| 1. |
- Koochakzadeh, Ali, et al.
(author)
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Multi-antenna assisted spectrum sensing in spatially correlated noise environments
- 2015
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In: Signal Processing. - : Elsevier BV. - 0165-1684 .- 1872-7557. ; 108, s. 69-76
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Journal article (peer-reviewed)abstract
- A significant challenge in spectrum sensing is to lessen the signal to noise ratio needed to detect the presence of primary users while the noise level may also be unknown. To meet this challenge, multi-antenna based techniques possess a greater efficiency compared to other algorithms. In a typical compact multi-antenna system, due to small interelement spacing, mutual coupling between thermal noises of adjacent receivers is significant. In this paper, unlike most of the spectrum sensing algorithms which assume spatially uncorrelated noise, the noises on the adjacent antennas can have arbitrary correlations. Also, in contrast to some other algorithms, no prior assumption is made on the temporal properties of the signals. We exploit low-rank/sparse matrix decomposition algorithms to obtain an estimate of noise and received source covariance matrices. Given these estimates, a Semi-Constant False Alarm Rate (S-CFAR) detector, in which the probability of false alarm is constant over the scaling of the noise covariance matrix, to examine the presence of primary users is proposed. In order to analyze the efficiency of our algorithm, we derive approximate probability of detection. Numerical simulations show that the proposed algorithm consistently and considerably outperforms state-of-the-art multiantenna based spectrum sensing algorithms.
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| 2. |
- Malek Mohammadi, Mohammadreza, et al.
(author)
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A Class of Nonconvex Penalties Preserving OverallConvexity in Optimization-Based Mean Filtering
- 2016
-
In: IEEE Transactions on Signal Processing. - : Institute of Electrical and Electronics Engineers (IEEE). - 1053-587X .- 1941-0476. ; 65:24, s. 6650-6664
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Journal article (peer-reviewed)abstract
- l1 mean filtering is a conventional, optimizationbasedmethod to estimate the positions of jumps in a piecewiseconstant signal perturbed by additive noise. In this method, the l1 norm penalizes sparsity of the first-order derivative of the signal.Theoretical results, however, show that in some situations, whichcan occur frequently in practice, even when the jump amplitudes tend to , the conventional method identifies false change points.This issue is referred to as stair-casing problem in this paper andrestricts practical importance of l1 mean filtering. In this paper, sparsity is penalized more tightly than the l1 norm by exploiting a certain class of nonconvex functions, while the strict convexity ofthe consequent optimization problem is preserved. This results in a higher performance in detecting change points. To theoretically justify the performance improvements over l1 mean filtering, deterministic and stochastic sufficient conditions for exact changepoint recovery are derived. In particular, theoretical results show that in the stair-casing problem, our approach might be able to exclude the false change points, while l1 mean filtering may fail. A number of numerical simulations assist to show superiorityof our method over l1 mean filtering and another state-of-theart algorithm that promotes sparsity tighter than the l1 norm. Specifically, it is shown that our approach can consistently detectchange points when the jump amplitudes become sufficiently large, while the two other competitors cannot.
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| 3. |
- Malek Mohammadi, Mohammadreza, et al.
(author)
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DOA estimation in partially correlated noise using low-rank/sparse matrix decomposition
- 2014
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In: 2014 IEEE 8th Sensor Array and Multichannel Signal Processing Workshop (SAM). - : IEEE Computer Society. - 9781479914814 ; , s. 373-376
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Conference paper (peer-reviewed)abstract
- We consider the problem of direction-of-arrival (DOA) estimation in unknown partially correlated noise environments where the noise covariance matrix is sparse. A sparse noise covariance matrix is a common model for a sparse array of sensors consisted of several widely separated subarrays. Since interelement spacing among sensors in a subarray is small, the noise in the subarray is in general spatially correlated, while, due to large distances between subarrays, the noise between them is uncorrelated. Consequently, the noise covariance matrix of such an array has a block diagonal structure which is indeed sparse. Moreover, in an ordinary nonsparse array, because of small distance between adjacent sensors, there is noise coupling between neighboring sensors, whereas one can assume that non-adjacent sensors have spatially uncorrelated noise which makes again the array noise covariance matrix sparse. Utilizing some recently available tools in low-rank/sparse matrix decomposition, matrix completion, and sparse representation, we propose a novel method which can resolve possibly correlated or even coherent sources in the aforementioned partly correlated noise. In particular, when the sources are uncorrelated, our approach involves solving a second-order cone programming (SOCP), and if they are correlated or coherent, one needs to solve a computationally harder convex program. We demonstrate the effectiveness of the proposed algorithm by numerical simulations and comparison to the Cramer-Rao bound (CRB).
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| 4. |
- Malek Mohammadi, Mohammadreza, et al.
(author)
-
Performance Guaranteesfor Schatten-p Quasi-Norm Minimization in Recovery of Low-Rank Matrices
- 2015
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In: Signal Processing. - : Elsevier BV. - 0165-1684 .- 1872-7557. ; 114, s. 225-230
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Journal article (peer-reviewed)abstract
- We address some theoretical guarantees for Schatten-p quasi-norm minimization (p∈(0,1]p∈(0,1]) in recovering low-rank matrices from compressed linear measurements. Firstly, using null space properties of the measurement operator, we provide a sufficient condition for exact recovery of low-rank matrices. This condition guarantees unique recovery of matrices of ranks equal or larger than what is guaranteed by nuclear norm minimization. Secondly, this sufficient condition leads to a theorem proving that all restricted isometry property (RIP) based sufficient conditions for ℓpℓp quasi-norm minimization generalize to Schatten-p quasi-norm minimization. Based on this theorem, we provide a few RIP-based recovery conditions.
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| 5. |
- Malek-Mohammadi, Mohammadreza, et al.
(author)
-
Successive Concave Sparsity Approximation for Compressed Sensing
- 2016
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In: IEEE Transactions on Signal Processing. - 1053-587X .- 1941-0476. ; 64:21, s. 5657-5671
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Journal article (peer-reviewed)abstract
- In this paper, based on a successively accuracy-increasing approximation of the l(0) norm, we propose a new algorithm for recovery of sparse vectors from underdetermined measurements. The approximations are realized with a certain class of concave functions that aggressively induce sparsity and their closeness to the l(0) norm can be controlled. We prove that the series of the approximations asymptotically coincides with the l(1) and l(0) norms when the approximation accuracy changes from the worst fitting to the best fitting. When measurements are noise-free, an optimization scheme is proposed that leads to a number of weighted l(1) minimization programs, whereas, in the presence of noise, we propose two iterative thresholding methods that are computationally appealing. A convergence guarantee for the iterative thresholding method is provided, and, for a particular function in the class of the approximating functions, we derive the closed-form thresholding operator. We further present some theoretical analyses via the restricted isometry, null space, and spherical section properties. Our extensive numerical simulations indicate that the proposed algorithm closely follows the performance of the oracle estimator for a range of sparsity levels wider than those of the state-of-the-art algorithms.
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| 6. |
- Malek Mohammadi, Mohammadreza, et al.
(author)
-
Upper bounds on the error of sparse vector and low-rank matrix recovery
- 2016
-
In: Signal Processing. - : Elsevier. - 0165-1684 .- 1872-7557. ; 120, s. 249-254
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Journal article (peer-reviewed)abstract
- Suppose that a solution x to an underdetermined linear system b=Ax is given. x is approximately sparse meaning that it has a few large components compared to other small entries. However, the total number of nonzero components of x is large enough to violate any condition for the uniqueness of the sparsest solution. On the other hand, if only the dominant components are considered, then it will satisfy the uniqueness conditions. One intuitively expects that x should not be far from the true sparse solution x0. It was already shown that this intuition is the case by providing upper bounds on ||x-x0|| which are functions of the magnitudes of small components of x but independent from x0. In this paper, we tighten one of the available bounds on ||x-x0|| and extend this result to the case that b is perturbed by noise. Additionally, we generalize the upper bounds to the low-rank matrix recovery problem.
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| 7. |
- Nimara, Doumitrou Daniil, et al.
(author)
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Model-Based Reinforcement Learning for Cavity Filter Tuning
- 2023
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In: Proceedings of the 5th Annual Learning for Dynamics and Control Conference, L4DC 2023. - : ML Research Press. ; , s. 1297-1307
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Conference paper (peer-reviewed)abstract
- The ongoing development of telecommunication systems like 5G has led to an increase in demand of well calibrated base transceiver station (BTS) components. A pivotal component of every BTS is cavity filters, which provide a sharp frequency characteristic to select a particular band of interest and reject the rest. Unfortunately, their characteristics in combination with manufacturing tolerances make them difficult for mass production and often lead to costly manual post-production fine tuning. To address this, numerous approaches have been proposed to automate the tuning process. One particularly promising one, that has emerged in the past few years, is to use model free reinforcement learning (MFRL); however, the agents are not sample efficient. This poses a serious bottleneck, as utilising complex simulators or training with real filters is prohibitively time demanding. This work advocates for the usage of model based reinforcement learning (MBRL) and showcases how its utilisation can significantly decrease sample complexity, while maintaining similar levels of success rate. More specifically, we propose an improvement over a state-of-the-art (SoTA) MBRL algorithm, namely the Dreamer algorithm. This improvement can serve as a template for applications in other similar, high-dimensional non-image data problems. We carry experiments on two complex filter types, and show that our novel modification on the Dreamer architecture reduces sample complexity by a factor of 4 and 10, respectively. Our findings pioneer the usage of MBRL which paves the way for utilising more precise and accurate simulators which was previously prohibitively time demanding.
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| 8. |
- Owrang, Arash, et al.
(author)
-
Consistent Change Point Detection for Piecewise Constant Signals With Normalized Fused LASSO
- 2017
-
In: IEEE Signal Processing Letters. - : Institute of Electrical and Electronics Engineers (IEEE). - 1070-9908 .- 1558-2361. ; 24:6, s. 799-803
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Journal article (peer-reviewed)abstract
- We consider the problem of offline change point detection from noisy piecewise constant signals. We propose normalized fused LASSO (FL), an extension of the FL, obtained by normalizing the columns of the sensing matrix of the LASSO equivalent. We analyze the performance of the proposed method, and in particular, we show that it is consistent in detecting change points as the noise variance tends to zero. Numerical experiments support our theoretical findings.
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