with memory. A new source coding method for lossless transmission of correlated sources, power series quantization (PSQ), was recently suggested. PSQ uses a separate linear or non-linear predictor for each quantizer region, and has shown increased performance compared to several common quantization schemes for sources with memory. We propose multiple description PSQ as a special case within our framework. The suggested scheme is shown to increase performance compared with previous state-of-the-art MDC methods.

A Gaussian mixture model (GMM)-based spatio-temporal error concealment approach has recently been proposed for packet video. The method improves peak signal-to-noise ratio (PSNR) compared to several famous error concealment methods, and it is asymptotically optimal when the number of mixture components goes to infinity. There are also drawbacks, however. The estimator has high online computational complexity, which implies that fewer surrounding pixels to the lost area than desired are used for error concealment. Moreover, GMM parameters are estimated without considering maximization of the error concealment PSNR. In this paper, we propose a mixture-based estimator and a least squares approach for solving the spatio-temporal error concealment problem. Compared to the GMM scheme, the new method may base error concealment on more surrounding pixels to the loss, while maintaining low computational complexity, and model parameters are found by an algorithm that increases PSNR in each iteration. The proposed method outperforms the GMM-based scheme in terms of computation-performance tradeoff.

In this paper, Gaussian mixture modeling is applied to error concealment for block-based packet video. A Gaussian mixture model for video data is obtained offline and is thereafter utilized online in order to restore lost blocks from spatial and temporal surrounding information. We propose estimators on closed form for missing data in the case of varying available neighboring contexts. Our error concealment strategy increases peak signal-to-noise ratio compared to previously proposed schemes. Examples of improved subjective visual quality by means of the proposed method are also supplied.

In this paper, a minimum mean square error-optimized mixture-based estimator is used for packet video error concealment. At the same time as on-line computational complexity is reduced, performance in peak signal-to-noise ratio (PSNR) is increased in comparison with a Gaussian mixture-based estimator that obtains its parameters through probability density estimation by means of the expectation maximization algorithm. Moreover, our method increases performance in PSNR compared to several other previous error concealment algorithms.

In this paper, a spatio-temporal Markov random field method is proposed for block-based packet video error concealment. We suggest the combined usage of two estimators, one for lost pixels, and one for lost motion vectors. The estimator for the lost pixel field takes surrounding pixels in the same frame where the loss occurred and motion-compensated pixels from a previous frame based on a motion field estimate into account, while the optimal estimator of the motion field takes surrounding pixels in the same frame where the loss occurred, pixels from a previous frame, and the estimator function for the pixel field into account. Our method increases performance in peak signal-to-noise ratio as well as subjective visual performance compared to several other previous error concealment algorithms.

We have developed a Gaussian mixture model-based technique for the compensation of lost pixel blocks during real time transmission of video. In this paper, we pursue an argument in order to better understand how the Gaussian mixture model-based estimator works. The discussion is supported with subjective evaluations and examples. Naive viewers preferred the result of our proposed technique 72 percent of the time in comparison with the linear minimum mean square error estimator. Our scheme increases performance measured in peak signal-to-noise ratio for all the 11 standard evaluation movie clips that were used

We have developed a statistical prediction technique to compensate for lost pixel blocks during real time transmission of video over packet-switched networks. The approach could as well be used for standard inter-frame coding. The method is based on the joint modeling of pixel statistics by Gaussian mixtures. Different EM variants for decreasing computational complexity and storage space are proposed. In the case of 4/spl times/4 luminance blocks, our method increases performance by 2.3 dB when augmenting the number of mixture components from 1 to 64. We show that these results are statistically significant.