Assume,guarantee or repair: a regular framework for non regular properties

We present Assume-Guarantee-Repair (AGR)—a novel framework which verifies that a program satisfies a set of properties and also repairs the program in case the verification fails. We consider communicating programs—these are simple C-like programs, extended with synchronous actions over communication channels. Our method, which consists of a learning-based approach to assume–guarantee reasoning, performs verification and repair simultaneously: in every iteration, AGR either makes another step towards proving that the (current) system satisfies the required properties, or alters the system in a way that brings it closer to satisfying the properties. To handle infinite-state systems we build finite abstractions, for which we check the satisfaction of complex properties that contain first-order constraints, using both syntactic and semantic-aware methods. We implemented AGR and evaluated it on various communication protocols. Our experiments present compact proofs of correctness and quick repairs.

     

On maximum-likelihood localization of coherent signals

We consider the problem of localizing multiple signal sources in the special case where all the signals are known a priori to be coherent. A maximum-likelihood estimator (MLE) is constructed for this special case, and its asymptotical performance is analyzed via the Cramer-Rao bound (CRB). It is proved that the CRB for this case is identical to the CRB for the case that no prior knowledge on coherency is exploited, thus establishing a quite surprising result that, asymptotically, the localization errors are not reduced by exploiting this prior knowledge. Also, we prove that in the coherent case the deterministic signals model and the stochastic signals model yield MLE's that are asymptotically identical. Simulation results confirming these theoretical results are included     

On blind beamforming for multiple non-Gaussian signals and theconstant-modulus algorithm

A new method for blindly separating multiple cochannel non-Gaussian signals received by a sensor array is presented. The method is based on a cumulant-based least-squares criterion that, for identically distributed negative-kurtosis signals, is proven to be identical to the “2-2” constant-modulus (CM) cost function commonly used by CM algorithms. A computationally simple algorithm is proposed to minimize the criterion. The algorithm performs well even when the number of samples is small, thus allowing its application in dynamic environments (e.g., moving emitters). For the special case of two signals only, the minimization is obtained analytically. Simulation results are included     

Direction finding of coherent signals via spatial smoothing foruniform circular arrays

We present a preprocessing technique that in conjunction with spatial smoothing circumvents the difficulty of direction-of-arrival estimation of coherent signals in the case of uniform circular arrays. Special consideration is given to problems arising in practice, such as mutual coupling and array geometry imperfections. Simulation results illustrating the performance of this scheme in conjunction with the MUSIC method are included     

Localization of multiple sources with moving arrays

We consider the problem of localizing multiple narrowband stationary signals using an arbitrary time-varying array such as an array mounted on a moving platform. We assume a Gaussian stochastic model for the received signals and employ the generalized least squares (GLS) estimator to get an asymptotically efficient estimation of the model parameters. In case the signals are a priori known to be uncorrelated, the estimator allows the exploitation of this prior knowledge to its benefit. For the important case of a translational motion of a rigid array, a computationally efficient spatial-smoothing method is presented. Simulation results confirming the theoretical results are included     

On the magic of SLIDE

Subspace-based line detection (SLIDE) is a novel approach for straight line fitting that has recently been suggested by Aghajan and Kailath. It is based on an analogy made between a straight line in an image and a planar propagating wavefront impinging on an array of sensors. Efficient sensor array processing algorithms are used to detect the parameters of the line. SLIDE is computationally cheaper than the Hough transform, but it has not been clear whether or not this is a magical free bonus. In particular, it has not been known how the breakpoints of SLIDE relate to those of the Hough transform. We compare the failure modes and limitations of the two algorithms and demonstrate that SLIDE is significantly less robust than the Hough transform.     

Direction finding with fewer receivers via time-varyingpreprocessing

We present a new technique for localizing multiple narrowband sources by a passive sensor array based on dimensionality-reducing time-varying preprocessing of the sensor outputs. The technique allows a significant reduction in the number of receivers required for the implementation with only two receivers sufficing in the extreme case. The estimation method we use is based on approximating the corresponding maximum likelihood estimator by a computationally simpler generalized least squares (GLS) estimator that is proved to be both consistent and asymptotically efficient. Simulation results confirming the theoretical results are included     

On the achievable localization accuracy of multiple sources at highSNR

The Cramer-Rao bound (CRB) for the problem of localizing multiple signal sources by an arbitrary passive sensor array is analyzed for the general case where the array is not necessarily simultaneously sampled and where the signals may a priori be known to be uncorrelated. It is shown that unlike in the case where the number of samples grows, wherein the CRB for the localization error always converges to zero, in the case where the number of snapshots is kept fixed and the signal-to-noise ratio (SNR) grows, the CRB converges to zero only if the number of sensors simultaneously sampled exceeds the signal subspace dimension