Unsourced random access (URA) is a particular form of grant-free uncoordinated multiple access wherein the users’ identities are not associated to specific waveforms at the physical layer. Tensor-based modulation (TBM) has been recently advocated as a promising technique for URA due to its ability to support a large number of active users transmitting simultaneously by exploiting tensor decomposition for user separation. In the present paper, we introduce a novel URA scheme that builds upon TBM by splitting the transmit message into two sub-messages. This first part is modulated according to a TBM scheme, while the second is encoded using a coherent non-orthogonal multiple access (NOMA) modulation. At the receiver side, we exploit the advantages of forward error correction (FEC) coding and interference cancellation techniques. The performance of the introduced scheme is compared with state-of-the-art URA schemes under a quasi-static Rayleigh fading model, proving the energy efficiency and robustness to large-scale fading of the proposed solution.

Under a simplified data model, this paper provides a theoretical analysis of learning from data that have an underlying low-rank tensor structure in both supervised and unsupervised settings. For the supervised setting, we provide an analysis of a Ridge classifier (with high regularization parameter) with and without knowledge of the low-rank structure of the data. Our results quantify analytically the gain in misclassification errors achieved by exploiting the low-rank structure for denoising purposes, as opposed to treating data as mere vectors. We further provide a similar analysis in the context of clustering, thereby quantifying the exact performance gap between tensor methods and standard approaches which treat data as simple vectors.

This paper considers a general framework for massive random access based on sparse superposition coding. We provide guidelines for the code design and propose the use of constant-weight codes in combination with a dictionary design based on Gabor frames. The decoder applies an extension of approximate message passing (AMP) by iteratively exchanging soft information between an AMP module that accounts for the dictionary structure, and a second inference module that utilizes the structure of the involved constant-weight code. We apply the encoding structure to (i) the unsourced random access setting, where all users employ a common dictionary, and (ii) to the “sourced” random access setting with user-specific dictionaries. When applied to a fading scenario, the communication scheme essentially operates non-coherently, as channel state information is required neither at the transmitter nor at the receiver. We observe that in regimes of practical interest, the proposed scheme compares favorably with state-of-the art schemes, in terms of the (per-user) energy-per-bit requirement, as well as the number of active users that can be simultaneously accommodated in the system. Importantly, this is achieved with a considerably smaller size of the transmitted codewords, potentially yielding lower latency and bandwidth occupancy, as well as lower implementation complexity.

Tensor-based modulation (TBM) [1] is a novel waveform design allowing massive random access in future wireless networks. In this article, we study the sensitivity of TBM to timing offsets when using orthogonal frequency division multiplexing (OFDM) transmissions. We show that as long as some mild conditions are met with respect to the mapping of the tensor elements on the OFDM time-frequency grid, it is still possible to separate the users, and to estimate and compensate their timing offsets on a per-user basis. We demonstrate the effectiveness of the estimator with both coherent and non-coherent modulation schemes.

We consider the joint constellation design problem for the noncoherent multiple-input multiple-output multiple-access channel (MAC). By analyzing the noncoherent maximum-likelihood detection error, we propose novel design criteria so as to minimize the error probability. As a baseline approach, we adapt several existing design criteria for the point-to-point channel to the MAC. Furthermore, we propose new design criteria. Our first proposed design metric is the dominating term in nonasymptotic lower and upper bounds on the pairwise error probability exponent. We give a geometric interpretation of the bound using Riemannian distance in the manifold of Hermitian positive definite matrices. From an analysis of this metric at high signal-to-noise ratio, we obtain further simplified metrics. For any given set of constellation sizes, the proposed metrics can be optimized over the set of constellation symbols. Motivated by the simplified metric, we propose a simple constellation construction consisting inpartitioninga single-user constellation. We also provide a generalization of our previously proposed construction based onprecodingindividual constellations of lower dimensions. For a fixed joint constellation, the design metrics can be further optimized over the per-user transmit power, especially when the users transmit at different rates. Considering unitary space-time modulation, we investigate the option of building each individual constellation as a set of truncated unitary matrices scaled by the respective transmit power. Numerical results show that our proposed metrics are meaningful, and can be used as objectives to generate constellations through numerical optimization that perform better, for the same transmission rate and power constraint, than a common pilot-based scheme and the constellations optimized with existing metrics.

We consider the use of deep neural networks (DNNs) in the context of channel state information (CSI)-based localization for Massive MIMO cellular systems. We discuss the practical impairments that are likely to be present in practical CSI estimates, and introduce a principled approach to feature design for CSI-based DNN applications based on the objective of making the features invariant to the considered impairments. We demonstrate the efficiency of this approach by applying it to a dataset constituted of geo-tagged CSI measured in an outdoors campus environment, and training a DNN to estimate the position of the UE on the basis of the CSI. We provide an experimental evaluation of several aspects of that learning approach, including localization accuracy, generalization capability, and data aging.

Channel charting is a data-driven baseband processing technique consisting in applying unsupervised machine learning techniques to channel state information (CSI), with the objective of reducing the dimension of the data and extracting the fundamental parameters governing the distribution of CSI samples observed by a given receiver. In this work, we focus on neural network-based approaches, and propose a new training strategy based on triplets of samples. It allows to simultaneously learn a meaningful similarity metric between CSI samples, on the basis of proximity in their respective acquisition times, and to perform the sought dimensionality reduction. The proposed approach is evaluated on a dataset of measured massive MIMO CSI, and is shown to perform well in comparison to the state-of-the-art methods (uniform manifold approximation and projection (UMAP), autoencoders, and siamese networks). In particular, we show that the obtained chart representation is topologically close to the geographical user position, despite the fact that the charting approach is not supervised by any geographical data.

We consider the joint constellation design problem for noncoherent multiple-input multiple-output multiple-access channels. By analyzing the noncoherent maximum-likelihood detection error, we propose novel design criteria so as to minimize the error probability. For any given set of constellation sizes, the proposed metrics can be optimized over the set of signal matrices. Based on these criteria, we propose a simple and efficient construction consisting in partitioning a single-user constellation. Numerical results show that our proposed metrics are meaningful, and can be used as objectives to generate constellations through numerical optimization that perform better, for the same transmission rate and power constraint, than a common pilot-based scheme and the constellations optimized with existing metrics.

Massive multiple-input multiple-output (MIMO) systems use antenna arrays with a large number of antenna elements to serve many different users simultaneously. The large number of antennas in the system makes, however, the channel state information (CSI) acquisition strategy design critical and particularly challenging. Interestingly, in the context of massive MIMO systems, channels exhibit a large degree of spatial correlation which results in strongly rank-deficient spatial covariance matrices at the base station (BS). With the final objective of analyzing the benefits of covariance-aided uplink multi-user CSI acquisition in massive MIMO systems, here we compare the channel estimation mean-square error (MSE) for (i) conventional CSI acquisition, which does not assume any knowledge on the user spatial covariance matrices and uses orthogonal pilot sequences; and (ii) covariance-aided CSI acquisition, which exploits the individual covariance matrices for channel estimation and enables the use of non-orthogonal pilot sequences. We apply a large-system analysis to the latter case, for which new asymptotic MSE expressions are established under various assumptions on the distributions of the pilot sequences and on the covariance matrices. We link these expressions to those describing the estimation MSE of conventional CSI acquisition with orthogonal pilot sequences of some equivalent length. This analysis provides insights on how much training overhead can be reduced with respect to the conventional strategy when a covariance-aided approach is adopted.

In this paper, we propose a practical structured constellation for non-coherent communication with a single transmit antenna over Rayleigh flat and block fading channel without instantaneous channel state information. The constellation symbols belong to the Grassmannian of lines and are defined up to a complex scaling. The constellation is generated by partitioning the Grassmannian of lines into a collection of bent hypercubes and defining a mapping onto each of these bent hypercubes such that the resulting symbols are approximately uniformly distributed on the Grassmannian. With a reasonable choice of parameters, this so-called cube-split constellation has higher packing efficiency, represented by the minimum distance, than the existing structured constellations. Furthermore, exploiting the constellation structure, we propose low-complexity greedy symbol decoder and log-likelihood ratio computation, as well as an efficient way to associate it to a multilevel code with multistage decoding. Numerical results show that the performance of the cube-split constellation is close to that of a numerically optimized constellation and better than other structured constellations. It also outperforms a coherent pilot-based scheme in terms of error probability and achievable data rate in the regime of short coherence time and large constellation size.

We consider the non-coherent single-input multiple-output (SIMO) multiple access channel with general signaling under spatially correlated Rayleigh block fading. We propose a novel soft-output multi-user detector that computes an approximate marginal posterior of each transmitted signal using only the knowledge about the channel distribution. Our detector is based on expectation propagation (EP) approximate inference and has polynomial complexity in the number of users, number of receive antennas and channel coherence time. We also propose two simplifications of this detector with reduced complexity. With Grassmannian signaling, the proposed detectors outperform a state-of-the-art non-coherent detector with projection-based interference mitigation. With pilot-assisted signaling, the EP detector outperforms, in terms of symbol error rate, some conventional coherent pilot-based detectors, including a sphere decoder and a joint channel estimation-data detection scheme. Our EP-based detectors produce accurate approximates of the true posterior leading to high achievable sum-rates. The gains of these detectors are further observed in terms of the bit error rate when using their soft outputs for a turbo channel decoder.

With the final objective of analyzing the benefits of covariance-aided uplink multi-user channel state information (CSI) acquisition in massive MIMO systems, in this paper we compare the channel estimation mean-square error (MSE) for (i) conventional CSI acquisition, which does not assume any knowledge on the users' individual spatial covariance matrices and uses orthogonal pilot sequences; and (ii) covariance-aided CSI acquisition, which exploits the individual covariance matrices (and especially their low rank) for channel estimation and possibly uses non-orthogonal pilot sequences. We apply a large-system analysis to the latter case and provide insights about how much the CSI acquisition process can be overloaded (in the sense of allowing estimating CSI with sufficient accuracy for more users than the number resource elements allocated for training) when a covariance-aided approach is adopted. This hints at potentially significant gains in the spectral efficiency of CSI acquisition in Massive MIMO.

One of the biggest challenges in operating massive multiple-input multiple-output systems is the acquisition of accurate channel state information at the transmitter. To take up this challenge, time division duplex is more favorable thanks to its channel reciprocity between downlink and uplink. However, while the propagation channel over the air is reciprocal, the radio-frequency front-ends in the transceivers are not. Therefore, calibration is required to compensate the RF hardware asymmetry. Although various over-the-air calibration methods exist to address the above problem, this paper offers a unified representation of these algorithms, providing a higher level view on the calibration problem, and introduces innovations on calibration methods. We present a novel family of calibration methods, based on antenna grouping, which improves accuracy and speeds up the calibration process compared to existing methods. We then provide the Cramér-Rao bound as the performance evaluation benchmark and compare maximum likelihood and least squares estimators. We also differentiate between the coherent and non-coherent accumulation of calibration measurements, and point out that enabling non-coherent accumulation allows the training to be spread in time, minimizing the impact to the data service. Overall, these results have special value in allowing the design of reciprocity calibration techniques that are both accurate and resource-effective.

This paper introduces a new quantization scheme for real and complex Grassmannian sources. The proposed approach relies on a structured codebook based on a geometric construction of a collection of bent grids defined from an initial mesh on the unit-norm sphere. The associated encoding and decoding algorithms have very low complexity (equivalent to a scalar quantizer), while their efficiency (in terms of the achieved distortion) is on par with the best known structured approaches, and compares well with the theoretical bounds. These properties make this codebook suitable for high-resolutions, real-time applications such as channel state feedback in massive multiple-input multiple-output (MIMO) wireless communication systems.

This paper extends the empirical minimum divergence approach for models, which satisfy linear constraints with respect to the probability measure of the underlying variable (moment constraints) to the case where such constraints pertain to its quantile measure (called here semiparametric quantile models). The case when these constraints describe shape conditions as handled by the L-moments is considered, and both the description of these models as well as the resulting nonclassical minimum divergence procedures are presented. These models describe neighbourhoods of classical models used mainly for their tail behavior, for example, neighborhoods of Pareto or Weibull distributions, with which they may share the same first L-moments. The properties of the resulting estimators are illustrated by simulated examples comparing maximum likelihood estimators on Pareto and Weibull models to the minimum chi-square empirical divergence approach on semiparametric quantile models, and others.