where C (m) (l) = C(m) k,d (l) =1, and {A, A k,d > } are ampltude factors. Denote the -pont untary nverse fast Fourer transform (IFFT) of (m) and (m) k,d by x(m) and, respectvely. After cyclc prefx (CP) nserton, the tme- Ths full text paper was peer revewed at the drecton of IEEE Communcatons Socety subject matter experts for publcaton n the IEEE GLOBECOM 25 proceedngs. A ew Rangng Method for OFDMA Systems Hlang Mnn, Member, IEEE and aoyu Fu, Student Member, IEEE Department of Electrcal Engneerng, Unversty of Texas at Dallas e-mal: {hlang.mnn, xxf31} @utdallas.edu Abstract We present a new ntal rangng method for OFDMA systems such as IEEE 2.16a. Frst, a new orthogonal rangng sgnal desgn s proposed by whch an effcent, lowcomplexty mult-user rangng sgnal detecton s developed. Based on the rangng sgnal detector results, power estmaton for the detected rangng subscrber statons s performed. Then, by utlzng the proposed orthogonal rangng sgnal desgn together wth the redundancy ntroduced by cyclc prefxes, a new teratve mult-user tmng offset estmator s presented. Compared wth the exstng methods utlzng the CDMA-type rangng codes (n frequency-doman) defned n IEEE 2.16a, the proposed method acheves a better performance and greater robustness aganst mult-user nterference and mult-path fadng channels. I. ITRODUCTIO In orthogonal frequency dvson multple access (OFDMA) systems (e.g., IEEE 2.16a [1]), the ssues of uplnk subcarrer orthogonalty and near/far problems are addressed by a process called rangng. Generally, a rangng process ncludes ntal rangng (for any rangng subscrber staton (RSS) that wants to synchronze to the system for the frst tme) and perodc rangng (to account for the user-movement over tme). Ths paper consders ntal rangng process at the base staton (BS) whch ncludes mult-user rangng code detecton, multuser tmng estmaton, and power estmaton. The rangng sgnals from IEEE 2.16a [1] use CDMA codes on all the rangng sub-carrers. Based on the rangng channel and rangng sgnals defned n [1], a rangng method based on a correlator bank n frequency-doman was presented n [2] and a tme-doman correlator bank based rangng method was proposed n [3]. The detects the multuser rangng codes by a fxed threshold. The method from [3] uses an adaptve detecton threshold and acheves an mproved detecton performance. In [4], a new rangng sgnal structure s presented whch dvdes all rangng opportuntes nto several groups. Rangng sgnals from dfferent groups do not nterfere wth each other whle wthn each group they nterfere wth each other. In ths scheme, the number of subcarrers n each sub-channel has to be equal to the length of the CDMA code and the sub-carrers must be assgned adjacently. Hence, t s not applcable n nterleaved OFDMA systems. Furthermore, same as the methods n [2] and [3], ts rangng performance wll depend on mult-path fadng channel effect and the correlaton propertes of CDMA codes. In ths paper, we present a new rangng sgnal desgn and a new rangng method for nterleaved OFDMA systems. The proposed rangng sgnal desgn s based on the orthogonalty prncple and the best channel dentfcaton condtons. Ths desgn results n robust, hgh performance, low-complexty mult-user rangng sgnal detecton and power estmaton. A new teratve estmaton of tmng offsets for all rangng subscrber statons s developed based on the proposed orthogonal rangng sgnal desgn and the cyclc prefx redundancy. If compared to exstng methods usng the exstng rangng sgnals, our rangng sgnal desgn and rangng method acheve a better performance and a greater robustness aganst nterference from other subscrber statons and mult-path fadng channel effects. II. SYSTEM DESCRIPTIO AD SIGAL MODEL We consder an uplnk of an OFDMA system wth sub-carrers n a tme-dvson duplexng setup. Durng a rangng tme-slot of M symbol ntervals, the sub-carrers are grouped nto Q R rangng sub-channels and Q D data subchannels. Each rangng sub-channel has 1R sub-carrers and each data sub-channel has 1D sub-carrers where 1R Q R + 1D Q D. In general, the sub-carrer assgnment of data and rangng sub-channels can be adaptve accordng to the system and channel condtons. The ndces of all the sub-carrers dedcated for the rangng channel and for the data subscrber statons (DSSs) are denoted by the sets J R and J D, and those allocated to -th RSS and k- th DSS are denoted by J and J k,d, respectvely. Each RSS uses q sub-channels where 1 q Q R. Durng the m-th symbol nterval of the rangng tme-slot, -th RSS transmts {C (m) (l) : l =,...,q 1R 1} on the sub-carrers defned by J whle k-th DSS transmts {C (m) k,d (l) : l =,..., k,d 1} on the sub-carrers defned by J k,d where k,d denotes the cardnalty of the set J k,d whch would be an nteger multple of 1D. In sub-carrer doman at m-th OFDM symbol nterval, the length- rangng code vector for -th RSS and the length- data vector for k-th DSS are denoted by (m) and (m) k,d, respectvely. Ther n-th elements (n {,..., 1}) are gven by < A C (m) (m) (n) = (l), : otherwse < A k,d C (m) (m) k,d (n) = k,d (l), : n = J(l), l =,...,q 1R 1 otherwse n = J k,d(l), l =,..., k,d 1 x (m) k,d (1) (2) IEEE Globecom 25 1435-73-9415-1/5/$2. 25 IEEE
Ths full text paper was peer revewed at the drecton of IEEE Communcatons Socety subject matter experts for publcaton n the IEEE GLOBECOM 25 proceedngs. doman transmtted sgnal samples of -th RSS are denoted by x >< (m) (l g), n = m( + g) +l, x (n) = l =,..., + g 1; m =,...,M 1, otherwse where {x (m) ( l) : and hence, x (m) DSS are denoted by ( l) =x(m) (3) l =1,..., g} represent CP samples ( l). Smlarly, those of k-th x >< (m) k,d (l g), n = m( + g) +l, x k,d (n) = l =,..., + g 1; m =, 1,..., n <. Suppose that there are R RSSs and D DSSs n the system and the system can support a maxmum of c smultaneous RSSs (correspondng to c rangng opportuntes or c dfferent rangng sgnals). The R RSSs rangng sgnal ndces are denoted by the set I R. For smplcty and wthout loss of generalty, we assume that -th RSS uses the rangng sgnal { (k)}, and hence I R = {,..., R 1} from the possble ndces {,..., c 1}. After obtanng the rangng channel nformaton through the control channel UL-MAP, each RSS chooses one of the c rangng sgnals randomly and performs ntal rangng process durng one rangng tmeslot. Snce the locatons of dfferent SSs are dfferent, the correspondng transmsson delays (d for -th RSS and d k,d for k-th DSS) are dfferent. Hence, at the begnnng of the rangng process, ther relatve delays wth respect to the BS s tme-slot boundary are dfferent. The maxmum possble relatve delay d max,r for a RSS s the round-trp transmsson delay for a RSS at the cell boundary. In practce, we can fnd ths maxmum relatve delay from the knowledge of cell radus. ote that g for RSSs should be desgned such that g d max,r + L. For DSSs, snce ntal rangng processes have already been completed, the maxmum possble delay d max,d s determned by the tmng requrement for the rangng process 1. We consder a mult-path Raylegh fadng channel wth L sample-spaced taps. The channel tap gans for -th RSS and k- th DSS (denoted by {h (l)} and {h k,d (l)}, l =,...,L 1, respectvely) are assumed to reman constant over one rangng tme-slot, and the average total energy of the channel taps s σh 2. Let the channel output samples for -th RSS sgnal be {y (n)} and those for k-th DSS be {y k,d (n)},.e., 2. L 1 y, (n) = h, (l)x, (n l d, ). (5) l= Then the n-th receved sgnal sample (n =, 1,...) at the BS can be expressed as R 1 D 1 y(n) = y (n) + y u,d(n) +w(n) (6) = u= where {w(n)} are ndependent and dentcally dstrbuted (d), crcularly-symmetrc complex Gaussan nose samples wth zero mean and varance σ 2 w. 1 The CP nterval for data transmsson can be desgned to be smaller than that of rangng symbols. 2 In the rest of the paper, the subscrpt * denotes whether R or D. (4) At the recever, we consder an observaton wndow of M( d + g )+ g samples to make sure that all receved rangng sgnals resde wthn ths observaton wndow regardless of ther possbly dfferent transmsson delays. There are M ISI-free wndows of samples each and (M +1) ISI-affected wndows of g samples each, n the observaton wndow. The sample ndces of m-th ISI-free wndow and m-th ISI-affected wndow are, respectvely, denoted by J (m) ISI free = {m( + g)+ g,...,(m +1)( + g) 1}, (7) m =,...,M 1 J (m) ISI = {m( + g),...,m( + g)+ g 1} () m =,...,M. otaton: We use the followng notatons: M = /M and [] M = modulo M. Hence = M M +[] M. III. PROPOSED RAGIG SIGAL DESIG We consder an nterleaved OFDMA system where 1R ( L) sub-carrers of each (ntal) rangng sub-channel are spread out across the sub-carrer doman wth an equal spacng of / 1R sub-carrers. Each RSS uses 1R sub-carrers (.e., q=1). The total number of rangng opportuntes provded by our desgn s c = Q R M. The c dfferent rangng sgnals (correspondng to the c rangng opportuntes) are dvded nto Q R groups. The sgnals from dfferent groups are transmtted on dfferent sub-carrers. The sub-carrer assgnment for -th RSS s defned by where J = {( n 1R + M ): n =,..., 1R 1} (9) M < 1R & M km f M k M. (1) A recommended choce for M s M /(Q R 1R ) whch assgns rangng sub-carrers of dfferent gorups equally spread out wth equal spacng across the entre bandwdth. ote that {J } and {J k,d } should be dsjont for all and k and {J } and {J k,r } are dsjont for all M k M but they are the same f M = k M. Due to the orthogonalty among sub-carrers, receved sgnals from dfferent groups would not nterfere wth each other f perfectly frequency-synchronzed. On the other hand, the M rangng sgnals n the same group are transmtted on the same 1R sub-carrers over M symbol ntervals. In order to separate these M rangng sgnals, we ntroduce phase-shft-orthogonalty over M symbol ntervals wthn each group as follows. The rangng sub-carrer symbols for -th RSS at m-th symbol nterval and -th symbol nterval are related by C (m) (l) =C() (l)ej2π[] M m/m, m =1,...,M 1. (11) The above orthogonal rangng code desgn provdes orthogonalty between any sgnal pars of the receved rangng and data sgnals and hence, t s optmal for mult-user rangng code detecton f perfectly frequency-synchronzed. ote that we set 1R L n our desgn so that the receved rangng sgnal from any RSS completely characterzes the correspondng channel 3. Our sub-carrer assgnment for rangng sub-channel apples the prncple of plot tone desgn for MIMO OFDM channel estmaton from [6] but we talor t to the rangng process. Hence, our rangng code desgn s optmal n terms of characterzng the correspondng channels 3 At least L plot tones are necessary for the dentfcaton of an L-tap channel. IEEE Globecom 25 1436-73-9415-1/5/$2. 25 IEEE
Ths full text paper was peer revewed at the drecton of IEEE Communcatons Socety subject matter experts for publcaton n the IEEE GLOBECOM 25 proceedngs. (may be useful n adaptve resource allocaton) whch n turn gves a better representaton of average power across the subcarrer doman for the RSS. It can be easly observed that all rangng codes are orthogonal to each other,.e., M 1 1 m= n= j (m) A (n)((m) k,r (n)) = 2 1RM, f = k, f k. Due to the orthogonalty, all rangng codes can be easly decoupled, renderng an effcent, low-complexty mult-user rangng code detecton as wll be dscussed n the next secton. IV. PROPOSED RAGIG METHOD Our frst performs mult-user rangng sgnal detecton based on the BS tmng reference. Then utlzng the rangng sgnal detecton results, a power estmaton and an teratve tmng estmaton are carred out for each detected RSS. Power and tmng estmates are compared wth rangng requrements and necessary control nformaton s broadcast back to the RSSs. A. Mult-User Rangng Sgnal Detecton Based on the BS tmng reference, we obtan frequencydoman receved k-th sub-carrer symbol (k {,..., 1}) at m-th symbol nterval (m {,...,M 1}) by-pont untary FFT of {y(n) : n J (m) ISI free } as = where (12) Y (m) (k) = 1 1 y(m( + g)+ g + l)e j2πlk/ (13) l= R 1 D 1 (m) (k)h(k) + (m) u,d (k)hu,d(k) +W (m) (k)(14) = u= j2πkd H (k) = e j2πkd,d H,D(k) = e W (m) (k) = L 1 l= L 1 h (l) e j2πlk (15) h,d(l) e j2πlk (16) l= 1 1 w(m( + g)+ g + l) e j2πlk. (17) l= Rangng codes usng dfferent rangng sub-carrers are already decoupled n the frequency-doman. Wthn each group of rangng codes usng the same rangng sub-carrers, the subcarrer symbols of dfferent rangng codes can easly be decoupled by utlzng the orthogonalty property (see (12), (1) and (11)) as Z (k) = = M 1 1 Y (m) (k)e j2π[] M m/m, k J (1) M m= ( () (k)h(k) + W (k), {,..., R 1} W (k) { R,..., c 1} (19) where { W (k)} are d crcularly symmetrc complex Gaussan random varables wth zero mean and varance σw/m 2. The decson varable D to decde the presence of the -th rangng sgnal s defned as D = = Z (k)z (k) (2) k J P >< (k)h(k) + W (k) 2, I R k J P W (k) 2 (21), / I R. k J The decson varable D s not affected by other RSSs and DSSs, resultng n an effcent, low-complexty mult-user rangng sgnal detecton. Our orthogonal rangng sgnal desgn s the key to ths effcent mult-user rangng sgnal detecton. The -th rangng sgnal detector decdes that the -th rangng sgnal s detected f D >η. The value of the threshold η s derved n the followng. Snce H (k) for k J are spread out across the whole bandwdth wth equal spacng and 1R n typcal OFDMA systems, {H (k) : k J } can be approxmately treated as ndependent random varables. Then D s a summaton of squares of 2 1R approxmatelyd real-valued random varables and can be consdered as a ch-square random varable wth 2 1R degrees of freedom. Hence, the probablty densty functon of D can be gven by where p D (x) x 1 σ 2 1R 2 1R Γ( x1r 1 2σ e 2,x (22) 1R) < A 2 σ 2 = σ2 h 2 + σ2 w 2M, I R : σ w 2 (23) 2M, otherwse. The detecton threshold η s derved from the followng maxmum-lkelhod crteron and obtaned as η = p D IR p D / IR (24) 2 1Rσ 2 / I R ln 1 σ2 / I R σ 2 I R σ 2 I R σ 2 / I R = 1Rσ2 w M (1 + 1R SR M )ln! 1+ SRM «1R where SR s the SR of -th rangng sgnal defned as SR = 1RA2 E[ H(k) 2 ] σ 2 w 1RA2 σ2 h σ 2 w ote that η s the same for all f transmt-powers of all RSSs are the same. Also, under fxed system parameters ( 1R,, M, σ 2 w), the changes n η value due to dfferent SR values (say wthn [-1dB 2dB]) s very small and can be neglected when compared wth the mean of D n the frst case ( I R ) of (21). So we can use a fxed detecton threshold as η = 1Rσ2 w M (1 + 1R SR f M ) ln 1+ SR «f M 1R where SR f s a fxed desgn SR for the detecton threshold and n our smulaton we use SR f = 1. To estmate the nose power σw 2 requred n the detecton threshold, we can keep one fxed rangng opportunty (say -th rangng code) unused. The correspondng D corresponds to the second case ( / I R ) of (21) from whch the BS recever can easly estmate the nose power as (25) (26) (27) (2) σˆ w 2 = D M/1R. (29) It s also possble to pre-measure the nose power by other means at the BS wthout sacrfcng a rangng opportunty. We can alternatvely use a fxed desgn value of σw 2 for the detecton threshold. For envronments wth varyng nose and nterference levels, nose (nterference ncluded) power estmator could be used, otherwse, a fxed desgn value of σw 2 would be a preferred choce. IEEE Globecom 25 1437-73-9415-1/5/$2. 25 IEEE
Ths full text paper was peer revewed at the drecton of IEEE Communcatons Socety subject matter experts for publcaton n the IEEE GLOBECOM 25 proceedngs. In the presence of resdual normalzed (by the sub-carrer spacng) frequency offsets, the σ 2 requred n the detecton threshold can be approxmated as >< 1 e j2π v 2 h PM 1 σ 2 (1 e j2π v/ ) l= G l, + σ 2 w /(2M), I R 1 e j2π v 2 h PM 1 (1 e j2π v/ ) l=,l G l, + σ 2 w /(2M), / I R (3) where v s a fxed desgn value of resdual normalzed frequency offset (upper end of possble resdual normalzed frequency offset range) and G l, = σ2 h 2M 2 A2 l 1 e j2π(m(+g ) v/+[l] M [] M ) 2 1 e j2π[(+g ) v/+([l] M [] M )/M ]. (31) The detecton threshold n the presence of resdual frequency offset can be calculated from (25) where σ 2 s gven by (3). B. Power Estmaton After -th rangng sgnal s detected, the next step n the rangng process s to estmate the correspondng (normalzed) receved power P defned by From (21), we obtan P (k) 2 H R,(k) 2 k J P =. (32) D P W (n) 2 P 2R[ (k)h (k) W (k)]} k J k J P =. (33) Snce the last term n the nomnator has a zero mean, we smply estmate the receved power of -th rangng sgnal as C. Iteratve Tmng Offset Estmaton ˆP = D σ2 w 1R/M. (34) The receved samples {y(n)} are the superposton of sgnals from R RSSs and D DSSs wth dfferent channels and dfferent tmng offsets. Rangng process estmates the tmng offsets of all detected RSSs based on the receved samples {y(n)} wthn the observaton wndow. We address ths mult-user tmng offset estmaton by means of R sngle RSS tmng offset estmators. For each detected RSS, an teratve tmng offset estmator s developed. Although multuser tmng offsets are not jontly estmated, each tmng offset estmator utlzes the tmng offset estmates of the other RSSs obtaned n the prevous teraton. The proposed tmng offset estmator explots the proposed orthogonal rangng sgnal desgn and the sgnal redundancy ntroduced by the CPs. Based on the orthogonalty among the RSSs and DSSs sgnals over M ISI-free wndows, we can obtan nterference-free clean samples (denoted by {, (n) : n =,..., 1}) of the channel-output m-th symbol (except nose contamnaton) for -th SS as (see (19) and (11)) (n) = 1,D (n) = 1 k J Z (k)e u J,D Y (m) (u)e j2πnk e j2πm[] M M (35) j2πnu. (36) From {, (n)}, we can reconstruct, for -th RSS (or DSS) wth transmsson delay d, a clean verson of the m- th symbol s CP, (d) (or ȳ(m) (d)) gven by ><,,CP (d) =,CP,D,CP h d, ȳ () T, ( g + d),...,ȳ(), ( 1), m = h ȳ (m 1), (),...,ȳ (m 1), (d 1), T, ( g + d),...,ȳ(m), ( 1), m where d s the all-zero vector of length d. On the other hand, we can obtan another verson of the CP (nterference-affected verson denoted by ŷ (m),cp ) by subtractng the clean verson of CPs of the other SSs from the receved CP wthn the ISI-affected wndow, y (m) CP, as follows: ŷ (m),cp = y(m) CP k I R,k D 1 k,r,cp (d k,r) u,d,cp (τ (D) ) (3) u= where τ (D) s the desgn parameter to replace the actual transmsson delays for all DSSs snce no tmng offset estmaton for DSS s performed. The ŷ (m),cp contans correct tmng nformaton d (embedded n y (m) CP ) and hence, the tmng offset estmate for -th RSS can be obtaned by maxmzng a sldng correlaton metrc between the clean verson and the nterference-affected verson as ˆd = arg max R d d max,r ( M 1 m= ) H,CP (d) ŷ(m),cp. (39) Constructng ŷ (m),cp requres the knowledge of {d k,r : k } whch are unknown and what the tmng offset estmator for k-th RSS s estmatng. However, we can apply an teratve () approach where {d k,r : k } are replaced wth { ˆd k,r : k } = τ (R) at the begnnng of the frst teraton to get the - (1) th RSS s tmng offset estmate { ˆd } at the end of the frst teraton. In general, at θ-th teraton, the nterference-affected verson ŷ (m,θ 1) (θ 1),CP s constructed by usng { ˆd k,r : k } and hence, the -th RSS s tmng offset estmate at the θ-th teraton s gven by ˆd (θ) = arg max R d d max,r ( M 1 m= ) H,CP (d) ŷ(m,θ 1),CP. (4) We assume that the tmng offset d k, s a random varable wth a unform dstrbuton n {,...,τ max } where τ max s equal to d max,r for RSS and d max,d for DSS. Then the best ntal tmng offset value τ whch gves the smallest tmngmsmatch-nterference energy s obtaned by Z τmax τ =argmn{ τ x τ τ max dx} = τmax 2. (41) Hence, the best ntal tmng offset estmates used n our tmng offset estmator are gven by τ (R) = dmax,r 2, τ (D) = dmax,d. (42) 2 V. SIMULATIO RESULTS AD DISCUSSIO The OFDMA system parameters are selected from [1]. The uplnk bandwdth s 3 MHz, the sub-carrer spacng s 1.67 KHz, and = 24. The rangng channel has 12 sub-carrers over M =2symbol ntervals. For the proposed rangng sgnal structure, the parameters used are: 1R =, q =1, Q R =16, M = 16 M, and (37) IEEE Globecom 25 143-73-9415-1/5/$2. 25 IEEE
Ths full text paper was peer revewed at the drecton of IEEE Communcatons Socety subject matter experts for publcaton n the IEEE GLOBECOM 25 proceedngs. c = 32. We use QPSK format for DSS. The combned transmt and receve flter s a rased-cosne flter g T (t) wth a roll-off factor of.5. The SUI-3 channel model wth 3 paths [5] s used and the (statstcal) average total energy of all channel taps σh 2 s set to unty. The channel mpulse response for the -thusersgvenbyh (l) = 2 = γ g T (lt s τ t ), l =,..., L 1; where {γ } and {τ } are the gans and delays of the channel paths, t s a tme shft for causalty, and 1/T s s tmes the sub-carrer spacng. The number of sample-spaced channel taps, L, s set to 7. Channels of dfferent users are assumed to be ndependent. We consder a cell radus of 5km whch gves the maxmum transmsson delay (round trp) d max,r =34µs = 12 samples. g s set to 12 samples satsfyng the condton d max,r < g L. The tmng requrement based on [1] s that all uplnk OFDM symbols should arrve at the BS wthn an accuracy of ±25% of the mnmum guard-nterval or better. In [1], g can be 1/4, 1/, 1/16, or1/32 of, and hence, the tmng offset should be wthn ±16 samples. We set d max,d =32. For comparson, we nclude the performance of the methods from [2] and [4] whch use the CDMA/GCL rangng codes. In the smulaton, the maxmum number of RSSs n one tme slot, R,max,sset to 15. We also nclude resdual normalzed frequency offsets n the range of [.2,.2] whch are assumed to be d for dfferent SSs. The value of nose power requred n settng the detecton threshold for the s obtaned by (29). A. Mult-User Detecton Performance Fg. 1 shows the probablty of correct detecton (P CD ) versus the number of RSSs for the condtons of DSS, 15 DSSs, and 3 DSSs n one rangng tme-slot. The P CD s defned as E[ Dc R ] where D c s the number of correct detecton n one rangng tme-slot. All three methods are robust to the data users nterference and resdual frequency offsets. However, the reference methods P CD performances degrade sgnfcantly as the number of RSSs ncreases (from 1. for R = 1 down to.65 for R = 15) whle the proposed method s performance remans the same at P CD =1.. Fg. 2 shows the probablty of detecton false-alarm (P FA ) versus the number of RSSs for the condtons of DSS, 15 DSSs, and 3 DSSs n one rangng tme-slot. The P FA s D defned as E[ a c R ] where D a s the number of rangng codes wthn one rangng tme-slot whch are detected at the BS but are not transmtted from any RSSs. All methods are robust to frequency offsets. Proposed method and the method from [2] are robust to RSS nterference and DSS nterference whle P FA performance of the degrades as the number of RSS ncreases. Proposed method has a better P FA performance than both reference methods under all condtons consdered. Fg. 3 shows the probablty of mssed detecton (P MD ) versus the number of RSSs for the condtons of DSS, 15 DSSs, and 3 DSSs n one rangng tme-slot. The P MD s defned as E[ Dm R ] where D m s the number of RSSs whch are transmtted by RSSs but are not detected at the BS. The s P MD performance s robust to the DSS nterference, RSS nterference and frequency offsets whle the reference methods performances degrade as the number of RSSs ncreases (from P MD =at R =1to P MD =5 at R =15). Hence, the has a much better performance than the two reference methods, especally n multple RSSs condtons. B. Power Estmaton Performance Fg. 4 shows the normalzed power estmaton MSE defned as E[(1 ˆP P ) 2 ] versus the number of RSSs for the condtons of DSS, 15 DSSs, and 3 DSSs n one rangng tme-slot. Snce there s no power estmator provded n [2] and [4], only the s performances n the absence/presence of frequency offsets are plotted. Power estmaton performance s robust to DSS nterference and the number of RSSs n the absence of frequency offsets. We observe that although the power estmaton performance degrades as the number of RSSs ncreases n the presence of frequency offsets, the performance s stll very good. C. Tmng Estmaton Performance Fg. 5 shows the standard devaton of the tmng offset estmate versus the number of RSSs for the condtons of DSS, 15 DSSs, and 3 DSSs n one rangng tme-slot. In each smulaton run, the true tmng offsets for RSSs and DSSs are taken randomly from the nterval [,d max,r ] and [,d max,d ], respectvely. All the three methods are robust to the DSS nterference and resdual frequency offsets. The performances of all tmng estmators degrade as the numbers of RSSs and DSSs ncrease but the gves a much better performance, especally n multple RSSs condton. Furthermore, the satsfes the tmng requrement provded n [1] all the tme whle the two reference methods satsfy the requrement only when the number of RSSs s small. We also evaluated the proposed tmng estmator wth dfferent number of teratons n the presence of frequency offsets (the plot s omtted due to space lmtaton). Twoteraton s the best choce snce more teratons do not brng n a notceable mprovement. VI. COCLUSIOS We have presented a new rangng sgnal desgn and a new ntal rangng method for OFDMA systems n multpath fadng channel envronments. The proposed rangng sgnal desgn s based on the orthogonalty prncple and the best channel dentfcaton condtons. Ths orthogonal rangng sgnal desgn results n robust, hgh performance, low-complexty mult-user rangng sgnal detecton and power estmaton. A new teratve estmaton of tmng offsets for all rangng subscrber statons s developed based on the proposed orthogonal rangng sgnal desgn and the cyclc prefx redundancy. The smulaton results show that the new approach s more robust to nterference from other rangng/data subscrber statons and mult-path fadng channel effects and also has better performance than the exstng methods whch use the CDMAtype rangng codes n frequency-doman. IEEE Globecom 25 1439-73-9415-1/5/$2. 25 IEEE
Ths full text paper was peer revewed at the drecton of IEEE Communcatons Socety subject matter experts for publcaton n the IEEE GLOBECOM 25 proceedngs. Fg. 1. Probablty of correct detecton 1.9..7.6.5 3s Probablty of correct detecton 1.9..7.6.5 Wth frequency offsets 3s The probablty of correct detecton for several rangng code detectors Probablty of detecton false alarm.2.1 3 data uesers Probablty of detecton false alarm.2.1 Wth frequency offsets 3 data uesers Fg. 2. The probablty of detecton false-alarm for several rangng code detectors ACKOWLEDGMET Ths work was supported n part by the Erk Jonsson School Research Excellence Intatve, the Unversty of Texas at Dallas, Texas, USA. REFERECES [1] IEEE LA/MA Standards Commttee, Broadband Wreless Access: IEEE MA standard, IEEE 2.16 a, 23. [2] Jerry Krnock, Manoneet Sngh, MIke Paff, Vncent, Arvnd Lonkar, Lawrence Fung and Chn-Chen Lee, Comments on OFDMA Rangng Scheme descrbed n IEEE 2.16ab-1/1r1, Document IEEE 2.16abc-1/24 [3] aoyu Fu, Hlang Mnn, Intal Uplnk Synchronzaton and Power Control (Rangng Process) for OFDMA Systems, Globecomm 24, pp. 3999-43. [4] angyang (Jeff) Zhuang, kevn Baum, Vjay anga, Mark Cudak Rangng Improvement for 2.16e OFDMA PHY, Document IEEE 2.16e-4/143r1 [5] IEEE LA/MA Standards Commttee, Channel Models for Fxed Wreless Applcatons, Document IEEE.2.16.3c-1/29r4. [6] H. Mnn and. Al-Dhahr, Optmal tranng sgnals for MIMO OFDM channel estmaton, IEEE Globecom 24, pp. 219-224. [7] IEEE LA/MA Standards Commttee, Broadband Wreless Access: IEEE MA standard, IEEE 2.16, 24. Fg. 3. Probablty of mssed detecton.5.2.1 3s Probablty of mssed detecton.5.2.1 Wth frequency offsets 3s The probablty of mssed-detecton for several rangng code detectors ormalzed MSE of power estmator Fg. 4. Standard devaton of tmng offset estmator 1 3 1 4 3s SR = 1 db wth frequency offsets wthout frequency offsets 1 5 The normalzed MSE of the power estmator at SR = 1 db 1 2 3s 1 1 1 Standard devaton of tmng offset estmator 1 2 1 1 Wth frequency offsets 3s 1 Fg. 5. The standard devaton (n samples) of the tmng offset estmators at SR = 1 db IEEE Globecom 25 144-73-9415-1/5/$2. 25 IEEE