The node’s reputation is evaluted based on the node’s state which will be obtained by the node’s behavior in RES-N. The tag T will record the node’s behavior as evidenceED. Then,T will includeEDas part of the response mes- sage when interacting with the next node Rn. After that, the message will be sent toOT by the nodeRn. Once receiving the response message,OT determines and then submitsR’s behavior to RMC. Finally, RMC updatesR’s reputation by R’s state which is determined by R’s behavior. In all, the node reputation evalutation process includes the following three steps.
– Node’s Behavior Determination
In order to perform operations on tagT, the node Rmust be authorized by the tag’s organization OT. Therefore,R requests authorization from OT by sending a request messageAU T H R to OT. Once being authorized,R can access to the tag. When the interaction between T and R is completed, T will generate an evidence ED to record the operation of the node. Specif- ically, ED=<IDR, OP, rand, seq> where IDR is the identity of R. ’OP’ stands for the performed operation such as data reading, writing or updat- ing. ‘seq’ is a sequence number which is initialized to 1 and will be increased by one after each operation. ‘rand’ is a random number generated by the tag. When the tag is requested by the next nodeRn,ED will be included in AU T H R=<IDT, IDRn, OPn, ED, > and sent to the tag’s organization OT byRn. Specifically,=Ek(Hash(ED)) which is obtained by first hash- ingED as Hash(ED) and then encrypting Hash(ED) by keyk, where kis the symmetric key shared byT andOT. Once receivingAU T H R,OT firstly verifies. If the receivedAU T H Rpass the verification,OT will then obtain R’s operation fromEDand determineR’s behavior as follows. Obviously,R’s behavior, either normal or malicious, can be observed accurately since each operation ofR will be sent toOT.
(a) normalbehaivor is detected, if nodeRonly performs operation permitted byOT.
(b) fault behaivor is detected, if node R performs unpermitted operation occasionally probably due to its random breakdown. This kind of fault behaivor such as data dropping or injection may not be allowed by OT
but won’t do harm toT.
(c) malicious behaivor is detected, if nodeRperforms operation strictly pro- hibited by OT such as compeletly wipe data.
– Node’s State Determination
After obtainingR’ behaviors from different organiztions, RMC can determine node R’s state according to R’s ‘Major Behavior’. The ‘Major Behavior’ is the behavior which occurs most frequently. For example, if the malicious, fault andnormal behavior occurs 6, 4 and 2 times during 10 min, the ‘Major Behavior’ ismalicious. According to Table1, we then find that the status of RisAttacked .
Table 1.Node state based on its major behavior Behavior Status
Normal Good
F ault T emporary breakdown Malicious Attacked
– Node’s Reputation Evaluation
Once obtaining the state of R, RMC can computeR’s reputation pR. If the state ofR is good,pR will be updated to the maximum reputation valuep0, where p0 denotes the initialization reputation value of a node. Or else, if R is in temporary breakdown or even attacked states, pR will be reduced to ζ∗p0 or even 0. Specifically,ζis an impact factor affecting the reputation of a breakdown node, where 0< ζ ≤1.
4 Simulation
In this section, we implement RES-N in a network covering over 1000*800 square meters. There are one RMC, 3 organizations, 30 tags and a large number of nodes. The moving speed of each node is 3 m/s. The available communication distance between a node and a tag is less than 30 m. The maximum communi- cation distance between two nodes is 150 m. Both the reputation of a node and an organization are initialized to 1.
Figure1 shows how the moving speed of tags affects the number of attacked nodes being detected for RES-N. We set that 30% of the nodes has been attacked.
Each organization deploys 100 readers and 5 tags. We can observe from Fig.1 that the number of attacked nodes being detected grows over time. This is because tags can encounter more readers and then capture the readers’ behavior over time with a high possibility.
0 20 40 60 80 100 0
1 2 3 4 5 6 7 8
Time (s)
Number of Attacked Nodes Being Detected
Fig. 1.Number of attacked nodes being detected over time
5 Conclusion
In this paper, we studied the trust issues in the IoT. In order to provide a general framework for trust management in IoT, we firstly design LTrust, a layered trust model for IoT. Then, a Reputation Evaluation Scheme for the Node (RES-N) and an a Reputation Evaluation Scheme for the Organization (RES-O) have been presented. The efficiency of RES-N and ORES is valided by the simulation results.
Acknowledgement. This research is supported in part by the Natural Science Foun- dation of China under grants No. 61300188 and 61601221; by the Fundamental Research Funds for the Central Universities No. 3132016024 and No. 3132017129; by Scientific Research Staring Foundation for the Ph.D in Liaoning Province No. 201601081; by Scientific Research Projects from Education Department in Liaoning Province No.
L2015056.
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system for the Internet of Things. Soft Comput.20, 1763–1779 (2016)
Estimation for Mixed Wideband Signals
Jiaqi Zhen(&), Yong Liu, and Yanchao Li College of Electronic Engineering, Heilongjiang University,
Harbin 150080, China zhenjiaqi2011@163.com
Abstract. Gain-phase error is inevitable in direction of arrival (DOA) estima- tion, it will lead to the mismatch between actual and ideal array manifold.
Therefore, a novel gain-phase error calculation approach in DOA estimation for mixed wideband signals is provided in this paper. First, the signals are trans- formed on the focusing frequency. Then peak searching is employed for determining the far-field sources. Finally, gain-phase error can be calculated according to the orthogonality of far-field signal subspace and noise subspace, simulation results manifest the effectiveness of the proposed approach.
Keywords: DOA estimationGain-phase errorFar-field signals Near-field signalsWideband signals
1 Introduction
With the development of array signal processing, more and more DOA estimation methods are springing up [1–8]. Such as multiple signal classification (MUSIC) [9], ESPRIT [10], maximum likelihood [11] and so on, all of them can achieve a high precision and resolution capability under ideal condition. But as a matter of fact, due to the processing technology and some disturbance, gain-phase error often exists in hardware, which leads to the deviation between actual and ideal array manifold, then most DOA estimation methods have deteriorated, so how to calculate this kind of error is very important.
In recent years, gain-phase error calculation has attracted many scholars: Fried- lander [12] analyzed its effect to MUSIC algorithm, then approximate expression of the estimation variance is given; Weiss and Friedlander [13] discussed thefirst and second order statistical properties of the spatial spectrum, then deduced the resolution threshold; Su et al. [14] inferred the expression of spatial spectrum, the relation
J. Zhen—This work was supported by the National Natural Science Foundation of China under Grant No. 61501176 and 61505050, University Nursing Program for Young Scholars with Creative Talents in Heilongjiang Province (UNPYSCT-2016017), China Postdoctoral Science Foundation (2014M561381), Heilongjiang Province Postdoctoral Foundation (LBH-Z14178), Heilongjiang Province Natural Science Foundation (F2015015), Outstanding Young Scientist Foundation of Heilongjiang University (JCL201504) and Special Research Funds for the Universities of Heilongjiang Province (HDRCCX-2016Z10).
©ICST Institute for Computer Sciences, Social Informatics and Telecommunications Engineering 2018 X. Gu et al. (Eds.): MLICOM 2017, Part I, LNICST 226, pp. 598–605, 2018.
https://doi.org/10.1007/978-3-319-73564-1_60
between gain-phase and resolution capacity; Wang et al. [15] concluded the quadric equation in one unknown of average signal to noise ratio (SNR) resolution threshold for MUSIC algorithm. All the research have shown the effect of the gain-phase error to the DOA estimation, they also greatly promoted the practical application of corre- sponding techniques, but there are rare published literatures in DOA estimation for mixed signals.
A novel gain-phase error calculation approach in DOA estimation for mixed far-field and near-field wideband signals (abbreviate as FS and NS) is provided in this paper. First, the signals are transformed on the focusing frequency. Then peak searching is employed for determining the far-field sources. Finally, Gain-phase error can be calculated according to the orthogonality of far-field signal subspace and noise subspace.
2 Array Signal Model
Define the wavelength of the signal is k, D is the array aperture, l is the distance between the signal and the reference. Generally speaking, ifl [ [ 2D2=k, it will be in the far-field; if l 2 ðk=2p; 2D2=kị, it will be in the near-field. As is shown in Fig.1, assume that N1 wideband far-field and N2 near-field sources impinge onto a 2Mỵ1-element uniform linear array from directions of h ẳ ẵh1; ; hN1;hN1ỵ1; ; hN, the middle sensor is treated as the reference, where N ẳ N1 ỵ N2, 0\h\p, the space of sensorsd equals half of the wavelength of the center fre- quency, andN1,N2 is assumed to be known in advance, then array output is
Xðfiị ẳ Aðfi;hịSðfiị ỵ Eðfiị ði ẳ 1; 2; ; Jị ð1ị
n1
θ
d 1
0 m M
1( )
s tn
2( )
s tn
n2
θ -m -1
-M
Y
O X
Fig. 1. Signal model
whereJis number of divided narrowband frequency bins,Aðfi; hịis the array manifold
Aðfi;hị ẳ ẵaFSðfi;h1ị; ; aFSðfi;hn1ị; ;aFSðfi;hN1ị; aNSðfi;hN1ỵ1ị; ;aNSðfi;hn2ị; ;aNSðfi;hNị
ẳ ẵAFSðfiị;ANSðfiị
ð2ị whereAFSðfiị ẳ ẵaFSðfi; h1ị; ; aFSðfi; hn1ị; ; aFSðfi; hN1ịis the array manifold of FS, andaFSðfi; hn1ịis the steering vector ofsn1ðtị;ANSðfiị ẳ ẵaNSðfi; hN1ỵ1ị; ; aNSðfi; hn2ị; ; aNSðfi; hNị is the array manifold of NS, and aNSðfi; hn2ị is the steering vector ofsn2ðtị, here
aFSðfi; hn1ị ẳ ẵexpðj2pfisMðhn1ịị; ; expðj2pfismðhn1ịị; ; 1; ; expðj2pfismðhn1ịị; ; expðj2pfisMðhn1ịịT ð3ị and
smðhn1ị ẳmd
ccoshn1 ðm ẳ M; ; m; ; 0; ; m; ; M;
n1ẳ1; 2; ; N1ị ð4ị
is the delay forsn1ðtịarriving at themth sensor with respect to the origin, on the other hand
aNSðfi;hn2ị ẳ ẵexpðj2pfisMðhn2ịị ; expðj2pfismðhn2ịị; ; 1; ; expðj2pfismðhn2ịị; ; expðj2pfisMðhn2ịịT ð5ị according to the geometrical relationship, we can deduce thesmðhn2ịfrom Fig.1
smðhn2ị ẳ ln2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi l2n2ỵðmdị22ln2mdcoshn2
q
c ð6ị
reference Taylor series, Eq. (6) can be transformed into [16]
smðhn2ị ẳ m2d2
4ln2ccos2hn2 þ 1
cmdcoshn2 m2d2
4ln2c ð7ị
and
Sðfiị ẳ ẵSFSðfiị; SNSðfiịT
ẳ ẵS1ðfiị; ; Sn1ðfiị; ; SN1ðfiị; SN1ỵ1ðfiị; ; Sn2ðfiị; ; SNðfiịT ð8ị here SFSðfiị ẳ ẵS1ðfiị; ; Sn1ðfiị; ; SN1ðfiịT is signal vector of FS, SNSðfiị ẳ
ẵSN1ỵ1ðfiị; ; Sn2ðfiị; ; SNðfiịT is that of NS. Eðfiịis the Gaussian white noise matrix with mean 0 and variancer2, then corresponding covariance matrix is
Rðfiị ẳ 1
ZXðfiịXHðfiị
ẳ 1
ZAðfi; hịSðfiịSHðfiịAHðfi; hị ỵ r2ðfiịI
ẳ RFSðfiị ỵ RNSðfiị ỵ r2ðfiịI
ð9ị
the covariance matrix of FS isRFSðfiị ẳ 1ZAFSðfiịSFSðfiịSHFSðfiịAHFSðfiị, that of NS is RNSðfiị ẳ Z1ANSðfiịSNSðfiịSHNSðfiịAHNSðfiị.
We can also model the gain-phase error as
Wðfiị ẳ diagẵWMðfiị; ; Wmðfiị; ; 1; ; Wmðfiị; ; WMðfiịT ð10ị where
Wmðfiị ẳ qmðfiịejumðfiị; m ẳ M; ; m; ;0; ; m; ; M; ð11ị is the gain-phase error of the sensorm,qmðfiị,umðfiịare the corresponding gain and phase errors, and they are independent with each other, so the array output with gain-phase error is
X0ðfiị ẳ A0ðfi; hịSðfiị ỵ Eðfiị ẳ WðfiịAðfi; hịSðfiị ỵ Eðfiị ð12ị
3 Estimation Theory
First, we need to estimate the covariance matrix with gain-phase error
R0ðfiị ẳ 1
ZX0ðfiịðX0ðfiịịH
ẳ 1
ZA0ðfi; hịSðfiịSHðfiịðA0ðfi; hịịH ỵ r2ðfiịI
ẳ 1
ZWðfiịAðfi; hịSðfiịSHðfiịAHðfi; hịWHðfiị ỵ r2ðfiịI
ẳ R0FSðfiị ỵ R0NSðfiị ỵ r2ðfiịI
ð13ị
where the covariance matrix of the FS isR0FSðfiị ẳ Z1WðfiịAFSðfiịSFSðfiịSHFSðfiị AHFS
ðfiịWHðfiị, that of the NS isR0NSðfiị ẳ Z1WðfiịANSðfiịSNSðfiịSHNSðfiị AHNSðfiịWHðfiị.
We can employ some coherent signal subspace methods to transform the received data on the focusing frequency
R00ðf0ị ẳ 1 J
XJ
iẳ1
TðfiịR0ðfiịTHðfiị ð14ị
hereTðfiị ẳ U0Sðf0ịU0SðfiịH
is the focusing matrix,U0Sðf0ị is the signal subspace of R0ðfiị,f0is the focusing frequency, then we can found the MUSIC spatial spectrum of FS
PMUFðhị ẳ 1
a0FSðf0; hị
H
UEðf0ịUHEðf0ịa0FSðf0; hị
ẳ 1
aHFSðf0; hịWHðf0ịUEðf0ịUHEðf0ịWðf0ịaFSðf0; hị
ẳ 1 Y
ð15ị
where UEðf0ị is the noise subspace of R00ðf0ị, in order to be convenient to the derivation, we express the gain-phase error with another form
wðfiị ẳ ẵqMðfiịejuMðfiị; ; qmðfiịejumðfiị; ;1; ; qmðfiịejumðfiị; ; qMðfiịejuMðfiịT ð16ị then we can simplify the denominator of the function above
Y ẳ aHFSðf0; hịWHðf0ịUEðf0ịUHEðf0ịWðf0ịaFSðf0; hị
ẳ XN1
n1ẳ1
aHFSðf0; hn1ịWHðf0ịUEðf0ịUHEðf0ịWðf0ịaFSðf0; hn1ị
ẳ XN1
n1ẳ1
wHðf0ịnðdiagðaFSðf0; hn1ịịịHUEðf0ịUHEðf0ịdiagðaFSðf0; hn1ịịo wðf0ị
ẳ wHðf0ịDðf0; hịwðf0ị
ð17ị
where Dðf0; hị ẳ PN1
n1ẳ1nðdiagðaFSðf0; hn1ịịịHUEðf0ịUHEðf0ịdiagðaFSðf0; hn1ịịo , the DOA of FS can be solved by minimizing (17). wðf0ị is not null matrix, so wHðf0ịDðfi; hịwðf0ị ẳ 0 holds only if Dðf0; hị is singular, then h1; hN1 can be estimated by searchingN1 peaks ofDðf0;hị.
Next, the orthogonality of signal subspace of FS and noise subspace can be utilized a0FSðhn1ị
H
U0E ẳ aHFSðhn1ịWHU0E ẳ 01ð2Mỵ1Nị ð18ị it can be transformed into
aHFSðhn1ịWHU0E ẳ wHf diagðaFSðhn1ịịgHU0E ẳ wHQðhn1ị ð19ị
here Qðhn1ị ẳ fdiagðaFSðhn1ịịgHU0E, define D as the middle row of U0E, as the middle row ofaFSðhn1ịequals 1, the middle element ofQðhn1ịisDtoo. Combining all FS, and letQðhị ẳ ẵQðh1ị; ; Qðhn1ị; ; QðhN1ị, therefore
wHQðhị ẳ wH
Q1ðhị D D Q2ðhị 2 64
3
75 ẳ ẵwH1; 1; wH2
Q1ðhị D D Q2ðhị 2 64
3
75ẳẵ0; ;01ð2Mỵ1NịN1
ð20ị wherew1is thefirstMrows ofw,w2is the latterMrows ofw,Q1ðhịis thefirstMrows ofQðhị,Q2ðhịis the latter M rows ofQðhị, define G ẳ ẵD D1ð2Mỵ1NịN1,w1
andw2 will be acquired according to (20), that is
^
w1 ẳ G Qð 1ðhịị#H
ð21ị
^
w2 ẳ G Qð 2ðhịị#H
ð22ị
^
w1andw^2is the estimation ofw1 andw2,ð ị#means solving pseudo-inverse, then we have
w^ ẳ w^T1; 1; w^T2
T
ð23ị Thus, estimation of gain-phase error can be calculated, and the number of sensors and the signals must satisfy 2M þ 1 [ N1 þ N2, the method is suitable for gain-phase error calculation in DOA estimation for mixed wideband signals, so we call it GPW for short.
4 Simulations
The structure of the array is illustrated as Fig.1, consider two FS and two NS impinge on a uniform linear array with 7 omnidirectional sensors from ð73; 85ị and ð40; 65ịsimultaneously, the frequency of the signals limited in 0.9 GHz–1.1 GHz.
The band is divided into 9 frequency bins, here the gain and phase errors are generated in [0, 0.5] and [20; 20] randomly respectively, 500 Monte-Carlo trials are repeated.
SNR is 6 dB, number of snapshots is 30, Figs.2 and 3 have shown gain and phase error estimation of different sensors at every frequency bin, whereith s-A means actual value ofith sensor, andith s-E means the corresponding estimation, we can see from Figs.2and3, GPW can estimate the gain and phase error of the array, especially when the frequency is near to the center point. As the center frequency corresponds to half of the wavelength, so it is more precise than the others.
5 Conclusion
A novel gain-phase error calculation approach in DOA estimation for mixed wideband signals is provided in this paper. First, the signals are transformed on the focusing frequency. Then peak searching is employed for determining the far-field sources.
1 2 3 4 5 6 7 8 9 10
0 0.1 0.2 0.3 0.4 0.5 0.6
Frequency bins
Gain error
-3th s-A -3th s-E -2th s-A -2th s-E -1th s-A -1th s-E 1th s-A 1th s-E 2th s-A 2th s-E 3th s-A 3th s-E
Fig. 2. Gain error estimation
1 2 3 4 5 6 7 8 9 10
-25 -20 -15 -10 -5 0 5 10 15 20 25
Frequency bins
Phase error /
-3th s-A -3th s-E -2th s-A -2th s-E -1th s-A -1th s-E 1th s-A 1th s-E 2th s-A 2th s-E 3th s-A 3th s-E
°
Fig. 3. Phase error estimation
Finally, Gain-phase error can be calculated according to the orthogonality of far-field signal subspace and noise subspace. However, it just applies to uniform linear array, we will be committed to study the technique for planar array in future.
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Comput. Harmon. Anal.38, 177–195 (2015)
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Estimation for Mixed Wideband Signals
Jiaqi Zhen(&), Yong Liu, and Yanchao Li College of Electronic Engineering, Heilongjiang University, Harbin 150080, China
zhenjiaqi2011@163.com
Abstract. With the electromagnetic frequency getting higher and higher, the distance between the sensors is becoming smaller and smaller, so the mutual coupling is increasingly obvious, it will lead to the mismatch between actual and ideal array manifold. Therefore, a novel mutual coupling error calculation approach in direction of arrival (DOA) estimation for mixed wideband signals is provided in this paper. First, the signals are transformed on the focusing fre- quency. Then root finding is employed for determining the far-field signals.
Finally, mutual coupling error can be calculated according to the orthogonality of far-field signal subspace and noise subspace.
Keywords: DOA estimationMutual couplingFar-field signals Near-field signalsWideband signals
1 Introduction
Direction of arrival (DOA) estimation has developed very rapidly in recent years [1–5], and many excellent algorithms has been proposed, such as multiple signal classification (MUSIC) [6], ESPRIT [7], maximum likelihood [8] and so on, all of them can achieve a high precision and resolution capability under ideal condition, but they are always not in common use due to the complex circumstance. One of the reasons is the mutual coupling effect in the array, it is the interference among sensors. Due to the unam- biguous demand for the array in direction of arrival (DOA) estimation, the interval of the adjacent sensor is often not allowed larger than half of the wavelength, which leads to the serious mutual coupling, then estimation result will deviate the actual direction, so we need to fundamentally resolve this kind of problem.
In recent years, mutual coupling error calculation has attracted many scholars.
Generally speaking, they can be classified into active calibration and passive
J. Zhen—This work was supported by the National Natural Science Foundation of China under Grant No. 61501176 and 61505050, University Nursing Program for Young Scholars with Creative Talents in Heilongjiang Province (UNPYSCT-2016017), China Postdoctoral Science Foundation (2014M561381), Heilongjiang Province Postdoctoral Foundation (LBH-Z14178), Heilongjiang Province Natural Science Foundation (F2015015), Outstanding Young Scientist Foundation of Heilongjiang University (JCL201504) and Special Research Funds for the Universities of Heilongjiang Province (HDRCCX-2016Z10).
©ICST Institute for Computer Sciences, Social Informatics and Telecommunications Engineering 2018 X. Gu et al. (Eds.): MLICOM 2017, Part I, LNICST 226, pp. 606–613, 2018.
https://doi.org/10.1007/978-3-319-73564-1_61