On Distributed Detection in EH-WSNs With Finite-State Markov Channel and Limited Feedback Ghazaleh Ardeshiri Azadeh V osoughi Senior Member IEEE University of Central Florida

2025-05-02 0 0 2.33MB 15 页 10玖币

侵权投诉

On Distributed Detection in EH-WSNs With

Finite-State Markov Channel and Limited Feedback

Ghazaleh Ardeshiri, Azadeh Vosoughi Senior Member, IEEE University of Central Florida

Email:gh.ardeshiri@knights.ucf.edu, azadeh@ucf.edu

Abstract—We consider a network, tasked with solving binary

distributed detection, consisting of Nsensors, a fusion center

(FC), and a feedback channel from the FC to sensors. Each sensor

is capable of harvesting energy and is equipped with a ﬁnite

size battery to store randomly arrived energy. Sensors process

their observations and transmit their symbols to the FC over

orthogonal fading channels. The FC fuses the received symbols

and makes a global binary decision. We aim at developing

adaptive channel-dependent transmit power control policies such

that J-divergence based detection metric is maximized at the FC,

subject to total transmit power constraint. Modeling the quan-

tized fading channel, the energy arrival, and the battery dynamics

as time-homogeneous ﬁnite-state Markov chains, and the network

lifetime as a geometric random variable, we formulate our power

control optimization problem as a discounted inﬁnite-horizon

constrained Markov decision process (MDP) problem, where

sensors’ transmit powers are functions of the battery states,

quantized channel gains, and the arrived energies. We utilize

stochastic dynamic programming and Lagrangian approach to

ﬁnd the optimal and sub-optimal power control policies. We

demonstrate that our sub-optimal policy provides a close-to-

optimal performance with a reduced computational complexity

and without imposing signaling overhead on sensors.

Index Terms—adaptive channel-dependent power control,

channel gain quantization, distributed detection, energy harvest-

ing, J-divergence, ﬁnite size battery, geometrically distributed

network lifetime, limited feedback, Markov decision process,

optimal and sub-optimal policies, time-homogeneous ﬁnite-state

Markov chain.

I. INTRODUCTION

Event detection for smarter cities, healthcare systems, farm-

ing, and greenhouse environmental monitoring systems is one

of the vital tasks in wireless sensor networks (WSNs) [1],

[2] and the Internet of things (IoT)-based WSNs [3], [4].

The classical studies of binary distributed detection in [5]–

[7] cannot be directly applied to these networks, since the

classical works are based on the assumption that the rate-

constrained communication channels between distributed sen-

sors and fusion center (FC) are error-free. This has motivated

researchers to study channel-dependent local decision rules

for sensors and decision fusion rules for the FC, such that

the effect of wireless communication channels in WSNs is

integrated into the system designs [8]–[11]. Even for channel-

dependent distributed detection system designs, providing a

guaranteed detection performance by a conventional WSN, in

which sensors are powered by conventional non-rechargeable

batteries and become inactive when the stored energy in their

batteries is exhausted, is impossible. Although adaptive signal

transmission strategies, including optimal channel-dependent

power control [12]–[14] and censoring [15], [16], can enhance

the energy efﬁciency and increase the lifetime of a conven-

tional WSN, they cannot change the fact that the network

lifetime is inherently limited. This limited lifetime disrupts

the event detection task and drastically degrades the detection

performance.

Energy harvesting (EH) from the environment is a promis-

ing solution to address the energy constraint problem in

conventional WSNs, and to render these networks to self

sustainable networks with perpetual lifetimes. The new class of

EH-powered WSNs, where nodes have EH capability and are

equipped with rechargeable batteries, will be also important for

the development of IoT-based WSNs. In EH-powered WSNs

power/energy management is necessary, in order to balance

the rates of energy harvesting and energy consumption for

transmission. If the energy management policy is overly ag-

gressive, sensors may stop functioning, due to energy outage.

On the other hand, if the policy is overly conservative, sensors

may fail to utilize the excess energy, due to energy overﬂow,

leading into a performance degradation. EH has been also

considered in the contexts of data communications [17], [18],

cognitive radio systems [19], distributed estimation [20], and

distributed detection [21]–[27]. The body of research on EH-

enabled communication systems can be grouped into two main

categories, depending on the adopted energy arrival model

[18], [28]: in deterministic models the transmitter has full

(causal and non-causal) knowledge of energy arrival instants

and amounts at the beginning of transmission, in stochastic

models, suitable for modeling ambient RF and renewable

energy sources that are intrinsically time-variant and sporadic,

the transmitter only has causal knowledge of energy arrival. In

addition, wireless communication channels change randomly

in time due to fading. These together prompt the need for

developing new power control/energy scheduling strategies for

an EH-enabled transmitter that can best exploit and adapt to

the random energy arrivals and time-varying fading channels.

Designing power control/energy scheduling schemes corre-

sponding to random energy arrivals and time-varying fading

channels can be viewed as a multistage stochastic optimization

problem, where the goal is to ﬁnd a sequence of decisions

a decision maker has to make, such that a speciﬁc metric

over a horizon spanning several time slots is optimized (e.g.,

optimizing transmission completion time, data throughput,

outage probability, or symbol error rate in a point-to-point EH-

powered wireless communication system [18]). A common

approach to solve this sequential decision making problem

is to adopt the mathematical framework of Markov decision

arXiv:2210.04953v1 [eess.SP] 10 Oct 2022

processes (MDP). The main ingredients of the MDP are states,

actions, rewards, and state transition probabilities. The state

could be a composite states of fading channel, energy arrival,

and battery condition. The action is the transmit power level

or the amount of energy to be consumed, and the reward is

a function of the states and the actions. The state transition

probability describes the transition probability from the current

state to the next state with respect to each action. The goal is

to ﬁnd the optimal policy, which speciﬁes the optimal action

in the state and maximizes the long-term expected discount

inﬁnite-horizon reward starting from the initial state [18].

In the context of distributed detection in WSNs, there are

only few studies that consider EH-powered sensors [21]–[27].

In the following we provide a concise review of these works,

highlight how our present work ﬁlls the knowledge gap in the

literature, and how it is different from our previous works in

[25]–[27].

A. Related Works and Knowledge Gap

Considering an EH-powered node, that is deployed to

monitor the change in its environment, the authors in [21]

formulated a quickest change detection problem, where the

goal is to detect the time at which the underlying distribution

of sensor observation changes. Considering an EH-WSN and

choosing deﬂection coefﬁcient as the detection performance

metric, the authors in [24] formulated an adaptive transmit

power control strategy based on PHY-MAC cross-layer design.

Considering an EH-WSN and choosing error probability as the

detection performance metric, the authors in [22] proposed

ordered transmission schemes, that can lead to a smaller

average number of transmitting sensors, without comprising

the detection performance. Modeling the randomly arriving

energy units during a time slot as a Bernoulli process, the

battery state as a K-state Markov chain, and choosing Bhat-

tacharya distance as the detection performance metric, the

authors in [23] have investigated the optimal local decision

thresholds at the sensors, such that the detection performance

is optimized. We note the system model in [24] lacks a battery

to store the harvested energy. Further, the adopted energy

arrival model in [24] is deterministic. On the other hand,

[21], [22] assumed sensor-FC channels are error-free and [23]

considered a binary asymmetric channel model for sensor-FC

links. The high level communication channel model, combined

with a simple stochastic model for random energy arrival is

limiting. Speciﬁcally, it does not allow one to study channel-

dependent transmit power control strategies. Such a study

requires a more realistic communication channel model and

stochastic energy arrival model that match the energy needed

for a channel-dependent transmission. This is the knowledge

gap that we address in this work.

To highlight how our present work is different from our

previous works in [25]–[27], we brieﬂy summarize them

in the following. Modeling the random energy arrival as a

Bernoulli process, the dynamics of the battery as a ﬁnite-

state Markov chain, and considering fading channel model,

in [25] we adopted channel-inversion transmit power control

policy, where allocated power is inversely proportional to

fading channel state information (CSI) in full precision, and

we found the optimal decision thresholds at sensors such that

Kullback-Leibler (KL) distance detection metric at the FC

is maximized. Different from [25], in [26] we modeled the

random energy arrival as an exponential process and assumed

that each sensor only knows its quantized CSI and adapts its

transmit power according to its battery state and its quantized

CSI, such that J-divergence based detection metric at the FC is

maximized. Modeling the random energy arrival as a Poisson

process in [27], we proposed a novel transmit power control

strategy that is parameterized in terms of the channel gain

quantization thresholds and the scale factors corresponding

to the quantization intervals, and found the jointly optimal

quantization thresholds and the scale factors such that J-

divergence based detection metric at the FC is maximized.

Our present work is different from our prior works in [25]–

[27] in several aspects. The transmit power control strategies in

these works are intrinsically different from our present work,

since in [25]–[27] we have assumed that the battery operates

at the steady-state and the energy arrival and channel models

are independent and identically distributed (i.i.d) across trans-

mission blocks. Consequently, the power optimization problem

in [25]–[27] became a deterministic optimization problem, in

terms of the optimization variables, and the obtained solutions

are different. In this work, the battery is not at the steady-state.

Also, both the channel and the energy arrival are modeled as

homogeneous ﬁnite-state Markov chains (FSMCs). Therefore,

the power control optimization problem at hand becomes a

multistage stochastic optimization problem, and can be solved

via the MDP framework. To the best of our knowledge, this

is the ﬁrst work that develops MDP-based channel-dependent

power control policy for distributed detection in EH-WSNs.

The MDP framework has been utilized before in [29], [30] to

address a quickest change detection problem.

B. Our Contribution

Given our adopted WSN model (see Fig. 1), we aim

at developing an adaptive channel-dependent transmit power

control policy for sensors such that a detection performance

metric is optimized. We choose the J-divergence between

the distributions of the detection statistics at the FC under

two hypotheses, as the detection performance metric. Our

choice is motivated by the fact that J-divergence is a widely

adopted metric for designing distributed detection systems

[12], [13], [27], [31]. We note that J-divergence and Peare

related through Pe>Π0Π1e−J/2, where Π0,Π1are the a-

priori probabilities of the null and the alternative hypothe-

ses, respectively [12], [13], [31]. Hence, maximizing the J-

divergence is equivalent to minimizing the lower bound on

Pe. Modeling the quantized fading channel, the energy arrival,

and the dynamics of the battery as homogeneous FSMCs, and

the network lifetime as a random variable with geometric dis-

tribution, we formulate J-divergence-optimal transmit power

control problem, subject to total transmit power constraint, as

adiscounted inﬁnite-horizon constrained MDP optimization

problem, where the control actions (i.e., transmit powers) are

functions of the battery state, quantized CSI, and the arrived

Ht=1:Ais present

Ht=0:Ais absent

Fusion Center

Feedback

sensor 1

x1,t

e1,t

b1,t

α1,t

g1,t w1,t

y1,t

...

sensor 2

x2,t

e2,t

b2,t

α2,t

g2,t w2,t

y2,t

sensor N

xN,t

eN,t

bN,t

αN,t

gN,t

wN,t

yN,t

Fig. 1: Our system model and the schematic of battery state in time slot t.

energy. We obtain the optimal and sub-optimal policies and

propose two algorithms based on value iterations in the MDP.

Our main contributions can be summarized as follow:

•Given our adopted system model, we develop the op-

timal power control policy, using dynamic programming and

utilizing the Lagrangian approach to transform the constrained

MDP problem into an equivalent unconstrained MDP problem.

For the optimal policy, the local action (i.e., a sensor’s transmit

power) depends on the network state (i.e., all sensors’ battery

states, quantized CSIs, and the arrived energies), and the com-

putational complexity of the algorithm grows exponentially in

number of sensors N. Implementing this solution requires each

sensor to report its battery state and arrived energy to the FC,

which imposes a signiﬁcant signaling overhead to the sensors.

•To eliminate this overhead, we develop a sub-optimal

power control policy, using a uniform Lagrangian multiplier to

transform the constrained MDP problem into Nunconstrained

MDP problems. For the sub-optimal policy, the local action

depends on only the local state (i.e., a sensor’s battery state,

quantized CSI, and the arrived energy), and the computational

complexity of the algorithm grows linearly in N.

•We numerically study the performance of our proposed

algorithms and showed that the sub-optimal policy has a close-

to-optimal performance.

•We study how our system setup and proposed solutions

can be extended to the scenario where sensors are randomly

deployed in the ﬁeld.

C. Paper Organization

The paper organization follows: Section II describes our

system and observation models, derives a closed-form expres-

sion for the total J-divergence and introduces our constrained

optimization problem. Sections III describes the optimal and

the sub-optimal policies. SectionIV discusses how our setup

can be extended to the scenario where sensors are randomly

deployed in the ﬁeld (i.e., sensors’ locations are unknown a-

priori). Section V illustrates our numerical results. Section VI

concludes our work.

II. SYSTEM MODEL

A. Observation Model at Sensors

We consider a WSN tasked with solving a binary distributed

detection problem (see Fig. 1). To describe our signal process-

ing blocks at sensors and the FC as well as energy harvesting

model, we divide time horizon into slots of equal length Ts.

Each time slot is indexed by an integer tfor t= 1,2, ..., T (see

Fig. 2). We model the underlying binary hypothesis Htin time

slot tas a binary random variable Ht∈ {0,1}with a-priori

probabilities ζ0= Pr(Ht= 0) and ζ1= Pr(Ht= 1) = 1−ζ0.

We assume that the hypothesis Htvaries over time slots in

an independent and identically distributed (i.i.d.) manner. Let

xn,t denote the local observation at sensor nin time slot t. We

assume that sensors’ observations given each hypothesis with

conditional distribution f(xn,t|Ht=ht)for ht∈ {0,1}are

independent across sensors. This model is relevant for WSNs

that are tasked with detection of a known signal in uncorrelated

Gaussian noises with the following signal model

Ht=1: xn,t =A+vn,t,

Ht=0: xn,t =vn,t,for n= 1, . . . , N, (1)

where Gaussian observation noises vn,t ∼N (0, σ2

vn)are inde-

pendent over time slots and across sensors. Given observation

xn,t sensor nforms local log-likelihood ratio (LLR)

Γn(xn,t),log f(xn,t|ht= 1)

f(xn,t|ht= 0),(2)

and uses its value to choose its non-negative transmission

symbol αn,t to be sent to the FC. In particular, when LLR

is below a given local threshold θn, sensor ndoes not

transmit and let αn,t = 0. When LLR exceeds the given local

threshold θn, sensor nchooses αn,t according to the available

information (will be explained later). In particular, we have

ζn,0= Pr(αn,t =0) = ζ0(1−Pfn) + ζ1(1−Pdn),

ζn,1= Pr(αn,t 6=0) = ζ0Pfn+ζ1Pdn,(3)

where the probabilities Pfnand Pdncan be determined using

our signal model in (1) and given the local threshold θn

Pfn=Pr(αn,t 6= 0|ht= 0) =Qθn+A2/2σ2

pA2/σ2

vn,

Pdn=Pr(αn,t 6= 0|ht= 1) =Qθn− A2/2σ2

pA2/σ2

vn.(4)

Instead of ﬁxing θn, one can ﬁx Pdnand let Pdn=Pd,∀n.

Then the false alarm probability in (4) can be written as Pfn=

QQ−1(Pd) + pA2/σ2

vn.

Note that sensors are typically deployed in hostile outdoor

environments (e.g., for forestry ﬁre and volcano monitoring

and detection, and battleﬁeld surveillance) in an unattended

and distributed manner. Therefore, they are highly suscepti-

ble to physical destruction. We include this factor into our

modeling by letting η∈[0,1) be the probability that a

sensor can survive physical destruction or hardware failure

and continue to function in time slot t. Deﬁning the network

lifetime Tas the time until the ﬁrst sensor fails, we ﬁnd that

文档加载中……请稍候！
如果长时间未打开，您也可以点击刷新试试。

下载文档到电脑，查找使用更方便

10 玖币 0人已下载

立即下载

摘要：

OnDistributedDetectioninEH-WSNsWithFinite-StateMarkovChannelandLimitedFeedbackGhazalehArdeshiri,AzadehVosoughiSeniorMember,IEEEUniversityofCentralFloridaEmail:gh.ardeshiri@knights.ucf.edu,azadeh@ucf.eduAbstractWeconsideranetwork,taskedwithsolvingbinarydistributeddetection,consistingofNsensors,afusi...

展开>> 收起<<

On Distributed Detection in EH-WSNs With Finite-State Markov Channel and Limited Feedback Ghazaleh Ardeshiri Azadeh V osoughi Senior Member IEEE University of Central Florida.pdf

共15页,预览3页

还剩页未读，继续阅读

声明：本站为文档C2C交易模式，即用户上传的文档直接被用户下载，本站只是中间服务平台，本站所有文档下载所得的收益归上传人(含作者)所有。玖贝云文库仅提供信息存储空间，仅对用户上传内容的表现方式做保护处理，对上载内容本身不做任何修改或编辑。若文档所含内容侵犯了您的版权或隐私，请立即通知玖贝云文库，我们立即给予删除！

On Distributed Detection in EH-WSNs With Finite-State Markov Channel and Limited Feedback Ghazaleh Ardeshiri Azadeh V osoughi Senior Member IEEE University of Central Florida

相关推荐

开通VIP享超值会员特权

作者详情

相关内容

热门标签

举报选择: