wide range of problems in communications and information theory can be cast as sparse recovery tasks, where the objective is to identify the active codewords in a linear superposition with random channel coefficients and additive noise. In multi-antenna systems, it is commonly assumed that the channel coefficients and noise are identically distributed across receive antennas, which implies that the activity pattern is shared among all antennas. By forming outer products of the received signals, such problems can be transformed into structured covariance estimation problems in which the unknown parameters are the variances of the channel coefficients, commonly referred to as large-scale fading coefficients. Characterizing the interplay among the number of receive antennas, pilot symbols, active users, total users, and the resulting error probability is therefore of fundamental importance for the design of efficient random access protocols. In this work, a general class of covariance estimators, defined by a real-valued functiongand a prescribed set of admissible covariance matrices, is studied. Given a possibly perturbed observation of an underlying covariance matrix, the estimator is defined as the minimizer of a sum ofgapplied to the eigenvalues of a suitably normalized matrix, subject to the constraint that the estimate lies in the admissible set. Under mild regularity conditions on the functiongand the constraint set, robustness of this class of estimators is established, in the sense that the estimation error can be made arbitrarily small as the perturbation vanishes. These general results are applied to activity detection in random access systems with multiple receive antennas. Recovery via nonnegative least squares and via a relaxed maximum-likelihood estimator is considered, and it is shown that, under suitable assumptions on the channel and noise distributions, the relaxed maximum-likelihood estimator belongs to the proposed class of covariance estimators. Finally, pilot codebooks satisfying a signed kernel condition are introduced and it is shown that, with such codebooks, reliable recovery of the large-scale fading coefficients is possible when the number of receive antennas is sufficiently large and the number of active users satisfiesS≤ [1/2M2] − 1, whereMdenotes the number of pilot symbols per user. For the finite-antenna regime, refined recovery conditions that explicitly capture the dependence on the number of receive antennas are derived.

In this paper we study fully asynchronous random access (RA) multiple antenna receiver in a Rayleigh block-fading AWGN channel with pure path delays. Although our approach can be used to detect users in a grant-free random access system, where each user sporadically and without waiting for a permission from a base station (BS) transmits short messages, we in particular consider the pilot-based unsourced random access (U-RA), where those messages are from a common codebook. The first and arguably the most important task of the pilotbased U-RA receiver is to detect the list of transmitted pilots. Due to the propagation through the considered channel, those pilots are received as a superposition at the BS with delays, due to the lack of perfect timing synchronization. We show that the output of the chip matched filter at the BS receiver can be seen as the superposition of two zero-padded versions of each transmitted pilot sequence. We include this observation in the compressed sensing (CS) formulation of the activity detection (AD) problem, and solve it using the multiple measurement vectors approximate message passing (MMV-AMP) algorithm and a dedicated parametrized 2-level hierarchical sparsity (P2-LHS) denoiser. Our numerical experiments show that the proposed scheme can accurately detect U-RA messages and shows excellent robustness to timing asynchronism. The proposed denoiser vastly outperforms the standard Bernoulli-Gaussian (BG) denoiser for a large range of signal-to-noise ratio (SNR) values. Furthermore, using outage rate analysis, we investigate the performance of the asynchronous U-RA receiver using a Gaussian codebook and minimum distance decoding in the data phase. Our results show that a significant gain in throughput can be achieved when users adopt rate control (RC).

Many algorithms for high-dimensional regression problems require the calibration of regularization hyperparameters. This, in turn, often requires the knowledge of the unknown noise variance in order to produce meaningful solutions. Recent works show, however, that there exist certain estimators that are pivotal, i.e., the regularization parameter does not depend on the noise level; the most remarkable example being the square-root lasso. Such estimators have also been shown to exhibit strong connections to distributionally robust optimization. Despite the progress in the design of pivotal estimators, the resulting minimization problem is challenging as both the loss function and the regularization term are non-smooth. To date, the design of fast, robust, and scalable algorithms with strong convergence rate guarantees is still an open problem. This work addresses this problem by showing that an iteratively reweighted least squares (IRLS) algorithm exhibits global linear convergence under the weakest assumption available in the literature. We expect our findings will also have implications for multi-task learning and distributionally robust optimization.

To efficiently utilize the scarce wireless resource, the random access scheme has been attaining renewed interest primarily in supporting the sporadic traffic of a large number of devices encountered in the Internet of Things (IoT). In this paper we investigate the performance of slotted ALOHA—a simple and practical random access scheme—in connection with the grant-free random access protocol applied for user-centric cell-free massive MIMO. More specifically, we provide the expression of the sum-throughput under the assumptions of the capture capability owned by the centralized detector in the uplink. Further, a comparative study of user-centric cell-free massive MIMO with other types of networks is provided, which allows us to identify its potential and possible limitation. Our numerical simulations show that the user-centric cell-free massive MIMO has a good trade-off between performance and fronthaul load, especially at low activation probability regime.

This work proposes a maximum likelihood-based parameter estimation framework for a multistatic millimeter wave integrated sensing and communication system using energy-efficient hybrid digital-analog arrays. Due to the typically large arrays used in the higher frequency bands to mitigate isotropic path loss, such arrays may operate in the near-field (NF) regime. To address this, we propose a two-step estimation process. Initially, we consider far-field (FF) propagation assumptions, followed by refined estimation based on NF assumptions, enhancing accuracy when the target is within the NF of the arrays. In particular, when operating in the NF of the transmitter (Tx), we select beamfocusing array weights designed to achieve constant gain over an extended spatial region. Subsequently, we re-estimate target parameters at the receivers (Rxs). The effectiveness of the proposed framework is evaluated over various scenarios through numerical simulations. In particular, the impact of customdesigned flat-gain beamfocusing codewords in improving both communication and sensing performance when the target is in the NF of the Tx is demonstrated. Additionally, the benefit of considering a correct NF channel model when the target is located near an Rx is shown.

The quantification of predictive uncertainties helps to understand where existing models struggle to find the correct prediction. A useful quality control tool is the task of detecting out-of-distribution (OOD) data by examining the model’s predictive uncertainty. For this task, deterministic single forward pass frameworks have recently been established as deep learning models and have shown competitive performance in certain tasks. The unique combination of spectrally normalized weight matrices and residual connection networks with an approximate Gaussian Process output layer can here offer the best trade-off between performance and complexity. We utilize this framework with a refined version that adds spectral batch normalization and an inducing points approximation of the Gaussian Process for the task of OOD detection in remote sensing image classification. This is an important task in the field of remote sensing because it provides an evaluation of how reliable the model’s predictive uncertainty estimates are. By performing experiments on the benchmark datasetsEurosatandSo2Sat LCZ42, we can show the effectiveness of the proposed adaptions to the residual networks. Depending on the chosen dataset, the proposed methodology achieves OOD detection performance up to 16% higher than previously considered distance-aware networks. Compared to other uncertainty quantification methodologies, the results are on the same level and exceed them in certain experiments by up to 2%. In particular, spectral batch normalization, which normalizes the batched data as opposed to normalizing the network weights by the spectral normalization, plays a crucial role and leads to performance gains of up to 3% in every single experiment. For reproducibility, the code can be found here: https://github.com/ChrisKo94/DUE Land Cover.

Deep neural networks based on unrolled iterative algorithms have achieved remarkable success in sparse reconstruction applications, such as synthetic aperture radar (SAR) tomographic inversion (TomoSAR). However, the currently available deep learning-based TomoSAR algorithms are limited to 3-D reconstruction. The extension of deep learning-based algorithms to 4-D imaging, i.e., differential TomoSAR (D-TomoSAR) applications, is impeded mainly due to the high-dimensional weight matrices required by the network designed for D-TomoSAR inversion, which typically contain millions of freely trainable parameters. Learning such huge number of weights requires an enormous number of training samples, resulting in a large memory burden and excessive time consumption. To tackle this issue, we propose an efficient and accurate algorithm called HyperLISTA-ABT. The weights in HyperLISTA-ABT are determined in an analytical way according to a minimum coherence criterion, trimming the model down to an ultra-light one with only three hyperparameters. Additionally, HyperLISTA-ABT improves the global thresholding by utilizing an adaptive blockwise thresholding (ABT) scheme, which applies block-coordinate techniques and conducts thresholding in local blocks, so that weak expressions and local features can be retained in the shrinkage step layer by layer. Simulations were performed and demonstrated the effectiveness of our approach, showing that HyperLISTA-ABT achieves superior computational efficiency with no significant performance degradation compared to the state-of-the-art methods. Real data experiments showed that a high-quality 4-D point cloud could be reconstructed over a large area by the proposed HyperLISTA-ABT with affordable computational resources and in a fast time.

This work proposes a maximum likelihood (ML)- based parameter estimation framework for a millimeter wave (mmWave) integrated sensing and communication (ISAC) system in a multistatic configuration using energy-efficient hybrid digital-analog (HDA) arrays. Due to the typically large arrays deployed in the higher frequency bands to mitigate isotropic path loss, such arrays may operate in the near-field (NF) regime. The proposed parameter estimation in this work consists of a two-stage estimation process, where the first stage is based on far-field (FF) assumptions, and is used to obtain a first estimate of the target parameters. In cases where the target is determined to be in the NF of the arrays, a second estimation based on NF assumptions is carried out to obtain more accurate estimates. In particular, when operating in the near-filed of the transmitter (Tx), we select beamfocusing array weights designed to achieve a constant gain over an extended spatial region and re-estimate the target parameters at the receivers (Rxs). We evaluate the effectiveness of the proposed framework in numerous scenarios through numerical simulations and demonstrate the impact of the custom-designed flat-gain beamfocusing codewords in increasing the communication performance of the system.

In this paper, we propose a novel channel estimation scheme for pulse-shaped multicarrier systems using smoothness regularization for ultra-reliable low-latency communication (URLLC). It can be applied to any multicarrier system with or without linear precoding to estimate challenging doubly-dispersive channels. A recently proposed modulation scheme using orthogonal precoding is orthogonal time-frequency and space modulation (OTFS). In OTFS, pilot and data symbols are placed in delay-Doppler (DD) domain and are jointly precoded to the time-frequency (TF) domain. On the one hand, such orthogonal precoding increases the achievable channel estimation accuracy and enables high TF diversity at the receiver. On the other hand, it introduces leakage effects which requires extensive leakage suppression when the piloting is jointly precoded with the data. To avoid this, we propose to precode the data symbols only, place pilot symbols without precoding into the TF domain, and estimate the channel coefficients by interpolating smooth functions from the pilot samples. Furthermore, we present a piloting scheme enabling a smooth control of the number and position of the pilot symbols. Our numerical results suggest that the proposed scheme provides accurate channel estimation with reduced signaling overhead compared to standard estimators using Wiener filtering in the discrete DD domain.

In this work, we propose a framework based on Deep Neural Networks (DNNs) for radar parameter estimation in an Integrated Sensing and Communication (ISAC) system em-ploying a realistic and hardware-efficient Hybrid Digital-Analog (HDA) architecture that uses Orthogonal Frequency Division Multiplexing (OFDM) digital modulation. This framework takes raw signals as input and utilizes a Variational Autoencoder (VAE) followed by a regression network to output the spatial extent and location of extended targets. Owing to the HDA setup, the co-located radar receiver uses multi-block measurements to perform parameter estimation. The proposed solution is motivated as a remedy for the increasing computational complexity associated with high-resolution extended target estimation in multi-carrier digital modulations such as OFDM. In addition, it is well known that off-grid delay-Doppler shifts which are present in the doubly-dispersive channels in the high mobility scenarios expected in ISAC applications, exhibit leakage effects that adversely affect the parameter estimation performance. Due to the data-centric nature of the proposed method, these effects can be learned by the network. We provide numerical results to showcase the effectiveness of the proposed framework for parameter estimation. 1

In this work, we propose a compressed sensing framework for radar parameter estimation in an Integrated Sensing and Communication (ISAC) system employing a realistic and hardware-efficient Hybrid Digital-Analog (HDA) architecture which uses Orthogonal Time Frequency Space (OTFS) digital modulation. In such a setup, the co-located radar receiver uses multi-block measurements to perform parameter estimation. OTFS is widely considered as a robust modulation to deal with the doubly-dispersive channel in the high mobility scenarios expected in ISAC applications, however it suffers from leakage effects in the presence of fractional Doppler/delay (i.e., off-grid) shifts. By taking the inherent structure of the leakage effect into consideration and casting the multi-block measurements in a Multiple Measurement Vector (MMV) setting, we develop the Joint Hierarchical Sparsity concept based on which, we formulate a soft-thresholding iterative parameter estimation framework. This framework exploits the jointly hierarchical structure of the MMV setting for improved (radar-) parameter estimation. We provide numerical results to showcase the effectiveness of the proposed framework for parameter estimation.

In this paper we study the message detection (MD) problem for a chip-asynchronous random access (RA) multiple antennas receiver and a Rayleigh block-fading AWGN channel with a pure path delay. Although our approach can be used to detect users in a grant-free random access system, where each user sporadically and without waiting for a permission from a base station (BS) transmits a short message, we in particular consider unsourced random access (U-RA), where those messages are from a common codebook. The first and arguably the most important task of the U-RA receiver is to detect the list of transmitted messages. Due to the propagation through the considered channel, those messages are received as a superposition at the BS with delays. In order to reduce the overhead for timing synchronisation, which would be wasteful for short messages, in this work we provide an asynchronous operating mode for MD in U-RA. To do this, we show that when using a chip matched filter at the BS, the contribution of each transmitted message in the sampled received signal can be described as a superposition of two zero-padded versions of that message. We include this observation in the compressed sensing (CS) formulation of the MD problem, and solve it using the multiple measurement vectors approximate message passing (MMV-AMP) algorithm and a dedicated 2-level hierarchical sparsity (2-LHS) denoiser. Our numerical experiments show that the proposed scheme can accurately detect U-RA messages in the considered channel without any overhead for timing synchronization.

Deep Learning models for classification often suffer from overconfidence, which naturally results in poor predictive uncertainty estimates. To overcome this, many calibration techniques have been established. These techniques operate on the labels or the output space of the network but ignore the input image space. A recently proposed approach considers the distances between different network inputs explicitly and theoretically propagates the distances through the network. The resulting predictive uncertainties of the model are then able to better reflect these distances. We test this approach in the context of remote sensing image classification for land use. To evaluate the predictive uncertainties, we set up an Out-of Distribution (OoD) detection framework based on class separation.

To achieve super-resolution synthetic aperture radar (SAR) tomography (TomoSAR), compressive sensing (CS)-based algorithms are usually employed, which are, however, computationally expensive, and thus is not often applied in large-scale processing. Recently, deep unfolding techniques have provided a good combination of physical model-based algorithms and the ability of neural networks to learn from data. In this vein, iterative CS-based algorithms can usually be un-rolled as neural networks with only 10 to 20 layers. When trained, it shows great computational efficiency for further TomoSAR processing. However, the learning architecture of neural networks built in this approach tends to result in error propagation and information loss, thus degrading the performance. In this paper, we propose to employ complex-valued sparse long short-term memory (CV-SLSTM) units to tackle this problem by incorporating historically updating information into the optimization procedure and preserving full information. Simulations are carried out to validate the performance of the proposed algorithm.

We consider the unsourced random access problem on a Rayleigh block-fading AWGN channel with multiple receive antennas. Specifically, we treat the slow fading scenario where the coherence blocklength is large compared to the number of active users and a message can be transmitted in a single fading coherence block. Unsourced random access refers to a form of grant-free random access where users are constrained to use the same codebook and therefore are a priori indistinguishable. The receiver must recover the list of transmitted messages up to permutations. In this paper, we propose an approach based on splitting the user messages into two parts. First, a small block of bits selects a relatively short codeword from a common “pilot” codebook. Then the remaining message bits are encoded by a standard block code for the Gaussian channel. The receiver makes use of a multiple measurement vector approximate message passing (MMV-AMP) algorithm to estimate the active user channels from the “pilot” part, and then uses the estimated channels to perform coherent maximum ratio combining (MRC) to decode the second part. We provide an accurate closed-form approximated analysis of the proposed scheme. Furthermore, we analyze the MRC decoding when successive interference cancellation is performed over groups of users, striking an attractive tradeoff between complexity and performance. Finally, we investigate the impact of power control policies, taking into account the unique nature of massive random access. As a byproduct, we also present an extension of the MMV-AMP algorithm which allows pathloss coefficients to be treated as deterministic unknowns by performing maximum likelihood estimation in each step of the MMV-AMP algorithm.

In this work, we introduce an iterative algorithm for the Euclidean distance matrix completion (EDMC) problem with noisy and incomplete distance measurements. The proposed method is based on semidefinite programming, utilizes a Pareto iterative approach, and performs a projection-free convex optimization over the spectrahedron to solve a level-set problem relevant to EDMC problems. The optimality trade-off between the trace of a positive semidefinite matrix and a loss function is pursued over Pareto optimal points with simple, derivative-free, costly efficient nonlinear equation root finding iterations called Illinois-type methods. We evaluate our approach numerically in a scenario where distance measurements are affected by multiplicative noise.

Finding sparse solutions of underdetermined linear systems commonly requires the solving ofL1regularized least squares minimization problem, which is also known as the basis pursuit denoising (BPDN). They are computationally expensive since they cannot be solved analytically. An emerging technique known asdeep unrollingprovided a good combination of the descriptive ability of neural networks, explainable, and computational efficiency for BPDN. Many unrolled neural networks for BPDN, e.g. learned iterative shrinkage thresholding algorithm and its variants, employ shrinkage functions to prune elements with small magnitude. Through experiments on synthetic aperture radar tomography (TomoSAR), we discover the shrinkage step leads to unavoidable information loss in the dynamics of networks and degrades the performance of the model. We propose a recurrent neural network (RNN) with novel sparse minimal gated units (SMGUs) to solve the information loss issue. The proposed RNN architecture with SMGUs benefits from incorporating historical information into optimization, and thus effectively preserves full information to the final output. Taking TomoSAR inversion as an example, extensive simulations demonstrated that the proposed RNN outperforms the state-of-the-art deep learning-based algorithm in terms of super-resolution power as well as generalization ability. It achieved 10% to 20% higher double scatterers detection rate and is less sensitive to phase and amplitude ratio difference between scatterers. Test on real TerraSAR-X spotlight images also shows high-quality 3-D reconstruction of test site.

Deep unfolding showed to be a very successful approach for accelerating and tuning classical signal processing algorithms. In this paper, we propose learned Gaussian-mixture AMP (L-GM-AMP) - a plug-and-play compressed sensing (CS) recovery algorithm suitable for any i.i.d. source prior. Our algorithm builds upon Borgerding’s learned AMP (LAMP), yet significantly improves it by adopting a universal denoising function within the algorithm. The robust and flexible denoiser is a byproduct of modelling source prior with a Gaussian-mixture (GM), which can well approximate continuous, discrete, as well as mixture distributions. Its parameters are learned using standard backpropagation algorithm. To demonstrate robustness of the proposed algorithm, we conduct Monte-Carlo (MC) simulations for both mixture and discrete distributions. Numerical evaluation shows that the L-GM-AMP algorithm achieves state-of-the-art performance without any knowledge of the source prior.

We combine three different approaches to greatly enhance the defect reconstruction ability of active thermographic testing. As experimental approach, laser-based structured illumination is performed in a stepwise manner. As an intermediate signal processing step, the virtual wave concept is used in order to effectively convert the notoriously difficult to solve diffusion-based inverse problem into a somewhat milder wave-based inverse problem. As a final step, a compressed-sensing-based optimization procedure is applied which efficiently solves the inverse problem by making advantage of the joint sparsity of multiple blind measurements. To evaluate our proposed processing technique, we investigate an additively manufactured stainless steel sample with eight internal defects. The concerted super resolution approach is compared to conventional thermographic reconstruction techniques and shows an at least four times better spatial resolution.

In this paper, we study the problem of user activity detection and large-scale fading coefficient estimation in a random access wireless uplink with a massive MIMO base station with a large number M of antennas and a large number of wireless single-antenna devices (users). We consider a block fading channel model where the M-dimensional channel vector of each user remains constant over a coherence block containing L signal dimensions in time-frequency. In the considered setting, the number of potential users Ktotis much larger than L but at each time slot only Katotof them are active. Previous results, based on compressed sensing, require that Ka≤ L, which is a bottleneck in massive deployment scenarios. In this work, we show that such limitation can be overcome when the number of base station antennas M is sufficiently large. More specifically, we prove that with a coherence block of dimension L and a number of antennas M such that Ka/M = o(1), one can identify Ka= O(L2/log2(Ktot/ Ka)) active users, which is much larger than the previously known bounds. We also provide two algorithms. One is based on Non-Negative Least-Squares, for which the above scaling result can be rigorously proved. The other consists of a low-complexity iterative componentwise minimization of the likelihood function of the underlying problem. While for this algorithm a rigorous proof cannot be given, we analyze a constrained version of the Maximum Likelihood (ML) problem (a combinatorial optimization with exponential complexity) and find the same fundamental scaling law for the number of identifiable users. Therefore, we conjecture that the low-complexity (approximated) ML algorithm also achieves the same scaling law and we demonstrate its performance by simulation. We also compare the discussed methods with the (Bayesian) MMV-AMP algorithm, recently proposed for the same setting, and show superior performance and better numerical stability. Finally, we use the discussed approximated ML algorithm as the inner decoder in a concatenated coding scheme for unsourced random access, a grant-free uncoordinated multiple access scheme where all users make use of the same codebook, and the receiver must produce the list of transmitted messages, irrespectively of the identity of the transmitters. We show that reliable communication is possible at any Eb/N0provided that a sufficiently large number of base station antennas is used, and that a sum spectral efficiency in the order ofO(Llog(L)) is achievable.

Unsourced random-access (U-RA) is a type of grant-free random access with a virtually unlimited number of users, of which only a certain number Kaare active on the same time slot. Users employ exactly the same codebook, and the task of the receiver is to decode the list of transmitted messages. We present a concatenated coding construction for U-RA on the AWGN channel, in which a sparse regression code (SPARC) is used as an inner code to create an effective outer OR-channel. Then an outer code is used to resolve the multiple-access interference in the OR-MAC. We propose a modified version of the approximate message passing (AMP) algorithm as an inner decoder and give a precise asymptotic analysis of the error probabilities of the AMP decoder and of a hypothetical optimal inner MAP decoder. This analysis shows that the concatenated construction under optimal decoding can achieve a vanishing per-user error probability in the limit of large blocklength and a large number of active users at sum-rates up to the symmetric Shannon capacity, i.e. as long as KaR2(1+KaSNR). This extends previous point-to-point optimality results about SPARCs to the unsourced multiuser scenario. Furthermore, we give an optimization algorithm to find the power allocation for the inner SPARC code that minimizes the SNR required to achieve a given target per-user error probability with the AMP decoder.

Orthogonal time frequency and space (OTFS) modulation is a pulse-shaped Gabor signaling scheme with additional time-frequency (TF) spreading using the symplectic finite Fourier transform (SFFT). With a sufficient amount of accurate channel information and sophisticated equalizers, it promises performance gains in terms of robustness for high mobility users. To fully exploit diversity in OTFS, the 2D-deconvolution implemented by a linear equalizer should approximately invert the doubly dispersive channel operation, which however is a twisted convolution. In theory, this is achieved in a first step by matching the TF grid and the Gabor synthesis and analysis pulses to the delay and Doppler spread of the channel. However, in practice, one always has to balance between supporting high granularity in delay-Doppler (DD) spread, and multi-user and network aspects. In this paper, we propose mobility modes with distinct grid and pulse matching for different doubly dispersive channels. To account for remaining self-interference, we tune the minimum mean square error (MMSE) linear equalizer without the need of estimating channel cross-talk coefficients. We evaluate our approach with the QuaDRiGa channel simulator and with OTFS transceiver architecture based on a polyphase implementation for orthogonalized Gaussian pulses. In addition, we compare OTFS to a IEEE 802.11p compliant design of cyclic prefix (CP) based orthogonal frequency-division multiplexing (OFDM). Our results indicate that with an appropriate mobility mode, the potential OTFS gains can be indeed achieved with linear equalizers to significantly outperform OFDM.

Unsourced random-access (U-RA) is a type of grant-free random access with a virtually unlimited number of users, of which only a certain number Kaare active on the same time slot. Users employ exactly the same codebook, and the task of the receiver is to decode the list of transmitted messages. Recently a concatenated coding construction for U-RA on the AWGN channel was presented, in which a sparse regression code (SPARC) is used as an inner code to create an effective outer OR-channel. Then an outer code is used to resolve the multiple-access interference in the OR-MAC. In this work we show that this concatenated construction can achieve a vanishing per-user error probability in the limit of large blocklength and a large number of active users at sum-rates up to the symmetric Shannon capacity, i.e. as long as KaR2(1 + KaSNR). This extends previous point-to-point optimality results about SPARCs to the unsourced multiuser scenario. Additionally, we calculate the algorithmic threshold, that is a bound on the sum-rate up to which the inner decoding can be done reliably with the low-complexity AMP algorithm.

Vehicle-to-everything (V2X) communication is seen as an enabler of high-density platooning as part of more environmentally friendly future transportation systems. Indeed, in high-density platooning, trucks are able to reduce their overall fuel consumption. Compared to platooning systems exclusively based on sensors, V2X enabled platooning systems can drive smaller inter-vehicle distances. They are then able to achieve this fuel consumption reduction thanks to the decreased air drag. It has been shown that the performance of the application is dependent on the performance of the communications system. The application therefore needs to be aware of the maximal tolerable communication degradation that keeps the platoon safe considering its driving parameters. In this article, we derive the relationship between the maximal tolerable packet losses, measured as the packet inter-reception time, and the intervehicle distance. We first study the relationship between these parameters through the analysis of simulation data. We then derive a functional link by fitting different statistical models. Finally, we apply the resulting models to packet inter-reception time measurements obtained in simulation of platoons supported by IEEE 802. 11p driving through varying surrounding traffic densities.

This work deals with the problem of distributed data acquisition under non-linear communication constraints. More specifically, we consider a model setup where M distributed nodes take individual measurements of an unknown structured source vector x0∈ ℝn, communicating their readings simultaneously to a central receiver. Since this procedure involves collisions and is usually imperfect, the receiver measures a superposition of non-linearly distorted signals. In a first step, we will show that an s-sparse vector x can be successfully recovered from O(s · log(2n/s)) of such superimposed measurements, using a traditional Lasso estimator that does not rely on any knowledge about the non-linear corruptions. This direct method however fails to work for several “uncalibrated” system configurations. These blind reconstruction tasks can be easily handled with the ℓ1,2-Group-Lasso, but coming along with an increased sampling rate of O(s · max{M, log(2n/s)}) observations - in fact, the purpose of this lifting strategy is to extend a certain class of bilinear inverse problems to non-linear acquisition. Our two algorithmic approaches are a special instance of a more abstract framework which includes sub-Gaussian measurement designs as well as general (convex) structural constraints. These results are of independent interest for various recovery and learning tasks, as they apply to arbitrary non-linear observation models. Finally, to illustrate the practical scope of our theoretical findings, an application to wireless sensor networks is discussed, which actually serves as the prototypical example of our methodology.

We investigate practical aspects of a recently introduced blind (noncoherent) communication scheme, called modulation on conjugate-reciprocal zeros (MOCZ). MOCZ is suitable for a reliable transmission of sporadic and short-packets at ultra-low latency and high spectral efficiency via unknown multipath channels, which are assumed to be static over the receive duration of one packet. The information is modulated on the zeros of the transmitted discrete-time baseband signal's z- transform. Because of ubiquitous impairments between the transmitter and receiver clocks, a carrier frequency offset occurs after down-conversion to the baseband. This results in a common rotation of the zeros. To identify fractional rotations of the base angle in the zero-pattern, we propose an oversampled direct zero-testing decoder to identify the most likely one. Integer rotations correspond to cyclic shifts of the binary message, which we determine by cyclically permutable codes (CPC). Additionally, the embedding of CPCs into cyclic codes, enables additive error-correction which reduces the bit-error-rate tremendously. Furthermore, we exploit the trident structure in the signal's autocorrelation for an energy based detector to estimate timing offsets and the effective channel delay spread. We finally demonstrate how this joint data and channel estimation can be largely improved by receive antenna diversity at low SNR.

This paper studies the optimal achievable performance of compressed sensing based unsourced random-access communication over the real AWGN channel. "Unsourced" means that every user employs the same codebook. This paradigm, recently introduced by Polyanskiy, is a natural consequence of a very large number of potential users of which only a finite number is active in each time slot. The resemblance of compressed sensing based communication and sparse regression codes (SPARCs), a novel type of point-to-point channel codes, allows us to design and analyse an efficient unsourced random-access code. Finite blocklength simulations show that the combination of AMP decoding, with suitable approximations, together with an outer code recently proposed by Amalladinne et. al. outperforms state of the art methods in terms of required energyper-bit at lower decoding complexity.

We investigate non-negative least squares (NNLS) for the recovery of sparse non-negative vectors from noisy linear and biased measurements. We build upon recent results from [1] showing that for matrices whose row-span intersects the positive orthant, the nullspace property (NSP) implies compressed sensing recovery guarantees for NNLS. Such results are as good as for ℓ1-regularized estimators but require no tuning at all. A bias in the sensing matrix improves this auto-regularization feature of NNLS and the NSP then determines the sparse recovery performance only. We show that NSP holds with high probability for shifted symmetric subgaussian matrices and its quality is independent of the bias. As tool for proving this result we established a debiased version of Mendelson's small ball method.

We introduce a novel blind (noncoherent) communication scheme, called modulation on conjugate-reciprocal zeros (MOCZ), pronounced as “Moxie,” to reliably transmit sporadic short-packets over unknown wireless multipath channels. In MOCZ, the information is modulated onto the zeros of the transmitted discrete-time baseband signal's z-transform, which yields to a codebook of non-orthogonal signals. In the absence of additive noise, the zero structure of the signal is perfectly preserved at the receiver, no matter what the channel impulse response (CIR) is. Furthermore, by a proper selection of the zeros, we show that MOCZ is not only invariant to the CIR but also robust against additive noise. Starting with the maximum-likelihood estimator, we define a low complexity and reliable decoder and compare it to various state-of-the-art noncoherent multipath schemes, such as OFDM index-modulation (IM), OFDM pilot-aided, OFDM differential-modulation, and pulse-position-modulation. Our scheme outperforms all schemes and maintains its performance even if the length becomes shorter than the CIR.

In this paper, we study the problem of activity detection (AD) in a massive MIMO setup, where the Base Station (BS) has M ≫ 1 antennas. We consider a block fading channel model where the M-dim channel vector of each user remains almost constant over a coherence block (CB) containing Dc signal dimensions. We study a setting in which the number of potential users Kcassigned to a specific CB is much larger than the dimension of the CB Dc(Kc≫ Dc) but at each time slot only Ac≪ Kcof them are active. Most of the previous results, based on compressed sensing, require that Ac≤ Dc, which is a bottleneck in massive deployment scenarios such as Internet-of-Things (IoT) and Device-to-Device (D2D) communication. In this paper, we show that one can overcome this fundamental limitation when the number of BS antennas M is sufficiently large. More specifically, we derive a scaling law on the parameters (M, Dc, Kc, Ac) and also Signal-to-Noise Ratio (SNR) under which our proposed AD scheme succeeds. Our analysis indicates that with a CB of dimension Dc, and a sufficient number of BS antennas M with Ac/M=o(1), one can identify the activity of Ac=O(Dc2/log2((Kc)/(Ac))) active users, which is much larger than the previous bound Ac=O(Dc) obtained via traditional compressed sensing techniques. In particular, in our proposed scheme one needs to pay only a poly-logarithmic penalty O(log2((Kc)/(Ac))) for increasing the number of potential users Kc, which makes it ideally suited for AD in IoT setups. We propose low-complexity algorithms for AD and provide numerical simulations to illustrate our results.

We consider simultaneous blind deconvolution of r source signals from their noisy superposition, a problem also referred to blind demixing and deconvolution. This signal processing problem occurs in the context of the Internet of Things where a massive number of sensors sporadically communicate only short messages over unknown channels. We show that robust recovery of message and channel vectors can be achieved via convex optimization when random linear encoding using i.i.d. complex Gaussian matrices is used at the devices and the number of required measurements at the receiver scales with the degrees of freedom of the overall estimation problem. Since the scaling is linear in r our result significantly improves over recent works.

We investigate recovery of nonnegative vectors from non-adaptive compressive measurements in the presence of noise of unknown power. In the absence of noise, existing results in the literature identify properties of the measurement that assure uniqueness in the non-negative orthant. By linking such uniqueness results to nullspace properties, we deduce uniform and robust compressed sensing guarantees for nonnegative least squares. No ℒ1-regularization is required. As an important proof of principle, we establish that m × n random i.i.d. 0/1-valued Bernoulli matrices obey the required conditions with overwhelming probability provided that m = O(s log(n/s)). We achieve this by establishing the robust nullspace property for random 0/1-matrices-a novel result in its own right. Our analysis is motivated by applications in wireless network activity detection.

We consider the pairing problem in network-assisted device-to-device communications. The pairing problem is stated as a rate estimation problem. To this end, we develop a framework that we call compressive rate estimation. We assume that the composite channel gain matrix (i.e., the matrix of all channel gains between all network nodes) is compressible and develop a novel sensing and reconstruction protocol for the estimation of achievable rates. The proposed sensing protocol exploits the superposition principle of the wireless channel and enables the receiving nodes to obtain non-adaptive random measurements of columns of the composite channel matrix. The random measurements are fed back to a central controller who decodes the composite channel gain matrix (or parts of it) and estimates individual user rates. We analyze the rate loss gap for a linear and a non-linear decoder and find the scaling laws according to the number of non-adaptive measurements.

Providing short-message communication and simultaneous channel estimation for sporadic and fast fading scenarios is a challenge for future wireless networks. In this work we propose a novel blind communication and deconvolution scheme by using Huffman sequences, which allows to solve three important tasks at once: (i) determination of the transmit power (ii) identification of the instantaneous discrete-time FIR channel if the channel delay is less than L/2 and (iii) simultaneously communicating L-1 bits of information. Our signal reconstruction uses a recent semi-definite program that can recover two unknown signals from their auto-correlations and cross-correlations. This convex algorithm shows numerical stability and operates fully deterministic without any further channel assumptions.

In this paper, we utilize the framework of compressed sensing (CS) for device detection and distributed resource allocation in large-scale machine-to-machine (M2M) communication networks. The devices are partitioned into clusters according to some pre-defined criteria, e.g., proximity or service type. Moreover, by the sparse nature of the event occurrence in M2M communications, the activation pattern of the M2M devices can be formulated as a particular block sparse signal with additional in-block structure in CS based applications. This paper introduces a novel scheme for distributed resource allocation to the M2M devices based on block-CS related techniques, which mainly consists of three phases: (1) In a full-duplex acquisition phase, the network activation pattern is collected in a distributed manner. (2) The base station detects the active clusters and the number of active devices in each cluster, and then assigns a certain amount of resources accordingly. (3) Each active device detects the order of its index among all the active devices in the cluster and accesses the corresponding resource for transmission. The proposed scheme can efficiently reduce the acquisition time with much less computation complexity compared with standard CS algorithms. Finally, extensive simulations confirm the robustness of the proposed scheme under noisy conditions.

In this paper, we study the capacity and degree-of-freedom (DoF) scaling for the continuous-time amplitude limited AWGN channels in radio frequency (RF) and intensity modulated optical communication (OC) channels. More precisely, we study how the capacity varies in terms of the OFDM block transmission time T, bandwidth W, amplitude A and the noise spectral density N0/2. We first find suitable discrete encoding spaces for both cases, and prove that they are convex sets that have a semi-definite programming (SDP) representation. Using tools from convex geometry, we find lower and upper bounds on the volume of these encoding sets, which we exploit to drive pretty sharp lower and upper bounds on the capacity. We also study a practical Tone-Reservation (TR) encoding algorithm and prove that its performance can be characterized by the statistical width of an appropriate convex set. Recently, it has been observed that in high-dimensional estimation problems under constraints such as those arisen in Compressed Sensing (CS) statistical width plays a crucial role. We discuss some of the implications of the resulting statistical width on the performance of the TR. We also provide numerical simulations to validate these observations.

We investigate recovery of nonnegative vectors from nonadaptive compressive measurements in the presence of noise of unknown power. It is known in the literature that under additional assumptions on the measurement design recovery of such vectors is possible with nonnegative least squares without any regularization. We show that uniqueness results known for the noiseless case carry over to robust guarantees in the noisy setting. We present guarantees which hold instantaneously by connecting the relation to the robust nullspace property. As an important example, we prove that an m × n random iid. 0/1-valued Bernoulli matrix with m = O(s log(n)) rows admits the robust nullspace property with high probability and meets the design requirements for nonnegative least squares recovery. Our analysis is motivated by applications in wireless network activity detection.

We consider a device-to-device scenario in a fragmented spectrum band. Multiple devices transmit complex symbols with a single antenna on distributed, but disjoint OFDM resources. The devices select sufficient frequency resources to enable channel estimation, if the receiver has complete knowledge of the resource map. However, in this scenario the actual allocation map is unknown to the receiver. Therefore, a receiver observing the superposition of all transmitted signals is faced with two problems, channel estimation and identification of the correct resources allocation map. In our previous work [1], we identified the channel and the allocation map of the corresponding users by applying an objective function based on the ℓ1-norm. In this work, we show that successful recovery is possible under different practical ITU channel models. Furthermore, we apply basis pursuit denoising (BPDN) from the compressed sensing framework for channel estimation and show the superior performance in contrast to classical least square estimators. These results show, that identifying non-adjacent multiuser allocations is possible.

In theory, coordinated multipoint transmission (CoMP) promises vast gains in spectral efficiency. However, industrial field trials show rather disappointing throughput gains, whereby the major limiting factor is proper sharing of channel state information. Many recent papers have considered this so-called limited feedback problem in the context of CoMP, usually taking the following assumptions, namely, infinite SNR regime, no user selection, and ideal link adaptation, rendering the analysis too optimistic. In this paper, we make a step forward toward a more realistic assessment of the limited feedback problem by introducing an improved metric for the performance evaluation, which better captures the throughput degradation. We find the relevant scaling laws (lower and upper bounds) and show that they are different from existing ones. Moreover, we provide a robust iterative interference alignment algorithm and corresponding feedback strategies achieving the obtained scaling laws. The main idea is that, instead of sending the complete channel matrix, each user fixes a receive filter and feeds back a quantized version of the effective channel. Finally, we underline our findings with simulations for the proposed system.

In this note we show that stable recovery of complex-valued signals x ϵ Cnup to a global sign can be achieved from the magnitudes of 4n - 1 Fourier measurements when a certain symmetrization and zero-padding is performed before measurement (4n - 3 is possible in certain cases). For real signals, symmetrization itself is linear and therefore our result is in this case a statement on uniform phase retrieval. Since complex conjugation is involved, such measurement procedure is not complex-linear but recovery is still possible from magnitudes of linear measurements on, for example, (Re(x), Im(x)).

In this paper we show that convolutions of sufficiently sparse signals always admit a non-zero lower bound in energy if oversampling of its Fourier transform is employed. This bound is independent of the signals and the ambient dimension and is determined only be the sparsity of both input signals. This result has several implications for blind system and signal identification and detection, noncoherent communication of sporadic and short-message type user data and strategies for its compressive reception. Furthermore, we give some first insights into the combinatorial nature of this problem, its scaling behavior and present numerical results as well.

This paper proposes a novel feedback protocol for relay-based two-hop networks, in which the channel state information matrix of the second hop is compressible due to the presence of spatial correlation and distance dependent path loss among the communication channels from the relay nodes to the users. The proposed protocol makes use of recent developments in the fields of low rank matrix recovery and compressed sensing to approximate the channel matrix by a low rank and sparse matrix. As a result, accurate channel state information can be provided to the base station for optimal relay selection, while significantly reducing pilot contamination and feedback overhead. Simulations demonstrate that approximately 50% of the training and feedback overhead can be saved if the compressibility of the channel matrix is taken into account.

For several communication models, the dispersive part of a communication channel is described by a bilinear operation T between the possible sets of input signals and channel parameters. The received channel output has then to be identified from the image T(X, Y) of the input signal difference sets X and the channel state sets Y. The main goal in this contribution is to characterize the compressibility of T(X, Y) with respect to an ambient dimension N. In this paper we show that a restricted norm multiplicativity of T on all canonical subspaces X and Y with dimension S resp. F is sufficient for the reconstruction of output signals with an overwhelming probability from O((S + F) log N) random sub-Gaussian measurements. Thus, in this case, the number of degrees of freedom of each output grows only additively instead of multiplicatively with the input dimensions (sparsity) S and F. This is a relevant improvement in the output compressibility and suggests a substantially reduced rate in compressed sampling algorithms.

We present and analyze a new robust feedback and transmit strategy for multiuser MIMO downlink communication systems, termed Rate Approximation (RA). RA combines the flexibility and robustness needed for reliable communications with the user terminal under a limited feedback constraint. It responds to two important observations. First, it is not so significant to approximate the channel but rather the rate, such that the optimal scheduling decision can be mimicked at the base station. Second, a fixed transmit codebook at the transmitter is often better when therefore the channel state information is more accurate. In the RA scheme the transmit and feedback codebook are separated and user rates are delivered to the base station subject to a controlled uniform error. The scheme is analyzed and proved to have better performance below a certain interference plus noise margin and better behavior than the classical Jindal formula. LTE system simulations sustain the analytic results showing performance gains of up to 50% or 70% compared to zeroforcing when using multiple antennas at the base station and multiple antennas or a single antenna at the terminals, respectively. A new feedback protocol is developed which inherently considers the transmit codebook and which is able to deal with the complexity issue at the terminal.

We consider the time-continuous doubly-dispersive channel with additive Gaussian noise and establish a capacity formula for the case where the channel correlation operator is represented by a symbol which is periodic in time and fulfills some further integrability and smoothness conditions. The key to this result is a new Szegö formula for certain pseudo-differential operators. The formula justifies the water-filling principle along time and frequency in terms of the time-continuous time-varying transfer function (the symbol).

In this paper we present a new paradigm for multiuser MIMO downlink communications called Rate Approximation with significant impact on the upcoming LTE standard. Rate Approximation combines flexibility and robustness needed for reliable communications with the terminal in the downlink and taking advantage of the channel state information. The scheme responds to two major developments in the recent literature: One observation is that it is not so important to approximate the channel but rather the rate itself. The second observation is that a fixed codebook at the transmitter is often better when simultaneously the channel state information is more accurate. Both observations are incorporated in the new scheme where the transmit and feedback codebook are strictly separated and user rates are brought to the base station subject to a controlled uniform error. The new metric is amenable to further numerical optimization. Analysis and simulations show the superior performance of the scheme and, furthermore, a strong impact on upcoming cooperative schemes is expected.

We present a new robust feedback and transmit strategy for multiuser MIMO downlink communication systems, termed Rate Approximation (RA), and analyze its performance. The new scheme combines flexibility and robustness needed for reliable communications with the user terminal, under a limited feedback constraint. The scheme responds to two major developments in the recent literature: One observation is that it is not so important to approximate the channel but rather the rate itself. The second observation is that a fixed codebook at the transmitter is often better when simultaneously the channel state information is more accurate. Both observations are incorporated in the new scheme where the transmit and feedback codebook are strictly separated and user rates are brought to the base station subject to a controlled uniform error. The analysis provides two astonishing results. First, under perfect channel state information at the transmitter RA outperforms zeroforcing beamforming (ZFBF) for a large fraction of the practically relevant signal-to-noise ratio range for the considered operating point. Second, under a limited feedback constraint the quantization error scaling of RA is shown to be doubly exponentially in the number of feedback bits, whereas the quantization error of ZFBF with random vector quantization was shown by Jindal to scale only exponentially. Simulations sustain our analytic results showing the superior performance of the new scheme.

In this contribution we present a novel method for constructing orthogonal pulses for UWB impulse radio transmission under the FCC spectral mask constraint. In contrast to previous work we combine a convex formulation of the spectral design with Lowdin's orthogonalization method [1], which delivers a shift--orthogonal basis optimally close (in energy) to the initial pulse, which generates (in a stable way) the shift--invariant space. The convex formulation of the spectral design is achieved by approximating the FCC mask with a finite--order filter matched to Gaussian monocycles as input. The output pulse then has high energy concentration in the passband (NESP value). Using Lowdin's orthogonalization we compute the corresponding shift--orthogonal pulse. We show that our approach is able to generate for finitely many shifts, orthogonal equal energy pulses with nearly the same NESP value. Furthermore, we show that the orthogonalization procedure can be well approximated using the Zak transform allowing for an efficient implementation with the discrete Fourier transform. Surprisingly, we could observe, that for certain parameters, this approximation yields almost the same performance as the exact Lowdin method.

We propose a new limited feedback scheme for the downlink of multiuser MIMO OFDM systems based on fixed linear beamforming, i.e. the linear beamforming vectors are chosen from a fixed transmit codebook. The proposed feedback method allows the base station to uniformly approximate all multiuser rates for any selection of users and any combination of beamforming vectors defined by the transmit codebook; thus providing all degrees of freedom for the user selection. The approximation of the multiuser rates is enabled by using an additional codebook for the feedback. This has several advantages: the transmit codebook can be designed independent of the feedback codebook, the accuracy of the approximated rates can be scaled by changing the size of the feedback codebook and the feedback codebook can be adapted to the environment. We show how feedback codebooks can be designed for arbitrary environments using the LBG algorithm. Moreover, we show how the computational complexity of the proposed feedback method can be reduced without a significant performance loss. In the simulations we demonstrate that the proposed method outperforms other methods within the LTE context.

In this article we show the relation between the theory of pulse shaping for WSSUS channels and the notion of approximate eigenstructure for time-varying channels. We consider pulse shaping for a general signaling scheme, called Weyl-Heisenberg signaling, which includes OFDM with cyclic prefix and OFDM/OQAM. The pulse design problem in the view of optimal WSSUS-averaged SINR is an interplay between localization and "orthogonality". The localization problem itself can be expressed in terms of eigenvalues of localization operators and is intimately connected to the concept of approximate eigenstructure of LTV channel operators. In fact, on the L2-level both are equivalent as we will show. The concept of "orthogonality" in turn can be related to notion of tight frames. The right balance between these two sides is still an open problem. However, several statements on achievable values of certain localization measures and fundamental limits on SINR can already be made as will be shown in the paper.

Optimal link adaption to the scattering function of wide sense stationary uncorrelated scattering (WSSUS) mobile communication channels is still an unsolved problem despite its importance for the next-generation system design. In a multicarrier transmission, such link adaption is performed by pulse shaping, i.e., by properly adjusting the transmit and receive filters. Pulse-shaped offset–quadratic-amplitude-modulation systems have been recently shown to have superior performance over standard cyclic prefix orthogonal frequency-division multiplexing (while operating at higher spectral efficiency). In this paper, we establish a general mathematical framework for joint transmitter and receiver pulse-shape optimization for so-called Weyl–Heisenberg or Gabor signaling, with respect to the scattering function of the WSSUS channel. In our framework, the pulse shape optimization problem is translated to an optimization problem over trace class operators, which in turn is related to fidelity optimization in quantum information processing. By convexity relaxation, the problem is shown to be equivalent to a convex constraint quasi-convex maximization problem, thereby revealing the nonconvex nature of the overall WSSUS pulse design problem. We present several iterative algorithms for optimization, providing applicable results even for large-scale problem constellations. We show that with transmitter-side knowledge of the channel statistics, a gain of 3–6 dB in signal-to-interference-plus-noise ratio can be expected.

Optimal link adaption to the scattering function of wide-sense stationary uncorrelated scattering (WSSUS) mobile communication channels is still an unsolved problem despite its importance for next-generation system design. In multicarrier transmission, such link adaption is performed by pulse shaping, i.e., by properly adjusting the transmit and receive filters. For example, pulse-shaped offset-quadrature amplitude modulation (OQAM) systems have recently been shown to have superior performance over standard cyclic prefix orthogonal frequency-division multiplexing (OFDM) (while operating at higher spectral efficiency). In this paper, we establish a general mathematical framework for joint transmitter and receiver pulse shape optimization for so-called Weyl-Heisenberg or Gabor signaling with respect to the scattering function of the WSSUS channel. In our framework, the pulse shape optimization problem is translated to an optimization problem over trace class operators which, in turn, is related to fidelity optimization in quantum information processing. By convexity relaxation, the problem is shown to be equivalent to a convex constraint quasi-convex maximization problem thereby revealing the nonconvex nature of the overall WSSUS pulse design problem. We present several iterative algorithms for optimization providing applicable results even for large-scale problem constellations. We show that with transmitter-side knowledge of the channel statistics a gain of 3-6 dB in signal-to-interference-and-noise-ratio (SINR) can be expected.

In this article new bounds on weighted p-norms of ambiguity functions and Wigner functions are derived. Such norms occur frequently in several areas of physics and engineering. In pulse optimization for Weyl-Heisenberg signaling in wide-sense stationary uncorrelated scattering channels for example it is a key step to find the optimal waveforms for a given scattering statistics which is a problem also well known in radar and sonar waveform optimizations. The same situation arises in quantum information processing and optical communication when optimizing pure quantum states for communicating in bosonic quantum channels, i.e. find optimal channel input states maximizing the pure state channel fidelity. Due to the non-convex nature of this problem the optimum and the maximizers itself are in general difficult find, numerically and analytically. Therefore upper bounds on the achievable performance are important which will be provided by this contribution. Based on a result due to E. Lieb, the main theorem status a new upper bound which is independent of the waveforms and becomes tight only for Gaussian weights and waveforms. A discussion of this particular important case, which tighten recent results on Gaussian quantum fidelity and coherent states, will be given. Another bound is presented for the case where scattering is determined only by some arbitrary region in phase space

The demand for wireless broadband access systems supporting mobility of the individual users has dramatically increased in recent years. To this end, we analyze the impact of user-mobility in the uplink of an OFDMA system on the performance of pilot-aided channel estimation. We analyze the mean square error (MSE) performance of two pilot-aided channel estimation schemes, the simple Gauss-Markov estimator and the optimal LMMSE estimator. We derive closed-form expressions for the MSE taking into account the impact of intercarrier-interference and time-variations of the channel. Different pilot allocation strategies are analyzed and their performances are compared. Finally, the results are illustrated by numerical simulations based on the WiMax 802.16e specifications

We consider the pulse design problem in multicarrier transmission where the pulse shapes are adapted to the second order statistics of the WSSUS channel. Even though the problem has been addressed by many authors analytical insights are rather limited. First we show that the problem is equivalent to the pure state channel fidelity in quantum information theory. Next we present a new approach where the original optimization functional is related to an eigenvalue problem for a pseudo differential operator by utilizing unitary representations of the Weyl-Heisenberg group. A local approximation of the operator for underspread channels is derived which implicitly covers the concepts of pulse scaling and optimal phase space displacement. The problem is reformulated as a differential equation and the optimal pulses occur as eigenstates of the harmonic oscillator Hamiltonian. Furthermore this operator-algebraic approach is extended to provide exact solutions for different classes of scattering environments

Phase noise and frequency offsets are, due to their time-variant behavior, one of the most limiting disturbances in practical orthogonal frequency-division multiplexing (OFDM) designs, and therefore, intensively studied by many authors. In this paper, we present a generalized framework for the prediction of uncoded system performance in the presence of time-variant distortions, including the transmitter and receiver pulse shapes, as well as the channel. Therefore, unlike existing studies, our approach can be employed for more general multicarrier schemes. To show the usefulness of our approach, we apply the results to OFDM in the context of frequency offset and Wiener phase noise, yielding improved bounds on the uncoded performance. In particular, we obtain exact formulas for the averaged performance in additive white Gaussian noise and time-invariant multipath channels.