Multiple-input multiple-output (MIMO) relay systems have received great attention for the development of future wireless networks, since they can be invoked for improving system capacity and extending the coverage are...
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Multiple-input multiple-output (MIMO) relay systems have received great attention for the development of future wireless networks, since they can be invoked for improving system capacity and extending the coverage area. Considering the fixed base station (BS) and relay station (RS) and the highly mobile users (UEs), the dual-hop MIMO relay channel possesses the two-timescale characteristics, i.e., the UEs-RS channel varies in a short-timescale manner whereas the RS-BS channel varies in a long-timescale manner. In order to acquire the knowledge of all individual channels at the BS directly, we propose two-timescale channel estimation algorithms with one-stage training (OST) scheme based on the above time-varying channel characteristics. Specifically, the two-timescale channel estimation problem is firstly formulated as an approximate maximum likelihood (AML) problem. Then, we design batch algorithm to solve the resultant optimization problem. Moreover, to overcome the drawbacks of batch algorithm, a low-complexity online algorithm is also proposed based on the two-stage stochastic optimization framework. Finally, simulation results are provided to verify the effectiveness of the proposed two-timescale channel estimation algorithms.
We propose two modified versions of the classical gradient ascent method to compute the capacity of finite-state channels with Markovian inputs. For the case that the channel mutual information rate is strongly concav...
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We propose two modified versions of the classical gradient ascent method to compute the capacity of finite-state channels with Markovian inputs. For the case that the channel mutual information rate is strongly concave in a parameter taking values in a compact convex subset of some Euclidean space, our first algorithm proves to achieve polynomial accuracy in polynomial time and, moreover, for some special families of finite-state channels our algorithm can achieve exponential accuracy in polynomial time under some technical conditions. For the case that the channel mutual information rate may not be strongly concave, our second algorithm proves to be at least locally convergent.
Geometric branch-and-bound solution methods, in particular the big square small square technique and its many generalizations, are popular solution approaches for non-convex global optimization problems. Most of these...
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Geometric branch-and-bound solution methods, in particular the big square small square technique and its many generalizations, are popular solution approaches for non-convex global optimization problems. Most of these approaches differ in the lower bounds they use which have been compared empirically in a few studies. The aim of this paper is to introduce a general convergence theory which allows theoretical results about the different bounds used. To this end we introduce the concept of a bounding operation and propose a new definition of the rate of convergence for geometric branch-and-bound methods. We discuss the rate of convergence for some well-known bounding operations as well as for a new general bounding operation with an arbitrary rate of convergence. This comparison is done from a theoretical point of view. The results we present are justified by some numerical experiments using the Weber problem on the plane with some negative weights.
The design of Finite Impulse Response (FIR) filters in one or several dimensions can be performed with good computational efficiency using a Weighted Least Square (WLS) design. Minimax design, which is often preferred...
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The design of Finite Impulse Response (FIR) filters in one or several dimensions can be performed with good computational efficiency using a Weighted Least Square (WLS) design. Minimax design, which is often preferred, is computationally burdensome, principally in two dimensions. This paper draws attention to the design of minimax filters using iterative WLS techniques for one-dimensional filters and extends the approach to two-dimensional filters. For two dimensions the techniques apply to both rectangular and hexagonal sampling grids. Examples demonstrate flexibility and good computational efficiency. The paper also illustrates a promising new approach to filter design which couples the very general WLS methodology to the less manageable but often preferred minimax performance criterion.
A method of yield derivative estimation for nondifferentiable or truncated probability-density functions (PDFs) is proposed and applied to yield optimization. The method applies convolution techniques and is based on ...
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A method of yield derivative estimation for nondifferentiable or truncated probability-density functions (PDFs) is proposed and applied to yield optimization. The method applies convolution techniques and is based on the recently introduced perturbation approach. It constructs some approximation to the original PDF and requires a small number of samples per yield-optimization-algorithm step. The method is efficient and provides fast convergence in the solution, especially for problems of high dimensionality. Several yield-gradient estimation formulas are given. Some theoretical and practical aspects of the proposed method are discussed. Practical applications are demonstrated on several analog filters, and the method is compared with some other existing methods.< >
This article develops a novel passive stochastic gradient algorithm. In passive stochastic approximation, the stochastic gradient algorithm does not have control over the location where noisy gradients of the cost fun...
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This article develops a novel passive stochastic gradient algorithm. In passive stochastic approximation, the stochastic gradient algorithm does not have control over the location where noisy gradients of the cost function are evaluated. Classical passive stochastic gradient algorithms use a kernel that approximates a Dirac delta to weigh the gradients based on how far they are evaluated from the desired point. In this article, we construct a multikernel passive stochastic gradient algorithm. The algorithm performs substantially better in high dimensional problems and incorporates variance reduction. We analyze the weak convergence of the multikernel algorithm and its rate of convergence. In numerical examples, we study the multikernel version of the passive least mean squares algorithm for transfer learning to compare the performance with the classical passive version.
In the barrier resilience problem (introduced by Kumar et al., Wireless Networks 2007), we are given a collection of regions of the plane, acting as obstacles, and we would like to remove the minimum number of regions...
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In the barrier resilience problem (introduced by Kumar et al., Wireless Networks 2007), we are given a collection of regions of the plane, acting as obstacles, and we would like to remove the minimum number of regions so that two fixed points can be connected without crossing any region. In this paper, we show that the problem is NP-hard when the collection only contains fat regions with bounded ply Delta (even when they are axis aligned rectangles of aspect ratio 1 : (1 + epsilon)). We also show that the problem is fixed parameter tractable (FPT) for unit disks and for similarly-sized beta-fat regions with bounded ply Delta and 0(1) pairwise boundary intersections. We then use our FPT algorithm to construct an (1 + epsilon)-approximation algorithm that runs in O(2f((Delta,epsilon,beta))n(5)) time, where f is an element of O (Delta(4)beta(8)/epsilon(4) log(beta Delta/epsilon)). (C) 2018 Elsevier B.V. All rights reserved.
Although millimeter wave (mmWave) communications can well support high-data-rate transmissions, the inherent shortcomings, e.g., high path loss and sensitivity to blockage, may cause severe outage problems if the netw...
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Although millimeter wave (mmWave) communications can well support high-data-rate transmissions, the inherent shortcomings, e.g., high path loss and sensitivity to blockage, may cause severe outage problems if the network is not configured properly. This paper aims to minimize the long-term outage probability of an mmWave communication network by optimizing the base station (BS) deployment and user association. For the BS deployment problem, existing works usually assumed that the positions of users are fixed and formulated it as a deterministic optimization problem. With the time-varying nature of positions of user equipments (UEs) taken into account, we establish a stochastic optimization framework for BS deployment optimization. The objective is to maximize the average number of physically accessible BSs of each UE under an inaccessible probability constraint, and a cooperative stochastic approximation (CSA)-based algorithm is developed to effectively search the optimal positions of BSs. For user association, our focus is to properly associate UEs with BSs to minimize the outage probability with balanced workloads among BSs. Combined with the proposed user association scheme, the proposed BS deployment scheme can significantly improve the network outage probability in the long term, especially when the aggregation degree of UEs is large.
We present a new hardness of approximation result for the Shortest Vector Problem in l(P) norm (denoted by SVPp). Assuming NP not subset of ZPP, we show that for every epsilon > 0, there is a constant p(epsilon) su...
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We present a new hardness of approximation result for the Shortest Vector Problem in l(P) norm (denoted by SVPp). Assuming NP not subset of ZPP, we show that for every epsilon > 0, there is a constant p(epsilon) such that for all integers p >= p(epsilon), the problem SVPp has no polynomial time approximation algorithm with approximation ratio p(1-epsilon). (c) 2005 Elsevier Inc. All rights reserved.
This article develops a new deep learning framework for general nonlinear filtering. Our main contribution is to present a computationally feasible procedure. The proposed algorithms have the capability of dealing wit...
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This article develops a new deep learning framework for general nonlinear filtering. Our main contribution is to present a computationally feasible procedure. The proposed algorithms have the capability of dealing with challenging (infinitely dimensional) filtering problems involving diffusions with randomly-varying switching. First, we convert it to a problem in a finite-dimensional setting by approximating the optimal weights of a neural network. Then, we construct a stochastic gradient-type procedure to approximate the neural network weight parameters, and develop another recursion for adaptively approximating the optimal learning rate. The convergence of the combined approximation algorithms is obtained using stochastic averaging and martingale methods under suitable conditions. Robustness analysis of the approximation to the network parameters with the adaptive learning rate is also dealt with. We demonstrate the efficiency of the algorithm using highly nonlinear dynamic system examples.
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