CA2698370A1

CA2698370A1 - Multi-tiered quantization of channel state information in multiple antenna systems

Info

Publication number: CA2698370A1
Application number: CA2698370A
Authority: CA
Inventors: Bartosz Mielczarek; Witold A. Krzymien
Original assignee: Bartosz Mielczarek; Witold A. Krzymien; Wi-Lan Inc.; Quarterhill Inc.
Current assignee: Quarterhill Inc
Priority date: 2007-09-07
Filing date: 2008-09-05
Publication date: 2009-03-12
Anticipated expiration: 2028-09-05
Also published as: WO2009030036A1; US20110274182A1; US9048891B2; CA2698370C; CN102084612A; HUE060441T2; EP3826200B1; EP2188927A1; EP2188927A4; CA2893295A1; CA2893295C; EP2188927B1; CN102084612B; EP3562069A1; EP3562069B1; US8036282B2; EP3826200A1; US20090067512A1

Abstract

A multi-tiered CSI vector quantizer (VQ) is provided for time-correlated channels. The VQ operates by quantizing channel state information by reference to both the current channel state information and a prior channel state quantization. A system is also provided that uses multi-tiered CSI quantizers. Enhanced signaling between the transmitter and receivers is provided in order to facilitate the use of multi-tiered CSI quantizers.

Description

Multi-tiered quantization of channel state information in multiple antenna systems BACKGROUND
[0001] One of the most promising solutions for increased spectral efficiency in high capacity wireless systems is the use of multiple antennas on fading channels.
The fundamental issue in such systems is the availability of the channel state information (CSI) at transmitters and receivers. In general, if the receivers and transmitter have an access to CSI, the system throughput can be significantly increased. While it is usually assumed that perfect CSI is available at the receivers, the transmitter may only have partial CSI available due to the feedback delay and noise, channel estimation errors and limited feedback bandwidth, which forces CSI to be quantized at the receiver to minimize feedback rate. There is described here an improvement in the quantization of channel state information in a multiple antenna system.

SUMMARY
100021 A multi-tiered CSI vector quantizer (VQ) is provided for time-correlated channels. The VQ operates for example by quantizing channel state information by reference to both current channel state information and a prior channel state quantization.
A system is also provided that uses multi-tiered CSI quantizers. Enhanced signaling between the transmitter and receivers is provided in order to facilitate the use of multi-tiered CSI quantizers. These and other aspects of the device and method are set out in the claims, which are incorporated here by reference.

BRIEF DESCRIPTION OF THE FIGURES
[0003] Embodiments will now be described with reference to the figures, in which like reference characters denote like elements, by way of example, and in which:
Fig. 1 is an illustration of a channel vector space according to known principles in the art;
Fig. 2 is an illustration of the channel vector space of Fig. 1 with a more fine-grained quantization;

Fig. 3 is an illustration of the channel vector space of Fig. 2 with a multi-tier quantization;
Fig. 4 shows the structure of a quantization system;
Fig. 5 shows the operation of an algorithm for designing a multi-tiered quantizer;
Fig. 6 shows a region of one codebook and the corresponding regions of the corresponding next higher tier codebook for use in a multi-tiered quantizer;
Fig. 7 shows an example of the operation of a multi-tiered quantizer;
Fig. 8 is a flow diagram showing the operation of a multi-tiered quantizer;
Fig. 9 shows the operation of the quantizer;
Fig. 10 shows typical eigenmode and singular value coherence times; and Fig. 11 shows the results of a simulation comparing a multi-tiered quantizer with non-tiered quantizers.

DETAILED DESCRIPTION
[0004] In a multiple antenna system as for example shown in Fig. 4, information is transmitted over multiple channels 34 corresponding to multiple antennas 36.
Each channel 34 has a state that affects the propagation of information over the channel. The state of multiple channels 34 between a transmitter 32 and one or more receivers 30 in a multiple antenna system can be expressed as a vector. As the channel state changes, this vector moves through the channel vector space. The channel vector space may be separated into regions (see Fig. 1). Each region may be represented by an index. If each region corresponds to the part of the space closest, by some metric, to a particular member of a set of points in the space, then the regions are known as Voronoi regions 20 and the points are known as centroids 22. In order to maximize throughput, it is preferred to associate each index to a centroid 22, which represents the Voronoi region 20 which is the part of space closer to that centroid 22 than any other.

[0005] A vector quantizer (VQ) with multi-tiered quantization is aimed at transmission channels with memory, in which there is a need to reduce the feedback bandwidth and allow the system to automatically adjust the quantizer resolution to the

2 rate of channel changes. In an exemplary design of a multi-tiered CSI vector quantizer (i.e., the description of centroids and Voronoi regions) for multiple-input, multiple-output (MIMO) channels with memory, the VQ uses multiple optimization steps.

[00061 In the typical CSI VQ, the quantization of the channel vector space can be illustrated as in Fig. 1: the CSI space is tessellated by Voronoi regions 20 with corresponding centroids 22 that represent all vector realizations within each Voronoi region (for each centroid, the corresponding Voronoi region is the set of points closer to that centroid than any other, according to some metric). The number of such regions (centroids) is defined by the number of available- bits, which also influence the quantization error of the VQ. Fig. 1 shows the situation when the channel CSI
is correlated in time and follows some trajectory 28 in time.

[0007] The quantization error can be decreased if the CSI VQ resolution is increased using more bits in feedback link. Fig.2 shows the identical trajectory 28 of the channel vector realization as in Fig. 1 with increased number of centroids 22 and Voronoi regions 20A. In Fig. 1 only two different centroid indices would be used to represent the channel trajectory, whereas in Fig. 2, four such indices would be used, which would result in more precise representation of the actual channel changes. The price for such improvement is a larger number of bits needed to characterize the quantized CSI indices that must be fed back to the transmitter.

[0008] The typical trajectory 28 of CSI vectors is partially predictable in a sense that the channel realizations between consecutive transmission epochs within the same frequency band are correlated. The correlation increases with decreasing relative speeds of receiver-transmitter pairs with the net effect of trajectories being statistically contained within a given Voronoi region for a predictable amount of time. The time metrics may be quantitative described in various ways such as using time metrics called eigemode coherence time and singular value coherence time. In CSI VQ context, the longer the coherence time, the less frequent the changes in VQ indices that need to be reported back to the transmitter.

3 [0009] A multi-tiered VQ allows for a significant reduction of the feedback rate for systems in which channel coherence times are fairly long. During the design of the quantizer, the Voronoi regions are optimized according to any chosen criterion in 2,3,4 and more tiers, in which consecutive Voronoi regions are embedded in the previous ones as shown for example in Fig. 3 for a 2-tiered design.

[0010] In the example of Fig. 3, a 2-tiered CSI VQ is divided into primary 23 and secondary 24 Voronoi regions and corresponding centroids 25, 26. In the first phase of the VQ operation, only the primary regions are used to assign the primary centroid indices to the channel vectors. In the second phase, only the secondary centroids and the primary centroid within the first identified primary region are reported to the base station until the channel vector realization leaves the primary region. In this way, as long as the channel vector does not change very rapidly, high quantization resolution can be obtained at much lower feedback rate as the quantization points are concentrated within a space of single primary Voronoi region. Moreover, this mechanism allows the receiver to automatically adjust the vector resolution to the rate of channel changes. The transmitter and receiver must have a way of identifying for which Voronoi regions (primary, secondary etc.) the VQ indices are reported.

[0011] The following notation is used in describing an exemplary multi-tiered VQ:
= M- the number of tiers in the CSI vector quantizer design = mk - the current tier index at receiver k = mk - the current base station tier index of receiver k = Nm - the number of bits for CSI representation at each tier of the CSI MIMO
VQ.

4 [0012] A system using a dual VQ codebook design for quantization of channel state information in a multiple antenna system is shown in Fig. 4. This example shows a system according to the inventors' United States patent application no.
11/754,965 filed May 29, 2007. A multi-tiered VQ may be used for eigenmode and singular value codebooks in systems ranging from only one active receiver at a time to systems with multiple receivers being active simultaneously (where we define being active as receiving transmissions). The design of the multi-tiered codebooks can be applied tomatrices of orthogonal eigenmodes, subsets of eigenmodes and scalar singular values as necessary.
The following descriptions may be applied to any type of CSI quantizing solution.

[0013] In Fig. 4, a transmitter 32 communicates with a receiver 30 over a feedforward channel 66 and a feedback channel 38 using antennas 36. The receiver 30 includes a channel estimator 40, linear processor 68 for decoding a transmission, a singular value processing unit 42, a power allocation and eigenmode selector 44, and codebooks 48 and 46. The receiver 30 may use various known electronic processors for its parts, and in one embodiment may use a monolithic application specific chip. The functions of the receiver 30 may be provided partly or entirely by hardware, firmware and/or software.
The transmitter 32 includes anindexer and optimizer 54 and stored modulation and power allocation matrices 56 and 58 respectively. An input data stream 60 is fed to a modulator 62 that applies a linear modulation matrix selected from the stored modulation matrices 56. The modulated data stream is fed to a power allocator 64, which applies a power allocation matrix selected from the stored power allocation matrices 58. The system of Fig. 4 works as follows:
1. Before the transmission epoch, each receiver 30 estimates 40 its channel matrix H
34 for the feedforward channel 66 and uses this information to perform 42 the singular value decomposition (SVD) of the matrix.
2. The eigenmode and singular value (power allocation) coinponents are separately quantized 44 using two codebooks V 46 and D 48, respectively.
3. The indices 50 of the selected codewords are fed back to the transmitter using a feedback channel 38.

4. The transmitter uses all the indices from all receivers 50, 52 in the system to choose 56, 58 the pre-computed linear modulation and power allocation matrices B 62, 64 and S, respectively. The choice is based on a predefined set of rules (maximum throughput, fairness, etc.).

5. The signal (x, to x NT ) 60 is modulated using the selected linear modulation and power allocation matrices B 62 and S 64 and transmitted via the feedforward channe166.

6. The transmitted modulated signal is processed by the receiver 68.
The transmitter 32 thus has a processor configured to carry out the above steps 4-5 and each receiver has one or more antennas 36 and a processor configured to carry out steps 1-3 and 6.

[0014] Referring to Fig. 5, design of the multi-tiered codebooks (D or 0 is performed as follows:
1. Based on the desired system parameters (types of channels, required feedback rate required performance etc.) set parameters M and N,n for each value of m=1,2,..,M.
2. Set m=1 (step 70).
3. Any of various vector quantizers may be used to design a receiver VQ using NI
resolution bits (step 72). An example is given below, from US patent application no. 11/754, 965, which is entitled "Quantization of Channel State Information in Multiple Antenna Systems".
4. Store the description of the Voronoi regions and centroids for m-tier of the VQ
(step 74).
5. If m is smaller than M (step 76), continue the design in the following way:
a) Create a large list of possible channel realizations (step 78).
b) Using the m-tier VQ, quantize (step 80) the above channel realizations.
c) Select channel realizations corresponding to each of the m-tier VQ indices (step 82).
d) Within each of the m-tier Voronoi regions, perform m+1 tier design of a vector quantizer using any of various VQ designs, such as in United States patent application no. 11/754,965 and shown below. The algorithm uses Nm+1 resolution bits within each region and forces one of the tier m+1 centroids within each region to be identical to the m-tier centroid corresponding to this region (step 84). The codebook entries of the new codebook for each region are now considered to be the group of tier m+1 entries associated with the tier m codebook entry for that region.
e) The reused m-tier centroid is assigned Nm+l index bits equal to 0.
f) Increase m by 1(step 86).
g) Go to step 4.
6. If m~M, finish the VQ design (step 76).

7. Design the modulation matrices corresponding to the designed multi-tiered VQ
using any of various modulation matrix design techniques such as the algorithrn shown in USPTO application no. 11/754,965, as shown below (step 88). The algorithm is now done (step 90).

[00151 The rationale behind re-using one of the m tier centroids at design phase of (m+1)-tier centroids and Voronoi regions (see bullet 5d above) is that the same set of modulation matrices can be used in a system where different users report their quantized channel information using different VQ tiers. As all m-tier centroids are contained in (m+1)-tier centroids, the effective indices can be easily used to decide which centroid must be used. Fig. 6 shows an example: a single primary region with index 1111 92 and secondary regions with indices of 000, 001, etc 94 thus giving them effective indices of 1111000, 1111001, etc. 96 Note that the primary centroid is in the same place as the secondary centroid with index 000. Moreover, thanks to such a design, the base station may support users with different implementations of the vector quantizers, e.g., varying number of VQ tiers. Thanks to the embedding of the codewords, all such situations will be supported.

[0016] The algotiffim fiaoim "Quantizatian of ehmwl state iufMatiIn in multi-gie antenna s}steMM7 is as follows:
[0817] For the case of a single receiv~er active at a tiimee, we iatrtraducae a hensis#ic disttsitim metric which is expressed as '7v (n; H), = I IDV "Q (n) - ~I p (1) where l(n) is the nth entry iu the predefined set of cbmm.e1 ttiagmabzzdm mua-tcic:es and I = Ilp is ikre Frobcnius rsomL We csmitted sobsctipt entries j in (1) for the Clazsty of presentation.

[0$18] We assuae dig n= 0,1, ...2NX - 1 Whete Nv is the mmberof bits pcr dmnel Iealzzalm in the feedb'Afk link needed to represent the vecL n V (n)_ 'T'o design the quauli= using (1), we divide the whole space of ehammt reahations H into 2N- regions Vi where V i = I H : W (i, H ) < 'l v(.?a H ) fcr aU9 ~ i}. (2) [0019] 'T'he aigcuithm st2ItS by creatiug a codrbaakof centroaids V and based on these resuK divides the quantization Wace iatD r*aans Vi- The c.ndebnok is created as follows:

1- Create a 1arge training set of L random, matrices H(t)-2- For each rmn:ciom matrix H(dj, perfÃnm singular valm decomposition to ab-taia D(t) and V (l) as Y, = Hjxj + nj = (ujD~~~ ) (Vtki) + n~ (3) 3. Set iteratiam counter 8= 0- Create a set of 2M- ramdam matrices H(n) -

8 4- For each matrix fi(n) calculate cacresgonding'VW(ra) using singular wat.uc deaanVositian_ S- For each rAining element H(I) and codebook enteg V()(n) calculate the metric in (1). For every I clmase indexes riw(!) coirespraading to ttie krtvesE
Values lDf =yv(n; g(d))-6_ Calculate a ncav set V('+')(n) as afom eEf spherical avemge of a3I entries V(~ contspmtiing to the sagte index n umng the fAkming mdhod. (The dsect ave:saging is impass:ible smce it does ncrt preserve orthogouality be-twem eigenvectors-) For all n calculate the sabsets L(n) _11:np,(o = n}
and if ffieir respective cardinah#iÃs (L(n) I # t} ft cnffespmding matsim 40+1) (n) can be abtained as I(~+)~ ~ V(1)10V(~$ (4) whcte 10 is an reT x saT all-zero- mairix vaith the escepption of t1e apper-left cmmcr ekment equal tÃt I_ FinaEly, ztsiug singulaÃ value deccsmposihonõ
calculateV'f+r+i) (~) from 4(;+') (n~ = V'+i) (n)W i~ ~"V(r+') (n))H ~
whem W is a sla.mmg vasiablEe-7- Calcutate the avcrage 6istmlion inetcic'~~'~ 1 ,(LF,, '~(np([); H(t)) & If distortion mr-tric falfills ~ry,('+') _40I,(^,~.~ C 9, sGp. O6awise inmase i by 1 anut go tn 5).

[0024] Upon c~moplctionafthe abBW atgorit.hm, the set af vectors ~' can tac used ta catculate the regions in (2).

9 [0021] Having cptimized gowff-independent entries in the codebook ofchannet eigenmode matrices Ii, the neYA step is to create a codebook f+ar paww allocahm RTe use a distarifiom mettic defumd as det[f + HQ.HH]
.~(~; ~; ~) _ ~[~ + ~(~)H (~)~] t~
vrhne g(k) is the kth entry in @te predefined set. of chanact water-filliug matrim and V(vpt) is the entry in ffie V' codebook that minitnizes metric (1) for the givm Ii We nsek= Oy 1, ...2NO -1 where Ns n th.e ammbeÃ af ints per dmnd reat-izatma mthe fee&ack lmlc needed to repesmt the vactrns S(k). lk~mg the metric in (6) is equiralent to minimizing the capacity loss beÃween the txptimmm ~y,.,,~~''`,,~g Q['~ QYl{i q~ i~iG F ~~ W .a,~.,,~.~M~1.-~ U~ ~D ~y~gpw ~Jr~Cj Q ~ ~ i~i. .
wdli".t~-~W~$
[0022] Similarly to the pxmous pÃoblem, we dmnde the wlmk space of cbannel ruliz3tit9tY5 H lYiti1 2N- regions S;(P) whCiC

S~(P) _(H : 7s(a; H; F') < 7s(?; H; P) for all j~ i}-and k- crea bc the codebook 9, we use the folCrxiag siethod:

1_ Create a large traiaing set of L random marrices H(O.

2. For each random matrix i4(t), gerfiom water-f~tiing operation tD obtain cqrti-mnut covariance:asa.tsic.es Q(dj and a(O, 3_ Sd dera.tios c(nmtu %= 0. Cseabe a set of 2ff$ taldom eiiagQnaT matdm 80)(k) with Tr P.

4. For every codebook entry S(+' (k) and matsis. Q(I). cak-Wate the mctFic as in (6). Choam andesc:s k,,t(i) carresgondang to Su lowesttvalues of'Ys(k;
H(t); F')-5_ If 7s (kpt(o; I-1(1); P) > 7a(H(d); F) whcrc 7õq(H(t); P) is &c metric cvr-lo, respanding to equal-pa~u~~er distrfttim defined as lreqtH(O; p) ~p + ~~.H~( )~ (O]' set &e cacre3poadigg entry kv(l ) = 2x". For all k calculate the RsbWb L(k) = {L : k%*(I) = k }.

6_ Far ag k=0,1, ...2Ng-1 Porwhieh IL(k)~ 7~ 0, caÃcutat+e a acw sct S({+r}
(k) as the arithmw& average (k) IL(k)I
7_ Calculate the averAp distaitinn metrfc.

~So +~a = ~ ~~~r~~~~~; H(I); P)j ~(x(~l; ~?. (10) 8. If distDrticm metric fiWl&lls < , swp.. O&eiwise inam e i with 1 and go t,D 4).

[0023] The set Gf m~dors S is then used tc- calcWa.te the regiama in (7).
Since w:ater-filling strog& depends on the power level F ancl Vp opfiimaly the A
slau1d be createx4 f r eve!iy power kue1 and unaber of bits Nv in eigenvectar mafim coddmk. (2)_ [0li24] In the mulft-user case, we fn3av the apprrnanc of Spencer et al, where each user perferrms singular value deca~ositian of Hk = LT,~V~ and ccmv9etts its res.pectivae Hk to anr-dimaeasicnat vectvr h" as bi, =u*RHit=s,-twLvff, (11) where A." is the largest smgular value of Sk and uk and v* are its caarespmdyn.g v ctm frcrn the untary mafirim Uk asu3 Vk, resgectivrlp.
[002' We use the linear blor-k dÃaganalizatian agproach, whi.ch chmmatm MLn by carmp smg ffie modulatung matrix B[S] of properiy chtrm nnti-sjsace, e*e;n-suxks far each se ,S . For each rccdvu i E S. the ith raw of Me matrix H[S1 is AÃst deleted to fom H[Si] - In ihe nW step, the skguIar va2uee de,conopositiion is perfnrnued to yidd H[S';] = u[A] S [,%] Vm [Sj]- By settireg the gth cÃdwnu of B[SI to be eguai to the ri,gblmast vecbx of V [S;], we force the sig[W #o thz tith receevm to be trasssmitted iu ffic null-sgaac of the other ustss and no A+ILTI wi11 appear_ In other vonds, dw channd uriIl be di.agana'lized aft d:i beiag ft en>am on lhe cliagond of H [S] B[S] . This leads to fimd[2 Rb- _ max [)Og2 (~ [S] 40 l+ (12) L_1 vvhcre C [S] is tk solution offhe xvater-filtmtg equatm.
[0026] We assme t2ut N,, is #he mmber of bits per cbanacl realizahn in the fecdbwk vnk. needed to rqresmt the vectars vt a (11). We dmce the space of ail poSSablc v'S mtt12a'r fegiQnS Ui ::; = {v : 7.($; v) <'7-(.7; v) f+or auj:~ i} (13) where,y, (n; v) is a distwtion fvn.ctim. Within each region %, vse def'ine a ecairaid vectDr v(i), which wi11 be used as arqpresentation of ihe region. The design of the codebook I can be done analytically andlar heuristically using for cumpie the Lloyd algoiidim.In this work, we defm The distartitan fimcticxse as the angle betwem thw actual vector v and it(i): v) = co -'(v(aj = v), wbich hs betu shown by Rcsh and Rhao iD maamisim ergodic capacity, and use Lloyd aT.gesddm tn train the vector quantizm Note that dLe conshuctivn nf ~ is inkkpendent of the trausmit power_ [0027] We assme that N, is the mgnber of bits per ctsmml realizativu in the feedback linle needed to r+epcesmt the scalar a.' in (11). We divide the space of ail possible channel realizations a= su into 21- regioas si s;_{S :I JW -~~~ 14.al-81 for anj0 i} (14) where A(i) ar.e scalar centQids r+epusenting regx.ans st. In this wt>rY, we ptifcrtm the design of the codebook I usiag the classical ncsa-unfbrin. quanfizer design algmthmn w ith diskffbn functicsn ,gm~n by quadratic function of the quantiaaWm ecror as e(i; n) _(s - s(i))2-[410281 The canstacticn of the codebook s is generally dependent un the trms-mit power lnmel,. However, the differeaices be'tw*om the codebooks A for dsff'ecent power regions are quite small. This a1l,ows us to create on[y one codebook A
and me it for alt trmsmit powers-[0029] The cal.culatiog of the atodsilation matrix h is based tm the gisen code-book,O. We assmme that the quantuation of the channel eig+eamodes is pel.f+oaamccl 2tthtmeiversic3e andesch usertczasmitsback. ift eocl6boak indeK 8k.
TIeisd,ices are don used at the Umsrnitter side iD stfect the moduiaticsn matrix $(ii, i2, ...ag)-SinM frvm the lineaÃ t2nsffiitter pomt of vWW, ardering of the asGrs is not impor-tant, we wi11 nse the cammntion fliat the indices (et, i2, ...iK) me almaays presented in the aseending c>rder. Farr e~ple, ist a sysle.m vaith K = 2, rrr =2 and I-bit veekir quantizers it, ffiere will exist osaly three possible modulation mahmes eatrespfmding t sets of v indices (1, 1), (1, 2) and (2, 2)-[00301 In dLe conhmt of vectox- quantizir& the desiga afthe the modt;da.tian ma-trfms can no hrnger be based on the algm-it5m presented for the single user case.
Using this method with quantized vemons of ht produces uvrtmg result when iden-tica1 indices t,k are re#uned and the receiver attempts to jointly optimize tr=cmis-sion to the users with seemmgF.y identicai channel veebass h~. lnsiead, we propose the following algorilhm to crpfiMize the set of uxatrices h(it, i2, ...%K):

1_ Create a 1argE set of Nnr aandamQ matrices Hx, where N is thc number of haming sets with raT users eaclz 2_ For each randmn matrix Hk, Perfam smgular value deecmposifina and ob-taia hk as in (11).

3_ For each vectDr ha sÃame the index % of the conr+espom,ding entry # (tiF).
4_ Dm& ffie entire set of matriees IHt intD N sets wit'h nr elcments eaek 5_ Scwtt the indiees tia within each sct t in the ascending order. Map aIl unique sets of sorted indices to a set of unique indices IB {fc-r example (I,1) -~
Ia 1,(172) - Iu =2j(2,2) -+Ig=3...)_ 6_ Iu each set I, reoader the corresponding channel vectm ht aecorrlÃng to their utds.ccs ia and caleulabc the opfimum Br using the bkkde diagana:Ta ti+an method descnGed abme.

7_ Calculate a set b(FB) as a column-wise spherical asrcrage of all eQtries B, c rztspnndi:ng to the same index I.

(903I1 ,AAfter ealculation Of (l$I modulation snaixiM B, the remaining part of system design is the caleulation of the watsr.-fiI1ing matrices. 1), which divide the psnvvers between the eigemnodea at the ttansmimcr _ The pracedwe for txealicra. of aadehaok D is similar to the alaOve alganthm, widY the ddEereaee ftt the r.nis~
~(%) are used iastead of I (ik), and the spherical averaging of the tvater-fillmg mahnms is puftmed diaganally ncat eDluMII-wis,e . ExplicdT

1. Cuate a Luge set of Nnr randOm matrices Hk, where N ir, the number of ttaining sets with n, us+ers earh-2. For each Emdom ma.trix IH't, pecfcsrm siflg,ular valae deeonnpcrsi(ion 2ad ab-tain hka.cit(11).

3_ For eacte vector ht stme the index ~i, of ilte conespErnd.isg entry i(nk).
4_ Oivx#e the entire set of matices 14 igbD N sets with nT elemmcnfs ea&

5_ Sort the indices nk withn each set t is3 the ascene3ing order. Map aU umque -;
sets of sorted indices to a sd of Ãnigw imdcrs ID (for examgsle (1, 1) ID = 1; (17 2) -- fD = ,2, (2,2) - ID = 3...).

6_ In each set 1. ieoz4a die ct}TfCspQflldfflg chzmel vectors }t e1CCMdiDg to their i.ndicm nA; and calcalate 1he optimum Di using the meUd of wabmfiUing trf (12).

7. Calcutate a set $(ID) as adiaganaÃ spbesical avraage afall enix ies I3t car-reqxmdmg to tlsc sane kmkz ID.

S

[0032] Referring to Figs. 7 and 8, based on the design of the multi-tiered codebooks D
and V as in the previous section, the system will operate as follows:

1. Initialize transmission epoch to t=1.
2. Set mk=1 at each receiver k, (all users will use separate indices mk) (step 112).
3. Set mk=1 separately for each receiver at the transmitter side. The transmitter-side indices mk should be mapped to their respective receiver-side indices mk (step 110).
4. Each receiver estimates its channel matrix H[t] (step 40).
5. Each receiver performs the vector quantization of the channel using m=1 tier quantizers described above (step 114).
6. The m-tier N,,, -bit long indices are fed back to the transmitter.
7. The transmitter performs the selection of active users using any method (maximum fairness, maximum throughput etc.) and chooses the optimum modulation matrices using a VQ method such as the method described in United States patent application no. 11/754,965.
8. The signal is transmitted to the selected active receivers.
9. Increase transmission epoch as t=t+1.

10. Each receiver estimates its channel matrix H[t] (step 40).

11. Each receiver performs the vector quantization of the channel using m-tier quantizers described above (step 114).

12. Each receiver that recognizes (step 116) that its quantized channel's mk-tier Voronoi region in the t+1 epoch is identical to the mk-tier Voronoi region in epoch t performs the following steps:
a) Unless 118 mk=M, increase the receiver's index to mk=mk+1(step 120).
b) The channel realization within the unchanged Voronoi region is quantized using the new mk-tier quantizer (step 114).
c) The receiver uses a known mechanism (see later in the document) to signal to the transmitter the new mk -tier of VQ.
d) The N,õk bits long indices are fed back to the transmitter (step 124).

e) Transmitter increases its index as mk=mk+1(step 126).

13. Each receiver that recognizes (step 116) that its quantized channel's mk-tier Voronoi region in the t+1 epoch is not identical to the mk-tier Voronoi region in epoch t performs the following steps:
a) Unless (step 128) mk=1, decrease the receiver's index mk to the last tier where the Voronoi regions mk_1 are identical in both t and t+1 epochs (step 130).
b) If no such tier can be found, set mk-1, otherwise update the mk to a value for which Voronoi regions mk_I are identical (step 130).
c) The channel realization is quantized using the mk-tier quantizer (step 114).
d) The receiver uses a known mechanism (see below) to signal to the transmitter the new mk tier of VQ.
e) The Nk bits long indices are fed back to the transmitter (step 124).
f) Transmitter decreases its index as mk=mk (step 134).

14. The transmitter selects the modulation matrices based on the indices fed from the receivers and each receiver's separate mk index stored at the transmitter side (step 136).

15. The modulation matrices are used to transmit the information to the selected receivers (step 138).

The example of the algorithm's operation shown in Figs.7-8 for one mobile receiver uses M=3 tiered quantizer. In this scenario, CSI vector stays in tier-1 Voronoi region 20 in first 5 frames Fl-F5, in the tier-2 region 24 in first 5 frames F1-F5, and tier-3 region 100 in frames F2 and F3. Receiver R1 recognizes the subsequent Voronoi regions and adjusts the tier (m) 104 of the used quantizer accordingly by increasing and decreasing quantizer resolution. The quantizer indices each representing the centroid 22,26,102 of its respective Voronoi region in the appropriate tier, are then fed to the base station B 1 that combines them properly so that the effective CSI resolution N varies in time (t increases from F 1-F6) depending on the rate of channel changes. Base station B 1 chooses modulation matrix 56 and transmits signal 60. At each time the resolution is equal to that of an untiered quantizer with a number of bits equal to the number of bits 106 representing the tier used (N,n) plus that for all lower tiers. It can be clearly seen that the proposed algorithm allows the system to automatically adjust the resolution to the speed of channel changes.
Fig. 9 shows a graphical representation of the algorithm.

[0033] The set of indices mk at the receivers should be matched to the indices m"` at the transmitter. If the transmitter uses the index mk that corresponds to the wrong mk -tier of the receiver VQ, the resulting loss of performance may be very significant. In general, the index of the quantized channel vector at the transmitter is reconstructed as:
AAAABBBCCC....
where AAAA corresponds to m=1 tier NI indexing bits, BBB corresponds to m=2 tier N2 indexing bits etc. (see Fig.6 for an example).
At any given time, the transmitter receives only m-tier index bits (AAAA, BBB, CCC
etc.). and it must be able to establish which tier those bits correspond to.
For example, there must be a signaling method allowing the transmitter to distinguish between two consecutive transmissions such as BBB, BBB where the channel vector moved away from one tier-2 centroid to another, from the BBB, CCC transmission, where the channel vector stayed in the same tier-2 region BBB and tier-3 quantization was used in the CCC
word.

[0034) Various methods may be used for transmitting index information from the receiver to the transmitter such as:
1. Direct indexing of VQ words. In order to let the transmitter know, which VQ
tier is used, the actual VQ codeword index is extended with the bit representation of the index mk of each receiver. Example:
MMAAAA, MMBBB, MMCCC ...
Where, for example, two bits MM are used to represent one of the four quantization tiers in the system. The drawback of this method is that the additional feedback load is required to transmit information about mk indices.
2. Varying length of different m tier VQ words. In this method, each m-tier of the CSI quantizer is characterized by different number of indexing bits N,n.
Example:

AAAA, BBB, CC, D ...
where four bits AAA are used to represent tier-1 quantization, 3 bits BBB are used to represent tier-2 quantization etc. The advantage of this system is that there is no need to transmit additional bits M as in the previous method. The drawback of this method is that there must be another mechanism allowing the transmitter to count how many bits were actually sent from the receiver and the varying feedback load.
3. Channel prediction based assessment of VQ tier. In this method, each m-tier of the CSI quantizer may be characterized by any number of bits Nm and the statistical channel characterization is used by the transmitter to decide whether the channel vector stayed in the previous m-tier Voronoi region or moved away from it. The advantage of this system is that it leaves a large degree of freedom for designing the feedback link. The drawback of this method is that the complexity of transmitter design grows and there may be erroneous decisions on the tier of quantizer used by the receivers.
4. Hybrid solutions combining the previous three methods in any way that is suitable from system design point of view.
[0035] In the course of the system operation, it may happen that some of the transmitter indices mk will no longer be synchronized with corresponding receiver indices mk Such a situation will typically happen when one of the feedback messages from a receiver has not been detected at the transmitter (i.e., the transmitter lacks channel quantization index for the current transmission epoch) or the received message with the indexing information does not agree with the expected quantization tier m.

[0036] In practical communication systems, two erroneous situations can occur:
= The received feedback message shows the situation when mk> mk+l. Such a situation is not allowed during the course of the normal operation since the receiver may only step back to the lower tier quantizers or increase the current one by 1.
= The transmitter did not receive any feedback information due to the feedback link problems.

[0037] Various methods may be used to solve the problem such as:
1. Use channel prediction to recover the incorrect index. The previously used indices are used to extrapolate the actual channel information index.
2. Deactivate the user for the next transmission epoch and send the VQ RESET
message to it. If the transmitter cannot reliably decide, which channel index was reported by the receiver, it sends a special VQ RESET message to, the receiver containing the last value of the effective index at the transmitter AAAABBBCC...
without the last tier of bits (in other words, bits up to the level mk-1 are communicated to the base station). The receiver than establishes, whether the saine tier of the VQ can be used or whether it has to step back to a lower tier. The new indices are sent to the transmitter and the system resumes the usual operation.

[0038] Fig. 10 shows a typical set of curves representing the eigenmode and singalar value coherence times for a 2x2 MIMO system. For definitions see B. Mielczarek and W.
Krzymien, "Influence of CSI feedback delay on capacity of linear multi-user MIMO
systems," in Proc. IEEE WCNC., Hong Kong, March 2007, pp.. 1188-1192. As one can see, the length of time in which the first tier Voronoi regions do not change decreases with increasing resolution and normalized Doppler frequency of the channel fDTfta,,,e. For example, with fDTf,õ,,0.02, the Voronoi regions of the eigenmode quantizers will stay the same for approximately 6 consecutive frames when the eigenmode quantizer uses N=4 bit resolution. When the quantizer uses N=7 bits, only 2-3 consecutive frames will have identical first tier Voronoi regions. In general, in order to improve system's throughput, it is preferable to use higher resolution of VQ but the price for the improvement is the high feedback burden and frequent changes of the high resolution indices. As shown in example below, by using a multi-tier VQ design, it is actually possible to achieve very good system performance and significantly reduce the required feedback bit rate.

100391 In Fig. 11, the simulation results are shown for a system with 2-tier eigenmode quantizer (M=2) using N1=4 and N2=3. The system has been designed using algorithms described in this application and starts by transmitting 4 bits (AAAA) and, if the 1-tier Voronoi regions are the same in the consecutive frames, only 3 bits (BBB) are sent to the transmitter. We compare them with 1-tier systems with N1=7 and N1=4. The implemented algorithms are tested on a system with 2 base station antennas and 10 users with 2 receive antennas each. We test three channels with maximum normalized Doppler frequencies equal to 0.01, 0.02 and 0.1 as in Fig.11. As one can see, the throughput gap between the conventional 1-tier vector quantizers for N1=7 and Nj=4 is quite large (around 3 dB at 10 bpcu) - any increase of throughput in such simple systems requires increase of feedback bandwidth. However, if the channel is assumed to have memory, by using our proposed approach, it is possible to attain almost the same performance with multi-tier CSI
quantization. In our example, the maximum feedback burden is set to 4 bits/frame/receiver for the 2-tier system but the performance is almost equivalent to 7 bit feedback system for a large range of Doppler frequencies. Hence, by proper choice of the number of tiers and their corresponding resolutions, it is possible to design the practical systems for a wide variety of channel conditions, required throughput performance and maximum feedback link bit rates.

[0040] In the claims, the word "comprising" is used in its inclusive sense and does not exclude other elements being present. The indefinite article "a" before a claim feature does not exclude more than one of the feature being present. Each one of the.individual features described here may be used in one or more embodiments and is not, by virtue only of being described here, to be construed as essential to all embodiments as defined by the claims.

[0041] Immaterial modifications may be made to the ernbodiments described here without departing from what is covered by the claims.

Claims

What is claimed is:

1. A method of quantizing channel state information in a multiple-input transmission system having at least a transmitter and a receiver, the method comprising the steps of:

quantizing information concerning a first channel state to produce first quantized information, and sending the first quantized information to the transmitter;
and quantizing information concerning a second channel state by reference to (1) the second channel state and (2) the first quantized information, to produce a second quantized information, and sending the second quantized information to the transmitter.

2. The method of claim 1 in which the quantization of the first channel state and the second channel stated is each carried out using a codebook, the codebook having codebook entries each representing a region of a space of possible channel states, the quantization comprising representing each channel state with a codebook entry which represents a region of the space of possible channel states which includes the channel state, and transmitting a codeword index representing the codebook entry.

3. The method of claim 2 in which a single codebook is used to quantize the first channel state and the second channel state, the codebook entries of the codebook being arranged in multiple tiers.

4. The method of claim 3, in which the codebook has a lowest tier , and for any tier other than the lowest tier, the codebook entries in each respective tier are arranged in groups, so that each such group is associated with one or more codebook entries in a lower tier; and each codebook entry in each tier other than the lowest tier is represented by an index which is unique among the codebook entries in that group.

5. The method of claim 3 in which in the case that the codebook entry used to represent the first channel state is in an initial tier, and at least one group of codebook entries in a tier higher than the initial tier has the property that the one or more codebook entries associated with the group includes the codebook entry used to represent the first channel state, and the one or more codebook entries associated with the group also includes an entry in the initial tier which represents a region of the space of possible channel states which includes the second channel state, then the second channel state is quantized using one of the at least one group of higher tier entries with that property.

6. The method of claim 4 in which each group of entries in any tier other than the lowest tier is uniquely associated with a single entry in a lower tier.

7. The method of claim 6 in which in the case that the first channel state is quantized using a first codebook entry, and the second channel state is not in the region of the space of possible channel states represented by that codebook entry, then a codebook entry which represents a region of the space of possible channels states containing both states is used, the codebook entry being in the highest tier that has a codebook entry which represents a region of the space of possible channel states containing both states.

8. The method of claim 6 in which in the case that the first channel state is quantized using a first codebook entry in a first group of codebook entries, and the second channel state is not in any of the regions of the space of possible channel states represented by each of the codebook entries in the group of codebook entries, then the second channel state is quantized using a codebook entry in a group of codebook entries in which the first channel state is in a region of the space of possible channel states represented by one of the codebook entries in the group, and the second channel state is also in a region of the space of possible channel states represented by one of the entries in the group, and if more than one such group exists, a group in the highest tier containing such groups is used, and if no such group exists, a codebook entry in the lowest tier is used to quantize the second channel state.

9. The method of claim 4 in which the regions of the space of possible channel states corresponding to codebook entries in each group of each tier other than the lowest tier, and codebook entries in the lowest tier, are Voronoi regions for some choice of centroids and a metric.

10. The method of claim 8 in which the centroids for a lower tier correspond to a subset of the centroids for a higher tier.

11. The method of claim 3 in which information concerning which tier the codebook entry used to quantize the second channel state belongs to is transmitted with the codeword indices.

12. The method of claim 3 in which information concerning which tier the codebook entry used to quantize the second channel state belongs to is transmitted by using codewords varying in length according to the tier being used.

13. The method of claim 3 in which channel prediction is used to predict which tier the codebook entry used to quantize the second channel state belongs to.

14. The method of claim 3 in which a hybrid of the methods of claims 11, 12, and 13 is used.

15. The method of claim 3 in which channel prediction is used to recover from synchronization error or missing information concerning which tier the codebook entry used to quantize the second channel state belongs to.

16. The method of claim 3 in which in order to recover from synchronization error or missing information concerning which tier the codebook entry used to quantize the second channel state belongs to, the transmitter sends a request to do another quantization in a way not directly depending on the missing or erroneous quantization.

17. The method of claim 16 in which the transmitter includes information concerning what to use as the first quantized information with the request.

18. A method of constructing a codebook suitable for the use of the method of claim 5, comprising the steps of:

constructing a single-tiered codebook, to be used as a lowest tier of a multiple tier codebook; and for each entry in the lowest tier, selecting a region of a space of possible channel states and constructing a finer codebook to quantize the region of the space of possible channel states, and using the entries of the finer codebook as a group of entries in a second tier associated with the entry of the lowest tier; and if more tiers are desired, constructing further tiers in relation to the second tier in the same way as the second tier is constructed in relation to the first.

19. The method of claim 18 in which the region of the space of possible channel states that is used to construct the group of entries of the next tier is the same as the region of the space of possible channel states represented by that entry.

20. The method of claim 19 in which the regions of the space of possible channel states represented by each entry of the codebook are Voronoi regions and each group of entries in each higher tier is forced to have a centroid of one of the Voronoi regions co-located with a centroid of the region represented by the lower tier entry with which it is associated.

21. An apparatus consisting of:

a receiver comprising one or more antennas and a processing module processing module, said module configured to carry out the method steps of claim 1; and a transmitter comprising antennas and a processing module configured to process channel state information quantized by the method of claim 1 from one or more receivers and modulate a signal sent to one or more of the receivers according to the channel state information.