conventional RLS criterion we derive a new Recursive. Least Square (RLS) adaptive beainfonning algoritlun for antenna arrays applied in an OFDM system.
2002 grd International Conference on Microwave and Millimeter Wave Technology Proceedings
A New RLS-based Adaptive Beamforming Algorithm for Smart Antennas Applied to an OFDM System I
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Lc Minh Tuan. Pliam Van So. JCI\~OOKim and Giwm Yoon Eng.. Infonnation & Co~nmunica~ions UniveEih (ICU) SX-4. Hivaarn-dong. Yusoag-gu, Taejon -305-348. Korca letuan@:icu.ac.kr Tel.: i82-42-866-6201 Fax.: t82-42-8664227 2 TclcCIS. Inc.. 418 South Abbott A\uioc. Milpitas. CA 95129. U.S.A. I Scliool of
Abstract
In tlus paper, we consider an OFDM s!stem witli coclraiuiel iiiierrereiice aiid U i i use o r adaplive aiitelula arrays to suppress siich interference. Based on llie conventional RLS criterion we derive a new Recursive Least Square (RLS) adaptive beainfonning algoritlun for antenna arrays applied in an OFDM system. Computer siiiiulation slion-s tliat. n-lien applied to tlie OFDM system. the proposed algoritluii is capable of combating cochamiel interference in both AWGN channel and iiiultipath Rayleigh fading clwmiel with AWGN. 1. Introduction Futux wireless conuouiucatioii S~SICIIISnus st bc able accomiiiodate a liugc iiuinbcr of subscribcrs In olher words. Ihcy ~ioistnieel the dcmands for high dala rale and large capacity. Noiletlieless, inultipatli fading effects and coclianncl i~iterrere~icearc tlic main limi~a~ioiisfacing such systcms. Tlicreforc. finding approaclics lo ovcrcomc ~lieselimi~alioiisis or great importance. One possible solulioii for tlicse sgslcms to bc rcalizcd is to iisc Ortliogoiial Frcqiiency Division Moitiplexing (OF'DM) combined with adaptive anlenna anays. OFDM [I1421 lias proven to be a potential candidate Tor increasing bit rate and capacity iii xirelcss coiiiiii~~iiications. By using OFDM, baudnidlli efficiency can be acliie\ed. Furlhermore. it is one of Ilie most eKecti\e approaches for cornb;iling ~ntillipatlidekiy spread i n wireless coiiuiiunicalion systems. Aiiotlier key advantage of using OFDM is that Ilie modulation and demodulalioii cau be acliieved in the discrete-domain b!. using a discrete Fourier transform (DFT) 1.31. w-luch is efficiently impleiiiented by nsing Uie FFT. 11 is also nell krioa-n Ilia1 adaptive antenna arrays have been introduced in the literatiire for TDMA and CDMA systems lo improve Uie performances of such systems [4]-lS]. By using aiteium srravs. rapid dispersive fading can be mitigated and co-channel interference can be suppressed. therefore coimnimicahon capacity can be improved. More receiiUy. snlilfi aiteimas have been applied to OFDM systems 161-171. In 161. the autllois esplore the combinalioli of adapuve aiiteniws and OFDM
for operalion io a faded delay-spread channel. AnteMa array is also used 10 suppress delay signal aiid Dopplershifted signal in [7]. Ho\vever. doe to the nse of the inverse FFT (IFFT) and FFT processing in traiisiiiil~erarid receiver. respectively- new adaplive beainfoniiing techniques are required for the OFDM system. In this paper. we propose a new RLS adaptive algorilliiii for an OFDM system. In the proposed algorithm. a short training process first updates the weight veclor. Then a decision-directed lecliiiique is used Cor updating the weight i'ector. Both processes are performed in the time domain. Simolation results slioiv thal the proposed ;ilgoritlun is able to extract tlie desired signal n-Iiile it coinpresses other undesirable cocliannel interferers Tlius. the resiiltiiig system has a ven good performance.
IO
11. OFDM System with adaptive antenna array First. Ict us considcr tlic traiisiiiitfcr sidc of tlic OFDM s~sleiii.N molliplcsed s!iiibols in tlie rreqiiencv-doiinin are craiisformed iii llie time domaiii signal by tlic IFFT as rollon s: .\' I
1,:(n)e,"+ .
I=0.1_...: N - 1
m.i
(1)
i=o
whcrc ~ ! , , , , ~ (isn )the sxmbol of thc
nil"
iiscr carricd by
tlic k" subcarricr of the n"' block. .X,,,~~(E) is the I" tiine-domain sample of the n'" block. Equatioii ( I ) can be rewritten in the vector fonn as foll0\\.5: -I m
(2)
( n ) = -U, y (njFH(n)
wlrrc
rl
1
...
represems (lie FFT operation matrix H dcnotcs tlic Hcniutian trruispose.
0-7803-7486-X/02/$17.00 Q 2002 IEEE. 672
1
1
f,'(n)=A(B)X(n)+ (;(n)
I n order to updatc tlic mcight vector. in this papcr n e proposc a ncw RLS algoritliiii. Thc iiiaiii principlc of this criterion is that bcforc transiiiitting the infomiation bits (or infonoation signal), tlic wiglit vcctor of the array is updatcd by a iiuinbcr of blocks of pilot signal, which are knoivn by both transmitter and reccivcr. After traiiiing the weiglit vector of the amy. inforination signal is transmitted. In tlie receiver side. the iveiglil vcctor non is updated by blind nietliod. That is, pilot signal is no longer used. The rererelice signal used Tor updatiiig the \\-eight J' (n).at the output vector is thc received sigiwl vector. r6n
\VIlCrc.
of tlie decoder.
. ~ , , , ( i ~ ) = l . ~ , ~ ,x ~ ,,,, ( /]~()n )
... sn,,,,(n)Jis tile sigiwl
{'ecloror the in"' user iii tlie time doniain.
(II)=b, o b )
L L',,.
I,.
Y,,,,1 b ) '.. Y
,I,,
is
A.l(I7)l
tlx
corresponding signal wctor in the freqoeny domain. Now \ye consider the receiver side. Assume tlut there are iM sigiials iiiipingiiig at an m a y of K elenleiits and ilvai K >_ M . TIIC signal matrix. L.'(I~).rcci ed at tlie am\- antenna is reprcscntcd by:
I . Truiningperiod:
First, let 11sconsider the training period in the receiver side. I n this period only training signal is transinitled so as to train the weight vecLor of the army anlenim Note that_ in the freclueiic!-doiiiiiin. both the received pilot signal and the received infonniitioii signal are given by eqiiation ( 5 ) . In tlic time-domain. tlic pilot signal vcctor (n)
1
zp,,,
and the received pilot signal vector
E,,,>(.)ctin be found
from tbc corresponding frequency-domain pilot signal vector -p,, y ' (n) and the received pilot signal \-eclor
y" (nj as follows:
-pn,
i
.
.i Ly"'
Herc. A(0) is tlic array rcsponsc iiiatrix for A,l iisers and G(n) is tlic K by N inatrix of additiw white
Gaussian noises. '
The desired signal vector of tile in"' iiser. givcn by:
s;(n): is
( n ) = l ~ , . ~ ( n2p,,~,1(n) ) ... ~ ~ , . ~ . ~ ( n ) l (6) = y (nF"(f7) -Prn
and
-
",,(.)=
c/",,,(n)=L,.,(d ..' = V(nF(n)F"(n)
and T denotes the trmspose. Tbc nciglitcd signal vcctor .r,"( n ) is then converted into the Crequeiicydoinain. thus yielding:
- (n)=s,,( n ) F ( n ) = ~(n)v(n)F(n) :
(.)=
(5)
Tliis sigiial vcctor vi11 bc dccodcd to recover the original data froru tlic tnnsii~I!tcr. Lct us dcnotc the signal ' vector at the output of tlie decoder I y (?I) . -4"
(7)
U . 2 O 7 ) F ( 1 7 F H0 7 )
IVIICK. F(n) is the FFT opcntion matrix. Now let
wllere.
L,,,
Ep (.F"
(4
!Lp,,,A~.l(41
(4
(8)
I
11'
",,,,, = b 4 : ,,,,i u p!,,,,(n) ' U .( i =O,l, ,..,AJ-l Then the receivcd pilot signal vector in equation (7) can be rewitten as: ''
:;:j
-
xr,(4=W:(~,>",(n)
II (9) = k.,,.o(n) .-,E",.,(n) " ' ,E .: Based on the coiivenlional cost fnnctioti for RLS algorilluii 181, we propose a new cost rumion for tlie RLS beainfonning algoritliiii applied in ai OFDM system as m n s : ,/.
111. The proposed RLS algorithm
673
v.1(41
Here. A! is ilie ncmmber of s!~mbols per OFDM block or number of subcamcn in a block. e, ( k ) is tile difference beiween llic ~irne-doinainrefcreiice sigcuil s,,,~,~ ( k ) and (lie time-doriiain array oulpul
-sy,,,,,(k)attime i; .That is_ e,@) is defined by:
-The received infonuation signal ciratris U,,,( I ? ) no\\ replaces h e received pilot sigilrtl inatris UP*,, (H) ond:is still calculated by using equation (8). -Thc timc-domain rcfercncc signal is non- clcared J' ( ~ 7 )and is gi~eri by: froiii the decoder output -
