the popular antcnna array structures in DOA systcms are ULA and UCA vvith sim plc antenna elem ents, such as dipoles.. The accuracy o f DOA estimation in 360° range vvith ULA and UCA
Trang 4BÁO CÁO TỎNG HỢP
I Đ Ặ T V Á N Đ Ề
“N g h iê n c ứ u cá c p h ư ơ n g p lĩá p và th u ậ t to á n x á c đ ịn h h ư ớ n g s ó n g đến, s ử d ụ n g dàn a nten có cấ u tr ú c đặc biệt, ứ n g d ụ n g clio h ệ a n te n th ô n g m in h " là m ộ t t r o n g c á c
II TỎNG QUAN CÁC VẤN ĐÈ N G H IÊ N c ứ u CỦA ĐÈ TÀI
Đ e tài “N g h iê n c ứ u các p h ư ơ n g p h á p và th u ậ t toán x á c đ ịn h h ư ớ n g só n g đến,
s ử d ụ n g dàn a n ten có cấ u trú c đặc b iệt, ứ n g d ụ n g c h o h ệ crnten tlíô n g m in h " t ậ p t r u n e
Trang 124 Nhận xét
T r o n g c ù n g m ộ t m ô h ì n h a n t e n v à tí n h i ệ u :
- X é t v ê đ ộ c h í n h x á c : h a i t h u ậ t t o á n c ó đ ộ c h í n h x á c n h ư n h a u
- X é t v ề t h ờ i g i a n t h ự c h iệ n : t h ờ i g i a n tí n h t o á n c ù a t h u ậ t t o á n E S P R I T ít h ơ n m ộ t Iiửa ll iu ậ l l u á n PvíU SIC p ỉg o à i ỉ'à, ílìu â í ío á iì C S í^ ív ỉT c h o r ì £ s y k í t Cjuả c ủ a 4
n g u ồ n t í n h i ệ u c ò n t h u ậ t t o á n M U S I C p h ả i c ó q u á t r ì n h t ì m c á c đ i ể m c ự c đ ạ i t r o n e
p h ổ k h ô n g g i a n V ì v ậ y , x é t t ổ n g t h ể t h u ậ t t o á n E S P R I T s ẽ c h o t h ờ i £ Ìa n t í n h t o á n
ít h ơ n n h i ề u v à t h e o đ ú n g ti ê u c h í c ủ a tá c e i ả t h u ậ t t o á n n h à m k h á c p h ụ c v ấ n đ ề
th ờ i g i a n tí n h t o á n t r o n g M Ư S I C
Trang 13T huật to án M US1C trong U C A vẫn đ ư ợc uiữ n g u v ẽ n n h ư đồi với U L A
II M Ô P H Ỏ N G T H U Ậ T T O Á N M U S IC VỚI DÀ N A N T E N ULA VẢ l CA
Trang 15b H ạ n cliế c ù a th u ậ t to á n M U S I C k lìi áp d ụ n g với (iíìn n n te n ƯLA và ƯCA
- Đ ổ i v ớ i c ấ u t r ú c U L A v à U C A k h i c h o s ố p h ầ n t ử a n t e n n h ỏ h a n s ố n g u ồ n tín
h iệ u d ế n thì v i ệ c m ô p h ỏ n e k h ô n e th e t h ự c h i ệ n đ ư ợ c d o t r o n g t h u ậ t to á n M U S I C
s ự p h â n t á c h e i ữ a k h ô n s s i a n c o n c ù a tín h i ệ u v à n h i ề u p h â n b iệ t bơi c á c 2ÍÚ trị
r i ê n g c ủ a m a t r ậ n h i ệ p p h ư ơ n g sai lối v à o ( m ụ c 1.2) V à vì v ậ y t h e o t h u ậ t to á n n ; n thì s ổ g i á trị r i ê n g ứ n g v ớ i k h ô n e e i a n tín h i ệ u p h ả i n h ò h ơ n s ố p h ầ n từ a n t e n tr o n u
m à n g N ó i c á c h k h á c , s ố n g u ồ n tín h i ệ u p h á t h i ệ n đ ư ợ c bị h ạ n c h ế b ờ i s ổ p h ầ n tử
a n t e n t r o n g i n ả n e
Trang 21MUSIC UCA + nonlinear W P A DOA - degree
H ìn h 11 - P h ổ k h ô n g g i a n c ủ a d à n U C A v ớ i m ỗ i p h ầ n t ử là m ộ t h ệ a n t e n p h a p h i t u y ê n
t r o n a t r ư ờ n g h ợ p 2 7 n a u ô n tí n h i ệ u đ ê n
Kết luận: N h ư v ậ y , v ớ i c ấ u tr ú c m ớ i - d à n U C A v ớ i m ỗ i p h ầ n t ư a n t e n là m ộ t h ệ a n l e n
p h a p h i t u y ế n , c ó th ể x á c đ ị n h c h í n h x á c c á c n g u ồ n tín h i ệ u đ ế n c à t r o n e t r ư ờ n g h ợ p so
Trang 23X I T À I L I Ệ U T H A M K H Ả O
1 T à i liệu T i ế n g V i ệ t
[1] P h a n A n h , L ý th u yết và K ỹ thuật a n te n, N X B K h o a h ọ c v à K ỹ t h u ậ t
2 T à i liệu T i ế n g A n h
[2] R i c h a r d R o y a n d T h o m a s K a i l a t h , E S P R IT - E stim a tio n o f S ig n a ì P aram eters Via
R otational In va ria n ce Techniques I E E E T r a n s a c t i o n s o n A c o u s t i c s S p e e c h a n d S i e n a l
P r o c e s s i n g , V o l 3 7 N o 7, J u l y 1 9 8 9
[3] H a m i d K r i m a n d M a t s V i b e r g , Two D ecades o f A rra y S ig n a l P ro cessin g R esearch
I E E E S i g n a l P r o c e s s i n g M a g a z i n e , J u l y 1 9 9 6 , p p 6 7 - 9 4
[4] J o s e p h C L i b e r t i , J r & T h e o d o r e S R a p p a p o r t , Sm art A n ten n a f o r ÌVire/es.s
C om m unications IS-95 a n d T hird G eneration CD M A A p p lic a tio n s, P r e n t i c a l H a ll.
Trang 243 K h ó a lu ậ n t ô t n g h i ệ p n ă m 2 0 1 0 : "N ghiên cứu, m ô p h ỏ n g ảnh h ư ờ n g ạhép ttivn g
hô g iữ a các p h á n tử anten đến kết quả p h ô M U S IC trong dàn an ten ULA
4 K h ó a lu ậ n t ố t n g h i ệ p n ă m 2 0 1 0 : '‘N ghiên cứu, m ô p h ỏ n g ảnh h ư ớ n g g h ép Iưưng
hô g iữ a các p h ầ n từ anten đến kết quà p h ô M U S IC trong dàn an ten UCA
5 K h ó a l u ậ n tố t n g h i ệ p n ă m 2 0 1 0 : "Tlĩiết kế đ ầ u thu p h ụ c vụ cho úu% d ụng DOA tân sổ hoạt độn g 915 M H z
25
Trang 252 0 1 0 In tern a tio n a l C on feren ce on
C om putational In tellig en ce an d V eh icu lar
Trang 262010 International Conference on Computational Intelligence and Vehicular System Proceedings
Trang 27Direction-Of-Arrival Estimation using Special Phase Pattem Antenna Elements in Uniíbrm C ircular Array*
tm tuanW m ic.go\ vn
A b s tr a c t - A t h í o r y m o d e l in w h ic h U n iío r m C ir c u la r A r r a y
(U C A ) u sin g s p e c ia l a n te n n a c le m e n ts Cor D ir e c tio n o f A r r iv a l
(D O A ) e s tim a tio n is p r e s e n le d S im u la tio n r e s u lts sh o w th at
DOA estimation is very importanl in smart antcnna
dcsigning and direction íìnding In most o f thc research papers
and real systems the popular antcnna array structures in DOA
systcms are ULA and UCA vvith sim plc antenna elem ents, such
as dipoles.
The accuracy o f DOA estimation in 360° range vvith ULA
and UCA structures is usually dcpendent on the numbcr o f
elements in array and elem ents arrangement The niore element
numbcr is largc, the more accuracy is higli With UCA
structure, unique disadvantage is: the algorithm can not detect
sourccs if the number o f antenna elem enls is not large enough
(smaller or little larger than the number ofin cident sources).
To increases accuracy and overcom es thc disadvantagc in
DOA cstimalion using UCA \vith traditional elem ents, vve
introducc a theorv m odel using ncw antcnna element structure
for UCA It will be dcscribcd in next scctions in details.
!n this papcr, \ve used well-kno\vn Multiple Signal
Classiíìcation (M U SIC ) algorithm [1] to estimatc DOA for
UCA in traditional elem cnts case and proposed elem ents casc
Afìer thai, dilĩerent spatial spectrum results o f these structures
vvill bc comparcd and discussed.
The paper is organizcd as follow s Section II presents an
overvievv description o f system proposed elem ent structure
and detailcd data modcl analysis Simulation results and
discussion arc givcn in section III Section IV is a short
conclusion MUS1C algorithm is given in Appendix in detail.
II S y s te m D e s c r ip t io n , T h e o r y M o d e l o f pROPOsnD
A n t e n n a A r r a y S t r u c t u r e a n d D a t a M o d e l
A O ve rvie w System D escriplion
Fig 1 shovvs the m odel o f DOA estim ation system \vith general antenna array structure
The system has tu o parts: Data Acquiremcnt part and
Signal Processing & Displa> part The former includes
antenna arra> RF-IF convcrtcr and A D C The laler includes MUSIC alcorithm and result displav.
tì Theory m o d eí o f P ro p o se d Antenna E lem ent j o r UCA
M odel and phase paticrn o f a tradilional elem ent (dipolc)
is shovved in Fig 2.
This vvork IS supporĩcd b> UET, VNUM Tlic conlcnt o f llus vvork \vas parllv snpp<irted b> the rescarch project ọ c 0 ’ 2 ! and o c 08 ] 5
Trang 28(a) <b)
where: d| is the distance betvveen 1-1 and 1-2 dipoles and d2 is
the distance betAveen II-1 and 11-2 dipoles.
11-2 Dipolc
am p/pltase excilalioii
dl d2 1/90“ 1/270" 1/0" 1/180" 0 5 \
vvhere \ is the operation vvavelength.
With parameters in Table 1 the special phase paltern is
presenled in Fig.4
Compare with traditional elenient, proposed elem ent has
phase pattern is very speciallv difĩerent from traditional
element It has nonlinear form and can be expressed by [2]:
Fig 2 M odcl (a) and phase patlem fb) o f tradilional element
According to [2], special phase patterns can be created by
dipoles com bine One o f them is show ed in Fig 3
Fig 4 Phasc Patlem o f the Proposed Elcmcni
c UCA w ith P ro p o se d Elem enls
Proposed antenna elem cnt u h ich includes 4 dipoles in Fig.3 can be considcred as one elem ent vvith phase pattcrn likes in Fig.4.
Then UCA wi(h proposed elem ents is shovvn in p'ig.5.
\ I' \ I
ĩ : : I
F(g 5 UCA vviilt 6 Proposcd Anlcnna Eleincnis
where R is the radius o f circular.
D D a ta m o d e l A nalvsis
A ssutne lliat am plilude pattern o f each proposed elcm enl
is constant; the number o í clem ents in UCA is N Data motlel can be dcscribed as Ibllous:
The antenna arrav reccives signals from L narrouhand sources, w hich are randomly distributed in the xv-plane in ihe far lleld o f antcnna arra\ Phase patlem s o f proposed elem ents are rotated step b> step by electricallv control systcrn íiach step is considcred as N elem ents in general antcnna arrav Ị hc
arrav steerinc vector o f 0 direction is expressed as:
a ( 0 ) = [ a , ( ơ ) a ,((? ) ÁO )] ( 2 )
\vhere
Trang 29where u„ is the matrix vvhich includes eigenvectors o f noise
subspace Orthogonality betxveen steering vectors and l ’n will
minimize the denom inator o f (5 ) and hence it vvill make up
peaks in MUS1C spectrum T hcse peaks \vill correspond to thc
DOAs o f the sources [3].
I I I S ỉM U L A T IO N R E S U L T S a n d D lS C U SS IO N
The sim ulation is carricd out for U C A with traditional
elements and U CA vvith proposed elem cnts over 1000
snapshots Arter that, perlòrm ance o f M U SIC algorithm using
thcse anlenna array structures vviỉl bc compared eaclì other
Some discussion w ill be prcsented at the end o f this section.
A Simulalion R esu ỉls
Simulation Parameters are dcscribed in table 2.
Fig 6 illustrates the spatial spcctrum for UCA \vitlì
traditional elem ents and U C A vviih proposcd elem ents As
shown, the former estim ated 16 peaks \vith ỉ desired peak 15
undesired peaks and all pcaks are not Sharp Meamvhilc, the
latlcr eslim ated 24 dcsircd pcaks vvith 5° resolution and íill
peaks are Sharp.
M-l is the number o f rotated steps, A 0 is rotated angle.
The acquired data after ( M - l) ,h step is given by:
x ( 0 = Ị a ( ớ , ) s , ( r ) + n ( r ) (3)
/«/
vvhere s ( / ) is source at 6 direclion vvhich is assumed that
uncorrelated with the others, n ( / ) is noise vector which is
modeled as tem porally A dd ilive White Gaussian N oise
(AWGN).
Aíìer that M U SIC algorithm is used to estim ate D O A s as
follows:
The covariance matrix o f X (tcmporaỉ averaging over K
snapshots) [4] is gi ven by:
ỉ K.7
vvhere (.) denotes con ip lcx con ịugate transpose.
The idea o f M US1C algorithm bases on eigenvectors and
eigenvalues o f R : the eigen vectors corrcsponding to (he
smallest eigenvalues form the noise subspace and also
orthogonal to the steering vectors [3] Thereíore MUSIC
spatial spectrum is expressed as:
24 elcm ents = 24 dipoles
() elcm ents - 24 dipolcs (R olaicd Stcp num ber
B D iscussion
A ccordine to introduction section MUSIC nlgorithm using UCA u ith proposed elem cnts can eslim ate DOAs in spatial spectrum cxactl) allhoueh thc nunibcr ol inuilcni sources is approxiinate or larger than the number o f anlcnn.i elem ents The sim ulation result in Fig 6 i11 Iistrated this idea The reason o f the results can be explaincd as follows: Theorv D O A estim ation o f proposed structure is similar to
U CA with traditional elcm ents To incrcasc accurac\ and can dctcct sources in ca.sc the number o f antenna clcm cnts is not large enough the proposcd melhotl madc inerease thc nunihci
Trang 30Each phase pattern rotated slep o f proposed elem ents is
corresponding to making up N traditional elem ents in UCA
Thereíòre, after M -l rotated sleps, proposed structure makes
up MxN elem ents.
A limitation o f this D O A method is amplitude pattern o f
proposed elem ent has not been considered in detail yet (In
II.D part, w e assum ed that it is constant).
However UCA using nonlinear phase pattern antenna
elements still has meaning in looking for a DOA estim ation
method vvhich has the number and accuracy o f DOA peaks in
spatial spectrum do not depend on the number o f real antenna
elements
I V C O N C L U S IO N
DOA estim ation algorithm (M U SIC ) using UCA with
new antenna elem ent struclure vvas investigated and compared
with tradilional UCA structure Investigation results assert
once again that: proposed antenna structure can be used to
estimate D O A s exactly in case the number o f antenna
elements is not large enough In the future vvork w e will
consider impact o f am plitude pattern on accuracy o f DOA
spectrum and look for a real antenna elem ent niodel \vhich has
the most optimal am plitude and phase pattern.
A p p e n d ix
A MUSIC algorithm wilh g e n e ra l antenna m o d e ì [ 5 ]
Assume that: in 2D spatial coordinates, there is a
narrowband signal im pinges on the l,h antenna elem ent like in
Fig 7.
Fig 1 General anlenna model
The output is m odeled by:
■'(')+"(') (6)
= a(e)s(t)+n{t)
vvith g ,(0) is radiation pattern o f /lh antenna elem ent.
If M signals inipinge on L sensors in the presence o f an
additive noise n (/) and assum e that 5,(0) is constant then the
outputs o f antenna elem ents are:
x ( / ) = A ( 0 ) s ( í ) + n ( í ) 0 )
\vhere:
x ( / ) = Ị í , ( í ) , r ( / ) v , ( / ) ] 7 is s i c n a l \ c c l o r a t a n t e n n a
A (0) — [ a (0( ) a(0 ) a (0Ay )] i s steering malrix
a (0) = [ a , ( e ) « , ( e ) a , (0)] is steering vector
« Í Ạ Ì = Ị c M c M V í / V Ị 7 ic c n i t r r e v ^ r l n r
n (r ) = [ í i ,0) is noise vector
MUSIC algorithm is exprcssed as lollovvs:
S t c p l: Calculate Spatial Covariance Matrix
R = E { x ( /) x " ( /) Ị = A e | s ( / ) s " ( /) Ị a " + e | h (/) ii (/)
= A P A t o i vvith
e Ị s ( / > " ( 0 Ị = p
E {n (/ )n " (/ ) } = ơ’1
( 8 )
<‘M( 1 0 )
Stcp2: D ecom position Spatial Covariance Matri\
R = A P A " + ơ 1 = U A U " ( I I ) with u is unitarv and A = d i a ẹ ị x X X , ) vvhich
X, > l : >0.
Depend on eigenvalues with X , > x , > > > ơ .
~ - ơ ' we can partilion thc
eigenvalue/eigenveclor pairs into signal and noi se subspaces
So w e can vvrite (11) into:
R = U A l ) ; + U A u " (12) From ( I I ) and (12) w c have:
R = A P A " + ơ 1 = U ,A ,U " + U f ơ ; U " (13) From (13) i I APA" is luII rank then eigcnveetors l in noise subspace are orthogonal to A So vve can \vritc:
vvilh 0 6 1 0 0 , 0 Af Ị
(15) Step3: Calculatc MUSIC spatial spcctrum
p | 0 ) = ^ Ì L
^ a"( 0) U„U>( G)
R N I KI N ( l:S
[ 11 R o Sclimidl " M u l u p k ’ 1‘I>IIIII'I h n a i n / n (111,1 M iỊ n a l p i i n i m c h r
cMimaiion llilĩi: Trans Anlennas and propagation vol AP-34 pp 271-
280 M ar 1986
[2 ] Phan A n h A n tn n n o m llio u l r i n n ư ( ự ìtic r a n d I h s i r III
Raiiiu ĩinịỉtnccrinự S enes M onograpli No 2? W rocl;m Poland IVM
ISSN 0324-9328
(3J Liu Jin Li li Hn.T7.hi NVang, "InvcMiịỉdlinn of D it/crenu’ 11/V» nf Arr,i\
S in u iurcs fo r Smari Antennas ", P roceedm gs o f ICMMT 2008
(4] Joseph c Libcrti Jr Ẵ; Theodore s R appapon Sntori Ânn-nna t(ir IVirelcxs Comnuimcalions I.S-95 ơnd Third Cmneratmn CI)MA
A p p lica iio m , Prentice Hall PTR
Ị5 ] Ham id Kri 111 and Mnls V iberg ' l u n lìeta d e* <<f Arra\ Siựnal
Proiưsuiìỉỉ IE1ÌÍÌ Siunal Pmccs^mi! \1aiM7.inc Julv 19% pp