Oshri Naparstek

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

Fully Distributed Optimal Channel Assignment for Open Spectrum Access

In this paper, we address the problem of fully distributed assignment of users to sub-bands such that the sum-rate of the system is maximized. We introduce a modified auction algorithm that can be applied in a fully distributed way using an opportunistic CSMA assignment scheme and is ε optimal. We analyze the expected time complexity of the algorithm and suggest a variant to the algorithm that has lower expected complexity. We then show that, in the case of i.i.d. Rayleigh channels, a simple greedy scheme is asymptotically optimal as SNR increases or as the number of users is increased to infinity. We conclude by providing simulated results of the suggested algorithms.

Fully distributed auction algorithm for spectrum sharing in unlicensed bands

In this paper we introduce a modified auction algorithm that can be applied in a fully distributed manner. The algorithm requires an auctioneer but does not require shared memory or message passing between bidders. We show that an opportunistic carrier sensing scheme can be used to replace the auctioneer in a manner that does not require any message passing, control channel or any other explicit information sharing between users. Bounds on optimality are given as well as simulated results.

A fast matching algorithm for asymptotically optimal distributed channel assignment

The channel assignment problem is a special case of a very well studied combinatorial optimization problem known as the assignment problem. In this paper we introduce an asymptotically optimal fully distributed algorithm for the maximum cardinality matching problem. We show that with high probability, the running time of the algorithm on random bipartite graphs is less than O (N log(N)/log Np)) . We then show that the proposed algorithm can be used to produce asymptotically optimal solutions for the max sum assignment problem.

Bounds on the expected optimal channel assignment in Rayleigh channels

The channel assignment problem is highly important to OFDMA cognitive radio systems. Tight bounds on the optimal channel assignment are crucial for the performance evaluation of various channel assignment schemes. In this paper we derive the mean of the maximal sum rate channel assignment for i.i.d Rayleigh fading channels. We provide upper and lower bounds on the expected optimal assignment. We then show that the bounds are asymptotically tight in both high SNR and as the number of users increases.

Information theoretic radar waveform design for multiple targets

In this paper we describe the optimization of an information theoretic criterion for radar waveform design. The method is used to design radar waveforms suitable for simultaneously estimating and tracking parameters of multiple targets. Our approach generalizes the information theoretic water-filling approach of Bell. The paper has two main contributions. First, a new information theoretic design criterion for designing multiple waveforms under a joint power constraint when beamforming is used both at transmitter and receiver. Then we provide a highly efficient algorithm for optimizing the transmitted waveforms, by approximating the information theoretic cost function. We show that using Lagrange relaxation the optimization problem can be decoupled into a parallel set of low-dimensional search problems at each frequency, with dimension defined by the number of targets instead of the number of frequency bands used.

Adaptive Radar Waveform Design for Multiple Targets: Computational Aspects

In this paper we describe the optimization of an information theoretic criterion for radar waveform design. The method is used to design radar waveforms suitable for simultaneously estimating and tracking parameters of multiple targets. Our approach generalizes the information theoretic water-filling approach of Bell. The paper has two main contributions. First, a new information theoretic design criterion for designing multiple waveforms under a joint power constraint when beamforming is used both at transmitter and receiver. Then we provide a highly efficient algorithm for optimizing the transmitted waveforms, by approximating the information theoretic cost function. We show that using Lagrange relaxation the optimization problem can be decoupled into a parallel set of low-dimensional search problems at each frequency, with dimension defined by the number of targets instead of the number of frequency bands used.

Expected time complexity of the auction algorithm and the push relabel algorithm for maximum bipartite matching on random graphs

In this paper we analyze the expected time complexity of the auction algorithm for the matching problem on random bipartite graphs. We first prove that if for every non-maximum matching on graph G there exist an augmenting path with a length of at most 2l + 1 then the auction algorithm converges after N i¾? l iterations at most. Then, we prove that the expected time complexity of the auction algorithm for bipartite matching on random graphs with edge probability p=clogNN and c > 1 is ONlog2NlogNp w.h.p. This time complexity is equal to other augmenting path algorithms such as the HK algorithm. Furthermore, we show that the algorithm can be implemented on parallel machines with OlogN processors and shared memory with an expected time complexity of ONlogN.

Parametric Spectrum Shaping for Downstream Spectrum Management of Digital Subscriber Lines

The performance of Digital Subscriber Line (DSL) systems is tightly dependent on network deployment. The users (lines) in the binder create mutual interference, thus decreasing the rates of all users. The Optimal Spectrum Balancing (OSB) algorithm solves the spectrum management problem to increase user rates. However, the computational complexity of the OSB algorithm is extremely high. In this paper we introduce a novel low-complexity sub-optimal algorithm, dubbed PArametric Spectrum Shaping (PASS). The complexity of the suggested algorithm is independent of the number of tones. Simulation results show that the PASS algorithm matches OSB performance in many typical DSL scenarios.

Joint adaptive waveform design and direction-of-arrival tracking

The ability to adapt waveforms to the changing properties of targets is a very important feature for radars. Adaptive waveform design can improve the estimation and tracking of targets dramatically. In this paper we propose a joint scheme for adaptive multiple waveforms design and multi-target parameter estimation and tracking for extended targets. We combine our previous work on information theoretic waveform design for multiple extended targets with an iterative joint direction-of-arrival and target frequency response estimation. The results can improve wide band high range resolution (HRR) applications. The method is computationally attractive, since the waveform design stage involves convex optimization. The performance gains of the adaptive design process are demonstrated in simulations. The proposed algorithm shows benefits of 2-3 dB compared to flat spectrum waveform in terms of received SNR, and yields better resolution capability due to the adaptive waveform design.