FDD Cooperative Channel Estimation and Feedback for 3D Massive MIMO System

In multiple measurement vector (MMV) problems, L measurement vectors each of which has length M are available for recovering jointly sparse signals that have a common support set of size K. In this paper, a fast and noise-robust greedy algorithm is proposed for joint sparse recovery in MMV problems, by exploiting a posteriori probability ratios for every index of sparse input signals. The essence of the algorithm is to transfer the information through iterations, which contributes to the performance improvement of support detection. When L is sufficiently large at M = K +1, we investigate the asymptotic performance of exact support recovery using a Gaussian assumption, power-law approximations, and order statistics, where the techniques are inspired by experimental results. In this case, we also present a sufficient condition on the number of measurements, or M = K + 1 = Ω (log N), for theoretical support recovery guarantee. The theoretical analysis reveals that the proposed algorithm can achieve reliable joint sparse recovery asymptotically at the theoretical limit of M = K + 1 with high probability. By examining the performance for various M, K, and L, simulation results demonstrate that if M is not too small, the proposed algorithm can be reliable, fast, and noise-robust, compared to the conventional ones, such as simultaneous orthogonal matching pursuit (SOMP), subspace augmented MUSIC (SA-MUSIC), and rank-aware order recursive matching pursuit (RA-ORMP).

The Kaczmarz algorithm is popular for iteratively solving an over determined system of linear equations. Randomized version of the Kaczmarz algorithm can converge exponentially and independent of number of equations. Recently an algorithm for finding sparse solution to a linear system of equations has been proposed based on weighted randomized Kaczmarz algorithm. These algorithms solves single measurement vector problem, however there are applications where multiple-measurements are available. In this work, the objective is to solve a multiple measurement vector problem with common sparse support by modifying the sparse randomized Kaczmarz algorithm. We have also modeled the problem of face recognition from video as the multiple measurement vector problem and solved using our proposed technique. We have compared the proposed algorithm with state-of-art spectral projected gradient algorithm for multiple measurement vectors on both real and synthetic datasets. The Monte Carlo simulations confirms that our proposed algorithm has better recovery and convergence rate than the MMV version of spectral projected gradient algorithm under fairness constraints.

This paper considers the sparse recovery problem of multiple measurement vector (MMV) model corrupted in impulsive noise. To ensure outlier-robust sparse recovery, we formulate an MMV problem that includes the generalized lp-norm (1 < p < 2) divergence data-fidelity term added to the l2,0 joint sparsity-promoting regularizer. The joint sparse penalty, however, is non-continuous and hence non-differentiable, which inevitably raises difficulty in optimization when using a gradient-based method. To address this, we build a smooth approximation for the l2,0-based sparse metric via the log-sum based sparse-encouraging surrogate function. Then, we propose a block successive upper-bound minimization algorithm for the smooth MMV problem by solving a series of subproblems based on the block coordinate descent (BCD) method. Furthermore, local convergence of the proposed algorithm to a stationary point of the smooth problem is proved. Experiments demonstrate its efficiency and robust recovery performance for suppressing impulsive noise.

This thesis is a reconciliation between multiple bodies of work with a shared objective that is ``to identify the active support" under different environment settings. The applications of focus within this thesis will be placed on electrical impedance tomography (EIT) and direction-of-arrival (DOA) estimation. The term ``active support" or only ``support" is commonly used in compressed sensing and sparse signal recovery communities which is essentially referring to ``the most contributing parameters" in a system of linear equations. Although with a common objective shared among the works that have been done within this thesis, this thesis can be divided into two major parts based on applications’ environment. The first part is the support identification under a process expressible by Fredholm integral equation of the first kind. For this problem, a research topic that is known as ``Electrical impedance tomography (EIT)," is chosen as a representative application for a collection of problems expressible by this integral equation. The physical laws (Physics) of EIT can be explained by Maxwell's equations under quasi-static environment. Under such condition, the energy dissipated from the source is spread throughout the region (domain) in a non-linear fashion. Together with the absent of phase or time delay information, the image reconstruction task for EIT usually faces the issue of low signal-to-noise-ratio (SNR) and support ambiguity. Multiple real-life applications typically fall under this category of problems such as medical and geophysical subsurface imaging, deconvolution, and image deblurring. The EIT is an imaging technique that estimates a distribution of electrical admittivity $\gamma$ of a ``subject under test (SUT)" sometimes called as ``medium" based on an inference from data captured from the medium's boundary. Although the name would suggests the value of `impedance' to be measured, in most practical scenario its reciprocal which is `admittance' (admittivity value) is commonly calculated instead. The admittivity value $\gamma$ encapsulates the information of medium's conductivity ($\sigma$) and permittivity ($\epsilon$) with the following expression $\gamma = \sigma + i\omega\epsilon$, where $\omega=2\pi f$ is the angular frequency (rad/s) and $f$ is frequency in Hz. The ``tomographic reconstruction" or ``the process of estimating the medium's internal admittivity distribution" can be accomplished by solving a mathematical problem that is commonly known as an ``inverse problem." Due to a quasi-static nature of this imaging modality, the image reconstruction of the EIT is known to be one of the most severely ill-posed inverse problems. The image reconstruction problem of EIT will be analyzed through two different viewpoints. Firstly, this problem will be analyzed through the lens of a discrete ill-posed inverse problem from the applied mathematics community viewpoint. Secondly, this problem will be re-analyzed through the lens of array signal processing/beamforming framework from the signal processing community viewpoint. While exploring the EIT image reconstruction techniques, it was observed that although the EIT system can be implemented economically, the implementation process is not completely straightforward. Therefore, a framework of a simple and reliable EIT prototyping system that could provide means to collect different data format (e.g. single measurement vector (SMV) and multiple measurement vectors (MMV)) were implemented in this thesis. This robust, economical, and straightforward implementation framework was developed with an aim that it could be beneficial for those who are interested in image reconstruction and inverse algorithms without the access of a full functioning commercialized EIT system. The second part is the support identification for DOA estimation under Gaussian and $\alpha-$stable distributed noises. Several improvements of a robust beamforming technique called MUSIC-like algorithm had been further investigated which helps improve the algorithm's performance. The main focus of this part is the performance improvement of the algorithm that can be used for support identification task under different noise scenarios. Three different approaches for estimating a relaxation parameter, an essential parameter used in the MUSIC-like algorithm, are presented. By experimenting with different approaches, an adaptive framework for relaxation parameter was observed to have the potential for further improvement. The performance of the MUSIC-like algorithm was then further explored through the directional adaptive framework under both Gaussian and $\alpha-$stable distributed noise. It was also compared with the conventional MUSIC algorithm coupled with a pre-conditioned covariance matrix.

Approximate message passing (AMP) algorithms break a (high-dimensional) statistical problem into manageable parts and then repeatedly solve each part in turn, akin to alternating projections. One notable characteristic is that their asymptotic behaviours can be accurately predicted via their associated state evolution equations. Orthogonal AMP (OAMP) was recently developed to avoid the need for computing the so-called Onsager term in traditional AMP algorithms, providing two clear benefits: the derivation of an OAMP algorithm is both straightforward and more broadly applicable. OAMP was originally demonstrated for statistical problems with a single measurement vector and single transform. This paper extends OAMP to statistical problems with multiple measurement vectors (MMVs) and multiple transforms (MTs). We name the resulting algorithms as OAMP-MMV and OAMP-MT, respectively, and their combination as augmented OAMP (A-OAMP). Whereas the extension of traditional AMP algorithms to such problems would be challenging, the orthogonal principle underpinning OAMP makes these extensions straightforward. <p xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">The MMV and MT models are widely applicable to signal processing and communications. We present an example of a MIMO relay system with correlated source data and signal clipping, which can be effectively modelled as a joint MMVMT system. While existing methods encounter challenges when applied to this example, OAMP offers an efficient solution with excellent performance.

The fact that the millimeter-wave (mmWave) multiple-input multiple-output (MIMO) channel has sparse support in the spatial domain has motivated recent compressed sensing (CS)-based mmWave channel estimation methods, where the angles of arrivals (AoAs) and angles of departures (AoDs) are quantized using angle dictionary matrices. However, the existing CS-based methods usually obtain the estimation result through one-stage channel sounding that have two limitations: (i) the requirement of large-dimensional dictionary and (ii) unresolvable quantization error. These two drawbacks are irreconcilable; improvement of the one implies deterioration of the other. To address these challenges, we propose, in this paper, a two-stage method to estimate the AoAs and AoDs of mmWave channels. In the proposed method, the channel estimation task is divided into two stages, Stage I and Stage II. Specifically, in Stage I, the AoAs are estimated by solving a multiple measurement vectors (MMV) problem. In Stage II, based on the estimated AoAs, the receive sounders are designed to estimate AoDs. The dimension of the angle dictionary in each stage can be reduced, which in turn reduces the computational complexity substantially. We then analyze the successful recovery probability (SRP) of the proposed method, revealing the superiority of the proposed framework over the existing one-stage CS-based methods. We further enhance the reconstruction performance by performing resource allocation between the two stages. We also overcome the unresolvable quantization error issue present in the prior techniques by applying the atomic norm minimization method to each stage of the proposed two-stage approach. The simulation results illustrate the substantially improved performance with low complexity of the proposed two-stage method.

A sparse global navigation satellite system (GLONASS) signal acquisition method based on compressive sensing and multiple measurement vectors is proposed. The nonsparse GLONASS signal can be represented sparsely on our proposed dictionary which is designed based on the signal feature. Then, the GLONASS signal is sensed by a normalized orthogonal random matrix and acquired by the improved multiple measurement vectors acquisition algorithm. There are 10 cycles of pseudorandom codes in a navigation message, and these 10 pseudorandom codes have the same row sparse structure. So, the acquisition probability can be raised by row sparse features theoretically. A large number of simulated GLONASS signal experiments show that the acquisition probability increases with the increase in the measurement vector column dimension. Finally, the practical availability of the new method is verified by acquisition experiments with the real record GLONASS signal. The new method can reduce the storage space and energy loss of data transmission. We hope that the new method can be applied to field receivers that need to record and transmit navigation data for a long time.

In Unlabeled Sensing, one observes a set of linear measurements of an underlying signal with incomplete or missing information about their ordering, which can be modeled in terms of an unknown permutation. In this paper, we study the case of multiple noisy measurement vectors (MMVs) resulting from a common permutation and investigate to what extent the number of MMVs m facilitates permutation recovery by "borrowing strength". We provide an affirmative answer for an oracle setting in which the matrix of signals is known by establishing matching upper and lower bounds on the required Signal-to-Noise Ratio (SNR), which – as distinguished from the case of a single measurement vector – involves a dependence on the stable rank of the matrix of signals. Specifically, a larger stable rank significantly reduces the required average SNR which can drop from n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Ω(1)</sup> for m = 1 to Ω(log n) for m = Ω(log n), where n denotes the number of measurements per MMV. Numerical results are well-aligned with our theoretical findings.

Massive MIMO has been proposed as a means of achieving huge spectral efficiency in cellular networks. However, its implementation is usually based on linear precoding schemes using Channel State Information (CSI). For this reason, the use of the Time Division Duplex (TDD) mode is typically assumed since it removes the dependence on the number of antennas at the transmitter to acquire CSI. Unfortunately, most of the cellular network operate in the Frequency Division Duplex (FDD) mode in which the acquisition of CSI depends proportionally to the number of transmit antennas. For this reason, the implementation of Massive MIMO is handicapped to few transmit antennas for the current cellular networks. In this paper we study the use of reconfigurable antennas that can switch among a set of preset modes, i.e., radiation patterns, through Blind Interference Alignment schemes. We show that it is a solution to exploit a very large number of antennas at the transmit side, overcoming the bottleneck that today constitutes the acquisition of CSI in Massive MIMO systems operating in FDD mode.

In this work, we provide non-asymptotic, probabilistic guarantees for successful recovery of the common nonzero support of jointly sparse Gaussian sources in the multiple measurement vector (MMV) problem. The support recovery problem is formulated as the marginalized maximum likelihood (or type-II ML) estimation of the variance hyperparameters of a joint sparsity inducing Gaussian prior on the source signals. We derive conditions under which the resulting nonconvex constrained optimization perfectly recovers the nonzero support of a joint-sparse Gaussian source ensemble with arbitrarily high probability. The support error probability decays exponentially with the number of MMVs at a rate that depends on the smallest restricted singular value and the nonnegative null space property of the self Khatri-Rao product of the sensing matrix. Our analysis confirms that nonzero supports of size as high as <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$O(m^{2})$ </tex-math></inline-formula> are recoverable from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula> measurements per sparse vector. Our derived sufficient conditions for support consistency of the proposed constrained type-II ML solution also guarantee the support consistency of any global solution of the multiple sparse Bayesian learning (M-SBL) optimization whose nonzero coefficients lie inside a bounded interval. For the case of noiseless measurements, we further show that a single MMV is sufficient for perfect recovery of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> -sparse support by M-SBL, provided all subsets of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k + 1$ </tex-math></inline-formula> columns of the sensing matrix are linearly independent.

We address the problem of finding sparse solutions to an underdetermined system of equations when there are multiple measurement vectors having the same, but unknown, sparsity structure. The single measurement sparse solution problem has been extensively studied in the past. Although known to be NP-hard, many single-measurement suboptimal algorithms have been formulated that have found utility in many different applications. Here, we consider in depth the extension of two classes of algorithms-Matching Pursuit (MP) and FOCal Underdetermined System Solver (FOCUSS)-to the multiple measurement case so that they may be used in applications such as neuromagnetic imaging, where multiple measurement vectors are available, and solutions with a common sparsity structure must be computed. Cost functions appropriate to the multiple measurement problem are developed, and algorithms are derived based on their minimization. A simulation study is conducted on a test-case dictionary to show how the utilization of more than one measurement vector improves the performance of the MP and FOCUSS classes of algorithm, and their performances are compared.

Deep learning (DL)-based channel state information (CSI) feedback improves the capacity and energy efficiency of massive multiple-input multiple-output (MIMO) systems in frequency division duplexing mode. However, multiple neural networks with different lengths of feedback overhead are required by time-varying bandwidth resources. The storage space required at the user equipment (UE) and the base station (BS) for these models increases linearly with the number of models. In this paper, we propose a DL-based changeable-rate framework with novel quantization scheme to improve the efficiency and feasibility of CSI feedback systems. This framework can reutilize all the network layers to achieve overhead-changeable CSI feedback to optimize the storage efficiency at the UE and the BS sides. Designed quantizer in this framework can avoid the normalization and gradient problems faced by traditional quantization schemes. Specifically, we propose two DL-based changeable-rate CSI feedback networks CH- CsiNetPro and CH- DualNetSph by introducing a feedback overhead control unit. Then, a pluggable quantization block (PQB) is developed to further improve the encoding efficiency of CSI feedback in an end-to-end way. Compared with existing CSI feedback methods, the proposed framework saves the storage space by about 50% with changeable-rate scheme and improves the encoding efficiency with the quantization module.

In the multiuser multiple-input multiple-output (MU-MIMO) system, to reduce the influence of channel correlation on system performance, the base station (BS) should select the appropriate subset of user equipments (UEs) according to their channel state information (CSI). Due to a lack of channel reciprocity, the downlink CSI needs to be fed back to the BS in frequency division duplexing (FDD) mode. Some scholars have exploited kinds of deep neural networks (DNNs) for sensing and recovering CSI. However, user selection after all the CSI is reconstructed by DNNs will bring a great time delay. In this paper, we propose a deep learning-based CSI feedback scheme called US-CsiNet. Based on adversarial autoencoder (AAE), US-CsiNet can explicitly cover user schedule information while representing CSI. At the UE side, the encoder of US-CsiNet maps the CSI into codewords of which part are feature information for user schedule. Then the BS applies these partial codewords to separate the UEs into different groups and select active UEs. Finally, the decoder of AAE reconstructs the CSI of these active UEs. US-CsiNet can not only simplify the user selection process but also guarantee the accuracy of CSI reconstruction. The simulation results show that the proposed approach outperforms maximum channel gain (MCG) user selection algorithms and achieves the nearly same performance with semiorthogonal user selection (SUS) which needs full CSI of all users at the BS.

This paper proposes an adaptive RF front-end (RFFE) architecture that uses an electrical-balance duplexer (EBD) and tuned surface acoustic wave (SAW) resonators to enable adaptive dual-frequency isolation suited for LTE’s frequency-division duplex (FDD) mode of operation. Alternatively, in the in-band full-duplex (IBFD) mode, the EBD cancels the in-band TX self-interference directly at RF for increased channel capacity. Furthermore, the EBD’s balance network is optimized to reduce the TX insertion loss (IL) below the nominal 3-dB limit in the FDD mode. A 0.18- $\mu \text{m}$ SOI CMOS prototype implements the EBD, low-noise amplifier, and SAW-tuning capacitor banks. The chip is mounted to a module substrate together with the SAWs and matching components. The RFFE achieves >50-dB dual-frequency isolation and 2.6–3.4-dB TX IL in FDD mode, has +58/+42-dBm TX/RX-path IIP3 for an increased IBFD-link budget and handles up to +27.5-dBm TX power in both modes.

This paper addresses the problem of compressively sensing a set of temporally correlated sources, in order to achieve faithful sparse signal reconstruction from noisy multiple measurement vectors (MMV). To this end, a simple sensing mechanism is proposed, which does not require the restricted isometry property (RIP) to hold near the sparsity level, whilst it provides additional degrees of freedom to better capture and suppress the inherent sampling noise effects. In particular, a reduced set of MMVs is generated by projecting the source signals onto random vectors drawn from isotropic multivariate stable laws. Then, the correlated sparse signals are recovered from the random MMVs by means of a recently introduced sparse Bayesian learning algorithm. Experimental evaluations on synthetic data with varying number of sources, correlation values, and noise strengths, reveal the superiority of our proposed sensing mechanism, when compared against well-established RIP-based compressive sensing schemes.