Discrete Stochastic Approximation Algorithms Research Articles

Software-Defined Device-to-Device (D2D) Communications in Virtual Wireless Networks With Imperfect Network State Information (NSI)

Software-defined networking (SDN) and network function virtualization (NFV) are a promising system architecture and control mechanism for future networks. Although some works have been done on wireless SDN and NFV, recent advancements in device-to-device (D2D) communications are largely ignored in this novel framework. In this paper, we study the integration of D2D communication in the framework of SDN and NFV. An inherent challenge in supporting software-defined D2D is the imperfectness of network state information, including channel state information (CSI) and queuing state information, in virtual wireless (QSI) networks. To address this challenge, we formulate the resource sharing problem in this framework as a discrete stochastic optimization problem and develop discrete stochastic approximation algorithms to solve this problem. Such algorithms can reduce the computational complexity compared with exhaustive search while achieving satisfactory performance. Both the static wireless channel and time-varying channels are considered. Extensive simulations show that users can benefit from both wireless network virtualization and software-defined D2D communications, and our proposed scheme can achieve considerable performance gains in both system throughput and user utility under practical network settings.

Resource Optimization-Based Interference Management for Hybrid Self-Organized Small-Cell Network

This paper jointly studies interference management (IM) and self-organization (SO) schemes in a hybrid-SO small-cell network, which is a combination of the centralized and distributed small-cell networks. From the view of downlink transmission, we formulate a resource optimization-based IM (ROIM) problem. In particular, to accommodate to the hybrid architecture, the problem is divided into two subproblems. The first is subchannel allocation, which is investigated with overall network interference alleviation under the assumption of imperfect channel-state information (CSI). The second is power assignment (PA), which aims at constraining the local interference while guaranteeing the network utility. To solve the ROIM problem, we propose a two-step SO-based IM (TSSOIM) scheme. At the first step, the operation and management (O&M) unit adopts an aggressive discrete stochastic approximation (ADSA) algorithm to find the proper channel set for users. At the second step, small cells employ the game-theory-based Kalai–Smorodinsky bargaining solution (KSBS) to assign power to the channels. Simulation results are presented to show the effectiveness of the proposed TSSOIM scheme.

Discrete Convexity and Stochastic Approximation for Cross-layer On– off Transmission Control

This paper considers the discrete convexity of a cross-layer on – off transmission control problem in wireless communications. In this system, a scheduler decides whether or not to transmit in order to optimize the long-term quality of service (QoS) incurred by the queueing effects in the data link layer and the transmission power consumption in the physical (PHY) layer simultaneously. Using a Markov decision process (MDP) formulation, we show that the optimal policy can be determined by solving a minimization problem over a set of queue thresholds if the dynamic programming (DP) is submodular. We prove that this minimization problem is discrete convex. In order to search the minimizer, we consider two discrete stochastic approximation (DSA) algorithms: 1) discrete simultaneous perturbation stochastic approximation (DSPSA) and 2) ${\bm{L}}^{\natural}$ -convex stochastic approximation ( ${\bm{L}}^{\natural}$ -convex SA). Through numerical studies, we show that the two DSA algorithms converge significantly faster than the existing continuous simultaneous perturbation stochastic approximation (CSPSA) algorithm in multiuser systems. Finally, we compare the convergence results and complexity of two DSA and CSPSA algorithms where we show that DSPSA achieves the best tradeoff between complexity and accuracy in multiuser systems.

Kronecker product‐based codebook design and optimisation for correlated 3D channels

AbstractDiscrete Fourier transform (DFT) codebook has been favoured by long term evolution because of its simplicity and effectiveness for two‐dimensional multi‐input multi‐output channels. In order to further explore vertical freedom, a Kronecker product‐based codebook (KPC), which is the Kronecker product of a horizontal DFT codebook and a vertical one, has been proposed. However, how to effectively design the codebook is still a challenge, because neither its effectiveness nor optimisation has been studied. In this paper, we demonstrate that the codewords in the KPC approximately match the distribution of the optimal beamforming vectors under spatially correlated three‐dimensional channels, showing the effectiveness of such codebook structure. Moreover, because the maximal cross‐correlation amplitude (Imax) of the original KPC is high, we investigate the structure of the codebook and then find a criterion of constructing the optimal KPC to achieve the lowest Imax, namely the Welch bound. Furthermore, considering the optimal codebook only exists under certain conditions, a modified discrete stochastic approximation algorithm is used to construct a near‐optimal codebook. Simulation results show that our algorithm greatly reduces Imax and respectively provides 1 and 0.5 dB coding gain compared to the traditional DFT codebook and the original KPC, which confirms the efficiency of the codebook design. Copyright © 2014 John Wiley & Sons, Ltd.

Adaptive opportunistic fair scheduling in power-controlled code division multiple access systems

The authors treat the multiuser scheduling problem for practical power-controlled code division multiple access (CDMA) systems under the opportunistic fair scheduling (OFS) framework. OFS is an important technique in wireless networks to achieve fair and efficient resource allocation. Power control is an effective resource management technique in CDMA systems. Given a certain user subset, the optimal power control scheme can be derived. Then the multiuser scheduling problem refers to the optimal user subset selection at each scheduling interval to maximise certain metric subject to some specific physical-layer constraints. The authors propose discrete stochastic approximation algorithms to adaptively select the user subset to maximise the instantaneous total throughput or a general utility. Both uplink and downlink scenarios are considered. They also consider the time-varying channels where the algorithm can track the time-varying optimal user subset. Simulation results to show the performance of the proposed algorithms in terms of the throughput/ utility maximisation, the fairness, the fast convergence and the tracking capability in time-varying environments are presented.

Joint Power Control and Receiver Optimization of CDMA Transceivers Using Successive Interference Cancellation

In a broadband uplink code-division multiple-access transmission, the interference among users, depending on the correlation of specific channels and codes, may be significant. Hence, when successive interference cancellation (SIC) is performed at the base station, the minimization of power consumption at the mobile terminals is achieved if a joint optimization of power control and ordering (JOPCO) of user detection is carried out. In this paper, we first investigate a closed-form solution to JOPCO, based on the assumption of perfect interference cancellation and complete knowledge of channel correlation among users. By describing the JOPCO problem as an optimization on a suitable graph, it is seen that the optimum solution is NP-hard, and we approximate it by a greedy algorithm. For a practical implementation, we then model JOPCO as a discrete stochastic optimization problem, and we derive a discrete stochastic approximation (DSA) algorithm that iteratively adapts the transmit powers and the SIC detection order. The DSA solution removes the hypothesis on perfect cancellation and explicit knowledge of the users' correlation. Moreover, by a suitable description of the problem, we obtain a simplified DSA algorithm having reduced requirements in both computational complexity and memory. Performance of the various algorithms is assessed by simulations in a universal mobile telecommunications system scenario

Discrete stochastic approximation algorithms for design of optimal sensor fusion rules

The basic idea of distributed detection is to have a number of independent sensors, each to make a local decision (typically a binary one) and then to combine their decisions at a fusion centre to make a global decision. Fault-tolerance has been considered as one of the main characteristics of wireless sensor networks. A fusion rule in the form of an error correction code has been recently proposed for better fault-tolerance in distributed sensor networks. In this paper, we propose to employ the powerful discrete stochastic approximation techniques to optimise the code matrix, that is, the fusion rule, with the objective of minimising the probability of decision error. We consider both the standard stochastic approximation algorithm and two newly proposed ones for this application. Extensive simulation results are provided to demonstrate the effectiveness of the proposed design paradigm in obtaining optimal fusion rules in distributed wireless sensor networks.

Adaptive MIMO antenna selection via discrete stochastic optimization

Recently it has been shown that it is possible to improve the performance of multiple-input multiple-output (MIMO) systems by employing a larger number of antennas than actually used and selecting the optimal subset based on the channel state information. Existing antenna selection algorithms assume perfect channel knowledge and optimize criteria such as Shannon capacity or various bounds on error rate. This paper examines MIMO antenna selection algorithms where the set of possible solutions is large and only a noisy estimate of the channel is available. In the same spirit as traditional adaptive filtering algorithms, we propose simulation based discrete stochastic optimization algorithms to adaptively select a better antenna subset using criteria such as maximum mutual information, bounds on error rate, etc. These discrete stochastic approximation algorithms are ideally suited to minimize the error rate since computing a closed form expression for the error rate is intractable. We also consider scenarios of time-varying channels for which the antenna selection algorithms can track the time-varying optimal antenna configuration. We present several numerical examples to show the fast convergence of these algorithms under various performance criteria, and also demonstrate their tracking capabilities.

Adaptive Opportunistic Fair Scheduling Over Multiuser Spatial Channels

We consider the problem of opportunistic fair scheduling (OFS) of multiple users in downlink time-division multiple-access (TDMA) systems employing multiple transmit antennas and beamforming. OFS is an important technique in wireless networks to achieve fair bandwidth usage among users, which is performed on a per-frame basis at the media access control layer. Multiple-transmit-antenna beamforming provides TDMA systems with the capability of supporting multiple concurrent transmissions, i.e., multiple spatial channels at the physical layer. Given a particular subset of users and their channel conditions, the optimal beamforming scheme can be calculated. The multiuser opportunistic scheduling problem then refers to the selection of the optimal subset of users for transmission at each time instant to maximize the total throughput of the system subject to a certain fairness constraint on each individual user's throughput. We propose discrete stochastic approximation algorithms to adaptively select a better subset of users. We also consider scenarios of time-varying channels for which the scheduling algorithm can track the time-varying optimal user subset. We present simulation results to demonstrate the performance of the proposed scheduling algorithms in terms of both throughput and fairness, their fast convergence, and the excellent tracking capability in time-varying environments.

Adaptive OFDM synchronization algorithms based on discrete stochastic approximation

This paper presents discrete stochastic approximation algorithms (DSA) for time synchronization in orthogonal frequency division multiplexing (OFDM) systems. It is shown that the discrete stochastic approximation algorithms can be effectively used to achieve a significant reduction in computational complexity compared to brute force maximum-likelihood (ML) methods for OFDM synchronization. The most important property of the proposed algorithms is their recursive self-learning capability-most of the computational effort is spent at the global or a local optimizer of the objective function. The convergence of the algorithms is analyzed. An adaptive version of the discrete stochastic approximation algorithm is also presented for tracking time-varying time delays and frequency offsets in time-selective fading channels. Detailed numerical examples illustrate the performance gains of these DSA-based synchronization algorithms.

Spreading Code Optimization and Adaptation in CDMA Via Discrete Stochastic Approximation

The aim of this paper is to develop discrete stochastic approximation algorithms that adaptively optimize the spreading codes of users in a code-division multiple-access (CDMA) system employing linear minimum mean-square error (MMSE) receivers. The proposed algorithms are able to adapt to slowly time-varying channel conditions. One of the most important properties of the algorithms is their self-learning capability-they spend most of the computational effort at the global optimizer of the objective function. Tracking analysis of the adaptive algorithms is presented together with mean-square convergence. An adaptive-step-size algorithm is also presented for optimally adjusting the step size based on the observations. Numerical examples, illustrating the performance of the algorithms in multipath fading channels, show substantial improvement over heuristic algorithms.