arXiv subjects

Amir Leshem

Publications and source records attributed to Amir Leshem.

85 records · Page 5Linked to original sources

arXiv2009

Closed form solution of the maximum entropy equations with application to fast radio astronomical image formation

In this paper we analyze the maximum entropy image deconvolution. We show that given the Lagrange multiplier a closed form can be obtained for the image parameters. Using this solution we are able to provide better understanding of some of the known behavior of the maximum entropy algorithm. The solution also yields a very efficient implementation of the maximum entropy deconvolution technique used in the AIPS package. It requires the computation of a single dirty image and inversion of an elementary function per pixel.

astro-ph.IM↗

arXiv2009

Game theory and the frequency selective interference channel - A tutorial

This paper provides a tutorial overview of game theoretic techniques used for communication over frequency selective interference channels. We discuss both competitive and cooperative techniques. Keywords: Game theory, competitive games, cooperative games, Nash Equilibrium, Nash bargaining solution, Generalized Nash games, Spectrum optimization, distributed coordination, interference channel, multiple access channel, iterative water-filling.

cs.IT↗

arXiv2009

MIMO decoding based on stochastic reconstruction from multiple projections

Least squares (LS) fitting is one of the most fundamental techniques in science and engineering. It is used to estimate parameters from multiple noisy observations. In many problems the parameters are known a-priori to be bounded integer valued, or they come from a finite set of values on an arbitrary finite lattice. In this case finding the closest vector becomes NP-Hard problem. In this paper we propose a novel algorithm, the Tomographic Least Squares Decoder (TLSD), that not only solves the ILS problem, better than other sub-optimal techniques, but also is capable of providing the a-posteriori probability distribution for each element in the solution vector. The algorithm is based on reconstruction of the vector from multiple two-dimensional projections. The projections are carefully chosen to provide low computational complexity. Unlike other iterative techniques, such as the belief propagation, the proposed algorithm has ensured convergence. We also provide simulated experiments comparing the algorithm to other sub-optimal algorithms.

cs.IT↗

arXiv2008

Finite Word Length Effects on Transmission Rate in Zero Forcing Linear Precoding for Multichannel DSL

Crosstalk interference is the limiting factor in transmission over copper lines. Crosstalk cancelation techniques show great potential for enabling the next leap in DSL transmission rates. An important issue when implementing crosstalk cancelation techniques in hardware is the effect of finite world length on performance. In this paper we provide an analysis of the performance of linear zero-forcing precoders, used for crosstalk compensation, in the presence of finite word length errors. We quantify analytically the trade off between precoder word length and transmission rate degradation. More specifically, we prove a simple formula for the transmission rate loss as a function of the number of bits used for precoding, the signal to noise ratio, and the standard line parameters. We demonstrate, through simulations on real lines, the accuracy of our estimates. Moreover, our results are stable in the presence of channel estimation errors. Finally, we show how to use these estimates as a design tool for DSL linear crosstalk precoders. For example, we show that for standard VDSL2 precoded systems, 14 bits representation of the precoder entries results in capacity loss below 1% for lines over 300m.

cs.IT↗

arXiv2008

Parametric high resolution techniques for radio astronomical imaging

The increased sensitivity of future radio telescopes will result in requirements for higher dynamic range within the image as well as better resolution and immunity to interference. In this paper we propose a new matrix formulation of the imaging equation in the cases of non co-planar arrays and polarimetric measurements. Then we improve our parametric imaging techniques in terms of resolution and estimation accuracy. This is done by enhancing both the MVDR parametric imaging, introducing alternative dirty images and by introducing better power estimates based on least squares, with positive semi-definite constraints. We also discuss the use of robust Capon beamforming and semi-definite programming for solving the self-calibration problem. Additionally we provide statistical analysis of the bias of the MVDR beamformer for the case of moving array, which serves as a first step in analyzing iterative approaches such as CLEAN and the techniques proposed in this paper. Finally we demonstrate a full deconvolution process based on the parametric imaging techniques and show its improved resolution and sensitivity compared to the CLEAN method.

astro-ph↗

arXiv2007

Cooperative game theory and the Gaussian interference channel

In this paper we discuss the use of cooperative game theory for analyzing interference channels. We extend our previous work, to games with N players as well as frequency selective channels and joint TDM/FDM strategies. We show that the Nash bargaining solution can be computed using convex optimization techniques. We also show that the same results are applicable to interference channels where only statistical knowledge of the channel is available. Moreover, for the special case of two players $2\times K$ frequency selective channel (with K frequency bins) we provide an $O(K \log_2 K)$ complexity algorithm for computing the Nash bargaining solution under mask constraint and using joint FDM/TDM strategies. Simulation results are also provided.

cs.IT↗

arXiv2006

An experimental uncertainty implied by failure of the physical Church-Turing thesis

In this paper we prove that given a black box assumed to generate bits of a given non-recursive real $Ω$ there is no computable decision procedure generating sequences of decisions such that if the output is indeed $Ω$ the process eventually accepts the hypothesis while if the output is different than $Ω$ than the procedure will eventually reject the hypothesis from a certain point on. Our decision concept does not require full certainty regarding the correctness of the decision at any point, thus better represents the validation process of physical theories. The theorem has strong implications on the falsifiability of physical theories entailing the failure of the physical Church Turing thesis. Finally we show that our decision process enables to decide whether the mean of an i.i.d. sequence of reals belongs to a specific $Δ_2$ set of integers. This significantly strengthens the effective version of the Cover-Koplowitz theorem, beyond computable sequences of reals.

math-ph↗

arXiv2006

Bargaining over the interference channel

In this paper we analyze the interference channel as a conflict situation. This viewpoint implies that certain points in the rate region are unreasonable to one of the players. Therefore these points cannot be considered achievable based on game theoretic considerations. We then propose to use Nash bargaining solution as a tool that provides preferred points on the boundary of the game theoretic rate region. We provide analysis for the 2x2 intereference channel using the FDM achievable rate region. We also outline how to generalize our results to other achievable rate regions for the interference channel as well as the multiple access channel. Keywords: Spectrum optimization, distributed coordination, game theory, interference channel, multiple access channel.

cs.IT↗

arXiv2006

Game theoretic aspects of distributed spectral coordination with application to DSL networks

In this paper we use game theoretic techniques to study the value of cooperation in distributed spectrum management problems. We show that the celebrated iterative water-filling algorithm is subject to the prisoner's dilemma and therefore can lead to severe degradation of the achievable rate region in an interference channel environment. We also provide thorough analysis of a simple two bands near-far situation where we are able to provide closed form tight bounds on the rate region of both fixed margin iterative water filling (FM-IWF) and dynamic frequency division multiplexing (DFDM) methods. This is the only case where such analytic expressions are known and all previous studies included only simulated results of the rate region. We then propose an alternative algorithm that alleviates some of the drawbacks of the IWF algorithm in near-far scenarios relevant to DSL access networks. We also provide experimental analysis based on measured DSL channels of both algorithms as well as the centralized optimum spectrum management.

cs.IT↗

arXiv2000

Radio astronomical imaging in the presence of strong radio interference

Radio-astronomical observations are increasingly contaminated by interference, and suppression techniques become essential. A powerful candidate for interference mitigation is adaptive spatial filtering. We study the effect of spatial filtering techniques on radio astronomical imaging. Current deconvolution procedures such as CLEAN are shown to be unsuitable to spatially filtered data, and the necessary corrections are derived. To that end, we reformulate the imaging (deconvolution/calibration) process as a sequential estimation of the locations of astronomical sources. This not only leads to an extended CLEAN algorithm, the formulation also allows to insert other array signal processing techniques for direction finding, and gives estimates of the expected image quality and the amount of interference suppression that can be achieved. Finally, a maximum likelihood procedure for the imaging is derived, and an approximate ML image formation technique is proposed to overcome the computational burden involved. Some of the effects of the new algorithms are shown in simulated images. Keywords: Radio astronomy, synthesis imaging, parametric imaging, interference mitigation, spatial filtering, maximum likelihood, minimum variance, CLEAN.

astro-ph↗

arXiv2000

On the consistency of the definable tree property on \aleph_1

In this paper we prove the equiconsistency of ``Every omega_1 tree which is first order definable over H_{omega_1} has a cofinal branch'' with the existence of a Pi^1_1 reflecting cardinal. The proof uses a definable version of Ramsey theorem on aleph_1 which is again equiconsistent with a Pi^1_1 reflecting cardinal. We also prove that the addition of $MA$ to the definable tree property increases the consistency strength to that of a weakly compact cardinal. Finally we comment on the generalization to higher cardinals.

math.LO↗

arXiv2000

0^# and elementary end extensions of V_k

In this paper we prove that if k is a cardinal in L[0^#], then there is an inner model M such that M |= (V_k,E) has no elementary end extension. In particular if 0^# exists then weak compactness is never downwards absolute. We complement the result with a lemma stating that any cardinal greater than aleph_1 of uncountable cofinality in L[0^#] is Mahlo in every strict inner model of L[0^#].

math.LO↗

arXiv2000

Multichannel interference mitigation methods in radio astronomy

Radio-astronomical observations are increasingly corrupted by RF interference, and online detection and filtering algorithms are becoming essential. To facilitate the introduction of such techniques into radio astronomy, we formulate the astronomical problem in an array signal processing language, and give an introduction to some elementary algorithms from that field. We consider two topics in detail: interference detection by rank estimation of short-term covariance matrices, and spatial filtering by subspace estimation and projection. We discuss experimental data collected at the Westerbork radio telescope, and illustrate the effectiveness of the space-time detection and blanking process on the recovery of a 3C48 absorption line in the presence of GSM mobile telephony interference.

astro-ph↗