Network Power Constraint Research Articles

On Distributed Estimation in Hierarchical Power Constrained Wireless Sensor Networks

We consider distributed estimation of a random source in a hierarchical power constrained wireless sensor network. Sensors within each cluster send their measurements to a cluster head (CH). CHs optimally fuse the received signals and transmit to the fusion center (FC) over orthogonal fading channels. To enable channel estimation at the FC, CHs send pilots, prior to data transmission. We derive the mean square error (MSE) corresponding to the linear minimum mean square error (LMMSE) estimator of the source at the FC, and obtain the Bayesian Cramér-Rao bound (CRB). Our goal is to find (i) the optimal training power, (ii) the optimal power that sensors in a cluster spend to transmit their amplified measurements to their CH, and (iii) the optimal weight vector employed by each CH for its linear signal fusion, such that the MSE is minimized, subject to a network power constraint. To untangle the performance gain that optimizing each set of these variables provide, we also analyze three special cases of the original problem, where in each special case, only two sets of variables are optimized across clusters. We define three factors that allow us to quantify the effectiveness of each power allocation scheme in achieving an MSE-power tradeoff that is close to that of the Bayesian CRB. Combining the information gained from the factors and Bayesian CRB with our computational complexity analysis provides the system designer with quantitative complexity-versus-MSE improvement tradeoffs offered by different power allocation schemes.

Localisation algorithm with node selection under power constraint in software‐defined sensor networks

In this study, the authors propose an improved localisation algorithm in the software-defined sensor networks (SDSNs). This algorithm includes a node-selection strategy under the whole network power constraint, based on the software-defined networking (SDN) technique for providing the centralised control of the network. The analogous Cramer-Rao lower bound (A-CRLB) value is derived for each participating node, which represents a fundamental bound on the variance of the position estimator and is used to evaluate the contribution of each node to localisation accuracy. On the basis of A-CRLB values, the most helpful nodes for localisation are selected to maximise the sum of the nodes' contributory values to the localisation accuracy. With the global network knowledge provided by the SDN controller in the SDSN, the node-selection strategy is formulated into a 0-1 programming problem on the premise of power satisfaction of each node. Furthermore, the proposed node-selection -based localisation algorithm is applied to both noncooperative and cooperative localisation scenarios. Simulation results show that the proposed algorithms provide efficient and effective localisation schemes in SDSNs, and can improve the performance in terms of both the selection convergence speed and the localisation accuracy.

Joint Resource Allocation Scheme for OFDM Wireless-Powered Cooperative Communication Networks

Energy harvesting techniques, particularly radio frequency energy harvesting (RF-EH) techniques, which are known to provide feasible solutions to enhance the performance of energy constrained wireless communication systems, have gained increasing attention. In this paper, we consider a wireless-powered cooperative communication network (WPCCN) for transferring energy in the downlink and forwarding signals in the uplink. The objective is to maximize the average transmission rate of the system, subject to the total network power constraint. We formulate such a problem as a form of wireless energy transmission based on resource allocation that searches for the joint subcarrier pairing and the time and power allocation, and this can be solved by using a dual approach. Simulation results show that the proposed joint optimal scheme can efficiently improve system performance with an increase in the number of subcarriers and relays.

JOINT POWER ALLOCATION FOR DF CONCATENATED MIMO SUCCESSIVE RELAYING SCHEME UNDER NETWORK POWER CONSTRAINTS

Power efficiency is a vital consideration in wireless system. In this paper, we propose a framework for efficient power allocation in decode and forward multiple input multiple output successive relaying systems under network power constraints. Our aim is to maximize the information rate at each link by an optimal power allocation scheme via the primal dual algorithm. Then, we jointly allocate power to the source and transmitting relay under network power constraints. The simulated results show that the proposed joint power allocation scheme under network power constraint can outperform the uniform power allocation under an aggregate power constraints.

Optimal Minimum Variance Distortionless Precoding (MVDP) for Decentralized Estimation in MIMO Wireless Sensor Networks

In this letter, we present a framework for optimal minimum variance distortionless precoder (MVDP) design towards decentralized estimation of a vector parameter in a coherent multiple access channel based multiple-input multiple-output (MIMO) wireless sensor network. The proposed MVDP scheme yields the optimal minimum variance distortionless parameter estimate at the fusion center without the necessity of any receive processing. A closed form expression is derived for the mean square estimation error of the MVDP and it is demonstrated that it asymptotically achieves the centralized minimum mean square error bound. Further, we derive the optimal decentralized estimation schemes with a total network power constraint (MVDP-T) and per-sensor power constraint (MVDP-P). Simulation results demonstrate the performance of the proposed optimal precoding schemes and also support the analytical results derived.

Optimal joint power allocation and sub‐carrier pairing in amplify‐and‐forward SC‐FDMA relaying networks

Optimal power allocation (PA) and sub-carrier pairing (SP) strategies for a dual-hop amplify-and-forward single-carrier frequency division multiple access network are derived. Frequency domain equalisers based on minimum mean square error (MMSE) and zero forcing (ZF) criteria are considered. For each equaliser, the problem of joint PA and SP is solved to maximise the system capacity subject to the total network power constraint. The optimality of ordered SP (OSP) and reverse OSP scenarios for MMSE and ZF equalisers, respectively, is proved.

Joint resource allocation with subcarrier pairing in cooperative OFDM DF multi‐relay networks

For conventional subcarrier pairing scheme in cooperative orthogonal frequency division multiplexing decode-and-forward multi-relay networks, to avoid interference, each subcarrier pair (SP) is assigned to a single relay. Over a specific subcarrier, the destination receives signals transmitted from the relay. In this study, to better exploit the degrees of spatial freedom, the authors propose to assign each SP to multiple relays. Thus, over a specific subcarrier, the destination receives signals transmitted from multiple relays. Under the total network power constraint, to maximise the sum transmission rate, they propose a joint resource allocation scheme, in which they jointly optimised the four types of resources: assisting relays selection, transmission mode selection, subcarrier pairing and power allocation. They further propose a suboptimal algorithm which can significantly reduce the computational complexity of the aforementioned optimal allocation scheme with sacrificing little on the performance. It is shown from simulation results that the author's proposed schemes have significant performance improvement over the resource allocation schemes in the literature.

Resource allocation in multi-relay multi-user OFDM systems for heterogeneous traffic

Resource allocation is an important issue that has not been well resolved in multi-relay multi-user Decode-and-Forward (DF) OFDM systems with subcarrier-pairing at relays in the presence of heterogeneous flows, i.e., simultaneous real-time (RT) and non-real-time (NRT) traffic. In this paper, we address the issue by first formulating it as a joint optimization problem of relay-user pair selection, subcarrier-pair assignment and power allocation and then solving it through dual decomposition and subgradient methods. Asymptotic optimal iterative algorithms with polynomial complexity are proposed with the objective of maximizing sum-transmission-rate of NRT traffic while providing quality-of-service (QoS) guarantee for RT traffic, in two cases: (i) with total network power constraint and (ii) with individual power constraints. Effective selections of initial dual variables and stepsize for the subgradient method are also presented. Simulation results are provided in multiple scenarios and they show that: (i) the proposed algorithms outperform the existing schemes in terms of providing QoS requirements of RT users and maximizing sum network transmission rates; (ii) algorithms designed under total power constraint exploit the power resource much better than those under individual power constraints.

Decentralized Estimation Under Correlated Noise

In this paper, we consider distributed estimation of an unknown random scalar by using wireless sensors and a fusion center (FC). We adopt a linear model for distributed estimation of a scalar source where both observation models and sensor operations are linear, and the multiple access channel (MAC) is coherent. We consider a fusion center with multiple antennas and single antenna. In order to estimate the source, best linear unbiased estimation (BLUE) is adopted. Two cases are considered: Minimization of the mean square error (MSE) of the BLUE estimator subject to network power constraint, and minimization of the network power subject to the quality of service (QOS). For a fusion center with multiple antennas, iterative solutions are provided and it is shown that the proposed algorithms always converge. For a fusion center with single antenna, closed-form solutions are provided, and it is shown that the iterative solutions will reduce to the closed-form solutions. Furthermore, the effect of noise correlation at the sensors and fusion center is investigated. It is shown that knowledge of noise correlation at the sensors will help to improve the system performance. Moreover, if correlation exists and not factored in, the system performance might improve depending on the correlation structure. We also show, by simulations, that when noise at the fusion center is correlated, even with knowing the correlation structure, the system performance degrades. Finally, simulations are provided to verify the analysis and present the performance of the proposed schemes.

Subcarrier-pair Based Power Allocation for Cooperative OFDM AF Multi-Relay Networks

For conventional subcarrier pairing schemes in cooperative orthogonal frequency division multiplexing amplify and forward multi-relay networks, to avoid interference, each subcarrier pair (SP) is assigned to only one relay. Over a specific subcarrier, the destination receives signals transmitted from only one relay. In our subcarrier pairing scheme, we assign each SP to all the relays. Thus, over a specific subcarrier, the destination receives signals transmitted from all the relays. Since it is assumed that there exists the direct link from the source to the destination, we assume that the source also transmits signals during the second time slot for the direct transmission mode. We propose an enhanced joint subcarrier pairing and power allocation optimization scheme which maximizes the transmission rate subject to total network power constraint. The problem is simplified and solved by using dual method. It is shown from simulation results that our proposed scheme outperforms the other schemes.

Joint Power Allocation and Subcarrier Pairing for Cooperative OFDM AF Multi-Relay Networks

For conventional subcarrier pairing scheme in cooperative orthogonal frequency division multiplexing amplify-and-forward multi-relay networks, to avoid interference, each subcarrier pair (SP) is assigned to only one relay, over a specific subcarrier, the destination receives signals transmitted from only one relay. In this letter, we propose to assign each SP to all the relays. Thus, over a specific subcarrier, the destination receives signals transmitted from all the relays. We propose a joint power allocation and subcarrier pairing scheme which maximizes the transmission rate subject to total network power constraint. The problem is simplified and solved by using dual method.

Optimum number of hops in linear multihop wireless networks

In this paper, we study the capacity of a multihop relay network with decode-and-forward strategy at each of the relay nodes. We consider both transmission power and processing power consumption at each link and a total network power constraint. We characterize the optimal number of hops that achieves maximum end-to-end throughput. In one special case, we derive an analytical expression for this optimal number of hops and show that it depends inversely on the computational power at each link. Both full-duplex (FD) and half-duplex (HD) operation of the nodes are considered and we also characterize situations in which HD operation provides higher throughput than FD operation. The effect of interference cancellation at the relay nodes is considered and the improvement in throughput is quantified.

Optimal Hop Distance and Power Control for a Single Cell, Dense, Ad Hoc Wireless Network

We consider a dense, ad hoc wireless network, confined to a small region. The wireless network is operated as a single cell, i.e., only one successful transmission is supported at a time. Data packets are sent between source-destination pairs by multihop relaying. We assume that nodes self-organize into a multihop network such that all hops are of length d meters, where d is a design parameter. There is a contention-based multiaccess scheme, and it is assumed that every node always has data to send, either originated from it or a transit packet (saturation assumption). In this scenario, we seek to maximize a measure of the transport capacity of the network (measured in bit-meters per second) over power controls (in a fading environment) and over the hop distance d, subject to an average power constraint. We first motivate that for a dense collection of nodes confined to a small region, single cell operation is efficient for single user decoding transceivers. Then, operating the dense ad hoc wireless network (described above) as a single cell, we study the hop length and power control that maximizes the transport capacity for a given network power constraint. More specifically, for a fading channel and for a fixed transmission time strategy (akin to the IEEE 802.11 TXOP), we find that there exists an intrinsic aggregate bit rate (\Theta_{opt} bits per second, depending on the contention mechanism and the channel fading characteristics) carried by the network, when operating at the optimal hop length and power control. The optimal transport capacity is of the form d_{opt}(\bar{P_t}) \times \Theta_{opt} with d_{opt} scaling as \bar{P_t}^{{1\over \eta}}, where \bar{P_t} is the available time average transmit power and \eta is the path loss exponent. Under certain conditions on the fading distribution, we then provide a simple characterization of the optimal operating point. Simulation results are provided comparing the performance of the optimal strategy derived here with some simple strategies for operating the network.

Optimal resource allocation for multiple network-coded two-way relay in orthogonal frequency division multiplexing systems

This paper studies optimal resource allocation for multiple network-coded two-way relay in orthogonal frequency division multiplexing systems. All the two-way relay nodes adopt amplify-and-forward and operate with analog network coding protocol. A joint optimization problem considering power allocation, relay selection, and subcarrier pairing to maximize the sum capacity under individual power constraints at each transmitter or total network power constraint is first formulated. By applying dual method, we provide a unified optimization framework to solve this problem. With this framework, we further propose three low-complexity suboptimal algorithms. The complexity of the proposed optimal resource allocation ORA algorithm and three suboptimal algorithms are analyzed, and it is shown that the complexity of ORA is only a polynomial function of the number of subcarriers and relay nodes under both individual and total power constraints. Simulation results demonstrate that the proposed ORA scheme yields substantial performance improvement over a baseline scheme, and suboptimal algorithms can achieve a trade-off between performance and complexity. The results also indicate that with the same total network transmit power, the performance of ORA under total power constraint can outperform that under individual power constraints. Copyright © 2012 John Wiley & Sons, Ltd.

Linear coherent distributed estimation over unknown channels

We study linear distributed estimation with coherent multiple access channel model and MMSE fusion rule. The flat fading channels are assumed unknown at the fusion center and need to be estimated. We adopt a two-phase approach, which first estimates channels and then estimates the source signal, to minimize the MSE of the estimated signal. We study optimal power allocation under a total network power constraint. We consider the optimal power allocation scheme in which training power and data power for each sensor are optimized, and the equal power allocation scheme in which training power is optimized while data power for each sensor is set equal. In both schemes, the problem is formulated as a constrained optimization problem and analytical closed-form solution is obtained. Analytic results reveal that (i) with estimated channels, the MSE approaches to a finite nonzero value as the number of sensors increases; (ii) the optimal training powers are the same in both schemes; (iii) the MSE performance compared with the case when channels are known shows the penalty caused by channel estimation becomes worse as the number of sensors increases. Simulation results verify our findings.

Subcarrier-pair based resource allocation for cooperative multi-relay OFDM systems

In this paper, we study the joint allocation of three types of resources, namely, power, subcarriers and relay nodes, in multi-relay assisted dual-hop cooperative OFDM systems. All the relays adopt the amplify-and-forward protocol and assist the transmission from the source to destination simultaneously but on orthogonal subcarriers. The objective is to maximize the system transmission rate subject to individual power constraints on each node or a total network power constraint. We formulate such a problem as a subcarrier-pair based resource allocation that seeks the joint optimization of subcarrier pairing, subcarrier-pair-to-relay assignment, and power allocation. Using a dual approach, we solve this problem efficiently in an asymptotically optimal manner. Specifically, for the optimization problem with individual power constraints, the computational complexity is polynomial in the number of subcarriers and relay nodes, whereas the complexity of the problem with a total power constraint is polynomial in the number of subcarriers.We further propose two suboptimal algorithms for the former to trade off performance for complexity. Simulation studies are conducted to evaluate the average transmission rate and outage probability of the proposed algorithms. The impact of relay location is also discussed.

Duality of MIMO multiple access channel and broadcast channel with amplify-and-forward relays

In this work, we consider a two-hop multiuser amplify-and-forward relay network with multi-antenna nodes. The results are three-fold. First, for any relay amplification matrix D in the multiple-access channel (MAC), we show that duality holds when ¿D <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">¿</sup> is employed in the broadcast channel (BC), and vice versa, where re is obtained from switching the total source and relay power constraints. Second, under a total network power constraint, we show that MAC-BC duality holds when D and D <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">¿</sup> are the relaying matrices in the MAC and BC respectively. Third, for any D in the MAC and cD <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">¿</sup> in the BC where c is any positive real scalar, MAC-BC duality under total network power constraint holds only for the above two cases.

The impact of CSI and power allocation on relay channel capacity and cooperation strategies

Capacity gains from transmitter and receiver cooperation are compared in a relay network where the cooperating nodes are close together. Under quasi-static phase fading, when all nodes have equal average transmit power along with full channel state information (CSI), it is shown that transmitter cooperation outperforms receiver cooperation, whereas the opposite is true when power is optimally allocated among the cooperating nodes but only CSI at the receiver (CSIR) is available. When the nodes have equal power with CSIR only, cooperative schemes are shown to offer no capacity improvement over non-cooperation under the same network power constraint. When the system is under optimal power allocation with full CSI, the decode-and-forward transmitter cooperation rate is close to its cut-set capacity upper bound, and outperforms compress-and-forward receiver cooperation. Under fast Rayleigh fading in the high SNR regime, similar conclusions follow. Cooperative systems provide resilience to fading in channel magnitudes; however, capacity becomes more sensitive to power allocation, and the cooperating nodes need to be closer together for the decode-and-forward scheme to be capacity-achieving. Moreover, to realize capacity improvement, full CSI is necessary in transmitter cooperation, while in receiver cooperation optimal power allocation is essential.

Sensor Selection and Power Allocation for Distributed Estimation in Sensor Networks: Beyond the Star Topology

Optimal power allocation for distributed parameter estimation in a wireless sensor network with a fusion center under a total network power constraint is considered. For the simple star topology, an analysis of the effect of the measurement noise variance on the optimal power allocation policy is presented. The optimal solution evolves from sensor selection, to water- filling, to channel inversion as the measurement noise variance increases; in the last solution, the sensor with the weakest channel signal-to-noise ratio (SNR) is allocated the largest fraction of the total power. Relaying nodes are then introduced to form the more complex branch, tree, and linear topologies. The optimal power allocation strategies for these complex topologies are then considered for both amplify-and-forward and estimate-and-forward transmission protocols. Analytical solutions for these cases appear to be intractable, and thus asymptotically optimal (for increasing measurement noise variance) solutions are derived. The solutions to this asymptotic problem offer near-optimal performance even for modest measurement noise. The optimal limiting power policy for the leaf nodes in branch and tree topologies is channel inversion, whereas in linear networks, the optimal solution is a form of weighted channel inversion. The results are extended to a multipath channel model and to the estimation of a vector of random parameters.

Type-Based Decentralized Detection in Wireless Sensor Networks

Distributed detection strategies for wireless sensor networks are studied under the assumption of spatially and temporally independent and identically distributed (i.i.d.) observations at the sensor nodes. Both intelligent (with knowledge of observation statistics) and dumb (oblivious of observation statistics) sensors are considered. Two types of communication channels are studied: a parallel access channel (PAC) in which each sensor has a dedicated additive white Gaussian noise (AWGN) channel to a decision center, and a multiple-access channel (MAC) in which the decision center receives a coherent superposition of the sensor transmissions. Our results show that the MAC yields significantly superior detection performance for any network power constraint. For intelligent sensors, uncoded (finite duration) communication of local log-likelihood ratios over the MAC achieves the optimal error exponent of the centralized (noise-free channel) benchmark as the number of nodes increases, even with sublinear network power scaling. Motivated by this result, we propose a distributed detection strategy for dumb sensors-histogram fusion-in which each node appropriately quantizes its temporal data and communicates its type or histogram to the decision center. It is shown that uncoded histogram fusion over the MAC is also asymptotically optimal under sublinear network power scaling with an additional advantage: knowledge of observation statistics is needed only at the decision center. Histogram fusion achieves exponential decay in error probability with the number of nodes even under a finite total network power. In principle, a vanishing error probability at a slower subexponential rate can be attained even with vanishing total network power in the limit. These remarkable power/energy savings with the number of nodes are due to the inherent beamforming gain in the MAC