arXiv subjects

Mahdi Barzegar Khalilsarai

Publications and source records attributed to Mahdi Barzegar Khalilsarai.

At least 19 recordsLinked to original sources

arXiv2025

Downlink CSIT under Compressed Feedback: Joint vs. Separate Source-Channel Coding

The acquisition of Downlink (DL) channel state information at the transmitter (CSIT) is known to be a challenging task in multiuser massive MIMO systems when uplink/downlink channel reciprocity does not hold (e.g., in frequency division duplexing systems). From a coding viewpoint, the DL channel state acquired at the users via DL training can be seen as an information source that must be conveyed to the base station via the UL communication channels. The transmission of a source through a channel can be accomplished either by separate or joint source-channel coding (SSCC or JSCC). In this work, using classical remote distortion-rate (DR) theory, we first provide a theoretical lower bound on the channel estimation mean-square-error (MSE) of both JSCC and SSCC-based feedback schemes, which however requires encoding of large blocks of successive channel states and thus cannot be used in practicesince it would incur in an extremely large feedback delay. We then focus on the relevant case of minimal (one slot) feedback delay and propose a practical JSCC-based feedback scheme that fully exploits the channel second-order statistics to optimize the dimension projection in the eigenspace. We analyze the large SNR behavior of the proposed JSCC-based scheme in terms of the quality scaling exponent (QSE). Given the second-order statistics of channel estimation of any feedback scheme, we further derive the closed-form of the lower bound to the ergodic sum-rate for DL data transmission under maximum ratio transmission and zero-forcing precoding. Via extensive numerical results, we show that our proposed JSCC-based scheme outperforms known JSCC, SSCC baseline and deep learning-based schemes and is able to approach the performance of the optimal DR scheme in the range of practical SNR.

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arXiv2023

Deep-Learning Aided Channel Training and Precoding in FDD Massive MIMO with Channel Statistics Knowledge

We propose a method for channel training and precoding in FDD massive MIMO based on deep neural networks (DNNs), exploiting Downlink (DL) channel covariance knowledge. The DNN is optimized to maximize the DL multi-user sum-rate, by producing a pre-beamforming matrix based on user channel covariances that maps the original channel vectors to effective channels. Measurements of these effective channels are received at the users via common pilot transmission and sent back to the base station (BS) through analog feedback without further processing. The BS estimates the effective channels from received feedback and constructs a linear precoder by concatenating the optimized pre-beamforming matrix with a zero-forcing precoder over the effective channels. We show that the proposed method yields significantly higher sum-rates than the state-of-the-art DNN-based channel training and precoding scheme, especially in scenarios with small pilot and feedback size relative to the channel coherence block length. Unlike many works in the literature, our proposition does not involve deployment of a DNN at the user side, which typically comes at a high computational cost and parameter-transmission overhead on the system, and is therefore considerably more practical.

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arXiv2022

FDD Massive MIMO Channel Training Optimal Rate Distortion Bounds and the Efficiency of one-shot Schemes

We study the problem of providing channel state information (CSI) at the transmitter in multi-user massive MIMO systems operating in frequency division duplexing (FDD). The wideband MIMO channel is a vector-valued random process correlated in time, space (antennas), and frequency (subcarriers). The base station (BS) broadcasts periodically beta_tr pilot symbols from its M antenna ports to K single-antenna users (UEs). Correspondingly, the K UEs send feedback messages about their channel state using beta_fb symbols in the uplink (UL). Using results from remote rate-distortion theory, we show that, as snr reaches infty, the optimal feedback strategy achieves a channel state estimation mean squared error (MSE) that behaves as Theta(1) if beta_tr < r and as Theta(snr^(-alpha)) when beta_tr >=r, where alpha = min(beta_fb/r, 1), where r is the rank of the channel covariance matrix. The MSE-optimal rate-distortion strategy implies encoding of long sequences of channel states, which would yield completely stale CSI and therefore poor multiuser precoding performance. Hence, we consider three practical one-shot CSI strategies with minimum one-slot delay and analyze their large-SNR channel estimation MSE behavior. These are: (1) digital feedback via entropy-coded scalar quantization (ECSQ), (2) analog feedback (AF), and (3) local channel estimation at the UEs and digital feedback. These schemes have different requirements in terms of knowledge of the channel statistics at the UE and at the BS. In particular, the latter strategy requires no statistical knowledge and is closely inspired by a CSI feedback scheme currently proposed in 3GPP standardization.

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arXiv2022

Structured Channel Covariance Estimation from Limited Samples for Large Antenna Arrays

In massive multiple-input multiple-output (MIMO) systems, the knowledge of the users' channel covariance matrix is crucial for minimum mean square error (MMSE) channel estimation in the uplink as well as it plays an important role in several multiuser beamforming schemes in the downlink. Due to the large number of base station antennas in massive MIMO, accurate covariance estimation is challenging especially in the case where the number of samples is limited and thus comparable to the channel vector dimension. As a result, the standard sample covariance estimator may yield a too large estimation error which in turn may yield significant system performance degradation with respect to the ideal channel covariance knowledge case. To address such problem, we propose a method based on a parametric representation of the channel angular scattering function. The proposed parametric representation includes a discrete specular component which is addressed using the well-known MUltiple SIgnal Classification (MUSIC) method, and a diffuse scattering component, which is modeled as the superposition of suitable dictionary functions. To obtain the representation parameters we propose two methods, where the first solves a non-negative least-squares problem and the second maximizes the likelihood function using expectation-maximization. Our simulation results show that the proposed methods outperform the state of the art with respect to various estimation quality metrics and different sample sizes.

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arXiv2022

Channel State Acquisition in FDD Massive MIMO: Rate-Distortion Bound and Effectiveness of "Analog" Feedback

We consider the problem of estimating channel fading coefficients (modeled as a correlated Gaussian vector) via Downlink (DL) training and Uplink (UL) feedback in wideband FDD massive MIMO systems. Using rate-distortion theory, we derive optimal bounds on the achievable channel state estimation error in terms of the number of training pilots in DL ($β_{tr}$) and feedback dimension in UL ($β_{fb}$), with random, spatially isotropic pilots. It is shown that when the number of training pilots exceeds the channel covariance rank ($r$), the optimal rate-distortion feedback strategy achieves an estimation error decay of $Θ(SNR^{-α})$ in estimating the channel state, where $α= min (β_{fb}/r , 1)$ is the so-called quality scaling exponent. We also discuss an "analog" feedback strategy, showing that it can achieve the optimal quality scaling exponent for a wide range of training and feedback dimensions with no channel covariance knowledge and simple signal processing at the user side. Our findings are supported by numerical simulations comparing various strategies in terms of channel state mean squared error and achievable ergodic sum-rate in DL with zero-forcing precoding.

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arXiv2020

WiFi-Based Channel Impulse Response Estimation and Localization via Multi-Band Splicing

Using commodity WiFi data for applications such as indoor localization, object identification and tracking and channel sounding has recently gained considerable attention. We study the problem of channel impulse response (CIR) estimation from commodity WiFi channel state information (CSI). The accuracy of a CIR estimation method in this setup is limited by both the available channel bandwidth as well as various CSI distortions induced by the underlying hardware. We propose a multi-band splicing method that increases channel bandwidth by combining CSI data across multiple frequency bands. In order to compensate for the CSI distortions, we develop a per-band processing algorithm that is able to estimate the distortion parameters and remove them to yield the "clean" CSI. This algorithm incorporates the atomic norm denoising sparse recovery method to exploit channel sparsity. Splicing clean CSI over M frequency bands, we use orthogonal matching pursuit (OMP) as an estimation method to recover the sparse CIR with high (M-fold) resolution. Unlike previous works in the literature, our method does not appeal to any limiting assumption on the CIR (other than the widely accepted sparsity assumption) or any ad hoc processing for distortion removal. We show, empirically, that the proposed method outperforms the state of the art in terms of localization accuracy.

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arXiv2020

Dual-Polarized FDD Massive MIMO: A Comprehensive Framework

We propose a comprehensive scheme for realizing a massive multiple-input multiple-output (MIMO) system with dual-polarized antennas in frequency division duplexing (FDD) mode. Employing dual-polarized elements in a massive MIMO array has been common practice recently and can, in principle, double the number of spatial degrees of freedom with a less-than-proportional increase in array size. However, processing a dual-polarized channel is demanding due to the high channel dimension and the lack of Uplink-Downlink (UL-DL) channel reciprocity in FDD mode. In particular, the difficulty arises in channel covariance acquisition for both UL and DL transmissions and in common training of DL channels in a multi-user setup. To overcome these challenges, we develop a unified framework consisting of three steps: (1) a covariance estimation method to efficiently estimate the UL covariance from noisy, orthogonal UL pilots; (2) a UL-DL covariance transformation method that obtains the DL covariance from the estimated UL covariance in the previous step; (3) a multi-user common DL channel training with limited DL pilot dimension method, which enables the BS to estimate effective user DL channels and use them for interference-free DL beamforming and data transmission. We provide extensive empirical results to prove the applicability and merits of our scheme.

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arXiv2020

Joint Approximate Covariance Diagonalization with Applications in MIMO Virtual Beam Design

We study the problem of maximum-likelihood (ML) estimation of an approximate common eigenstructure, i.e. an approximate common eigenvectors set (CES), for an ensemble of covariance matrices given a collection of their associated i.i.d vector realizations. This problem has a direct application in multi-user MIMO communications, where the base station (BS) has access to instantaneous user channel vectors through pilot transmission and attempts to perform joint multi-user Downlink (DL) precoding. It is widely accepted that an efficient implementation of this task hinges upon an appropriate design of a set of common "virtual beams", that captures the common eigenstructure among the user channel covariances. In this paper, we propose a novel method for obtaining this common eigenstructure by casting it as an ML estimation problem. We prove that in the special case where the covariances are jointly diagonalizable, the global optimal solution of the proposed ML problem coincides with the common eigenstructure. Then we propose a projected gradient descent (PGD) method to solve the ML optimization problem over the manifold of unitary matrices and prove its convergence to a stationary point. Through exhaustive simulations, we illustrate that in the case of jointly diagonalizable covariances, our proposed method converges to the exact CES. Also, in the general case where the covariances are not jointly diagonalizable, it yields a solution that approximately diagonalizes all covariances. Besides, the empirical results show that our proposed method outperforms the well-known joint approximate diagonalization of eigenmatrices (JADE) method in the literature.

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arXiv2019

Randomized Channel Sparsifying Hybrid Precoding for FDD Massive MIMO Systems

We propose a novel randomized channel sparsifying hybrid precoding (RCSHP) design to reduce the signaling overhead of channel estimation and the hardware cost and power consumption at the base station (BS), in order to fully harvest benefits of frequency division duplex (FDD) massive multiple-input multiple-output (MIMO) systems. RCSHP allows time-sharing among multiple analog precoders, each serving a compatible user group. The analog precoder is adapted to the channel statistics to properly sparsify the channel for the associated user group, such that the resulting effective channel (product of channel and analog precoder) not only has enough spatial degrees of freedom (DoF) to serve this group of users, but also can be accurately estimated under the limited pilot budget. The digital precoder is adapted to the effective channel based on the duality theory to facilitate the power allocation and exploit the spatial multiplexing gain. We formulate the joint optimization of the time-sharing factors and the associated sets of analog precoders and power allocations as a general utility optimization problem, which considers the impact of effective channel estimation error on the system performance. Then we propose an efficient stochastic successive convex approximation algorithm to provably obtain Karush-Kuhn-Tucker (KKT) points of this problem.

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arXiv2019

Uplink-Downlink Channel Covariance Transformations and Precoding Design for FDD Massive MIMO

A large majority of cellular networks deployed today make use of Frequency Division Duplexing (FDD) where, in contrast with Time Division Duplexing (TDD), the channel reciprocity does not hold and explicit downlink (DL) probing and uplink (UL) feedback are needed in order to achieve spatial multiplexing gain. To support massive MIMO, the overhead incurred by conventional DL probing and UL feedback schemes scales linearly with the number of BS antennas and, therefore, may be very large. In this paper, we present a new approach to achieve a very competitive trade-off between spatial multiplexing gain and probing-feedback overhead in such systems. Our approach is based on two novel methods: (i) an efficient regularization technique based on Deep Neural Networks (DNN) that learns the Angular Spread Function (ASF) of users channels and permits to estimate the DL covariance matrix from the noisy i.i.d. channel observations obtained freely via UL pilots (UL-DL covariance transformation), (ii) a novel "sparsifying precoding" technique that uses the estimated DL covariance matrix from (i) and imposes a controlled sparsity on the DL channel such that given any assigned DL pilot dimension, it is able to find an optimal sparsity level and a corresponding sparsifying precoder for which the "effective" channel vectors after sparsification can be estimated at the BS with a low mean-square error. We compare our proposed DNN-based method in (i) with other methods in the literature via numerical simulations and show that it yields a very competitive performance. We also compare our sparsifying precoder in (ii) with the state-of-the-art statistical beamforming methods under the assumption that those methods also have access to the covariance knowledge in the DL and show that our method yields higher spectral efficiency since it uses in addition the instantaneous channel information after sparsification.

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arXiv2019

Structured Channel Covariance Estimation from Limited Samples in Massive MIMO

Obtaining channel covariance knowledge is of great importance in various Multiple-Input Multiple-Output MIMO communication applications, including channel estimation and covariance-based user grouping. In a massive MIMO system, covariance estimation proves to be challenging due to the large number of antennas ($M\gg 1$) employed in the base station and hence, a high signal dimension. In this case, the number of pilot transmissions $N$ becomes comparable to the number of antennas and standard estimators, such as the sample covariance, yield a poor estimate of the true covariance and are undesirable. In this paper, we propose a Maximum-Likelihood (ML) massive MIMO covariance estimator, based on a parametric representation of the channel angular spread function (ASF). The parametric representation emerges from super-resolving discrete ASF components via the well-known MUltiple SIgnal Classification (MUSIC) method plus approximating its continuous component using suitable limited-support density function. We maximize the likelihood function using a concave-convex procedure, which is initialized via a non-negative least-squares optimization problem. Our simulation results show that the proposed method outperforms the state of the art in various estimation quality metrics and for different sample size to signal dimension ($N/M$) ratios.

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arXiv2019

Machine Learning for Geometrically-Consistent Angular Spread Function Estimation in Massive MIMO

In the spatial channel models used in multi-antenna wireless communications, the propagation from a single-antenna transmitter (e.g., a user) to an M-antenna receiver (e.g., a Base Station) occurs through scattering clusters located in the far field of the receiving antenna array. The Angular Spread Function (ASF) of the corresponding M-dim channel vector describes the angular density of the received signal power at the array. The modern literature on massive MIMO has recognized that the knowledge of covariance matrix of user channel vectors is very useful for various applications such as hybrid digital analog beamforming, pilot decontamination, etc. Therefore, most literature has focused on the estimation of such channel covariance matrices. However, in some applications such as uplink-downlink covariance transformation (for FDD massive MIMO precoding) and channel sounding some form of ASF estimation is required either implicitly or explicitly. It turns out that while covariance estimation is well-known and well-conditioned, the ASF estimation is a much harder problem and is in general ill-posed. In this paper, we show that under additional geometrically-consistent group-sparsity structure on the ASF, which is prevalent in almost all wireless propagation scenarios, one is able to estimate ASF properly. We propose sparse dictionary-based algorithms that promote this group-sparsity structure via suitable regularizations. Since generally it is difficult to capture the notion of group-sparsity through proper regularization, we propose another algorithm based on Deep Neural Networks (DNNs) that learns this structure. We provide numerical simulations to assess the performance of our proposed algorithms. We also compare the results with that of other methods in the literature, where we re-frame those methods in the context of ASF estimation in massive MIMO.

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arXiv2019

WiFi-Based Indoor Localization via Multi-Band Splicing and Phase Retrieval

We study the problem of indoor localization using commodity WiFi channel state information (CSI) measurements. The accuracy of methods developed to address this problem is limited by the overall bandwidth used by the WiFi device as well as various types of signal distortions imposed by the underlying hardware. In this paper, we propose a localization method that performs channel impulse response (CIR) estimation by splicing measured CSI over multiple WiFi bands. In order to overcome hardware-induced phase distortions, we propose a phase retrieval (PR) scheme that only uses CSI magnitude values to estimate the CIR. To achieve high localization accuracy, the PR scheme involves a sparse recovery step, which exploits the fact that the CIR is sparse over the delay domain, due to the small number of contributing signal paths in an indoor environment. Simulation results indicate that our approach outperforms the state of the art by an order of magnitude (cm-level localization accuracy) for more than 90% of the trials and for various SNR regimes.

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arXiv2018

Wideband Massive MIMO Channel Estimation via Sequential Atomic Norm Minimization

The recently introduced atomic norm minimization (ANM) framework for parameter estimation is a promising candidate towards low overhead channel estimation in wireless communications. However, previous works on ANM-based channel estimation evaluated performance on channels with artificially imposed channel path separability, which cannot be guaranteed in practice. In addition, direct application of the ANM framework for massive MIMO channel estimation is computationally infeasible due to the large dimensions. In this paper, a low-complexity ANM-based channel estimator for wideband massive MIMO is proposed, consisting of two sequential steps, the first estimating the channel over the spatial and the second over the frequency dimension. Its mean squared error performance is analytically characterized in terms of tight lower bounds. It is shown that the proposed algorithm achieves excellent performance that is close to the best that can be achieved by any unbiased channel estimator in the regime of low to moderate number of channel paths, without any restrictions on their separability.

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arXiv2018

FDD Massive MIMO via UL/DL Channel Covariance Extrapolation and Active Channel Sparsification

We propose a novel method for massive Multiple-Input Multiple-Output (massive MIMO) in Frequency Division Duplexing (FDD) systems. Due to the large frequency separation between Uplink (UL) and Downlink (DL), in FDD systems channel reciprocity does not hold. Hence, in order to provide DL channel state information to the Base Station (BS), closed-loop DL channel probing and Channel State Information (CSI) feedback is needed. In massive MIMO this incurs typically a large training overhead. For example, in a typical configuration with M = 200 BS antennas and fading coherence block of T = 200 symbols, the resulting rate penalty factor due to the DL training overhead, given by max{0, 1 - M/T}, is close to 0. To reduce this overhead, we build upon the well-known fact that the Angular Scattering Function (ASF) of the user channels is invariant over frequency intervals whose size is small with respect to the carrier frequency (as in current FDD cellular standards). This allows to estimate the users' DL channel covariance matrix from UL pilots without additional overhead. Based on this covariance information, we propose a novel sparsifying precoder in order to maximize the rank of the effective sparsified channel matrix subject to the condition that each effective user channel has sparsity not larger than some desired DL pilot dimension T_{dl}, resulting in the DL training overhead factor max{0, 1 - T_{dl} / T} and CSI feedback cost of T_{dl} pilot measurements. The optimization of the sparsifying precoder is formulated as a Mixed Integer Linear Program, that can be efficiently solved. Extensive simulation results demonstrate the superiority of the proposed approach with respect to concurrent state-of-the-art schemes based on compressed sensing or UL/DL dictionary learning.

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arXiv2018

Multi-Band Covariance Interpolation with Applications in Massive MIMO

In this paper, we study the problem of multi-band (frequency-variant) covariance interpolation with a particular emphasis towards massive MIMO applications. In a massive MIMO system, the communication between each BS with $M \gg 1$ antennas and each single-antenna user occurs through a collection of scatterers in the environment, where the channel vector of each user at BS antennas consists in a weighted linear combination of the array responses of the scatterers, where each scatterer has its own angle of arrival (AoA) and complex channel gain. The array response at a given AoA depends on the wavelength of the incoming planar wave and is naturally frequency dependent. This results in a frequency-dependent distortion where the second order statistics, i.e., the covariance matrix, of the channel vectors varies with frequency. In this paper, we show that although this effect is generally negligible for a small number of antennas $M$, it results in a considerable distortion of the covariance matrix and especially its dominant signal subspace in the massive MIMO regime where $M \to \infty$, and can generally incur a serious degradation of the performance especially in frequency division duplexing (FDD) massive MIMO systems where the uplink (UL) and the downlink (DL) communication occur over different frequency bands. We propose a novel UL-DL covariance interpolation technique that is able to recover the covariance matrix in the DL from an estimate of the covariance matrix in the UL under a mild reciprocity condition on the angular power spread function (PSF) of the users. We analyze the performance of our proposed scheme mathematically and prove its robustness under a sufficiently large spatial oversampling of the array. We also propose several simple off-the-shelf algorithms for UL-DL covariance interpolation and evaluate their performance via numerical simulations.

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arXiv2017

FDD Massive MIMO: Efficient Downlink Probing and Uplink Feedback via Active Channel Sparsification

In this paper, we propose a novel method for efficient implementation of a massive Multiple-Input Multiple-Output (massive MIMO) system with Frequency Division Duplexing (FDD) operation. Our main objective is to reduce the large overhead incurred by Downlink (DL) common training and Uplink (UL) feedback needed to obtain channel state information (CSI) at the base station. Our proposed scheme relies on the fact that the underlying angular distribution of a channel vector, also known as the angular scattering function, is a frequency-invariant entity yielding a UL-DL reciprocity and has a limited angular support. We estimate this support from UL CSI and interpolate it to obtain the corresponding angular support of the DL channel. Finally we exploit the estimated support of the DL channel of all the users to design an efficient channel probing and feedback scheme that maximizes the total spectral efficiency of the system. Our method is different from the existing compressed-sensing (CS) based techniques in the literature. Using support information helps reduce the feedback overhead from O(s*log M) in CS techniques to O(s) in our proposed method, with $s$ and $M$ being sparsity order of the channel vectors and the number of base station antennas, respectively. Furthermore, in order to control the channel sparsity and therefore the DL common training and UL feedback overhead, we introduce the novel concept of active channel sparsification. In brief, when the fixed pilot dimension is less than the required amount for reliable channel estimation, we introduce a pre-beamforming matrix that artificially reduces the effective channel dimension of each user to be not larger than the DL pilot dimension, while maximizing both the number of served users and the number of probed angles. We provide numerical experiments to compare our method with the state-of-the-art CS technique.

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arXiv2017

Efficient Downlink Channel Probing and Uplink Feedback in FDD Massive MIMO Systems

Massive Multiple-Input Multiple-Output (massive MIMO) is a variant of multi-user MIMO in which the number of antennas at each Base Station (BS) is very large and typically much larger than the number of users simultaneously served. Massive MIMO can be implemented with Time Division Duplexing (TDD) or Frequency Division Duplexing (FDD) operation. FDD massive MIMO systems are particularly desirable due to their implementation in current wireless networks and their efficiency in situations with symmetric traffic and delay-sensitive applications. However, implementing FDD massive MIMO systems is known to be challenging since it imposes a large feedback overhead in the Uplink (UL) to obtain channel state information for the Downlink (DL). In recent years, a considerable amount of research is dedicated to developing methods to reduce the feedback overhead in such systems. In this paper, we use the sparse spatial scattering properties of the environment to achieve this goal. The idea is to estimate the support of the continuous, frequency-invariant scattering function from UL channel observations and use this estimate to obtain the support of the DL channel vector via appropriate interpolation. We use the resulting support estimate to design an efficient DL probing and UL feedback scheme in which the feedback dimension scales proportionally with the sparsity order of DL channel vectors. Since the sparsity order is much less than the number of BS antennas in almost all practically relevant scenarios, our method incurs much less feedback overhead compared with the currently proposed methods in the literature, such as those based on compressed-sensing. We use numerical simulations to assess the performance of our probing-feedback algorithm and compare it with these methods.

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