Sajad Daei - Academia.edu (original) (raw)

Papers by Sajad Daei

arXiv (Cornell University), May 13, 2024

In this work, we address the challenge of accurately obtaining channel state information at the t... more In this work, we address the challenge of accurately obtaining channel state information at the transmitter (CSIT) for frequency division duplexing (FDD) multiple input multiple output systems. Although CSIT is vital for maximizing spatial multiplexing gains, traditional CSIT estimation methods often suffer from impracticality due to the substantial training and feedback overhead they require. To address this challenge, we leverage two sources of prior information simultaneously: the presence of limited local scatterers at the base station (BS) and the time-varying characteristics of the channel. The former results in a redundant angular sparsity of users' channels exceeding the spatial dimension (i.e., the number of BS antennas), while the latter provides a prior non-uniform distribution in the angular domain. We propose a weighted optimization framework that simultaneously reflects both of these features. The optimal weights are then obtained by minimizing the expected recovery error of the optimization problem. This establishes an analytical closedform relationship between the optimal weights and the angular domain characteristics. Numerical experiments verify the effectiveness of our proposed approach in reducing the recovery error and consequently resulting in decreased training and feedback overhead.

arXiv (Cornell University), Dec 27, 2022

This work is about recovering an analysis-sparse vector, i.e. sparse vector in some transform dom... more This work is about recovering an analysis-sparse vector, i.e. sparse vector in some transform domain, from undersampled measurements. In real-world applications, there often exist random analysis-sparse vectors whose distribution in the analysis domain are known. To exploit this information, a weighted 1 analysis minimization is often considered. The task of choosing the weights in this case is however challenging and non-trivial. In this work, we provide an analytical method to choose the suitable weights. Specifically, we first obtain a tight upper-bound expression for the expected number of required measurements. This bound depends on two critical parameters: support distribution and expected sign of the analysis domain which are both accessible in advance. Then, we calculate the nearoptimal weights by minimizing this expression with respect to the weights. Our strategy works for both noiseless and noisy settings. Numerical results demonstrate the superiority of our proposed method. Specifically, the weighted 1 analysis minimization with our near-optimal weighting design considerably needs fewer measurements than its regular 1 analysis counterpart.

arXiv (Cornell University), Jun 21, 2023

Resource allocation and multiple access schemes are instrumental for the success of communication... more Resource allocation and multiple access schemes are instrumental for the success of communication networks, which facilitate seamless wireless connectivity among a growing population of uncoordinated and non-synchronized users. In this paper, we present a novel random access scheme that addresses one of the most severe barriers of current strategies to achieve massive connectivity and ultra reliable and low latency communications for 6G. The proposed scheme utilizes wireless channels' angular continuous group-sparsity feature to provide low latency, high reliability, and massive access features in the face of limited time-bandwidth resources, asynchronous transmissions, and preamble errors. Specifically, a reconstruction-free goal oriented optimization problem is proposed which preserves the angular information of active devices and is then complemented by a clustering algorithm to assign active users to specific groups. This allows to identify active stationary devices according to their line of sight angles. Additionally, for mobile devices, an alternating minimization algorithm is proposed to recover their preamble, data, and channel gains simultaneously, enabling the identification of active mobile users. Simulation results show that the proposed algorithm provides excellent performance and supports a massive number of devices. Moreover, the performance of the proposed scheme is independent of the total number of devices, distinguishing it from other random access schemes. The proposed method provides a unified solution to meet the requirements of machine-type communications and ultra reliable and low latency communications, making it an important contribution to the emerging 6G networks.

arXiv (Cornell University), Aug 7, 2023

We consider the problem of gridless blind deconvolution and demixing (GB2D) in scenarios where mu... more We consider the problem of gridless blind deconvolution and demixing (GB2D) in scenarios where multiple users communicate messages through multiple unknown channels, and a single base station (BS) collects their contributions. This scenario arises in various communication fields, including wireless communications, the Internet of Things, over-the-air computation, and integrated sensing and communications. In this setup, each user's message is convolved with a multi-path channel formed by several scaled and delayed copies of Dirac spikes. The BS receives a linear combination of the convolved signals, and the goal is to recover the unknown amplitudes, continuousindexed delays, and transmitted waveforms from a compressed vector of measurements at the BS. However, in the absence of any prior knowledge of the transmitted messages and channels, GB2D is highly challenging and intractable in general. To address this issue, we assume that each user's message follows a distinct modulation scheme living in a known low-dimensional subspace. By exploiting these subspace assumptions and the sparsity of the multipath channels for different users, we transform the nonlinear GB2D problem into a matrix tuple recovery problem from a few linear measurements. To achieve this, we propose a semidefinite programming optimization that exploits the specific low-dimensional structure of the matrix tuple to recover the messages and continuous delays of different communication paths from a single received signal at the BS. Finally, our numerical experiments show that our proposed method effectively recovers all transmitted messages and the continuous delay parameters of the channels with a sufficient number of samples. Index Terms-Atomic norm minimization, blind channel estimation, blind data recovery, blind deconvolution, blind demixing.

arXiv (Cornell University), Jan 9, 2023

The multiuser linearly-separable distributed computing problem is considered here, in which N ser... more The multiuser linearly-separable distributed computing problem is considered here, in which N servers help to compute the real-valued functions requested by K users, where each function can be written as a linear combination of up to L (generally non-linear) subfunctions. Each server computes a fraction γ of the subfunctions, then communicates a function of its computed outputs to some of the users, and then each user collects its received data to recover its desired function. Our goal is to bound the ratio between the computation workload done by all servers over the number of datasets. To this end, we here reformulate the real-valued distributed computing problem into a matrix factorization problem and then into a basic sparse recovery problem, where sparsity implies computational savings. Building on this, we first give a simple probabilistic scheme for subfunction assignment, which allows us to upper bound the optimal normalized computation cost as γ ≤ K N that a generally intractable 0-minimization would give. To bypass the intractability of such optimal scheme, we show that if these optimal schemes enjoy γ ≤ −r K N W −1 −1 (− 2K eN r) (where W−1(•) is the Lambert function and r calibrates the communication between servers and users), then they can actually be derived using a tractable Basis Pursuit 1-minimization. This newly-revealed connection opens up the possibility of designing practical distributed computing algorithms by employing tools and methods from compressed sensing.

Cornell University - arXiv, May 14, 2022

Emerging communication networks are envisioned to support massive wireless connectivity of hetero... more Emerging communication networks are envisioned to support massive wireless connectivity of heterogeneous devices with sporadic traffic and diverse requirements in terms of latency, reliability, and bandwidth. Providing multiple access to an increasing number of uncoordinated users and sharing the limited resources become essential in this context. In this work, we revisit the random access (RA) problem and exploit the continuous angular group sparsity feature of wireless channels to propose a novel RA strategy that provides low latency, high reliability, and massive access with limited bandwidth resources in an allin-one package. To this end, we first design a reconstructionfree goal-oriented optimization problem, which only preserves the angular information required to identify the active devices. To solve this, we propose an alternating direction method of multipliers (ADMM) and derive closed-form expressions for each ADMM step. Then, we design a clustering algorithm that assigns the users in specific groups from which we can identify active stationary devices by their angles. For mobile devices, we propose an alternating minimization algorithm to recover their data and their channel gains simultaneously, which allows us to identify active mobile users. Simulation results show significant performance gains in terms of active user detection and false alarm probabilities as compared to state-of-the-art RA schemes, even with limited number of preambles. Moreover, unlike prior work, the performance of the proposed blind goal-oriented massive access does not depend on the number of devices.

IEEE Communications Letters, 2022

ArXiv, 2021

Abstract—Matrix completion refers to completing a low-rank matrix from a few observed elements of... more Abstract—Matrix completion refers to completing a low-rank matrix from a few observed elements of its entries and has been known as one of the significant and widely-used problems in recent years. The required number of observations for exact completion is directly proportional to rank and the coherency parameter of the matrix. In many applications, there might exist additional information about the low-rank matrix of interest. For example, in collaborative filtering, Netflix and dynamic channel estimation in communications, extra subspace information is available. More precisely in these applications, there are prior subspaces forming multiple angles with the groundtruth subspaces. In this paper, we propose a novel strategy to incorporate this information into the completion task. To this end, we designed a multi-weight nuclear norm minimization where the weights are such chosen to penalize each angle within the matrix subspace independently. We propose a new scheme for optimally c...

This work is about the total variation (TV) minimization which is used for recovering gradient-sp... more This work is about the total variation (TV) minimization which is used for recovering gradient-sparse signals from compressed measurements. Recent studies indicate that TV minimization exhibits a phase transition behavior from failure to success as the number of measurements increases. In fact, in large dimensions, TV minimization succeeds in recovering the gradient-sparse signal with high probability when the number of measurements exceeds a certain threshold; otherwise, it fails almost certainly. Obtaining a closed-form expression that approximates this threshold is a major challenge in this field and has not been appropriately addressed yet. In this work, we derive a tight lower-bound on this threshold in case of any random measurement matrix whose null space is distributed uniformly with respect to the Haar measure. In contrast to the conventional TV phase transition results that depend on the simple gradient-sparsity level, our bound is highly affected by generalized notions of...

Compressed Sensing refers to extracting a low-dimensional structured signal of interest from its ... more Compressed Sensing refers to extracting a low-dimensional structured signal of interest from its incomplete random linear observations. A line of recent work has studied that, with the extra prior information about the signal, one can recover the signal with much fewer observations. For this purpose, the general approach is to solve weighted convex function minimization problem. In such settings, the convex function is chosen to promote the low-dimensional structure and the optimal weights are so chosen to reduce the number of measurements required for the optimization problem. In this paper, we consider a generalized non-uniform model in which the structured signal falls into some partitions, with entries of each partition having a definite probability to be an element of the structure support. Given these probabilities and regarding the recent developments in conic integral geometry, we provide a method to choose the unique optimal weights for any general low-dimensional signal mo...

This work presents a novel framework for random access in crowded scenarios of multiple-input mul... more This work presents a novel framework for random access in crowded scenarios of multiple-input multiple-output(MIMO) systems. A multi-antenna base station (BS) and multiple single-antenna users are considered in these systems. A huge portion of the system resources is dedicated as orthogonal pilots for accurate channel estimation which imposes a huge training overhead. This overhead can be highly mitigated by exploiting intrinsic angular domain sparsity of massive MIMO channels and the sporadic traffic of users, i.e., few number of users are active to sent or receive data in each coherence interval. In fact, the angles of arrivals (AoAs) coming from active users are continuous parameters and can take any arbitrary values. Besides, the AoAs corresponding to each active user are alongside each other forming a specific cluster. This work revolves around exploiting these features. Specifically, a blind clustering-based algorithm is proposed that not only recovers the transmitted data by ...

Weighted nuclear norm minimization has been recently recognized as a technique for reconstruction... more Weighted nuclear norm minimization has been recently recognized as a technique for reconstruction of a low-rank matrix from compressively sampled measurements when some prior information about the column and row subspaces of the matrix is available. In this work, we study the recovery conditions and the associated recovery guarantees of weighted nuclear norm minimization when multiple weights are allowed. This setup might be used when one has access to prior subspaces forming multiple angles with the column and row subspaces of the ground-truth matrix. While existing works in this field use a single weight to penalize all the angles, we propose a multi-weight problem which is designed to penalize each angle independently using a distinct weight. Specifically, we prove that our proposed multi-weight problem is stable and robust under weaker conditions for the measurement operator than the analogous conditions for single-weight scenario and standard nuclear norm minimization. Moreover...

In this paper, we provide a method to recover off-the-grid frequencies of a signal in two-dimensi... more In this paper, we provide a method to recover off-the-grid frequencies of a signal in two-dimensional (2-D) line spectral estimation. Most of the literature in this field focuses on the case in which the only information is spectral sparsity in a continuous domain and does not consider prior information. However, in many applications such as radar and sonar, one has extra information about the spectrum of the signal of interest. The common way of accommodating prior information is to use weighted atomic norm minimization. We present a new semidefinite program using the theory of positive trigonometric polynomials that incorporate this prior information into 2-D line spectral estimation. Specifically, we assume prior knowledge of 2-D frequency subbands in which signal frequency components are located. Our approach improves the recovery performance compared with the previous work that does not consider prior information. Through numerical experiments, we find out that the amount of th...

One-bit compressive sensing (CS) is an advanced version of sparse recovery in which the sparse si... more One-bit compressive sensing (CS) is an advanced version of sparse recovery in which the sparse signal of interest can be recovered from extremely quantized measurements. Namely, only the sign of each measurement is available to us. In many applications, the ground-truth signal is not sparse itself, but can be represented in a redundant dictionary. A strong line of research has addressed conventional CS in this signal model including its extension to one-bit measurements. However, one-bit CS suffers from the extremely large number of required measurements to achieve a predefined reconstruction error level. A common alternative to resolve this issue is to exploit adaptive schemes. Adaptive sampling acts on the acquired samples to trace the signal in an efficient way. In this work, we utilize an adaptive sampling strategy to recover dictionary-sparse signals from binary measurements. For this task, a multi-dimensional threshold is proposed to incorporate the previous signal estimates i...

Matrix sensing is the problem of reconstructing a low-rank matrix from a few linear measurements.... more Matrix sensing is the problem of reconstructing a low-rank matrix from a few linear measurements. In many applications such as collaborative filtering, the famous Netflix prize problem, and seismic data interpolation, there exists some prior information about the column and row spaces of the ground-truth low-rank matrix. In this paper, we exploit this prior information by proposing a weighted optimization problem where its objective function promotes both rank and prior subspace information. Using the recent results in conic integral geometry, we obtain the unique optimal weights that minimize the required number of measurements. As simulation results confirm, the proposed convex program with optimal weights requires substantially fewer measurements than the regular nuclear norm minimization.

arXiv: Signal Processing, 2020

In this paper, we address the line spectral estimation problem with multiple measurement corrupte... more In this paper, we address the line spectral estimation problem with multiple measurement corrupted vectors. Such scenarios appear in many practical applications such as radar, optics, and seismic imaging in which the signal of interest can be modeled as the sum of a spectrally sparse and a blocksparse signal known as outlier. Our aim is to demix the two components and for that, we design a convex problem whose objective function promotes both of the structures. Using positive trigonometric polynomials (PTP) theory, we reformulate the dual problem as a semi-definite program (SDP). Our theoretical results states that for a fixed number of measurements N and constant number of outliers, up to O(N) spectral lines can be recovered using our SDP problem as long as a minimum frequency separation condition is satisfied. Our simulation results also show that increasing the number of samples per measurement vectors, reduces the minimum required frequency separation for successful recovery.

ArXiv, 2017

Compressed Sensing refers to extracting a low-dimensional structured signal of interest from its ... more Compressed Sensing refers to extracting a low-dimensional structured signal of interest from its incomplete random linear observations. A line of recent work has studied that, with the extra prior information about the signal, one can recover the signal with much fewer observations. For this purpose, the general approach is to solve weighted convex function minimization problem. In such settings, the convex function is chosen to promote the low-dimensional structure and the optimal weights are so chosen to reduce the number of measurements required for the optimization problem. In this paper, we consider a generalized non-uniform model in which the structured signal falls into some partitions, with entries of each partition having a definite probability to be an element of the structure support. Given these probabilities and regarding the recent developments in conic integral geometry, we provide a method to choose the unique optimal weights for any general low-dimensional signal mo...

IEEE Access, 2020

Matrix sensing refers to recovering a low-rank matrix from a few linear combinations of its entri... more Matrix sensing refers to recovering a low-rank matrix from a few linear combinations of its entries. This problem naturally arises in many applications including recommendation systems, collaborative filtering, seismic data interpolation and wireless sensor networks. Recently, in these applications, it has been noted that exploiting additional subspace information might yield significant improvements in practical scenarios. This information is reflected by two subspaces forming angles with column and row spaces of the ground-truth matrix. Despite the importance of exploiting this information, there is limited theoretical guarantee for this feature. In this work, we aim to address this issue by proposing a novel hybrid nuclear norm regularization which besides low-rankness, encourages subspace prior information. Our proposed regularizer is a weighted combination of deformed nuclear norm functions. We derive a closed-form accurate expression for the mean squared error (MSE) of the pro...

ArXiv, 2017

In this paper, we provide a method to recover off-the-grid frequencies of a signal in two-dimensi... more In this paper, we provide a method to recover off-the-grid frequencies of a signal in two-dimensional (2-D) line spectral estimation. Most of the literature in this field focuses on the case in which the only information is spectral sparsity in a continuous domain and does not consider prior information. However, in many applications such as radar and sonar, one has extra information about the spectrum of the signal of interest. The common way of accommodating prior information is to use weighted atomic norm minimization. We present a new semidefinite program using the theory of positive trigonometric polynomials that incorporate this prior information into 2-D line spectral estimation. Specifically, we assume prior knowledge of 2-D frequency subbands in which signal frequency components are located. Our approach improves the recovery performance compared with the previous work that does not consider prior information. Through numerical experiments, we find out that the amount of th...

arXiv (Cornell University), May 13, 2024

In this work, we address the challenge of accurately obtaining channel state information at the t... more In this work, we address the challenge of accurately obtaining channel state information at the transmitter (CSIT) for frequency division duplexing (FDD) multiple input multiple output systems. Although CSIT is vital for maximizing spatial multiplexing gains, traditional CSIT estimation methods often suffer from impracticality due to the substantial training and feedback overhead they require. To address this challenge, we leverage two sources of prior information simultaneously: the presence of limited local scatterers at the base station (BS) and the time-varying characteristics of the channel. The former results in a redundant angular sparsity of users' channels exceeding the spatial dimension (i.e., the number of BS antennas), while the latter provides a prior non-uniform distribution in the angular domain. We propose a weighted optimization framework that simultaneously reflects both of these features. The optimal weights are then obtained by minimizing the expected recovery error of the optimization problem. This establishes an analytical closedform relationship between the optimal weights and the angular domain characteristics. Numerical experiments verify the effectiveness of our proposed approach in reducing the recovery error and consequently resulting in decreased training and feedback overhead.

arXiv (Cornell University), Dec 27, 2022

This work is about recovering an analysis-sparse vector, i.e. sparse vector in some transform dom... more This work is about recovering an analysis-sparse vector, i.e. sparse vector in some transform domain, from undersampled measurements. In real-world applications, there often exist random analysis-sparse vectors whose distribution in the analysis domain are known. To exploit this information, a weighted 1 analysis minimization is often considered. The task of choosing the weights in this case is however challenging and non-trivial. In this work, we provide an analytical method to choose the suitable weights. Specifically, we first obtain a tight upper-bound expression for the expected number of required measurements. This bound depends on two critical parameters: support distribution and expected sign of the analysis domain which are both accessible in advance. Then, we calculate the nearoptimal weights by minimizing this expression with respect to the weights. Our strategy works for both noiseless and noisy settings. Numerical results demonstrate the superiority of our proposed method. Specifically, the weighted 1 analysis minimization with our near-optimal weighting design considerably needs fewer measurements than its regular 1 analysis counterpart.

arXiv (Cornell University), Jun 21, 2023

Resource allocation and multiple access schemes are instrumental for the success of communication... more Resource allocation and multiple access schemes are instrumental for the success of communication networks, which facilitate seamless wireless connectivity among a growing population of uncoordinated and non-synchronized users. In this paper, we present a novel random access scheme that addresses one of the most severe barriers of current strategies to achieve massive connectivity and ultra reliable and low latency communications for 6G. The proposed scheme utilizes wireless channels' angular continuous group-sparsity feature to provide low latency, high reliability, and massive access features in the face of limited time-bandwidth resources, asynchronous transmissions, and preamble errors. Specifically, a reconstruction-free goal oriented optimization problem is proposed which preserves the angular information of active devices and is then complemented by a clustering algorithm to assign active users to specific groups. This allows to identify active stationary devices according to their line of sight angles. Additionally, for mobile devices, an alternating minimization algorithm is proposed to recover their preamble, data, and channel gains simultaneously, enabling the identification of active mobile users. Simulation results show that the proposed algorithm provides excellent performance and supports a massive number of devices. Moreover, the performance of the proposed scheme is independent of the total number of devices, distinguishing it from other random access schemes. The proposed method provides a unified solution to meet the requirements of machine-type communications and ultra reliable and low latency communications, making it an important contribution to the emerging 6G networks.

arXiv (Cornell University), Aug 7, 2023

We consider the problem of gridless blind deconvolution and demixing (GB2D) in scenarios where mu... more We consider the problem of gridless blind deconvolution and demixing (GB2D) in scenarios where multiple users communicate messages through multiple unknown channels, and a single base station (BS) collects their contributions. This scenario arises in various communication fields, including wireless communications, the Internet of Things, over-the-air computation, and integrated sensing and communications. In this setup, each user's message is convolved with a multi-path channel formed by several scaled and delayed copies of Dirac spikes. The BS receives a linear combination of the convolved signals, and the goal is to recover the unknown amplitudes, continuousindexed delays, and transmitted waveforms from a compressed vector of measurements at the BS. However, in the absence of any prior knowledge of the transmitted messages and channels, GB2D is highly challenging and intractable in general. To address this issue, we assume that each user's message follows a distinct modulation scheme living in a known low-dimensional subspace. By exploiting these subspace assumptions and the sparsity of the multipath channels for different users, we transform the nonlinear GB2D problem into a matrix tuple recovery problem from a few linear measurements. To achieve this, we propose a semidefinite programming optimization that exploits the specific low-dimensional structure of the matrix tuple to recover the messages and continuous delays of different communication paths from a single received signal at the BS. Finally, our numerical experiments show that our proposed method effectively recovers all transmitted messages and the continuous delay parameters of the channels with a sufficient number of samples. Index Terms-Atomic norm minimization, blind channel estimation, blind data recovery, blind deconvolution, blind demixing.

arXiv (Cornell University), Jan 9, 2023

The multiuser linearly-separable distributed computing problem is considered here, in which N ser... more The multiuser linearly-separable distributed computing problem is considered here, in which N servers help to compute the real-valued functions requested by K users, where each function can be written as a linear combination of up to L (generally non-linear) subfunctions. Each server computes a fraction γ of the subfunctions, then communicates a function of its computed outputs to some of the users, and then each user collects its received data to recover its desired function. Our goal is to bound the ratio between the computation workload done by all servers over the number of datasets. To this end, we here reformulate the real-valued distributed computing problem into a matrix factorization problem and then into a basic sparse recovery problem, where sparsity implies computational savings. Building on this, we first give a simple probabilistic scheme for subfunction assignment, which allows us to upper bound the optimal normalized computation cost as γ ≤ K N that a generally intractable 0-minimization would give. To bypass the intractability of such optimal scheme, we show that if these optimal schemes enjoy γ ≤ −r K N W −1 −1 (− 2K eN r) (where W−1(•) is the Lambert function and r calibrates the communication between servers and users), then they can actually be derived using a tractable Basis Pursuit 1-minimization. This newly-revealed connection opens up the possibility of designing practical distributed computing algorithms by employing tools and methods from compressed sensing.

Cornell University - arXiv, May 14, 2022

Emerging communication networks are envisioned to support massive wireless connectivity of hetero... more Emerging communication networks are envisioned to support massive wireless connectivity of heterogeneous devices with sporadic traffic and diverse requirements in terms of latency, reliability, and bandwidth. Providing multiple access to an increasing number of uncoordinated users and sharing the limited resources become essential in this context. In this work, we revisit the random access (RA) problem and exploit the continuous angular group sparsity feature of wireless channels to propose a novel RA strategy that provides low latency, high reliability, and massive access with limited bandwidth resources in an allin-one package. To this end, we first design a reconstructionfree goal-oriented optimization problem, which only preserves the angular information required to identify the active devices. To solve this, we propose an alternating direction method of multipliers (ADMM) and derive closed-form expressions for each ADMM step. Then, we design a clustering algorithm that assigns the users in specific groups from which we can identify active stationary devices by their angles. For mobile devices, we propose an alternating minimization algorithm to recover their data and their channel gains simultaneously, which allows us to identify active mobile users. Simulation results show significant performance gains in terms of active user detection and false alarm probabilities as compared to state-of-the-art RA schemes, even with limited number of preambles. Moreover, unlike prior work, the performance of the proposed blind goal-oriented massive access does not depend on the number of devices.

IEEE Communications Letters, 2022

ArXiv, 2021

Abstract—Matrix completion refers to completing a low-rank matrix from a few observed elements of... more Abstract—Matrix completion refers to completing a low-rank matrix from a few observed elements of its entries and has been known as one of the significant and widely-used problems in recent years. The required number of observations for exact completion is directly proportional to rank and the coherency parameter of the matrix. In many applications, there might exist additional information about the low-rank matrix of interest. For example, in collaborative filtering, Netflix and dynamic channel estimation in communications, extra subspace information is available. More precisely in these applications, there are prior subspaces forming multiple angles with the groundtruth subspaces. In this paper, we propose a novel strategy to incorporate this information into the completion task. To this end, we designed a multi-weight nuclear norm minimization where the weights are such chosen to penalize each angle within the matrix subspace independently. We propose a new scheme for optimally c...

This work is about the total variation (TV) minimization which is used for recovering gradient-sp... more This work is about the total variation (TV) minimization which is used for recovering gradient-sparse signals from compressed measurements. Recent studies indicate that TV minimization exhibits a phase transition behavior from failure to success as the number of measurements increases. In fact, in large dimensions, TV minimization succeeds in recovering the gradient-sparse signal with high probability when the number of measurements exceeds a certain threshold; otherwise, it fails almost certainly. Obtaining a closed-form expression that approximates this threshold is a major challenge in this field and has not been appropriately addressed yet. In this work, we derive a tight lower-bound on this threshold in case of any random measurement matrix whose null space is distributed uniformly with respect to the Haar measure. In contrast to the conventional TV phase transition results that depend on the simple gradient-sparsity level, our bound is highly affected by generalized notions of...

Compressed Sensing refers to extracting a low-dimensional structured signal of interest from its ... more Compressed Sensing refers to extracting a low-dimensional structured signal of interest from its incomplete random linear observations. A line of recent work has studied that, with the extra prior information about the signal, one can recover the signal with much fewer observations. For this purpose, the general approach is to solve weighted convex function minimization problem. In such settings, the convex function is chosen to promote the low-dimensional structure and the optimal weights are so chosen to reduce the number of measurements required for the optimization problem. In this paper, we consider a generalized non-uniform model in which the structured signal falls into some partitions, with entries of each partition having a definite probability to be an element of the structure support. Given these probabilities and regarding the recent developments in conic integral geometry, we provide a method to choose the unique optimal weights for any general low-dimensional signal mo...

This work presents a novel framework for random access in crowded scenarios of multiple-input mul... more This work presents a novel framework for random access in crowded scenarios of multiple-input multiple-output(MIMO) systems. A multi-antenna base station (BS) and multiple single-antenna users are considered in these systems. A huge portion of the system resources is dedicated as orthogonal pilots for accurate channel estimation which imposes a huge training overhead. This overhead can be highly mitigated by exploiting intrinsic angular domain sparsity of massive MIMO channels and the sporadic traffic of users, i.e., few number of users are active to sent or receive data in each coherence interval. In fact, the angles of arrivals (AoAs) coming from active users are continuous parameters and can take any arbitrary values. Besides, the AoAs corresponding to each active user are alongside each other forming a specific cluster. This work revolves around exploiting these features. Specifically, a blind clustering-based algorithm is proposed that not only recovers the transmitted data by ...

Weighted nuclear norm minimization has been recently recognized as a technique for reconstruction... more Weighted nuclear norm minimization has been recently recognized as a technique for reconstruction of a low-rank matrix from compressively sampled measurements when some prior information about the column and row subspaces of the matrix is available. In this work, we study the recovery conditions and the associated recovery guarantees of weighted nuclear norm minimization when multiple weights are allowed. This setup might be used when one has access to prior subspaces forming multiple angles with the column and row subspaces of the ground-truth matrix. While existing works in this field use a single weight to penalize all the angles, we propose a multi-weight problem which is designed to penalize each angle independently using a distinct weight. Specifically, we prove that our proposed multi-weight problem is stable and robust under weaker conditions for the measurement operator than the analogous conditions for single-weight scenario and standard nuclear norm minimization. Moreover...

In this paper, we provide a method to recover off-the-grid frequencies of a signal in two-dimensi... more In this paper, we provide a method to recover off-the-grid frequencies of a signal in two-dimensional (2-D) line spectral estimation. Most of the literature in this field focuses on the case in which the only information is spectral sparsity in a continuous domain and does not consider prior information. However, in many applications such as radar and sonar, one has extra information about the spectrum of the signal of interest. The common way of accommodating prior information is to use weighted atomic norm minimization. We present a new semidefinite program using the theory of positive trigonometric polynomials that incorporate this prior information into 2-D line spectral estimation. Specifically, we assume prior knowledge of 2-D frequency subbands in which signal frequency components are located. Our approach improves the recovery performance compared with the previous work that does not consider prior information. Through numerical experiments, we find out that the amount of th...

One-bit compressive sensing (CS) is an advanced version of sparse recovery in which the sparse si... more One-bit compressive sensing (CS) is an advanced version of sparse recovery in which the sparse signal of interest can be recovered from extremely quantized measurements. Namely, only the sign of each measurement is available to us. In many applications, the ground-truth signal is not sparse itself, but can be represented in a redundant dictionary. A strong line of research has addressed conventional CS in this signal model including its extension to one-bit measurements. However, one-bit CS suffers from the extremely large number of required measurements to achieve a predefined reconstruction error level. A common alternative to resolve this issue is to exploit adaptive schemes. Adaptive sampling acts on the acquired samples to trace the signal in an efficient way. In this work, we utilize an adaptive sampling strategy to recover dictionary-sparse signals from binary measurements. For this task, a multi-dimensional threshold is proposed to incorporate the previous signal estimates i...

Matrix sensing is the problem of reconstructing a low-rank matrix from a few linear measurements.... more Matrix sensing is the problem of reconstructing a low-rank matrix from a few linear measurements. In many applications such as collaborative filtering, the famous Netflix prize problem, and seismic data interpolation, there exists some prior information about the column and row spaces of the ground-truth low-rank matrix. In this paper, we exploit this prior information by proposing a weighted optimization problem where its objective function promotes both rank and prior subspace information. Using the recent results in conic integral geometry, we obtain the unique optimal weights that minimize the required number of measurements. As simulation results confirm, the proposed convex program with optimal weights requires substantially fewer measurements than the regular nuclear norm minimization.

arXiv: Signal Processing, 2020

In this paper, we address the line spectral estimation problem with multiple measurement corrupte... more In this paper, we address the line spectral estimation problem with multiple measurement corrupted vectors. Such scenarios appear in many practical applications such as radar, optics, and seismic imaging in which the signal of interest can be modeled as the sum of a spectrally sparse and a blocksparse signal known as outlier. Our aim is to demix the two components and for that, we design a convex problem whose objective function promotes both of the structures. Using positive trigonometric polynomials (PTP) theory, we reformulate the dual problem as a semi-definite program (SDP). Our theoretical results states that for a fixed number of measurements N and constant number of outliers, up to O(N) spectral lines can be recovered using our SDP problem as long as a minimum frequency separation condition is satisfied. Our simulation results also show that increasing the number of samples per measurement vectors, reduces the minimum required frequency separation for successful recovery.

ArXiv, 2017

Compressed Sensing refers to extracting a low-dimensional structured signal of interest from its ... more Compressed Sensing refers to extracting a low-dimensional structured signal of interest from its incomplete random linear observations. A line of recent work has studied that, with the extra prior information about the signal, one can recover the signal with much fewer observations. For this purpose, the general approach is to solve weighted convex function minimization problem. In such settings, the convex function is chosen to promote the low-dimensional structure and the optimal weights are so chosen to reduce the number of measurements required for the optimization problem. In this paper, we consider a generalized non-uniform model in which the structured signal falls into some partitions, with entries of each partition having a definite probability to be an element of the structure support. Given these probabilities and regarding the recent developments in conic integral geometry, we provide a method to choose the unique optimal weights for any general low-dimensional signal mo...

IEEE Access, 2020

Matrix sensing refers to recovering a low-rank matrix from a few linear combinations of its entri... more Matrix sensing refers to recovering a low-rank matrix from a few linear combinations of its entries. This problem naturally arises in many applications including recommendation systems, collaborative filtering, seismic data interpolation and wireless sensor networks. Recently, in these applications, it has been noted that exploiting additional subspace information might yield significant improvements in practical scenarios. This information is reflected by two subspaces forming angles with column and row spaces of the ground-truth matrix. Despite the importance of exploiting this information, there is limited theoretical guarantee for this feature. In this work, we aim to address this issue by proposing a novel hybrid nuclear norm regularization which besides low-rankness, encourages subspace prior information. Our proposed regularizer is a weighted combination of deformed nuclear norm functions. We derive a closed-form accurate expression for the mean squared error (MSE) of the pro...

ArXiv, 2017

In this paper, we provide a method to recover off-the-grid frequencies of a signal in two-dimensi... more In this paper, we provide a method to recover off-the-grid frequencies of a signal in two-dimensional (2-D) line spectral estimation. Most of the literature in this field focuses on the case in which the only information is spectral sparsity in a continuous domain and does not consider prior information. However, in many applications such as radar and sonar, one has extra information about the spectrum of the signal of interest. The common way of accommodating prior information is to use weighted atomic norm minimization. We present a new semidefinite program using the theory of positive trigonometric polynomials that incorporate this prior information into 2-D line spectral estimation. Specifically, we assume prior knowledge of 2-D frequency subbands in which signal frequency components are located. Our approach improves the recovery performance compared with the previous work that does not consider prior information. Through numerical experiments, we find out that the amount of th...