International audience

Tensor-based modulation (TBM) provides a multi-linear spreading framework for blind multi-user separation in unsourced random access. In this paper, we show that TBM is a coded modulation built on a non-binary linear block code over $\mathbb{Z}_M$, whose symbols are mapped to $M$-PSK modulation, defining a geometrically uniform signal space code. We explicitly derive this generator matrix, characterize its rank deficiency, and show that reference symbols for tensor identifiability correspond to code shortening, producing a quasi-systematic or a systematic code, depending on the number of considered reference symbols for the TBM. Simulations in single-user AWGN and multi-user non-coherent multi-antenna fading channels demonstrate strong robustness and interference resilience, establishing TBM as a scalable, algebraically structured modulation-coding scheme bridging tensor representations and modern coding theory.

Wireless channel charting consists in the application of dimensionality reduction methods to the channel state information (CSI) collected during the operation of wireless communication systems. In the context of streaming data and due to hardware limitations, it is desirable to minimize the stored information during training; hence we propose online sample selection to perform dynamic channel charting. More specifically, we introduce a dual-memory approach consisting of a short-term buffer for recently received CSI samples and a longterm memory that retains key samples accumulated over time. We present novel unsupervised replay-based continual learning strategies for triplet-based channel charting from streaming CSI data. In particular, we develop three sample selection strategies for memory updates that are compatible with real-time operation and based on the channel chart, the loss function, or its gradient. Validation using real data demonstrate that our methods outperform existing replay-based unsupervised approaches.

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.

The high-SNR capacity of the noncoherent MIMO channel has been derived for the case of independent and identically distributed (IID) Rayleigh block fading by exploiting the Gaussianity of the channel matrix. This implies the optimal degrees of freedom (DoF), i.e., the capacity pre-log factor. Nevertheless, as far as the optimal DoF is concerned, IID Rayleigh fading is apparently a sufficient but not necessary condition. In this paper, we show that the optimal DoF for the IID Rayleigh block fading channel is also the optimal DoF for a more general class of generic block fading channels, in which the random channel matrix has finite power and finite differential entropy. Our main contribution is a novel converse proof based on the duality approach.

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.

The optimal degree-of-freedom (DoF) region of the non-coherent multiple-access channels is still unknown in general. In this paper, we make some progress by deriving the entire optimal DoF region in the case of the two-user single-input multiple-output (SIMO) generic block fading channels. The achievability is based on a simple training-based scheme. The novelty of our result lies in the converse using a genie-aided bound and the duality upper bound. As a by-product, our result generalizes previous proofs for the single-user Rayleigh block fading channels.

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.

In this paper, we study the two-user non-coherent multiple-input multiple-output broadcast channel with spatially correlated Rayleigh block fading. We propose a scheme to exploit the statistical channel state information (CSI), namely, the knowledge of the covariance matrix, and derive the corresponding achievable degrees of freedom region. The main idea of the proposed scheme is based on rate-splitting, additive superposition coding, and channel training. Our result shows that statistical CSI can play an important role in enhancing the degrees of freedom of a non-coherent broadcast channel.

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.

In interference channels (ICs), channel state information (CSI) can be utilized to design transmit signals that are optimally adapted to the state of the channels. This requires feeding CSI back to the transmitters. The CSI available at the transmitters (CSIT) is usually degraded, due to the limited capacity of the feedback link and the delays involved in the channel estimation and feedback. We discuss the scenario of fast fading and delayed CSIT, which is highly relevant in mobile environments with short channel coherence times. We consider the two-user multiple-input-multiple-output (MIMO) IC where the transmitters are provided with delayed CSIT. The DoF region for this channel was characterized by Vaze and Varanasi. We devise a simple and intuitive achievable scheme, which has a unified structure for different antenna configurations. We show that the proposed scheme also achieves the DoF region of the two-user MIMO broadcast channel (BC). In the IC, our scheme does not require the knowledge of direct channels at the transmitters. Moreover, we show that the amount of feedback can be further reduced by exploiting the invariances of the problem. Our approach can be helpful when analyzing more complicated networks.

A simple channel state information (CSI) feedback scheme is proposed for interference alignment (IA) over the K-user constant multiple-input-multiple-output interference channel (MIMO IC). The proposed technique relies on the identification of invariants in the IA equations, which enables the reformulation of the CSI quantization problem as a single quantization on the Grassmann manifold at each receiver. The scaling of the number of feedback bits with the transmit power sufficient to preserve the multiplexing gain that can be achieved under perfect CSI is established. We show that the CSI feedback requirements of the proposed technique are better (lower) than what is required when using previously published methods (including state-of-the-art codebook-based as well as analog feedback techniques), for system dimensions (number of users and antennas) of practical interest. Furthermore, we show through simulations that this advantage persists at low SNR, in the sense that the proposed technique yields a higher sum-rate performance for a given number of feedback bits. Finally, to complement our analysis, we introduce a statistical model that faithfully captures the properties of the quantization error obtained for random vector quantization (RVQ) on the Grassmann manifold for large codebooks; this enables the numerical (Monte Carlo) analysis of general Grassmannian RVQ schemes for codebook sizes that would be impractically large to simulate.

We consider the two-user Multiple-Input-Multiple-Output Interference Channel (MIMO-IC) with outdated channel state information at the transmitters (CSIT). For a fast- fading scenario, the degrees-of-freedom (DoF) region for this channel has been characterized by Vaze and Varanasi in [1]. We devise a simple achievable scheme, which has a unified structure for different antenna configurations. In the proposed scheme, matrices with random entries chosen from a continuous probability distribution are used in the process of designing the precoders. The unified structure of the precoders involving random matrices makes our scheme suitable for generalization to other networks.

Cellular systems that employ time division duplexing (TDD) transmission are good candidates for implementation of interference alignment (IA) in the downlink since channel reciprocity enables the estimation of the channel state by the base stations (BS) in the uplink phase. However, the interfering BSs need to share their channel estimates via backhaul links of finite capacity. A quantization scheme is proposed which reduces the amount of information exchange (compared to conventional methods) required to achieve IA in such a system. The scaling (with the transmit power) of the number of bits to be exchanged between the BSs that is sufficient to preserve the multiplexing gain of IA is derived. Furthermore, assuming that the BSs have accurate estimates of their outgoing channels, new methods are proposed to further improve the performance of the network in a distributed manner.

In this paper link adaptation for interference alignment (IA) based on imperfect channel state information (CSI) is investigated. We consider a MIMO interference channel where the transmit and receive spaces are determined by IA. We look at maximizing a weighted sum of the average rates provided that a certain set of bit-error-rate and power constraints are satisfied by dynamically adjusting coding, modulation and powers. The problem is quite general and intractable. We resort to some approximations and provide simulations to show the accuracy of the approximations in the regimes with practical interest.

We introduce an iterative solution to the problem of interference alignment (IA) over MIMO channels based on a message-passing formulation. We propose a parameterization of the messages that enables the computation of IA precoders by a min-sum algorithm over continuous variable spaces - under this parameterization, suitable approximations of the messages can be computed in closed-form. We show that the iterative leakage minimization algorithm of Gomadam et al. is a special case of our message-passing algorithm, obtained for a particular schedule. Finally, we show that the proposed algorithm compares favorably to iterative leakage minimization in terms of convergence speed, and discuss a distributed implementation.

We study the problem of interference alignment in the multiple-input multiple-output interference channel. Aiming at minimizing the interference leakage power relative to the receiver noise level, we use the deterministic annealing approach to solve the optimization problem. In the corresponding probabilistic formulation, the precoders and the orthonormal bases of the desired signal subspaces are variables distributed on the complex Stiefel manifold. To enable analytically tractable computations, we resort to the variational mean field approximation and thus obtain a novel iterative algorithm for interference alignment. We also show that the iterative leakage minimization algorithm by Gomadam et al. and the alternating minimization algorithm by Peters and Heath, Jr. are instances of our method. Finally, we assess the performance of the proposed algorithm through computer simulations.

In this paper, interference alignment (IA) based on imperfect channel state information (CSI) is investigated. As the accuracy of the CSI at the transmitter side is crucial for IA, we analyze the statistics of the imperfect CSI and design an adaptive scheme based on the available imperfect CSI. We consider a multiple-input-multiple-output (MIMO) interference channel where the transmit and receive spaces are determined by IA. Using practical modulation schemes, we consider the maximization of a weighted sum of the average rates provided that a certain set of bit-error-rate and power constraints is satisfied by dynamically adapting coding, modulation, and power settings. The problem in such a general form is intractable. Therefore, we resort to some approximations and provide simulations to show the accuracy of the approximations in the regimes with practical interest.

Cellular systems that employ time division duplexing (TDD) transmission are good candidates for implementation of interference alignment (IA) in the downlink since channel reciprocity enables the estimation of the channel state by the base stations (BS) in the uplink phase. However, the interfering BSs need to share their channel estimates via backhaul links of finite capacity. A quantization scheme is proposed which reduces the amount of information exchange (compared to conventional methods) required to achieve IA in such a system. The scaling (with the transmit power) of the number of bits to be exchanged between the BSs that is sufficient to preserve the multiplexing gain of IA is derived1.

Network MIMO provides significant gains compared to transmission schemes based on the interference channel in cellular networks. However, the interference channel is adopted very often in particular due to data sharing limitations of network MIMO. These limitations are due to backhaul links which have finite capacity and also introduce delay. In interference channels, even though data is not exchanged between the transmitters, the global channel state information (CSI) needs to be shared in order to attain the degrees of freedom (DoF) of the channel. This highlights the necessity of reducing the amount of CSI exchange and relying more on local CSI to design the precoders in particular when the local CSI is accurate. In this contribution, cellular downlink transmission using time division duplexing (TDD) is considered where the base stations (BS) can estimate their own channels through reciprocity during the uplink phase. The interfering BSs share their channel estimates via backhaul links of finite capacity. We propose a distributed precoding method based on interference alignment (IA) which is shown to require relatively less CSI exchange compared to other methods.

Relative calibration has been proposed as a simple way to practically exploit the reciprocity of the wireless channel. It is based on a simple convolutional model for the relationship between the channel impulse responses in both directions, and accounts for the discrepancies between transmit and receive radiofrequency components, without the need for specific calibration hardware. However, the relative calibration methods developed so far have been shown to lack robustness with respect to frequency offset between the devices on both sides of the considered channel. In this article, we introduce a relative calibration algorithm that properly deals with the presence of frequency offset. We verify its robustness and assess its performance through simulations, and validate experimentally the proposed model on measured channels.

A simple limited feedback scheme is proposed for interference alignment on the K-user Multiple-Input-Multiple-Output Interference Channel (MIMO-IC). The scaling of the number of feedback bits with the transmit power required to preserve the multiplexing gain that can be achieved using perfect channel state information (CSI) is derived. This result is obtained through a reformulation of the interference alignment problem in order to exploit the benefits of quantization on the Grassmann manifold, which is well investigated in the single-user MIMO channel. Furthermore, through simulations we show that the proposed scheme outperforms the naive feedback scheme consisting in independently quantizing the channel matrices, in the sense that it yields a better sum rate performance for the same number of feedback bits.

We consider the application of interference alignment (IA) to the cellular case with constant MIMO channel coefficients. Neglecting the weakest interferers in the network, we introduce an algorithm to obtain a partially connected (in particular, L-interfering) network, over which the feasibility of IA can be analyzed simply. We consider the application of IA over the obtained L-interfering network, while the rest of the interference is treated as noise. We benchmark this technique through extensive Monte-Carlo simulations, and introduce an approximate, compact expression for the ergodic mutual information achievable in the considered network setting.

We consider interference alignment (IA) in the L-interfering multiple access channels (MACs) network, a particular case of the partially connected interfering MACs network whereby the number of interference links per MAC is bounded regardless of the total number of MACs in the network. Conversely to the fully-connected case, we show that interference alignment can be achievable in a network of arbitrary size, while the per-user signaling dimension remains bounded. We provide necessary conditions for the feasibility of IA, discuss their sufficiency, and introduce an algorithm capable of providing practical solutions. These results also apply to the dual case of partially connected interfering broadcast channels (IBCs), and have practical applications to both the uplink and downlink of large cellular networks.

Wireless networks are fundamentally limited by the intensity of the received signals and the mutual interference caused by many concurrent transmissions. We consider large wireless ad hoc networks whose underlying node distribution is a Poisson cluster process. Under the assumption that multiple antennas are available at each node, we evaluate the performance of interference alignment (IA) inside each cluster. We extend our previous analysis of the outage probability achieved by this technique by generalizing it to IA with receive diversity. Furthermore, we provide a simplified expression applicable at high Signal-to-Interference Ratio, along the lines of the analysis recently proposed by Ganti, Andrews and Haenggi.

Spatial interference alignment among a finite number of users is investigated as a technique to increase the probability of successful transmission in an interference limited clustered wireless ad hoc network. Using techniques from stochastic geometry, we build on the work of Ganti and Haenggi dealing with Poisson cluster processes with a fixed number of cluster points and provide a numerically integrable expression for the outage probability using an intra-cluster interference alignment strategy with multiplexing gain one. For a special network setting we derive a closed-form upper bound. We demonstrate significant performance gains compared to single-antenna systems without local cooperation.

Spatial interference alignment among a cluster of base stations is considered as a technique to mitigate inter-cell interference in the downlink of a large cellular network using OFDMA. We derive an expression for the mutual information achieved by clustered base station cooperation together with a zero-forcing receiver. Numerical performance results with throughput gains of up to 30% with respect to the non-cooperating base stations case are demonstrated for users located in the central area of the cells. Those results provide insight into the applicability of interference alignment methods in upcoming cellular networks.

An improved SINR metric is proposed for the random beamforming scheme introduced by Sharif and Hassibi, when the channel observation used to compute the SINR is known to be noisy or outdated. The effect of noise on the MIMO channel estimate is accounted for using results on the perturbation of the eigenspaces of Hermitian matrices. The new metric, designed as a conservative estimate of the real SINR, is based on expectations of bounds on the signal and interference power. It is shown through simulations that it can noticeably reduce the outage probability, in the realistic setting of a 4 times 2 antennas system, at the cost of a minor reduction of the achievable sum-rate.

We consider the use of entropy maximization methods as a tool to generate fading models for multiple-input multiple-output (MIMO) spatially correlated flat-fading channels. We focus in particular on various assumptions about the degree of knowledge on the full covariance matrix of the channel (namely in the power constraint, rank constraint, and average constraint case). We show that this method can provide closed-form probability density functions in all cases. In a second part, we analyze the statistical properties of the singular values of the resulting fading channel. In general, they are more spread out that in the classical Gaussian i.i.d. case, which incurs less optimistic ergodic capacity figures.

In this paper, we address the potential benefits of dual-polarized arrays in multi-antenna wireless systems. After an extensive literature overview of experimental data, we present a new and simple analytical framework to model dual-polarized Rayleigh and Ricean fading channels for arbitrary array sizes. The model relies on a limited number of physical parameters, such as the channel spatial correlations, the channel co-polar and the cross-polar ratios and the antenna cross-polar discrimination. Then, we investigate the multiplexing advantage of dual-polarized transmissions through the evaluation of the ergodic mutual information, for both TITO and MIMO systems. Finally, the performance of two space-time coding schemes (Alamouti OSTBC and uncoded spatial multiplexing) is evaluated via a detailed analysis of the pairwise error probability.

We investigate the problem of establishing the joint probability distribution of the entries of a multiple-input multiple-output (MIMO) spatially correlated flat-fading channel, when little or no information about the channel properties are available. We show that the entropy of a random positive semidefinite matrix is maximized by the Wishart distribution. We subsequently obtain the maximum entropy distribution of the MIMO transfer matrix by establishing its distribution conditioned on the covariance, and by later marginalizing over the covariance matrix. The obtained distribution is isotropic, and is described analytically as a function of the Frobenius norm of the channel matrix.

This paper considers the use of nrtimes ntdual-polarized arrays for improving the mutual information of MIMO communications. We first develop an elegant model of the multi-polarized MIMO channel, which allows to account for spatial correlation and depolarization effects. The major advantage of the model lies in its analytical expression, whose parameters have a clear physical meaning. In a second part, we investigate the ergodic mutual information of multi-polarized schemes, and derive a condition upon which multi-polarized transmissions offer a higher capacity than equivalent uni-polarized schemes using the same number of antennas under the same overall array dimensions.

This contribution provides a fresh look at the asymptotic (in terms of number of antennas) design of multiple-antenna wireless systems, with the goal of giving useful insights on the deployment of future MIMO systems. For the i.i.d. Gaussian and double-directional models, we provide guidelines in terms of the repartition of the antennas between the transmitter and the receiver, and study the influence of array geometry on the ergodic mutual information per antenna. Furthermore, we compare the LOS and NLOS situations, and evaluate the relative importance of the LOS component and path loss in Ricean fading, as well as in the low-rank Ricean component case.

We address the problem of OFDM transmission over a time-varying, frequency-selective channel with high Doppler spread. This creates situations where the channel significantly evolves over the time span of one OFDM symbol. We analyze the CP-OFDM transmission mechanism, and the impairments due to channel variations, using a decomposition of these variations over a base of sinusoid functions sampling the Doppler spectrum at subcarrier frequencies. On the one hand, this leads to a fairly parsimonious parameterization of the time-varying channel impulse response. On the other hand we show that, considering a whole CP-OFDM symbol, this leads to a duality between equalization of the delay spread of a time-varying channel in the time domain, and the equalization of the Doppler spread of a frequency selective channel in the frequency domain. Using this duality, we show that equalization in the frequency domain can benefit from all known time domain equalization methods.