multisensor data fusion: from algorithm and …€¦ · 2multisensor data fusion: from algorithm...

H. Fourati

Multisensor Data Fusion:

From Algorithm and

Architecture Design to

Applications

Decision Fusion in CognitiveWireless Sensor Networks

Andrea Abrardo,1 Marco Martalo,2,3 and Gianluigi Ferrari2

1: University of Siena, Italy2: University of Parma, Italy3: E-Campus University, Novedrate (CO), Italy

Abstract

In this chapter, we focus on a cognitive wireless sensor network (WSN), wherea primary WSN (PWSN) is co-located with a cognitive (or secondary) WSN(CWSN). The shared frequency spectrum can be “freely” assigned by thePWSN. In particular, this spectrum is divided into disjoint “subchannels”and each subchannel is assigned (in a unique way) to a node of the PWSN.We assume that the nodes of the CWSN cooperate to sense the frequencyspectrum and estimate the free subchannels which can be used to transmittheir data. The key contribution of this work is two-fold. First, the sensingcorrelation among the secondary nodes is exploited to improve the reliabilityof the decision, taken by a secondary fusion center (FC), on the occupationstatus (by a node of the PWSN) of each subchannel. In this context, weprovide a simple model for characterizing the local sensing performance persubchannel, in terms of probabilities of missed detection (MD) and false alarm(FA). Then, we analyze the use of joint source channel coding (JSCC) schemesin the CWSN, in order to further exploit the source correlation to make thefinal decision of the secondary FC on the status of the frequency subchannelsmore reliable.

Keywords

Cognitive networks, information fusion, false alarm, missed detection, corre-lated sources.

1

2Multisensor Data Fusion: From Algorithm and Architecture Design to Applications

20.1 Introduction

With the development of wireless communications in the last years, most ofthe available spectrum has been fully allocated. On the other hand, recentinvestigations on the actual spectrum utilization have shown that a portionof the licensed spectrum is largely underutilized [2]. As a matter of fact, theso-called spectrum scarcity problem is mostly due to an inefficient spectrumallocation policy rather than to actual physical spectrum shortage. Accord-ingly, in order to “chase” the explosion of wireless communications, novelsolutions should be envisaged.

Dynamic spectrum access (DSA) has been considered to get a more effi-cient radio spectrum utilization [12], [11]. In DSA, part of the spectrum canbe allocated to one or more users, which are called primary users (PUs). Suchspectrum is not exclusively dedicated to PUs, although they have higher pri-ority than other users, which are referred to as secondary users (SUs). Inparticular, SUs can access the same spectrum as long as the PUs are not tem-porally using it or can share the spectrum with the PUs as long as the PUscan be properly protected. By doing so, the radio spectrum can be reused inan opportunistic manner or shared all the time: thus, the spectrum utilizationefficiency can significantly be improved.

To support DSA, SUs are required to capture or sense the radio environ-ment, and a SU with such a capability is also called a cognitive radio (CR)[8], [9]. One of the main tasks of CR is represented by spectrum sensing (SS),defined as the task of finding spectrum holes [16], i.e., portions of spectrumallocated (licensed) to some primary users but left unused for a certain time.On the other hand, SS from a single node does not always guarantee satis-factory performance due to noise uncertainty, the intrinsic random nature ofthe nodes’ positions, and unpredictable channel fluctuations. For example, aCR user cannot detect the signal from a primary transmitter behind a highbuilding and it may decide to access the licensed channel, thus interfering withthe primary receiver.

On the other hand, collaboration of multiple users in SS may highly im-prove SS performance by introducing a form of spatial diversity [5], [6]. Incooperative SS, CR users first send the collected data to a combining user orfusion center (FC). Alternatively, each user may independently perform localdecisions and then report binary decisions to the FC. Finally, the FC takes adecision on the presence or absence of the licensed signal based on the receivedinformation.

In this chapter, we focus on a cognitive WSN, where a primary wirelesssensor network (PWSN) is co-located with a cognitive (or secondary) sensornetwork (CWSN). In particular, the nodes of the CWSN reach their associatedaccess point (AP) directly (single hop). The shared (by PWSN and CWSN)frequency spectrum is divided into subchannels, which can be assigned by the

Decision Fusion in Cognitive Wireless Sensor Networks 3

PWSN, whereas the nodes of the CWSN cooperate to sense the frequencyspectrum and estimate the free subchannels which can be used to transmittheir data. The secondary nodes transmit the packets containing the observa-tions on the channels’ statuses to their fusion center (FC), embedded in thesecondary AP, which makes a final decision about the status (free or busy)of each subchannel and broadcast this information to all secondary nodes.The correlation, in the sensing operation, among the secondary nodes is takeninto account. In particular, we provide a simple analytical model to charac-terize the local sensing performance per subchannel, in terms of probabilitiesof missed detection (MD) and false alarm (FA). Moreover, we propose a jointsource channel coding (JSCC) scheme, in the CWSN, to exploit the sourcecorrelation in order to improve the reliability of the final decision taken by thesecondary FC. By relying on recent results on the design of practical decodingand fusion rules for multiple access schemes with correlated sources [4], wederive an effective fusion rule and an associated iterative decoding strategyfor joint channel decoding (JCD) at the secondary FC.

The rest of the chapter is structured as follows. In Section 20.2, we presentthe reference scenario. In Section 20.3, we analyze the performance from asingle node perspective. Then, in Section 20.4 we analyze the performancefrom a network point of view, distinguishing between uncoded and codedscenarios. In Section 20.5, both theoretical and simulation results are provided.Finally, concluding remarks are given in Section 20.6.

20.2 System Model

The scenario of interest is shown in Figure 20.1. The FC is placed at the centerof the cell, while secondary and primary nodes are independent and identicallydistributed (i.i.d.) according to a uniform distribution in a circular cell witha given radius R. A logical description of the scenario is given in Figure 20.2.Let us denote as cognitive user equipment (CUE) and primary user equipment(PUE) the secondary and primary nodes, respectively.1 The number of PUEsand CUEs is equal to P andN , respectively. Each PUE is assigned one channelamong a set of Nch orthogonal subchannels, e.g., a set of non-overlapping Nch

frequency bands. Moreover, each subchannel is assigned to at most one PUE,which transmits its own data (when available) with fixed power PT over theassigned subchannel. The status of the i-th (i ∈ {1, . . . , Nch}) subchannel Si

1This a slight abuse of notation, as CUE and PUE are notations typically adopted incellular systems. However, as smartphones are today advanced sensing systems, we keepthis notation also in the realm of WSNs.


CELL

FCR

user (PUE)primary

secondaryuser (CUE)

FIGURE 20.1

Cognitive scenario of interest.

is assumed binary, namely:

Si =

{S0 with probability P (S0)

S1 with probability P (S1) = 1− P (S0).

Data transmissions follow a classical model for cellular environments, wherethe path-loss is thoroughly characterized by two parameters: (i) the distanceattenuation factor α (adimensional, in the range 2-4) and (ii) the standarddeviation σ (in dB) of the log-normal shadowing [7].

Each CUE scans all Nch channels in order to detect the presence of a pri-mary signal transmission. In other words, the CUEs perform a binary hypoth-esis test on the presence of primary signals in each subchannel: a subchannelis idle under hypothesis S0 and busy under hypothesis S1. As for the signalmodel, we assume that the primary signal can be modeled as a zero-meanstationary white Gaussian process: this is a reasonable assumption when theCWSN has no a-priori knowledge about the possible modulation and pulseshaping formats adopted by the PWSN.

On the basis of the model assumptions above, the k-th CUE (k = 1, . . . , N)has to distinguish, for the i-th subchannel (i = 1, . . . , Nch), between two in-dependent Gaussian sequences:

νk,i(ℓ) =

{nk,i(ℓ) if S0

sk,i(ℓ) + nk,i(ℓ) if S1

ℓ = 1, . . . ,m (20.1)

where m is the number of observed samples—for simplicity, the time indexℓ refers to a single block of observations. Note that an implicit assumption


subchannel

1

subchannel

2· · · subchannel

NchNch − 1subchannel

PUEPPUE2PUE1 · · ·

CUEN· · ·CUE2CUE1

FC

CWSN

PWSN

FIGURE 20.2

Logical description of the scenario of interest.

in (20.1) is that the phenomenon status (S0 or S1) does not change over mconsecutive observations: this is realistic given thatm is typically much shorterthan the duration of a primary signal transmission. Moreover, the fact that thek-th node takesm consecutive observations {νk,i(ℓ)}mℓ=1 on the i-th subchannelguarantees a sort of time diversity in the sensing operation. In (20.1), sk,i(ℓ)is the received signal by the k-th CUE on the i-th subchannel, which is asequence of i.i.d. zero-mean complex Gaussian random variables with variance

P(k,i)R , which corresponds to the received power. The power P

(k,i)R depends

on the transmitted power PT and on the path-loss and shadowing terms ofeach CUE-PUE pair. Note that it is reasonable to assume that the path-loss and shadowing terms are constant over all m acquisitions. The noiseterms {nk,i(ℓ)} are also modeled as i.i.d. zero-mean complex Gaussian randomvariables with fixed variance PN, constant for all CUEs and subchannels.

Under the observation model (20.1), an energy detection (ED) scheme isthe optimal detector in the Neyman-Pearson sense [10]. In particular, thefollowing decision variable has to be evaluated:

Wk,i =m∑

ℓ=1

|νk,i(ℓ)|2

and the binary decision of the CUE is given by

xk,i =

{0 if Wk,i < τ

1 if Wk,i ≥ τ(20.2)

where τ is a proper decision threshold. In other words, each CUE decides for


0 if the channel is sensed idle, whereas it decides for 1 if the channel is sensedbusy. The local FA and MD probabilities, under the proposed ED scheme, canbe defined as follows:

P(k,i)FA , P (xk,i = 1|S0)

P(k,i)MD , P (xk,i = 0|S1).

Consequently, the correct detection (CD) probability is

P(k,i)CD = 1− P

(k,i)MD .

The k-th CUE then generates the decision vector xxxk = (xk,1, . . . , xk,Nch)

(k = 1, . . . , N), where xk,i ∈ {0, 1} (i = 1, . . . , Nch) corresponds to its lo-cal decision on the absence (0) or presence (1) of a primary signal in thei-th subchannel. This vector is then transmitted to the secondary FC, which,upon receiving decision vectors from all nodes of the CWSN, applies a properfusion strategy to make a final decision on the status (free or busy) of each sub-channel. The FC can thus broadcast this information to all secondary nodes(possibly with the assignment of the free subchannels to a subset of them, inorder to avoid multiple access interference.

20.3 Single Node Perspective

We now analyze the performance from a single node perspective. Being thesubchannels independent, without loss of generality we focus on a single sub-channel and derive the corresponding FA and MD probabilities—for nota-tional simplicity, we drop the superscript/subscript referring to the subchan-nel.. Since each subchannel is assigned to at most one PUE, without loss ofgenerality we also focus on a single PUE.

With reference to Figure 20.1, assume that CUEs and PUEs are uniformlydistributed within the cell with radius R and that the FC is positioned at thecell center. Denote as Xk = xke

2πθk and Xp = ye2πφ the positions of thek-th CUE and the PUE, respectively, where 0 ≤ xk, y ≤ R and 0 ≤ θk, φ ≤ 2π.The distance d between the two nodes is

dk = |Xp −Xk| =√

x2k + y2 − 2xky cos(θk − φ).

Assuming a fixed transmit power PT for primary nodes, the power P(k)R re-

ceived by the CUEs can be expressed as:

P(k)R =

K

dαkhkPT

where: K is the gain at one meter from the emitter; hk is the log-normal


shadowing coefficient of the link between the PUE and the k-th CUE; and dkis the distance between the PUE and the k-th CUE. Therefore, the sensingsignal-to-noise ratio (SNR) experienced by the k-th CUE, with respect to thePUE, can be expressed as follows:

γk(dk, h) =P

(k)R

PN=

KhkPT

PNdαk.

The local FA and MD probabilities for ED can then be evaluated as [10]

P(k)FA = Γu (mτN,m)

P(k)MD = 1− Γu

(mτN

1 + γk(dk, h),m

)

where τN = PNτ is the normalized threshold (with τ introduced in (20.2)) andΓu is the upper incomplete gamma function:

Γu(a, n) ,

∞∫

a

xn−1e−x dx.

Note that the FA probability is the same for all CUEs and does not depend on

their distances from the PUE, i.e., P(k)FA = PFA. The MD probability, instead,

depends on the distance dk and on the shadowing term hk. Averaging withrespect to the statistical distribution of the shadowing term, the followingexpression for the average MD probability at distance dk is obtained:

P(k)

MD = 1− 1√2πσ2

∞∫

−∞

Γu

(mτN

1 + γk(dk, 10S/10),m

)

e−S2

2σ2 dS. (20.3)

Even though the integral in (20.3) has no closed-form solution, it can benumerically evaluated. Finally, the average MD probability for any CUE, de-noted as PMD, can be obtained from (20.3) by averaging over the distance dk,thus obtaining:

PMD =

∫

ρ

P(k)

MD(ρ)fD(ρ) dρ (20.4)

where fD(ρ) is the probability density function (PDF) of the CUE-PUE dis-tance. The average CD probability for CUE, denoted as PCD, can be straight-forwardly expressed as

PCD = 1− PMD.

Expression (20.4) for PMD is an average measure for all possible CUEs. ThePDF fD(ρ) is associated with the distance between two randomly chosen


points in a circle and, according to the Crofton fixed points theorem [13], canbe given by the following expression:

fD(ρ) = 2ρ

R2

[

2

πarccos

( ρ

2R

)

− ρ

πR

√

1− ρ2

4R2

]

0 ≤ ρ ≤ 2R.

The choice of a proper value for the threshold τN is crucial to maximize theultimate system performance. Indeed, a small value of τN yields frequent FAs,whereas a high value of τN entails a high MD probability. The optimized valueof τN obviously depends on the sensing SNR experienced by each CUE, which,in turn, depends on several other uncontrollable characteristics, such as thepositions of CUEs/PUEs and shadowing. We preliminarily observe that theselection of a different and optimized threshold for each CUE would involve ahuge amount of message exchange between the FC and the CUEs. Therefore,we make the reasonable assumption that the threshold is a predefined systemparameter to be optimized off-line (e.g., in a training phase) through statisticalconsiderations. More generally, we make the assumption that the FC has noknowledge about the actual positions of CUEs and PUEs inside the cell.

20.4 Network Perspective

We now analyze the performance from a network perspective, considering theuse of the local decisions coming from all the CUEs, considering possible datafusion rules. In particular, in Subsection 20.4.1 we first focus on an uncodedscenario with error-free communication links. Then, in Subsection 20.4.2 weextend our analysis to the presence of communication noise and channel cod-ing.

20.4.1 Uncoded Scenario with No Communication Noise

We first consider the case where data (i.e., local decisions on the statuses ofthe subchannels) are transmitted as uncoded by each CUE to the secondaryFC, using a set of orthogonal error-free communication channels: this allows toderive the ultimate performance limits which can be achieved in this scenario.In reality, noisy communications from CUEs to the secondary FC are likelyto degrade the system performance, as shown by means of simulations inSection 20.5.

In order to derive the network-wide performance in the absence of channelcoding, we now consider all the Nch subchannels, where the characteristicsof the local decisions by the CUEs, in terms of FA and MD probabilities,have been derived in Section 20.3. Using the considered observation model,it is possible to write the a priori joint (among all CUEs) probability mass


function (PMF) of the decisions for the i-th subchannel (i ∈ {1, . . . , Nch})as [15]

P (xxxi) = P (xxxi|Si = S0)P (S0) + P (xxxi|Si = S1)P (S1)

= P (S0)∏

k∈X0

(1− PFA)k∏

k∈X1

(PFA)N−k +

P (S1)∏

k∈X0

(1− PCD

)k ∏

k∈X1

(PCD

)N−k(20.5)

where

X0 = {h ∈ {1, . . . , N} : xk,h = 0}X1 = {j ∈ {1, . . . , N} : xk,j = 1}.

Obviously, X0 ∪ X1 = {1, . . . , N}.Since the communication channels between the CUEs and the secondary

FC are error-free, the transmitted data are received correctly and the fusionrule at the FC can be written as:

Λi =

N∑

k=1

xk,i

S1

≷S0

T (20.6)

where T is a “global” decision threshold (i.e., equal for all subchannels) tobe optimized. In other words, the hypothesis testing problem turns out be acounting problem: the number of local decisions, at the CUEs, in favor of S1 isfirst counted and then compared with the threshold T . The fusion rule (20.6)is shown to be optimal under the assumption, as in this chapter, of blinddetection, i.e., the FC has no knowledge about the actual sensing accuracy(in terms of local FA and MD probabilities) of each CUE [14].

Let us now evaluate the performance at the FC by computing the finalCD and FA probabilities, denoted as PCD,f and PFA,f , respectively—note thatthese probabilities do not depend on the subchannel. To this end, we ap-proximate the performance of the system following an approach similar tothat in [14]. In particular, we assume that all users are characterized by thesame PMD given by (20.4), regardless of the position of the PUE. However,unlike [14], we do not consider a Gaussian approximation for Λ, since thenumber of CUEs may not necessarily be large. Since the observations {xk}are i.i.d. with a Bernoulli distribution, one can write

PCD,f = P (Λ > T |S1)

≃N∑

k=T

(N

k

)(PCD

)k (1− PCD

)N−k. (20.7)

Since the local FA probability does not depend on the position of the PUE,


the FA probability at the FC has exactly the following expression:

PFA,f = P (Λ > T |S0)

=N∑

k=T

(N

k

)

(PFA)k (1− PFA)

N−k . (20.8)

At this point, one can observe that the probabilities in (20.7) and (20.8)depend on the local and global thresholds, i.e., one can write:

PCD,f = G (τN, T )

PFA,f = F (τN, T )

where G(·, ·) and F(·, ·) are proper functions. The optimized values of thelocal (τN) and global (T ) thresholds can be determined by observing thatprotecting primary users against secondary interference is, in general, moreimportant than giving opportunities to secondary users. Therefore, we con-sider a Neyman-Pearson detector at the FC where we fix the requested CDprobability, i.e., we impose PCD,f = PCD,tgt. For each possible value of τN, theoptimal value of the threshold T , denoted as T ∗, can be determined by findingthe maximum value (if existing) of T which allows to achieve PCD,tgt, i.e.,:

T ∗(τN) = max{T ∈ N : G (τN, T ) = PCD,tgt}. (20.9)

In (20.9), the maximum value is considered because G(τN, T ) is, as shown later,a decreasing function of T for fixed τN. The optimal value of τN, denoted asτ∗N, is then selected as the value which allows to achieve the minimum PFA,f :

τ∗N = argminτN

F [τN, T∗(τN)] .

We now show an illustrative example of the general scenario of interestshown in Figure 20.1. In particular, the main system parameters are the fol-lowing: R = 1 km, PT = 30 mW, α = 4, σ = 5 dB, PN = −110 dBm, andm = 10. In Figure 20.3, PCD,f is shown, as a function of T , for N = 15 andvarious values of τN. In all cases, the target CD probability PCD,tgt is set to0.95. One can observe that the optimal value of T depends on τN: for in-stance, for τN = 1 the optimal threshold is T = 6, whereas T = 1 for τN = 1.6.These values are then used to determine the optimal values of τN, as shownin Figure 20.4, where PFA,f is shown, as a function of τN, for various valuesof T . The points highlighted with circles correspond to those obtained fromFigure 20.3. Since the optimized thresholds correspond to the minimum FA,in the considered settings the optimized thresholds are (T ∗, τ∗N) = (1, 1.8).

20.4.2 Coded Scenario with Communication Noise

Consider now a scenario where the data transmitted by the CUEs to theFC are corrupted by communication noise. For simplicity, assume that the


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15T

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

PCD,f

τN

= 1

τN

= 1.2

τN

= 1.4

τN

= 1.6

τN

= 1.8

PCD,tgt

= 0.95

FIGURE 20.3

PCD,f , as a function of T , for N = 15 and various values of τN. In all cases,the target CD probability PCD,tgt is set to 0.95.

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2τ

N

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

PFA,f

T = 1T = 2T = 4T = 6

FIGURE 20.4

PFA,f , as a function of τN, for various values of T . The points highlighted withcircles correspond to those obtained from Figure 20.3.


communication links are orthogonal and affected by additive white Gaussiannoise (AWGN), so that the observable model at the FC is

rk,i = xk,i + wk,i k = 1, . . . , N i = 1, . . . , Nch (20.10)

where {xk,i}Nch

i=1 is the binary data sequence obtained by channel encoding

(with coding rate rcod) the decision sequence {xk,i}Nch

i=1 . The communication

channel is characterized by an SNR denoted as γ(k)ch .2 In Section 20.5, a com-

mon average value of the communication SNR, denoted as γch, will be con-sidered. The choice of proper channel coding strategies is an interesting openissue, due to the fact that the decision packet length is typically small (infact, it corresponds to the number Nch of subchannels). However, this problemgoes beyond the scope of this chapter—in Section 20.5, a regular low-densityparity-check (LDPC) code will be considered.

Since the transmitted data are inherently correlated according to the PMFin (20.5), inspired by the work in [4], we use JCD at the receiver to improve thedetection/decoding performance. In this case, N subdecoders, one per CUE,are present at the AP. Each subdecoder works on the basis of its channelLLRs and the a priori soft information obtained from the soft-output infor-mation generated by the other subdecoders (associated with the remainingCUEs), properly combined taking into account the source correlation. Thecorresponding scheme of the JCD receiver is shown in Figure 20.5. This pro-cedure is then iterated in order to refine at each step the decisions of eachdecoder.

The log-likelihood ratio (LLR) relative to the i-th observable at the inputof the k-th subdecoder can be written as follows [1]:

L(k)i,in =

L(k)i,ch + L(k)

i,ap i = 1, . . . , Nch

L(k)i,ch i = Nch + 1, . . . , Nch/rcod

where the channel LLR can be written as

L(k)i,ch =

2ri,kσ2N

k = 1, . . . , N

being σ2N the variance of the AWGN. The a priori component of the LLR can

be instead written as [4]

P (xi,k) =∑

xxx′

i

P (xi,k = 0|xxx′i)

︸︷︷︸

a priori source correl.

N∏

ℓ=1ℓ 6=k

P (xi,ℓ)︸︷︷︸

from decoder ℓ

.

2We are making the reasonable assumption that the SNR is constant over the transmis-sion of an entire packet xxxk = (xk,1, . . . , xk,Nch

) and changes independently from CUE toCUE.


DECN

L(2)ch

DEC2

DEC1

DECk

L(N )ch

COMB

L(k)ch

L(1)ch

FIGURE 20.5

JCD algorithm and iterative decoding.

Since each decoder outputs the LLRs on the bits of the information se-quence, the following soft-input fusion (SF) rule can be used

Si = argmaxSi=0,1

βi

∑

{xxxi}

P (xxxi|Si)P (Si)∑

S∗=0,1 P (xxxi|S∗)P (S∗)︸︷︷︸

from the correlation model

n∏

j=1

P (xi,j |L(j)i )

︸︷︷︸

from decoder LLRs

(20.11)

whereβi , β(1− Si) + (1− β)Si i ∈ {0, 1}

with β ∈ (0, 1). In other words, the fusion rule (20.11), derived in [4] from amaximum a posteriori probability (MAP) criterion, can still be used in thisscenario using proper coefficients β0 = β and β1 = 1− β to obtain proper FAand CD probabilities. These coefficient needs to be optimized according to agiven criterion: in particular, in this chapter we consider the same procedureused in Section 20.4.1 to optimize T . In other words, for each value of τN,the optimal value of the threshold β, denoted as β∗, can be determined byfinding the maximum value (if existing) of β which allows to achieve PCD,tgt.The optimal value of τN, denoted as τ∗N, is then selected as the value whichallows to achieve, for β = β∗, the minimum PFA,f . Note also that these optimalvalues obviously depend on the sensing SNR.

Moreover, a hard-input fusion (HF) rule can be considered if the LLRs atthe output of the channel decoders are quantized, thus obtaining an estimateof the local decisions xxxi (i = 1, . . . , Nch). From a fusion point of view, the


estimated decisions {xxxi}Nch

i=1 are uncoded and, therefore, the same fusion ruleas in (20.6) can be applied:

Λi,cod =

N∑

k=1

xk,i

S1

≷S0

Tcod

where Tcod is a proper global threshold. The same optimization procedure forlocal τN and global Tcod thresholds described at the end of Subsection 20.4.1can be applied in this case as well.

20.5 Numerical Results

In this section, we present simulation results considering the same scenarioof Subsection 20.4.1. We assume that the frequency band is divided intoNch = 100 subchannels and, in the presence of channel coding, a half-rate(i.e., rcod = 1/2) (3,6) regular LDPC code, with pseudo-random parity-checkmatrix generation, is considered. The JCD algorithm summarized in Subsec-tion 20.4.2 is performed with 5 external iterations, while each LDPC decoderperforms internal iterations until a valid codeword is obtained or a maximumnumber of 50 internal iterations is reached. In order to eliminate statisticalfluctuations of the communication noise, the results in the presence of channelcoding are averaged over 100 different trials. In both uncoded and coded sce-narios, results are presented in terms of the receiver operating characteristic(ROC) curve, for the binary hypothesis testing problem of interest, showingthe CD probability as a function of the FA probability [3].

20.5.1 Uncoded Scenario

In Figure 20.6, the uncoded ROC is shown forN = 15 and various values of τN.Each point of the curves corresponds to a different value of T ∈ {1, 2, . . . , N}:in particular, T = 1 corresponds to the point in the upper right corner of thefigure.3 Note that for increasing values of T , a smaller FA probability can beobtained at the price of a lower CD probability. Moreover, increasing τN for afixed value of T allows to reduce both FA and CD probabilities, thus showingthe inherent tradeoff between these two quantities

In Figure 20.7, the uncoded ROC is shown for various values of N , con-sidering the optimal values of T and τN obtained with PCD,tgt = 0.95. Inparticular, for N = 5 the optimal point is (T ∗ = 1, τN = 1.1), for N = 10(T ∗ = 1, τN = 1.5), and for N = 15 (T ∗ = 1, τN = 1.8), as will be detailed inTable 20.1. Note that in all presented cases T = 1, i.e., the optimal decision

3Simulation results for the uncoded case, not shown here for brevity, are in agreementwith the theoretical results obtained from our analytical framework in Section 20.4.1.


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1P

FA,f

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

PCD,f

τN

= 1.4

τN

= 1.6

τN

= 1.8

FIGURE 20.6

Uncoded ROC for N = 15 and various values of τN.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1P

FA,f

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

PCD,f

N = 5N = 10N = 15

PCD,tgt

FIGURE 20.7

Uncoded ROC for various values of N , considering the optimal values of Tand τN obtained with PCD,tgt = 0.95.


TABLE 20.1

Optimal working points for the uncoded case and various values of N andPCD,tgt.

PCD,tgt N = 5 N = 10 N = 150.9 T ∗ = 1, τ∗N = 1.2 T ∗ = 1, τ∗N = 1.6 T ∗ = 1, τ∗N = 2.10.95 T ∗ = 1, τ∗N = 1.1 T ∗ = 1, τ∗N = 1.5 T ∗ = 1, τ∗N = 1.80.99 T ∗ = 1, τ∗N = 1 T ∗ = 2, τ∗N = 1.1 T ∗ = 1, τ∗N = 1.4

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1P

FA,f

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

PCD,f

uncodedcoded, γ

ch = 10 dB, SF

coded, γch

= 10 dB, HF

coded, γch

= 2 dB, SF

coded, γch

= 2 dB, HF

coded, γch

= 0 dB, SF

coded, γch

= 0 dB, SF

PCD,tgt

FIGURE 20.8

ROC curves for N = 10, PCD,tgt = 0.9, and different values of γch. Theperformance of SF is compared with that of HF.

rule is the OR decision rule. This means that, if CUE observations are avail-able without errors are the FC, it is sufficient to have at least one of them infavor of S1 to decide for this status. Moreover, for increasing values of N bothτN and T increases as well and the minimum possible PFA,f can be noticeablyreduced from 0.88 (N = 5) to 0.52 (N = 10) and 0.21 (N = 15). Obviously,these results depends on the considered target CD probability, as summarizedin Table 20.1. In particular, one can observe that with N = 10 and PCD,tgt

the minimum FA probability is achieved by fusing 2 decisions instead of 1.

20.5.2 Coded Scenario

In Figure 20.8, we show the ROC curves obtained considering N = 10,PCD,tgt = 0.9, and different values of γch. The performance of SF is com-pared with that of HF. One can observe that the better the communicationchannels (i.e., the higher the channel SNR), the closer the performance to thetheoretical limit given by the uncoded system: in particular, the performance


with γch = 10 dB overlaps with the theoretical limit given by the uncoded sys-tem. Moreover, in the presence of a bad communication link quality, the use ofSF allows to obtain better performance than HF, due to the fact that the like-lihood information coming from the decoder is properly exploited. The ROCcurves are shown for the optimal values of thresholds, e.g., T ∗ and τ∗N in theuncoded case (indicated as reference in Figure 20.8), β∗ and τ∗N for the codedcase and SF, and T ∗

cod and τ∗N for the coded case and HF. In particular, forhigh SNR (i.e., γch = 10 dB) the optimal value is τ∗N = 1.6 for both uncodedand coded (either HF or SF) cases. When the SNR reduces, e.g., γch = 2 dB,the optimal value is, in the coded case (either HF or SF), τ∗N = 1.7. Finally,for very bad communication link quality, e.g., γch = 0 dB, τ∗N 1.3 with HFand 2 with SF. The fact that the optimized threshold differs in the codedcase for at least medium-low communication SNRs, leads to the conjecturethat the choice of τN changes the correlation model, which should be properlytaken into account. Therefore, the dimensionality of the optimization problemincreases. This issue will be the subject of our future work.

20.6 Concluding Remarks

In this chapter, we have analyzed a cognitive WSN, where CUEs sense thefrequency spectrum and cooperate to estimate the free subchannels which canbe used to transmit their data. First, a simple analytical framework for char-acterizing the local sensing performance per subchannel, in terms of MD andFA probabilities, has been derived for a scenario with uncoded transmissionsover error-free communication channels. This allows to determine the ulti-mate achievable performance in such a scenario. Then, we have considered arealistic scenario with communication noise and the use of channel coding. Inthis context, the performance of JSCC schemes with JCD at the receiver hasbeen investigated. Our results have shown the beneficial impact of JCD atthe receiver (with improved quality of the subchannel status estimation), thusallowing to achieve performance close to the theoretical limit for sufficientlylarge values of the SNR.

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