We consider the problem of waveform design for Multiple-Input Multiple-Output (MIMO) radar in the presence of signal-dependent interference embedded in white Gaussian disturbance. We present two sequential optimizatio...
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We consider the problem of waveform design for Multiple-Input Multiple-Output (MIMO) radar in the presence of signal-dependent interference embedded in white Gaussian disturbance. We present two sequentialoptimization procedures to maximize the Signal to Interference plus Noise Ratio (SINR), accounting for a constant modulus constraint as well as a similarity constraint involving a known radar waveform with some desired properties (e. g., in terms of pulse compression and ambiguity). The presented sequential optimization algorithms, based on a relaxation method, yield solutions with good accuracy. Their computational complexity is linear in the number of iterations and trials in the randomized procedure and polynomial in the receive filter length. Finally, we evaluate the proposed techniques, by considering their SINR performance, beam pattern as well as pulse compression property, via numerical simulations.
We study the intrinsic limitations of sequential convex optimization through the lens of feedback information theory. In the oracle model of optimization, an algorithm queries an oracle for noisy information about the...
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We study the intrinsic limitations of sequential convex optimization through the lens of feedback information theory. In the oracle model of optimization, an algorithm queries an oracle for noisy information about the unknown objective function and the goal is to (approximately) minimize every function in a given class using as few queries as possible. We show that, in order for a function to be optimized, the algorithm must be able to accumulate enough information about the objective. This, in turn, puts limits on the speed of optimization under specific assumptions on the oracle and the type of feedback. Our techniques are akin to the ones used in statistical literature to obtain minimax lower bounds on the risks of estimation procedures;the notable difference is that, unlike in the case of i.i.d. data, a sequentialoptimization algorithm can gather observations in a controlled manner, so that the amount of information at each step is allowed to change in time. In particular, we show that optimizationalgorithms often obey the law of diminishing returns: the signal-to-noise ratio drops as the optimization algorithm approaches the optimum. To underscore the generality of the tools, we use our approach to derive fundamental lower bounds for a certain active learning problem. Overall, the present work connects the intuitive notions of "information" in optimization, experimental design, estimation, and active learning to the quantitative notion of Shannon information.
The paper considers the properties of feasible and optimal scheduling of jobs on one machine under constraints on the terms of the beginning and completion of jobs and on partial sequences of job performance. The esta...
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The paper considers the properties of feasible and optimal scheduling of jobs on one machine under constraints on the terms of the beginning and completion of jobs and on partial sequences of job performance. The established properties and the lower-bound estimates of the length of the optimal schedule are used to develop methods for the exact and approximate solutions of the formulated problem by sequential optimization algorithms. The proposed algorithms are illustrated by numerical examples and can be successfully applied to solve these problems in the absence of constraints.
We consider the problem of waveform design for Multiple-Input Multiple-Output (MIMO) radar in the presence of signal-dependent interference embedded in white Gaussian disturbance. We present two sequential optimizatio...
详细信息
ISBN:
(纸本)9781479920358
We consider the problem of waveform design for Multiple-Input Multiple-Output (MIMO) radar in the presence of signal-dependent interference embedded in white Gaussian disturbance. We present two sequentialoptimization procedures to maximize the Signal to Interference plus Noise Ratio (SINR), accounting for a constant modulus constraint as well as a similarity constraint involving a known radar waveform with some desired properties (e.g., in terms of pulse compression and ambiguity). The presented sequential optimization algorithms, based on a relaxation method, yield solutions with good accuracy. Their computational complexity is linear in the number of iterations and trials in the randomized procedure and polynomial in the receive filter length. Finally, we evaluate the proposed techniques, by considering their SINR performance, beam pattern as well as pulse compression property, via numerical simulations.
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