Damoun Nashtaali, Omid Mashayekhi, Pedram Pad, Seyed Reza Moghadasi, Farokh Marvasti
In CDMA systems, the received user powers vary due to moving distance of users. Thus, the CDMA receivers consist of two stages. The first stage is the power estimator and the second one is a Multi-User Detector (MUD). Conventional methods for estimating the user powers are suitable for underor fully-loaded cases (when the number of users is less than or equal to the spreading gain). These methods fail to work for overloaded CDMA systems because of high interference among the users. Since the bandwidth is becoming more and more valuable, it is worth considering overloaded CDMA systems. In this paper, an optimum user power estimation for over-loaded CDMA systems with Gaussian inputs is proposed. We also introduce a suboptimum method with lower complexity whose performance is very close to the optimum one. We shall show that the proposed methods work for highly over-loaded systems (up to m(m + 1) =2 users for a system with only m chips). The performance of the proposed methods is demonstrated by simulations. In addition, a class of signature sets is proposed that seems to be optimum from a power estimation point of view. Additionally, an iterative estimation for binary input CDMA systems is proposed which works more accurately than the optimal Gaussian input method.
Elaheh Mohammadi, Farokh Marvasti
In this paper, the optimal sampling strategies (uniform or nonuniform) and distortion tradeoffs for Gaussian bandlimited periodic signals with additive white Gaussian noise are studied. Our emphasis is on characterizing the optimal sampling locations as well as the optimal pre-sampling filter to minimize the reconstruction distortion. We first show that to achieve the optimal distortion, no pre-sampling filter is necessary for any arbitrary sampling rate. Then, we provide a complete characterization of optimal distortion for low and high sampling rates (with respect to the signal bandwidth). We also provide bounds on the reconstruction distortion for rates in the intermediate region. It is shown that nonuniform sampling outperforms uniform sampling for low sampling rates. In addition, the optimal nonuniform sampling set is robust with respect to missing sampling values. On the other hand, for the sampling rates above the Nyquist rate, the uniform sampling strategy is optimal. An extension of the results for random discrete periodic signals is discussed with simulation results indicating that the intuitions from the continuous domain carry over to the discrete domain. Sparse signals are also considered, where it is shown that uniform sampling is optimal above the Nyquist rate.
Azra Abtahi, M. Modarres-Hashemi, Farokh Marvasti, Foroogh S. Tabataba
Multiple-input multiple-output (MIMO) radars offer higher resolution, better target detection, and more accurate target parameter estimation. Due to the sparsity of the targets in space-velocity domain, we can exploit Compressive Sensing (CS) to improve the performance of MIMO radars when the sampling rate is much less than the Nyquist rate. In distributed MIMO radars, block CS methods can be used instead of classical CS ones for more performance improvement, because the received signal in this group of MIMO radars is a block sparse signal in a basis. In this paper, two new methods are proposed to improve the performance of the block CS-based distributed MIMO radars. The first one is a new method for optimal energy allocation to the transmitters, and the other one is a new method for optimal design of the measurement matrix. These methods are based on the minimization of an upper bound of the sensing matrix block-coherence. Simulation results show an increase in the accuracy of multiple targets parameters estimation for both proposed methods.
Nematollah Zarmehi, Farokh Marvasti
In this letter, we propose an algorithm for recovery of sparse and low rank components of matrices using an iterative method with adaptive thresholding. In each iteration, the low rank and sparse components are obtained using a thresholding operator. This algorithm is fast and can be implemented easily. We compare it with one of the most common fast methods in which the rank and sparsity are approximated by $\ell_1$ norm. We also apply it to some real applications where the noise is not so sparse. The simulation results show that it has a suitable performance with low run-time.
Sahar Sadrizadeh, Shahrzad Kiani, Mahdi Boloursaz, Farokh Marvasti
This paper studies the problem of Simultaneous Sparse Approximation (SSA). This problem arises in many applications which work with multiple signals maintaining some degree of dependency such as radar and sensor networks. In this paper, we introduce a new method towards joint recovery of several independent sparse signals with the same support. We provide an analytical discussion on the convergence of our method called Simultaneous Iterative Method with Adaptive Thresholding (SIMAT). Additionally, we compare our method with other group-sparse reconstruction techniques, i.e., Simultaneous Orthogonal Matching Pursuit (SOMP), and Block Iterative Method with Adaptive Thresholding (BIMAT) through numerical experiments. The simulation results demonstrate that SIMAT outperforms these algorithms in terms of the metrics Signal to Noise Ratio (SNR) and Success Rate (SR). Moreover, SIMAT is considerably less complicated than BIMAT, which makes it feasible for practical applications such as implementation in MIMO radar systems.
Nematollah Zarmehi, Sina Shahsavari, Farokh Marvasti
In this paper, we will provide a comparison between uniform and random sampling for speech and music signals. There are various sampling and recovery methods for audio signals. Here, we only investigate uniform and random schemes for sampling and basic low-pass filtering and iterative method with adaptive thresholding for recovery. The simulation results indicate that uniform sampling with cubic spline interpolation outperforms other sampling and recovery methods.
M. Amin Rahimian, Ali Ayremlou, Farokh Marvasti
It has been recently brought into spotlight that through the exploitation of network coding concepts at physical-layer, the interference property of the wireless media can be proven to be a blessing in disguise. Nonetheless, most of the previous studies on this subject have either held unrealistic assumptions about the network properties, thus making them basically theoretical, or have otherwise been limited to fairly simple network topologies. We, on the other hand, believe to have devised a novel scheme, called Real Amplitude Scaling (RAS), that relaxes the aforementioned restrictions, and works with a wider range of network topologies and in circumstances that are closer to practice, for instance in lack of symbol-level synchronization and in the presence of noise, channel distortion and severe interference from other sources. The simulation results confirmed the superior performance of the proposed method in low SNRs, as well as the high SNR limits, where the effect of quantization error in the digital techniques becomes comparable to the channel.
Mohammad Tofighi, Ali Ayremlou, Farokh Marvasti
A modular method was suggested before to recover a band limited signal from the sample and hold and linearly interpolated (or, in general, an nth-order-hold) version of the regular samples. In this paper a novel approach for compensating the distortion of any interpolation based on modular method has been proposed. In this method the performance of the modular method is optimized by adding only some simply calculated coefficients. This approach causes drastic improvement in terms of signal-to-noise ratios with fewer modules compared to the classical modular method. Simulation results clearly confirm the improvement of the proposed method and also its superior robustness against additive noise.
Ali Haghi, Reza K. Farsani, Mohammad Reza Aref, Farokh Marvasti
This paper investigates the capacity problem for some multiple-access scenarios with cooperative transmitters. First, a general Multiple-Access Channel (MAC) with common information, i.e., a scenario where p transmitters send private messages and also a common message to q receivers and each receiver decodes all of the messages, is considered. The capacity region of the discrete memoryless channel is characterized. Then, the general Gaussian fading MAC with common information wherein partial Channel State Information (CSI) is available at the transmitters (CSIT) and perfect CSI is available at the receivers (CSIR) is investigated. A coding theorem is proved for this model that yields an exact characterization of the throughput capacity region. Finally, a two-transmitter/one-receiver Gaussian fading MAC with conferencing encoders with partial CSIT and perfect CSIR is studied and its capacity region is determined. For the Gaussian fading models with CSIR only (transmitters have no access to CSIT), some numerical examples and simulation results are provided for Rayleigh fading.
Mohammad Javad Faraji, Pedram Pad, Farokh Marvasti
In this paper we wish to introduce a method to reconstruct large size Welch Bound Equality (WBE) codes from small size WBE codes. The advantage of these codes is that the implementation of ML decoder for the large size codes is reduced to implementation of ML decoder for the core codes. This leads to a drastic reduction of the computational cost of ML decoder. Our method can also be used for constructing large Binary WBE (BWBE) codes from smaller ones. Additionally, we explain that although WBE codes are maximizing the sum channel capacity when the inputs are real valued, they are not necessarily appropriate when the input alphabet is binary. The discussion shows that when the input alphabet is binary, the Total Squared Correlation (TSC) of codes is not a proper figure of merit.
Ashkan Esmaeili, Kayhan Behdin, Sina Al-E-Mohammad, Farokh Marvasti
In this paper, we propose a novel approach in order to recover a quantized matrix with missing information. We propose a regularized convex cost function composed of a log-likelihood term and a Trace norm term. The Bi-factorization approach and the Augmented Lagrangian Method (ALM) are applied to find the global minimizer of the cost function in order to recover the genuine data. We provide mathematical convergence analysis for our proposed algorithm. In the Numerical Experiments Section, we show the superiority of our method in accuracy and also its robustness in computational complexity compared to the state-of-the-art literature methods.
Ashkan Esmaeili, Farokh Marvasti
In this paper, we introduce a novel and robust approach to Quantized Matrix Completion (QMC). First, we propose a rank minimization problem with constraints induced by quantization bounds. Next, we form an unconstrained optimization problem by regularizing the rank function with Huber loss. Huber loss is leveraged to control the violation from quantization bounds due to two properties: 1- It is differentiable, 2- It is less sensitive to outliers than the quadratic loss. A Smooth Rank Approximation is utilized to endorse lower rank on the genuine data matrix. Thus, an unconstrained optimization problem with differentiable objective function is obtained allowing us to advantage from Gradient Descent (GD) technique. Novel and firm theoretical analysis on problem model and convergence of our algorithm to the global solution are provided. Another contribution of our work is that our method does not require projections or initial rank estimation unlike the state- of-the-art. In the Numerical Experiments Section, the noticeable outperformance of our proposed method in learning accuracy and computational complexity compared to those of the state-of- the-art literature methods is illustrated as the main contribution.
Ashkan Esmaeili, Farokh Marvasti
Sparse Inverse Covariance Estimation (SICE) is useful in many practical data analyses. Recovering the connectivity, non-connectivity graph of covariates is classified amongst the most important data mining and learning problems. In this paper, we introduce a novel SICE approach using adaptive thresholding. Our method is based on updates in a transformed domain of the desired matrix and exponentially decaying adaptive thresholding in the main domain (Inverse Covariance matrix domain). In addition to the proposed algorithm, the convergence analysis is also provided. In the Numerical Experiments Section, we show that the proposed method outperforms state-of-the-art methods in terms of accuracy.
Milad Soltany Kadarvish, Hesam Mojtahedi, Hossein Entezari Zarch, Amirhossein Kazerouni, Alireza Morsali, Azra Abtahi, Farokh Marvasti
Implicit Neural Representation (INR) has recently attracted considerable attention for storing various types of signals in continuous forms. The existing INR networks require lengthy training processes and high-performance computational resources. In this paper, we propose a novel sub-optimal ensemble architecture for INR that resolves the aforementioned problems. In this architecture, the representation task is divided into several sub-tasks done by independent sub-networks. We show that the performance of the proposed ensemble INR architecture may decrease if the dimensions of sub-networks increase. Hence, it is vital to suggest an optimization algorithm to find the sub-optimal structure of the ensemble network, which is done in this paper. According to the simulation results, the proposed architecture not only has significantly fewer floating-point operations (FLOPs) and less training time, but it also has better performance in terms of Peak Signal to Noise Ratio (PSNR) compared to those of its counterparts.
Fateme Ghayem, Farokh Marvasti
In this paper, the problem of Magnetic Resonance (MR) image reconstruction from partial Fourier samples has been considered. To this aim, we leverage the evidence that MR images are sparser than their zero-filled reconstructed ones from incomplete Fourier samples. This information can be used to define an optimization problem which searches for the sparsest possible image conforming with the available Fourier samples. We solve the resulting problem using the well-known Alternating Direction Method of Multipliers (ADMM). Unlike most existing methods that work with small over-lapping image patches, the proposed algorithm considers the whole image without dividing it into small blocks. Experimental results prominently confirm its promising performance and advantages over the existing methods.
Ali Mottaghi, Kayhan Behdin, Ashkan Esmaeili, Mohammadreza Heydari, Farokh Marvasti
In this paper, we design a system in order to perform the real-time beat tracking for an audio signal. We use Onset Strength Signal (OSS) to detect the onsets and estimate the tempos. Then, we form Cumulative Beat Strength Signal (CBSS) by taking advantage of OSS and estimated tempos. Next, we perform peak detection by extracting the periodic sequence of beats among all CBSS peaks. In simulations, we can see that our proposed algorithm, Online Beat TrAckINg (OBTAIN), outperforms state-of-art results in terms of prediction accuracy while maintaining comparable and practical computational complexity. The real-time performance is tractable visually as illustrated in the simulations.
Zahra Sadeghigol, Hadi Zayyani, Hamidreza Abin, Farokh Marvasti
In this letter, the problem of sparse signal reconstruction from one bit compressed sensing measurements is investigated. To solve the problem, a variational Bayes framework with a new statistical multivariate model is used. The dependency of the wavelet decomposition coefficients is modeled with a multivariate Gaussian copula. This model can separate marginal structure of coefficients from their intra scale dependency. In particular, the drawable Gaussian vine copula multivariate double Lomax model is suggested. The reconstructed signal is derived by variational Bayes algorithm which can calculate closed forms for posterior of all unknown parameters and sparse signal. Numerical results illustrate the effectiveness of the proposed model and algorithm compared with the competing approaches in the literature.
Ashkan Esmaeili, Arash Amini, Farokh Marvasti
In this paper, we investigate the recovery of a sparse weight vector (parameters vector) from a set of noisy linear combinations. However, only partial information about the matrix representing the linear combinations is available. Assuming a low-rank structure for the matrix, one natural solution would be to first apply a matrix completion on the data, and then to solve the resulting compressed sensing problem. In big data applications such as massive MIMO and medical data, the matrix completion step imposes a huge computational burden. Here, we propose to reduce the computational cost of the completion task by ignoring the columns corresponding to zero elements in the sparse vector. To this end, we employ a technique to initially approximate the support of the sparse vector. We further propose to unify the partial matrix completion and sparse vector recovery into an augmented four-step problem. Simulation results reveal that the augmented approach achieves the best performance, while both proposed methods outperform the natural two-step technique with substantially less computational requirements.
Mohammad Hadi, Farokh Marvasti, Mohammad Reza Pakravan
The common and traditional method for dispersion compensation in optical domain is concatenating the transmit optical fiber by a compensating optical fiber having high-negative dispersion coefficient. In this paper, we take an opposite direction and show how an optical fiber with high-positive dispersion coefficient can also be used for dispersion compensation. Our optical dispersion compensating structure is the optical implementation of an iterative algorithm in signal processing. The proposed dispersion compensating system is constructed by cascading a number of compensating sub-systems and its compensation capability is improved by increasing the number of embedded sub-systems. We also show that the compensation capability is a trade-off between transmission length and bandwidth. We use simulation results to validate the performance of the introduced dispersion compensating module. Photonic crystal fibers with high-positive dispersion coefficient can be used for constructing the proposed optical dispersion compensating module.
Mahdi Boloursaz Mashhadi, Farokh Marvasti
This letter considers the problem of sparse signal reconstruction from the timing of its Level Crossings (LC)s. We formulate the sparse Zero Crossing (ZC) reconstruction problem in terms of a single 1-bit Compressive Sensing (CS) model. We also extend the Smoothed L0 (SL0) sparse reconstruction algorithm to the 1-bit CS framework and propose the Binary SL0 (BSL0) algorithm for iterative reconstruction of the sparse signal from ZCs in cases where the number of sparse coefficients is not known to the reconstruction algorithm a priori. Similar to the ZC case, we propose a system of simultaneously constrained signed-CS problems to reconstruct a sparse signal from its Level Crossings (LC)s and modify both the Binary Iterative Hard Thresholding (BIHT) and BSL0 algorithms to solve this problem. Simulation results demonstrate superior performance of the proposed LC reconstruction techniques in comparison with the literature.