13-SEP-2001 1s:4~
`
`I-RA
`
`CE:.NTER FOR PERSONKOMM.
`
`Tll 0014048947883
`
`5.02/04
`
`.. -
`
`Georgia Tech Research Corporation
`Office of Technology Licensing
`Georgia Institute of Tec:hnology
`
`Confidentf1l and Proprietary
`f nvention Disclosure
`
`Title of lnv•ntion: Efficient Training and Synchronization Sequonee
`StructurOJ for MIMO OFOM
`
`Short Titlo: Sequence structure design for MIMO OFDM Systems. - - - - - - - - - -
`
`2
`
`l
`
`Inventors (Ple~H in,lude •II inventors: Use additional sheets as neccu:uy}
`~ull H•mo ADlll'Vll Narendra Moctv
`FvllN•- Gordon Lothar Stutrer
`Graduato Rasearcn AU1&111111
`Prolenor
`Tlli-
`71t1'1
`··-
`llt111 "..i MC ECE 2Sil
`0"!'1 >tld MC !!CE 0250
`11111dl119.AooGCATT. RM 549
`luild1no,lh1~.~TI. RM 51!0
`OlllCo I',,.... 404-81ii4-292:J
`o"""' ""°"'404·a94-e370
`"'"
`404-894-1&83
`F ..
`a11urva@ece.oalacn.ee1u
`em•ll
`Cillzanshljl
`Ha .... Mdnl.32715$ Gemota Teen Slallon
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`404-894-7883
`$1tlbertmecs.aatech.6du
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`4
`
`Did ltlis ln¥P.ntion result from sponsoroct research? Jr so, pl•;aH giv• detaifi;,
`
`Sponsor. Yamactaw
`Sponsor: ______ _
`
`G.I. T. Project Number:
`G.t.T. Project Number:
`
`E:-21-105;21021
`
`W;is thls project ec:mduetc:d thrQl.lg" or assoe;iated with a Georgia Tech Center?
`If YES, liat nilfne of Center
`..;;G;;.;C:;.A-.TT ________ _
`YH
`ll
`No
`
`s
`
`Has tho Invention been disclosed in an abstract. paper, ~lk. projGct report or thea1s?
`
`YES
`
`NO X
`
`----
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`QlscloHrc Date:
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`Typo of Olsclos11teConte1once_P_a .. !)e_r - - - - - - - - - - - - - - - - - - - - - -
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`6
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`Is a publicallori or othlilt dlselosure planned within 6 months? YES: JC.
`NO:
`T)'P9 of dl5cfosu1'll:
`Dis.c:lo.s1.1r1t Da«r:?reaentatian due 1()119/Z
`-c;;;;;ence F'aper
`q/ t<$/01
`
`ERIC-1035
`Ericsson v. IV, IPR2014-01185
`Page 1 of 10
`
`

`
`TIL 001404894'7883
`
`T
`
`Brief de$criptlon of the: invention (attach more detailed deterlptlon)!
`T~ iffll!N'll\on presentt tralniM seguenc:. atructures wtiic;h also hrle a1 aym:tiron!Zation aegllttlc• stnic:turu IOf
`MIMO OFOM SVSi.tft11;. We p1t1$11m :i technique by which Ille fnltlamia!li()ll ""'"''"' for o.1Ch ~ ia
`made urntary. tien<:e 1at1sCy1119 ll'ltl MMSi lllltlrtcn IOI the Ct'ISl'lf! chollnnel atimallfS. A IGQl'l:fl II ean1ad out ror
`&lrucl\ll'll with the laweS.t p• to ulr!r!qtl povm! l'illlOI. For sy!IMms ornpJcyr!i 2. 4. and 8 ll'iln:mut anlennas,
`optimal ~eguence ilrvc1111u are obtairulcl.
`
`8
`
`!i
`
`Po.s the dncrlptlon provided above en~le one sldlled In this ar&a ot technology to make
`NO:
`and use the inV11ntlon?
`YES:
`X
`If not, pleue ellplilin.
`
`tfave you dl&Closed the best mode- known to you at !Ins tlrrl& of e:mylng out your invention?
`If not. pleuo ezplain:
`YES:
`X
`NO·
`
`10
`
`Date of conception:
`
`8126/01
`
`11 Hu the invenllon be<1n 1'9ducc:d to a<;tual proichc;e (I.it., h~11 pfOduc:ts, apparaws or compoiltions,
`5/21'ilQ1
`elc. xtually been m.ade •nd tested?)
`YES:
`X
`NO:
`lfYES, Wilt• of reductlun to practice:
`Being lll'lolemented io a softwaro cad!o iel up
`
`12
`
`13
`
`14
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`1S
`
`Doe.s the 1rw11n!lon appear to IUIS5 the following 1HIS for patanr::ibility~
`No¥elty; Yn
`Useftdnau;
`Non-Obviousness:
`Ye;
`
`Has a patent or literature- search been und«taken?
`
`Are related pat11nt11 or other publlc:itions known to you?
`(II f""' pl•U• ac:t•cft ll•IJ
`
`ves:
`
`Y~S;
`
`NO:
`
`NO:
`
`/111 taboratory records and data aw:rilabl•7
`
`Y!S~
`
`x
`
`NO:
`
`"
`
`1e What ant the lmmodlat~ and/or future appl1c1ucma for the invention?
`The a!g.Orilhm can be used lo form ~J!.alning and synchronization seguQl'lce !ltructura 1n all the
`current and future wireless systoms I.hat employ MIMO OFDM
`
`1a
`
`Ant 1her& any !imitations to bl overcome poor to practical .11pplic1tion?
`No
`
`tll
`
`10
`
`1& work on the: ln¥11'ntion continuing?
`
`YES:
`
`)(
`
`NO:
`
`C>o you know of any appropriate 1ndus1r1a1 orgamz3llOM wl"ticl'I may 1:1• Interested in licensing
`this tecnnelogy7
`
`ERIC-1035
`Page 2 of 10
`
`

`
`13-SEP-.:::Wl
`
`1!::1•44
`
`Le.NII:.!< I-~ l"'tRSONKDMM.
`
`Ill 001404894?883
`
`5.04/04
`
`Compaf1y Name: WI-Lan Inc.
`Company Name:
`Company H;ame:
`Comp41ny Name:
`Company Name:
`PIHH ttt.tCh lddl-1 olwOl If....,, •po•• lt f"CIUlnnl
`
`Broadcorn Inc:.
`
`Cont1et: _________ _
`
`Contact:---------(cid:173)
`Contact:---------(cid:173)
`ContKt: - - - - - - - - - (cid:173)
`Conmt: - - - - - - - - - -
`
`Execution by lnventor(s}.
`
`I/We rnventor(1) hereby solemnly sw.ar and affirm under oattt that I/We am/arc: lhe only inventor(&)
`of th•& invention and tnat IJwo !lave not knowingly omitted the lnc:lu:sc1on ot any other lnventor(s)
`bt'sidu me/ull. and that the informatic:in provided In this dili.:losure is, to the best of my/our
`knowtlld;o, true ~d 1ccur1te.
`
`;1, ~~ L~~
`r
`
`r
`
`I
`
`g:::
`
`Oale
`Datt
`Datt
`
`Execution by Witnesses
`
`Date:
`
`1/11/zc-ei
`
`j
`
`This :nvention was dlsclo5ed and expl;lned to me by the invanl0f{$) whose s19nature{s) apprears
`above on Lh• l ' day of
`t:.x_ f i.
`, 20 [; f-
`-:; h ·;;?~
`7 - ~IUAOIWlln•u
`
`/
`Thi5 i11vention wu dlsclOlilild and ••Plained to 1'1'111 b)! tne lnventor(5) whose s19n.:lture(s) appro:irs
`. zo o!i
`llbovun t1'11 /G day ot Se,,;t-
`
`Date:
`
`Return tnl:i; form {wilb •ny .ntac:luMnta) to lb• Offlco of T.eMololJy ~1eens•n11,
`GTRC, C•ntennllll Ftehatcll au1l1Slng, Room 275, 400 Tenth StrHl Atlanta, QA 30332·0415.
`If you hav• any queatlllJlt. ?le•H call (404) 89'-6287.
`
`ANTAL 5.04
`
`ERIC-1035
`Page 3 of 10
`
`

`
`Efficient Training and Synchronization Sequence
`Structures for MIMO OFDM
`
`Apurva N. Mody1 and Gordon L. Stilber1•2
`1 School of Electrical and Computer Engineering
`Georgia Institute of Technology
`Atlanta, GA 30332
`2 Wi-LAN, Wireless Data Communications Inc., Atlanta, GA, USA
`stuber@ece.gatech.edu
`
`In this invention we present a general
`Abstract-
`method of forming efficient sequence structures which
`can be used for parameter estimation as well as synchro(cid:173)
`nization. As a specific example we fabricate a struc(cid:173)
`ture using directly modulatable orthogonal polyphase se(cid:173)
`quences. We presente a technique by which the transmis(cid:173)
`sion matrices for each subcarrier is made unitary hence
`satisfying the MMSE criterion for channel estimation. A
`search was then carried out for structures with lowest
`peak to average power ratios. For systems employing 2
`transmit antennas, Alamouti' s structure and the simpli(cid:173)
`fied orthogonal structure are found to be optimal. The
`simplified structure obtained from orthogonal design is
`also optimal for systems employing 4 and 8 transmit an(cid:173)
`tennas. For systems employing 3 transmit antennas, cir(cid:173)
`culant structure is the most suitable.
`
`I. INTRODUCTION
`
`synchronization signal must have a low Peak to Aver(cid:173)
`age Power Ratio (PAPR).
`In the IEEE 802.lla Standard [I] synchronization
`and training sequence consists of a short sequence fol(cid:173)
`lowed by a long sequence. The short sequence is used
`for time synchronization and coarse frequency off set es(cid:173)
`timation whereas the long sequnce is used for fine fre(cid:173)
`quency off set and channel estimation. This sequence is
`not designed for use in MIMO OFDM systems.
`In this paper we will be using the words "train(cid:173)
`ing" and "synchronization" sequence interchangeably
`since we propose an efficient sequence structure that
`can be used for both synchronization as well as train(cid:173)
`ing. We propose to use directly modulatable orthogonal
`polyphase sequences to form the MIMO synchroniza(cid:173)
`tion sequence. The sequence structure is modified such
`that it is also suitable for MIMO parameter estimation.
`
`Orthogonal Frequency Division Multiplexing (OFDM)
`has become popular for wireless communications [1].
`A multicarrier system can be efficiently implemented
`in discrete time using Inverse Discrete Fourier Trans(cid:173)
`form (IDFT) to act as a modulator. The actual data to be
`transmitted, now reperesent "frequency" domain coeffi(cid:173)
`cients of the signal and the samples at the output of the
`IDFT stage are in the "time" domain.
`In this paper we present efficient training and syn(cid:173)
`chronization sequence structures for Multi Input Multi
`Output (MIMO) OFDM systems. For OFDM systems
`synchronization must be carried out both in time and
`frequency. In addition, OFDM systems require parame(cid:173)
`ter estimation of the channel and the noise variance. Pa(cid:173)
`rameter estimation is normally carried out using a suit(cid:173)
`able training sequence. An efficient sequence structure
`must be suitable for synchronization as well as param(cid:173)
`eter estimation. Additionally for OFDM systems the
`
`The authors wish to thank the Yamacraw initiative, of the State
`of Georgia, U. S. A. http:/lwww.yamacraw.org for supporting this
`research.
`
`II.ANALYSIS
`
`A block of N samples at the output of the OFDM
`modulator represents an OFDM symbol and the net time
`required to transmit one symbol is called the symbol
`time, Ts. Later, a cyclic prefix consisting of the last G
`samples of the output of the IDFT block are inserted in
`front of the OFDM symbol samples. The time length
`of the cyclic prefix should be greater than the maxi(cid:173)
`mum length of the channel impulse response. The main
`function of the cyclic prefix is to guard the OFDM sym(cid:173)
`bol against Inter Symbol Interference (ISi), hence, this
`cyclic prefix is called the guard interval of the OFDM
`symbol and has a time duration T9 • The samples are
`then applied to a pair of balanced D/ A converters, and
`the analog I and Q signals are later upconverted to RF.
`The OFDM signal is transmitted over the channel, re(cid:173)
`ceived and downconverted to base band. The guard in(cid:173)
`terval is removed from the received discretized down(cid:173)
`converted signal and the signal is demodulated using a
`Discrete Fourier Transform (DFT) on a block of N sam-
`
`1
`
`ERIC-1035
`Page 4 of 10
`
`

`
`pies. In this paper, samples in the frequency domain are
`represented by Capital alphabet and those in the time
`domain are expressed using small alphabet.
`The general transmission format for a Q x L space(cid:173)
`time system is shown in Fig. 1. Such a space-time sys(cid:173)
`tem consists of Q Antennas at the transmitter and L
`Antennas at the receiver separated from each other in
`such a manner that the received signals have a mini(cid:173)
`mum correlation. A system employing such a scheme
`can provide a diversity of the order of Q x L. Let
`
`s,
`Sa.,
`
`s,
`• • • .. .. • .. • .. • • . •
`
`So.,,
`
`S20
`
`t+T.
`
`s.
`
`The time period T9 corresponds to the transmission of G
`samples. Often it is a good practice to double the length
`of the guard time in the training period [lJ. This helps in
`synchronization, frequency offset estimation and equal(cid:173)
`ization for channel shortening in case that the length of
`the channel exceeds the length of the guard time. An
`IDFT/ DPT pair is used as the OFDM modulator/ de(cid:173)
`modulator. The N point IDFT output sequence for the
`qth OFDM symbol is given by
`
`Sq,n = . f"f:j L Sq,kexp j]:[
`1 N-l
`{ 2rmk}
`
`0 Sn SN - Xl)
`
`TFOM
`
`Mod
`
`Mo<t
`
`t+(Q-1)T,
`
`rFOM
`
`Mod
`..............
`
`T TFOM
`I I .I
`
`_I ha.
`
`-...:·a
`I
`--J
`
`Q M-l
`
`i=l m=O
`
`(2)
`
`V 1V k=O
`where { Sq,k}f,:01 is the transmitted data sequence from
`l)Q + c
`the ith transmit Antenna such that q = (i -
`where 1 s c S Q. The signal is then sent over the
`channel. The notation for the received signals vectors
`for the time instants (t, t+ Ts, ... , t+ ( Q-1 )Ts) are (z:1,
`2:2• · ·., Z:Q)T, ... , ('.LQ·(l-1)+1• Z.:Q·(l-1)+2• · ·., fQ.zf ,. .. ,
`(Z.:(L-l)·Q+l• Z.:(L-l)·Q+2' .. ., 'fQLf for the Antennas
`1, 2, .. ., L. The received sample sequence after the re(cid:173)
`moval of the guard interval for the ( vT8 ) th training slot
`is
`rz,n = L L hiJ,m,v(N+G)+nsi,(n-m)N + W[,n
`
`~ ~ ~ Oemod
`
`0 -
`
`R,
`Ri
`
`R,
`
`R,
`
`Rt,k
`
`R20
`
`• • • • • • • • • • • • • · • • •
`
`Rex.
`
`t+(Q..1)T,
`
`Fig. 1. Block diagram of a system with Q x L transmit(cid:173)
`receive diversity
`
`···~
`
`.5'.n=(transmitted OFDM symbol), 77. =(vector of chan-
`-iJ
`nel coefficients in the frequency domain between the ith
`transmit and the jth receive antenna) and Ri=(the re(cid:173)
`ceived demodulated OFDM symbol). Pilots in the form
`of known OFDM symbols are sent for at least Q sym(cid:173)
`bol periods ( QTs) in order to obtain a unique solution
`for the channel coefficient estimates. If the pilots are
`sent for more than Q symbol periods then we would
`obtain a Least Squares (LS) solution at an expense of
`a larger overhead. The OFDM symbol period is given
`by Ts = NT+ T9 where 1/T is the sample rate into
`the OFDM modulator (bit rate for BPSK modulation).
`
`2
`
`where hiJ,m,v(N+G)+n is the channel impulse response
`at lag m and instant v(N + G) + n and l can be ex(cid:173)
`pressed as l = (j - l)Q + d for 1 S d S Q. The Wt,n
`are complex additive white Gaussian noise samples with
`1
`variance No. The received sample sequence {rz,n};;',:0
`is demodulated as [2]
`
`DFT{q}(k)
`Q
`= L Si,k'T/ij,k + Wt,k·
`
`(3)
`
`(4)
`
`i=l
`Hence the received demodulated OFDM sample matrix
`Rk of dimension ( Q x L) for the kth subcarrier can be
`expressed in terms of the transmitted sample matrix S k
`of dimension ( Q x Q), the channel coefficient matrix T/ k
`of dimension ( Q x L) and the additive white Gaussian
`noise matrix Wk of dimension ( Q x L) as
`Rk,QxL = sk,QxQ. T/k,QxL + Wk,QxL
`(5)
`R, T/ and W can either be seen as N, Q x L dimensional
`matrices or as Q x L length-N vectors.
`The total energy emenated from the Q transmit an(cid:173)
`tennas is restricted to unity [2] such that,
`
`E {~ l•,,nl 2
`
`}
`
`I
`
`n
`
`0, 1, 2,. .. , N.
`
`(6)
`
`ERIC-1035
`Page 5 of 10
`
`

`
`where 1 :::; i:::; Q, 1 :::; j:::; L.
`The Q x L length-N vectors {9i,j,m};;;:;;;;6 are then
`passed through a rectangular window such that
`
`Ji.. _ { 9i,j,m 0:::; m:::; (G - 1)
`m;::: G
`0
`i,3,m -
`
`(9)
`
`The time domain fine channel estimates hi 1· m are
`',
`then converted using FFT to fine channel estimates
`{ili,j,k}f~1 in the frequency domain such that
`
`-i,J
`
`ij . = FFTN{lii,J} 1 ::::; i:::; Q, 1:::; j ~ L
`'T1 + w .
`=
`(10)
`
`:.Li,J
`
`-i,J
`
`R,•
`
`Fig. 2. 3-D representation of the matrix R
`
`This means that the energy allocated to the symbols for
`each of the transmit antennas is reduced by a factor of
`Q. This can be advantageous since cheaper, smaller
`and less linear power amplifiers can be used in the sys(cid:173)
`tem [2].
`
`Because of the windowing operation, the noise variance
`in the fine channel estimates is reduced to No ¥t- In [2]
`we also discuss the noise variance estimation for MIMO
`OFDM systems however we do not include that over
`here.
`
`III.EFFICIENT SEQUENCE STRUCTURE DESIGN
`FOR MIMO OFDM SYSTEMS
`An efficient sequence structure must be suitable for
`both synchronization as well as parameter estimation.
`In this section we provide a brief overview of the tech(cid:173)
`nique used for parameter estimation and synchroniza(cid:173)
`tion for MIMO OFDM systems followed by the se(cid:173)
`quence structure design and its properties.
`
`Parameter Estimation for MIMO OFDM Systems
`
`In [2] we discuss a way to perform parameter estima(cid:173)
`tion for MIMO OFDM systems. We quickly summarize
`.i , this technique to lay a foundation for the sequence struc(cid:173)
`fi'"" ture design.
`The coarse channel estimates itiJ,k for each of the N
`subcarriers are obtained by multiplying N, Q x L ma(cid:173)
`trices Rk by the inverse of the pilot symbol matrices
`Sk,
`• Rk = 11 k + Wk k = 0, 1, ... , N - 1 (7)
`flk = Sk" 1
`where Wk = s,;; 1 ·Wk assuming that all the Sk'
`In addition, each of the Sk for
`s are non-singular.
`k = 0, 1, ... , N - 1 must be unitary, to obtain a Mini(cid:173)
`mum Mean Squared Error (MMSE) solution for coarse
`channel estimates.
`The channel estimates are further improved by first
`taking N -point IFFT of the Q x L coarse channel es(cid:173)
`timate vectors to convert them to the time domain such
`that
`
`g .. = IFFTN{fJ .. }
`-i,J
`-i,J
`
`(8)
`
`3
`
`Synchronization for MIMO OFDM Systems
`
`In [3] we show a way to perform time and frequency
`synchronization for MIMO OFDM systems using chirp
`like orthogonal polyphase sequences proposed by Sue(cid:173)
`hiro et al [3]. They are ( P - 1) orthogonal sequences of
`period P 2 each where P is a prime number. Orthogo(cid:173)
`nality of the various transmit sequences is important for
`achieving fine time synchronization. Hence in the time
`domain, the sequence sq,n transmitted from Antenna q
`is represented by
`
`1
`sq,n = v1Qbi 1 · exp
`
`(j27rqioi1)
`p
`
`,
`
`(11)
`
`whereO:=:;io :::;P-1, O:=:;i1 :=:;P-1,n=io·P+ii.
`These sequences show optimum correlation properties
`viz. 1. The time domain periodic autocorrelation of each
`sequence is an impulse function.
`
`¢(k) =
`
`1 p2_1
`L s~,n. Sq,(n+k)p2 =
`
`n=O
`
`{ 1
`0
`
`k=O
`k=/=O
`
`where * means complex conjugate operation and P 2
`is the period of the synchronization sequence and 2.
`The full period cross-correlation between different se(cid:173)
`quences is given by
`
`1 p2_1
`1
`'lj;(k) = p2 L s;,n. Sq',(n+k)p2 :::; p2,
`
`n=O
`
`(12)
`
`for all q =I= q'. The bi1 sin (11) are complex coefficients
`of magnitude 1.0 and form a diagonal matrix which can
`
`ERIC-1035
`Page 6 of 10
`
`

`
`be used to modulate these orthogonal sequences. These
`sequences maintain their orthogonality irrespective of
`the value assigned to bi1 s. Another advantage of us(cid:173)
`ing these sequences is that their PAPR is unity. Cyclic
`prefix of a suitable length can be appended to these se(cid:173)
`quences and then transmitted over Q OFDM symbol pe(cid:173)
`riods from Q Antennas. The parameter P can be chosen
`such that P 2 > N. The reason for choosing P 2 > N
`is that the channel estimates obtained after synchroniza(cid:173)
`tion can be decimated to N values to be used later in the
`demodulation process. However these sequences can
`also be used to construct short sequences as done in the
`IEEE 802.1 la Standard [lJ by chasing a smaller value
`of P. Shorter sequences lead to shorter computation re(cid:173)
`quirements for correlation and less complexity in DSP
`implementation. This in turn leads to faster start-up time
`for the system.
`
`Training/Synchronization Sequence Structures
`
`In [2] we did not show how to design a sequence
`structure such that the matrices Sks are unitary and at
`the same time have a low PAPR in the time domain.
`The matrices Sks must be unitary in order to obtain an
`MMSE solution to the coarse channel estimates. We
`extend the ideas of the previous sections so as to make
`each of the Sks unitary and at the same time ensure that
`they are suitable for synchronization. We also discuss
`the advantages and disadvantages of each structure.
`One of the simplest sequence structure is obtained
`when S is made diagonal such that
`
`So= [ r ~2
`
`.. : t j,
`
`(13)
`
`- [ ~~+1
`
`SQ2 -
`
`a chirp sequence which in the time domain is given by
`
`Sn= exp (3;'), n = 0, !, ... ,N -1.
`
`(14)
`
`The PAPR of the chirp sequence is unity. This struc(cid:173)
`ture is a direct extension of Single Input Single Output
`(SISO) systems however for MIMO it has the follow(cid:173)
`ing disadvantage. The transmitted power will have to
`be increased by a factor of Q during the training phase
`in order to achieve a comparable synchronization and
`parameter estimation performance to SISO. Hence this
`technique will require power amplifiers with a large dy(cid:173)
`namic range and will increase the system cost. Hence
`in order to avoid increased dynamic range requirements
`and to ensure accurate synchronization and channel es(cid:173)
`timation, we need to find ways to transmit signals from
`all the transmitter antennas at the same time.
`In [3] we suggested the use of orthogonal polyphase
`sequences given in (11) for synchronization for MIMO
`OFDM systems. As a particular example we make use
`of these sequences to construct the different structures.
`If we choose P > Q2 then we have more sequences
`than needed for transmission.
`For a 2 x 2 scheme, the space-time block code struc(cid:173)
`ture proposed by Alamouti [5] also serves as an optimal
`training sequence structure. This structure is given by
`
`SA = [ - ~~ ~i ] ,
`
`(15)
`
`For systems employing more than two transmit and
`receive antennas, following sequence structures can be
`thought of. We can form a sequence structure using Q2
`different orthogonal sequences such that
`
`This choice leads to two simplifications. The first sim(cid:173)
`plification is that we can transmit the same sequence
`over Q symbol times. The second simplification is
`that we no longer need to use specialized orthogo(cid:173)
`nal polyphase sequences since each sequence can be
`uniquely identified because of the diagonal sequence
`structure. This means that we are no longer bound to use
`an OFDM blocksize (P2 ) derived from a prime number
`P. In order to ensure that the diagonal matrix is also
`unitary, we must choose a sequence whose frequency
`domain samples are obtained from the unit circle in the
`complex domain. One example is to construct the se(cid:173)
`quence using the points from any of the Phase Shift
`Keying (PSK) constellations [IJ. Another example is
`
`4
`
`I ~~ ~:
`
`Sc=
`
`.
`£2
`or symmetric such that
`
`Ss =
`
`(17)
`
`(18)
`
`£Q l £Q-1
`
`.
`
`... ~1
`
`~~+2 : : : ~~Q l
`
`,
`
`(16)
`
`:
`:
`.
`.
`£Q2
`£Q(Q-1)+1
`or we can make the sequence structure cyclic/circulant
`such that
`
`ERIC-1035
`Page 7 of 10
`
`

`
`Another sequence structure can be fanned based on
`the orthogonal designs suggested by Tarokh et al. [5].
`These structures exist only for Q = 2, 4, 8. For Q = 4
`the transmission matrix in the frequency domain would
`be
`
`(19)
`
`However just by using these structures without any
`modifications to the sequences does not ensure that S ks
`are unitary. Hence some modifications must be made
`on Sks so that they have these properties. This modifi(cid:173)
`cation is carried out using a Gram-Schmidt orthogonal(cid:173)
`ization procedure listed in the Appendix.
`Two issues need to be addressed for the Gram(cid:173)
`Schmidt orthogonalization to be successful. Firstly, the
`rows of Sks must be linearly independent before orthog(cid:173)
`onalization is carried out. Secondly, the matrices must
`be chosen such that after the orthogonalization, the sig(cid:173)
`nal structure has a low PAPR.
`If orthogonal polyphase sequences are used then the
`complex coefficient bi1 s that modulate the sequences are
`extremely useful. This is because they can not only
`make the rows of the matrices Sks linearly indepen(cid:173)
`dent before the orthogonalization but they also reduce
`the PAPR of the resultant sequence structure.
`The Alamouti' s structure and the structure obtained
`from orthogonal designs can be further simplified by
`transmitting the same sequence from all the antennas
`such that
`
`s
`
`s
`AS=
`
`and
`
`[ S..1
`-8* 8*
`-1 -1
`
`'
`
`Srs =
`
`[ £1
`-S
`- 1
`-S..1
`-S..1
`
`S..1
`S..1
`S..1
`-S..1
`
`S..1
`-S..1
`S..1
`S..1 -~~ .
`S..1
`
`S..1 l
`£1 l
`
`(20)
`
`(21)
`
`Algorithm to form the sequence structure
`
`I. Choose sequences which have good correlation prop(cid:173)
`erties and low PAPR in the time domain.
`2. Take their FFf to convert them to the frequency do(cid:173)
`main and form the sequence structure by negating or
`conjugating the FFf coefficients as required.
`3. Make sure that the rows of Sks are linearly indepen(cid:173)
`dent. If not, then restart the design using different se(cid:173)
`quences.
`4. Subject Sks to Gram-Schmidt procedure to make
`them unitary.
`5. Check the PAPR of the resultant sequence structure
`in the time domain.
`6. If the PAPR is higher than desired then restart the
`design using different sequences.
`
`IV. SIMULATION RESULTS
`
`In this section we compare the properties of the dif(cid:173)
`ferent sequence structures. The sequence structures
`are fonned using polyphase orthogonal sequences with
`P
`l 7. Hence we obtain 16 orthogonal sequences of
`period P 2 = 289 each. It is found that by modulat(cid:173)
`ing the sequences by complex coefficients bi 1 we not
`only guarantee that all the Sks are unitary but also ob(cid:173)
`tain a low PAPR for the sequence structure. The com(cid:173)
`plex coefficients are generated randomly as points on
`the unit circle in the complex domain using a uniform
`random generator. Once these sequences are generated,
`they are converted to the frequency domain using FFT.
`In the frequency domain these sequences are modified
`to match the different configurations suggested earlier.
`The matrices Sks are then subjected to Gram-Schmidt
`orthogonalization to make them unitary and ensure that
`the 1\.1.MSE criterion for channel estimates is satisfied.
`A search is then carried out for a structure with a lowest
`PAPR over 1000 randomly generated sets. Since Gram(cid:173)
`Schmidt orthogonalization does not change the orthogo(cid:173)
`nal sequences in the first row of S, these structures have
`optimum correlation properties [3]. This is illustrated
`in figures 3 and 4 where orthogonal sequences obtained
`from the cyclic structure are transmitted over a flat and
`a frequency selective channel. The frequency selective
`channels are formed using 6 taps that are sample spaced,
`and having an exponential power delay profile. All the
`channels are uncorrelated. The received samples are
`correlated with one of the transmitted sequences. The
`SNR at the receiver is 6 dB.
`Table I illustrates the simulation results for the differ(cid:173)
`ent structures. From the table it can be concluded that
`for a system using 2 transmit antennas, the Alamouti'
`
`For both the above structures all the Sks are naturally
`unitary. Also, the PAPR of these sequence structures
`will be unity if we use chirp like sequences to fabricate
`it. The other advantage is that we can avoid using spe(cid:173)
`cialized orthogonal polyphase sequences as long as we
`choose a sequence whose samples in the frequency do(cid:173)
`main are obtained from the unit circle in the complex
`domain. However Alamouti' s structure exists only for
`Q = 2 and the Srs structure exists only for Q = 2, 4, 8.
`
`5
`
`ERIC-1035
`Page 8 of 10
`
`

`
`0.45
`
`0.1
`
`700
`
`750
`
`800
`
`Fig. 3. Correlation of the received signal with the signal from
`one of the transmit antennas in a non dispersive channel.
`SNR=6dB
`
`0.2
`
`Fig. 4. Correlation of the received signal with the signal
`from one of the transmit antennas in a dispersive channel.
`SNR=6 dB
`
`s structure SA and the simplified orthogonal structure
`STs are the most suitable. For Q
`3, the structure
`STs does not exist and hence the cyclic structure Sc
`can be used. For Q = 4, STs exists and is the most
`suitable sequence structure.
`
`V.CONCLUDING REMARKS
`
`In this invention we presented a general method of
`forming efficient sequence structures which can be used
`for parameter estimation as well as synchronization.
`As a specific example we fabricated a structure using
`directly modulatable orthogonal polyphase sequences.
`We presented a technique by which the transmission
`matrices for each subcarrier is made unitary hence sat(cid:173)
`isfying the MMSE criterion for channel estimation. A
`search was then carried out for structures with lowest
`peak to average power ratios. For systems employing 2
`transmit antennas, Alamouti' s structure and the simpli(cid:173)
`fied orthogonal structure are found to be optimal. The
`simplified structure obtained from orthogonal design is
`also optimal for systems employing 4 and 8 transmit an-
`
`6
`
`TABtEI
`COMPARISON BETWEEN VARIOUS SEQUENCE
`STRUCTURES
`s
`SA
`SAs
`Sys
`SQ2
`Sc
`ST
`Sc
`SQ2
`Ss
`Sys
`Sc
`Ss
`SQ2
`Sy
`
`Q
`2
`
`3
`
`4
`
`PAPR
`1.00
`1.00
`1.00
`3.37
`12.29
`12.05
`3.28
`4.44
`7.50
`1.00
`4.37
`5.12
`6.21
`9.17
`
`tennas. For systems employing 3 transmit antennas, cir(cid:173)
`culant structure is the most suitable.
`
`APPENDIX
`GRAM-SCHMIDT ORTHOGONALIZATION
`
`Given a matrix S~ whose rows are not orthonormal
`we can use the Gram-Schmidt procedure [4] to orthogo(cid:173)
`nalize the rows. The matrix Sk that is formed as a result
`of this procedure is unitary as long as we ensure that
`the rank of S~ is Q or that the rows of S~s are linearly
`independent.
`We can keep the first row of S~ as it is and based on
`the first row perform Gram-Schmidt procedure to make
`the remaining rows orthonormal.
`The following example shows the conversion of a 4 x
`4 matrix S~ to Sk. Given S~,
`
`s' =
`k
`
`.5e-.03J
`.5e·OOj
`.se-· 89~ .se-.49j
`.5e-.so1
`.se-.69J
`.5e-l.3J
`.5e-.72J
`
`[
`
`.5e·OOj
`.Se·17J
`.Se·201 .
`.se-.701
`
`.se-.32j
`.se-.2sj
`.se-.741
`
`{A 1)
`
`.5e·07J l
`
`after the Gram-Schmidt orthogonalization, we obtain a
`unitary sk as follows.
`
`S -
`k -
`
`[ 5e-03j
`.62e-2.0J
`.47e.75J .
`.37e-2·6J
`
`.5e·OOJ
`.16e-l.4j
`.83e-2·2j
`.17e-2.41
`
`.5e·ooj
`.76el.3J
`.24el.3J
`.34e-2·0J
`
`.5e·07j
`.1e-·2J
`.14el.Oj
`.85e·88J
`
`] (A 2)
`
`ERIC-1035
`Page 9 of 10
`
`

`
`REFERENCES
`
`( 1]
`
`IEEE Standard 802.11 a-1999, Part 11: Wireless LAN Medium
`Access Control (MAC) and Physical Layer (PHY) specifica(cid:173)
`tions: High-speed Physical Layer in the 5 GHz Band.
`[2] A. N. Mody and G. L. Sttiber, "Parameter Estimation for
`OFDM with Transmit Receive Diversity," VTC 2001, Rhodes,
`Greece.
`[3] A. N. Mody and G. L. Stuber, "Synchronization for MIMO
`OFDM Systems," to be presented at GLOBECOM 2001. San
`Antonio. TX, U. S. A.
`[4] G. Strang, Linear Algebra and its Applications, Saunders, Har(cid:173)
`court College Publishrng, 3rd. ed., New York, 1986.
`[5] V. Tarokh, H. Jafarkhani and A. R. Calderbank, "Space-Time
`Block Codes from Orthogonal Designs," IEEE Transactions
`on Information Theory, Vol. 45, No. 5, July 1999.
`
`7
`
`ERIC-1035
`Page 10 of 10