Amir Leshem

Information Theoretic Adaptive Radar Waveform Design for Multiple Extended Targets

In this paper, we use an information theoretic approach to design radar waveforms suitable for simultaneously estimating and tracking parameters of multiple extended targets. Our approach generalizes the information theoretic water-filling approach of Bell to allow optimization for multiple targets simultaneously. Our paper has three main contributions. First, we present a new information theoretic design criterion for a single transmit waveform using a weighted linear sum of the mutual informations between target radar signatures and the corresponding received beams (given the transmitted waveforms). We provide a family of design criteria that weight the various targets according to priorities. Then, we generalize the information theoretic design criterion for designing multiple waveforms under a joint power constraint when beamforming is used both at the transmitter and the receiver. Finally, we provide a highly efficient algorithm for optimizing the transmitted waveforms in the cases of single waveform and multiple waveforms. We also provide simulated experiments of both algorithms based on real targets and comment on the generalization of the proposed technique for other design criteria, e.g., the linearly weighted noncausal MMSE design criterion

Robust Adaptive Beamforming Based on Interference Covariance Matrix Reconstruction and Steering Vector Estimation

Adaptive beamformers are sensitive to model mismatch, especially when the desired signal is present in training snapshots or when the training is done using data samples. In contrast to previous works, this correspondence attempts to reconstruct the interference-plus-noise covariance matrix instead of searching for the optimal diagonal loading factor for the sample covariance matrix. The estimator is based on the Capon spectral estimator integrated over a region separated from the desired signal direction. This is shown to be more robust than using the sample covariance matrix. Subsequently, the mismatch in the steering vector of the desired signal is estimated by maximizing the beamformer output power under a constraint that prevents the corrected steering vector from getting close to the interference steering vectors. The proposed adaptive beamforming algorithm does not impose a norm constraint. Therefore, it can be used even in applications where gain perturbations affect the steering vector. Simulation results demonstrate that the performance of the proposed adaptive beamformer is almost always close to the optimal value across a wide range of signal to noise and signal to interference ratios.

Joint estimation of time delays and directions of arrival of multiple reflections of a known signal

We present an efficient algorithm for estimating the time delays and the directions-of-arrival (DOAs) of multiple reflections of a known signal. The algorithm is based on an iterative scheme that transforms the multidimensional maximum likelihood criterion into two sets of simple one-dimensional (1-D) maximization problems. Simulation results illustrating the performance of the algorithm in comparison with the Cramer-Rao bound are included.

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 player 2 times K frequency selective channel (with K frequency bins) we provide an O(K log2 K) complexity algorithm for computing the Nash bargaining solution under mask constraint and using joint FDM/TDM strategies. Simulation results are also provided.

MULTICHANNEL INTERFERENCE MITIGATION TECHNIQUES IN RADIO ASTRONOMY

Radio-astronomical observations are increasingly corrupted by radio frequency interference, and on-line 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 Synthesis Radio Telescope and illustrate the effectiveness of the spacetime detection and blanking process on the recovery of a 3C 48 absorption line in the presence of GSM mobile telephony interference.

Multichannel Opportunistic Carrier Sensing for Stable Channel Access Control in Cognitive Radio Systems

In this paper we propose to use the well known game theoretic Gale-Shapley stable marriage theorem from game theory as a basis for spectrum allocation in cognitive radio networks. We analyze the performance of the proposed solution and provide tight lower and upper bounds on both the stable allocation and the optimal allocation performance. Then we present a novel opportunistic multichannel medium access control technique that achieves stable allocation within a single CSMA contention window. We discuss practical implementation issues and put forward two other varieties of the algorithm which have lower implementation complexity. Finally, we provide simulated examples.

Game theory and the frequency selective interference channel

As discussed in this paper, the frequency selective interference channel is important, both from a practical as from an information theoretic point of view. We show that it has many intriguing aspects from a game theoretic point of view as well, and that various levels of interference admit different types of game theoretic techniques.

Array calibration in the presence of multipath

We present an algorithm for the calibration of sensor arrays in the presence of multipath. The algorithm is based on two sets of calibration data obtained from two angularly separated transmitting points. We show the similarity between the calibration problem and blind identification of SIMO systems and analyze the identifiability of the problem. Simulation results demonstrating the performance of the algorithm are included.

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 2times2 interference 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

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 for 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, but also the formulation allows the insertion of 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 (ML) 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.