arXiv subjects

Farzan Haddadi

Publications and source records attributed to Farzan Haddadi.

31 records · Page 2Linked to original sources

arXiv2018

Strong Interference Alignment

Interference alignment (IA) adjusts signaling scheme such that all interfering signals are squeezed in interference subspace. IA mostly achieves its performance via infinite extension of the channel, which is a major challenge for IA in practical systems. In this paper, we make part of interference very strong and achieve perfect IA within limited number of channel extensions. A single-hop $3$ user single antenna interference channel (IFC) is considered and it is shown that only one of the interfering signal streams needs to be strong so that perfect IA is feasible.

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arXiv2018

Robustness of Two-Dimensional Line Spectral Estimation Against Spiky Noise

The aim of two-dimensional line spectral estimation is to super-resolve the spectral point sources of the signal from time samples. In many associated applications such as radar and sonar, due to cut-off and saturation regions in electronic devices, some of the numbers of samples are corrupted by spiky noise. To overcome this problem, we present a new convex program to simultaneously estimate spectral point sources and spiky noise in two dimensions. To prove uniqueness of the solution, it is sufficient to show that a dual certificate exists. Construction of the dual certificate imposes a mild condition on the separation of the spectral point sources. Also, the number of spikes and detectable sparse sources are shown to be a logarithmic function of the number of time samples. Simulation results confirm the conclusions of our general theory.

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arXiv2018

Sample Complexity of Total Variation Minimization

This work considers the use of Total variation (TV) minimization in the recovery of a given gradient sparse vector from Gaussian linear measurements. It has been shown in recent studies that there exist a sharp phase transition behavior in TV minimization in asymptotic regimes. The phase transition curve specifies the boundary of success and failure of TV minimization for large number of measurements. It is a challenging task to obtain a theoretical bound that reflects this curve. In this work, we present a novel upper-bound that suitably approximates this curve and is asymptotically sharp. Numerical results show that our bound is closer to the empirical TV phase transition curve than the previously known bound obtained by Kabanava.

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arXiv2017

Two-Dimensional Super-Resolution via Convex Relaxation

In this paper, we address the problem of recovering point sources from two dimensional low-pass measurements, which is known as super-resolution problem. This is the fundamental concern of many applications such as electronic imaging, optics, microscopy, and line spectral estimation. We assume that the point sources are located in the square $[0,1]^2$ with unknown locations and complex amplitudes. The only available information is low-pass Fourier measurements band-limited to integer square $[-f_c,f_c]^2$. The signal is estimated by minimizing Total Variation $(\mathrm{TV})$ norm, which leads to a convex optimization problem. It is shown that if the sources are separated by at least $1.68/f_c$, there exist a dual certificate that is sufficient for exact recovery.

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arXiv2017

Off-the-grid Two-Dimensional Line Spectral Estimation With Prior Information

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 this improvement depends on prior information we have about the locations of the true frequencies.

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arXiv2017

How to exploit prior information in low-complexity models

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 model. This class of low-dimensional signal model includes many popular examples such as $\ell_1$ analysis (entry-wise sparsity in an arbitrary redundant dictionary), $\ell_{1,2}$ norm (block sparsity) and total variation semi-norm (for piece-wise constant signals). We show through precise analysis and simulations that the weighted convex optimization problem significantly improves the regular convex optimization problem as we choose the unique optimal weights.

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arXiv2016

Double-detector for Sparse Signal Detection from One Bit Compressed Sensing Measurements

This letter presents the sparse vector signal detection from one bit compressed sensing measurements, in contrast to the previous works which deal with scalar signal detection. In this letter, available results are extended to the vector case and the GLRT detector and the optimal quantizer design are obtained. Also, a double-detector scheme is introduced in which a sensor level threshold detector is integrated into network level GLRT to improve the performance. The detection criteria of oracle and clairvoyant detectors are also derived. Simulation results show that with careful design of the threshold detector, the overall detection performance of double-detector scheme would be better than the sign-GLRT proposed in [1] and close to oracle and clairvoyant detectors. Also, the proposed detector is applied to spectrum sensing and the results are near the well known energy detector which uses the real valued data while the proposed detector only uses the sign of the data.

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arXiv2016

Channel Aided Interference Alignment

Interference alignment (IA) techniques mostly attain their degrees of freedom (DoF) benefits as the number of channel extensions tends to infinity. Intuitively, the more interfering signals that need to be aligned, the larger the number of dimensions needed to align them. This requirement poses a major challenge for IA in practical systems. This work evaluates the necessary and sufficient conditions on channel structure of a fully connected interference network with time-varying fading to make perfect IA feasible within limited number of channel extensions. We propose a method based on the obtained conditions on the channel structure to achieve perfect IA. For the case of $3$ user interference channel, it is shown that only one condition on channel coefficients is required to make perfect IA feasible at all receivers. IA feasibility literature have mainly focused on network topology so far. In contrast, derived channel aiding conditions in this work can be considered as the perfect IA feasibility conditions on channel structure.

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arXiv2016

Perfect Interference Alignment for an Interference Network with General Message Demands

Dimensionality requirement poses a major challenge for Interference alignment (IA) in practical systems. This work evaluates the necessary and sufficient conditions on channel structure of a fully connected general interference network to make perfect IA feasible within limited number of channel extensions. So far, IA feasibility literature have mainly focused on network topology, in contrast, this work makes use of the channel structure to achieve total number of degrees of freedom (DoF) of the considered network by extending the channel aided IA scheme to the case of interference channel with general message demands. We consider a single-hop interference network with $K$ transmitters and $N$ receivers each equipped with a single antenna. Each transmitter emits an independent message and each receiver requests an arbitrary subset of the messages. Obtained channel aiding conditions can be considered as the optimal DoF feasibility conditions on channel structure. As a byproduct, assuming optimal DoF assignment, it is proved that in a general interference network, there is no user with a unique maximum number of DoF.

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arXiv2016

On feasibility of perfect interference alignment in interference networks

Interference alignment(IA) is mostly achieved by coding interference over multiple dimensions. Intuitively, the more interfering signals that need to be aligned, the larger the number of dimensions needed to align them. This dimensionality requirement poses a major challenge for IA in practical systems. This work evaluates the necessary and sufficient conditions on channel structure of a 3 user interference channel(IC) to make perfect IA feasible within limited number of channel extensions. It is shown that if only one of interfering channel coefficients can be designed to a specific value, interference would be aligned perfectly at all receivers.

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arXiv2009

Direction-of-Arrival Estimation for Temporally Correlated Narrowband Signals

signal direction-of-arrival estimation using an array of sensors has been the subject of intensive research and development during the last two decades. Efforts have been directed to both, better solutions for the general data model and to develop more realistic models. So far, many authors have assumed the data to be iid samples of a multivariate statistical model. Although this assumption reduces the complexity of the model, it may not be true in certain situations where signals show temporal correlation. Some results are available on the temporally correlated signal model in the literature. The temporally correlated stochastic Cramer-Rao bound (CRB) has been calculated and an instrumental variable-based method called IV-SSF is introduced. Also, it has been shown that temporally correlated CRB is lower bounded by the deterministic CRB. In this paper, we show that temporally correlated CRB is also upper bounded by the stochastic iid CRB. We investigate the effect of temporal correlation of the signals on the best achievable performance. We also show that the IV-SSF method is not efficient and based on an analysis of the CRB, propose a variation in the method which boosts its performance. Simulation results show the improved performance of the proposed method in terms of lower bias and error variance.

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arXiv2009

Statistical Performance Analysis of MDL Source Enumeration in Array Processing

In this correspondence, we focus on the performance analysis of the widely-used minimum description length (MDL) source enumeration technique in array processing. Unfortunately, available theoretical analysis exhibit deviation from the simulation results. We present an accurate and insightful performance analysis for the probability of missed detection. We also show that the statistical performance of the MDL is approximately the same under both deterministic and stochastic signal models. Simulation results show the superiority of the proposed analysis over available results.

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arXiv2009

On The Positive Definiteness of Polarity Coincidence Correlation Coefficient Matrix

Polarity coincidence correlator (PCC), when used to estimate the covariance matrix on an element-by-element basis, may not yield a positive semi-definite (PSD) estimate. Devlin et al. [1], claimed that element-wise PCC is not guaranteed to be PSD in dimensions p>3 for real signals. However, no justification or proof was available on this issue. In this letter, it is proved that for real signals with p<=3 and for complex signals with p<=2, a PSD estimate is guaranteed. Counterexamples are presented for higher dimensions which yield invalid covariance estimates.

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