arXiv:0802.4344v1 [cs.IT] 29 Feb 2008 An Improved Scheme for Initial Ranging in OFDMA-based Networks Luca Sanguinetti* and Michele Morelli H. Vincent Poor Department of Information Engineering University of Pisa Pisa, Italy luca.sanguinetti, michele.morelli@iet.unipi.it Department of Electrical Engineering Princeton University Princeton, NJ USA poor@princeton.edu Abstract— An efficient scheme for initial ranging has recently been proposed by X. Fu et al. in the context of orthogonal frequency-division multiple-access (OFDMA) networks based on the IEEE 802.16e-2005 standard. The proposed solution aims at estimating the power levels and timing offsets of the ranging subscriber stations (RSSs) without taking into account the effect of possible carrier frequency offsets (CFOs) between the received signals and the base station local reference. Motivated by the above problem, in the present work we design a novel ranging scheme for OFDMA in which the ranging signals are assumed to be misaligned both in time and frequency. Our goal is to estimate the timing errors and CFOs of each active RSS. Specifically, CFO estimation is accomplished by resorting to subspacebased methods while a least-squares approach is employed for timing recovery. Computer simulations are used to assess the effectiveness of the proposed solution and to make comparisons with existing alternatives. I. I NTRODUCTION The main impairment of an orthogonal frequency-division multiple-access (OFDMA) network is represented by its remarkable sensitivity to timing errors and carrier frequency offsets (CFOs) between the uplink signals and the base station (BS) local references. For this reason, the IEEE 802.16e-2005 standard for OFDMA-based wireless metropolitan area networks (WMANs) specifies a synchronization procedure called Initial Ranging (IR) where subscriber stations that intend to establish a link with the BS can use some dedicated subcarriers to transmit their specific ranging codes [1]. Once the BS has revealed the presence of ranging subscriber stations (RSSs), it has to estimate some fundamental parameters including timing errors, CFOs and power levels. Two prominent schemes for initial synchronization and power control in OFDMA were proposed in [2] and [3]. In these works, a long pseudo-noise sequence is transmitted by each RSS over the available ranging subcarriers. Timing recovery is then accomplished on the basis of suitable correlations computed in the frequency- and time-domain, respectively. The main drawback of these methods is their sensitivity to *This work was completed while the author was with Princeton University and it was supported by the U.S. National Science Foundation under Grants ANI-03-38807 and CNS-06-25637. multipath distortion, which destroys orthogonality among the employed codes and gives rise to multiple access interference (MAI). Better results are obtained in [4] by using a set of generalized chirp-like (GCL) sequences, which echibits increased robustness against the channel selectivity. A different approach to managing the IR process has recently been proposed in [5]. Here, the pilot streams transmitted by RSSs are spread in the time-domain over adjacent OFDM blocks using orthogonal codes. In this way, signals of different RSSs can be easily separated at the BS as they remain orthogonal after propagating through the channel. Timing information is eventually acquired in an iterative fashion by exploiting the autocorrelation properties of the received samples induced by the use of the cyclic prefix (CP). Unfortunately, this scheme is derived under the assumption of perfect frequency alignment between the received signals and the BS local reference. Actually, the occurrence of residual CFOs results into a loss of orthogonality among ranging codes and may lead to severe degradations of the system performance in terms of misdetection probability and estimation accuracy. In the present work we propose a novel ranging scheme for OFDMA systems that is robust to time and frequency misalignments. The goal is to estimate timing errors and CFOs of all active RSSs. The number of active codes is found by resorting to the minimum description length (MDL) principle [6] while the multiple signal classification (MUSIC) algorithm [7] is employed to detect which codes are actually active and to determine their corresponding CFOs. Timing estimation is eventually achieved through least-squares (LS) methods. Although the proposed solution allows one to estimate the timing errors of each RSS in a decoupled fashion, it may involve huge computational burden in applications characterized by large propagation delays. For this reason, we also present an alternative scheme derived from ad hocreasoning which results into substantial computational saving. It is worth noting that timing synchronization in OFDMA uplink transmissions has received little attention so far. A well-established way to handle timing errors is to design the CP length large enough to include both the channel delay spread and the two-way propagation delay between the BS and the user station [8]. This leads to a quasi-synchronous system in which timing errors can be viewed as part of the channel impulse response (CIR) and are compensated for by the channel equalizer. Unfortunately, this approach poses an upper limit to the maximum tolerable propagation delay or, equivalently, to the maximum distance between the BS and the subscriber stations [9]. For this reason, its application to a scenario with large cells (as envisioned in next broadband wireless networks) is hardly viable. In the latter case, accurate knowledge of the timing errors is required in order to align the uplink signals to the BS time scale. II. S YSTEM DESCRIPTION AND SIGNAL MODEL A. System description The investigated OFDMA network employs N subcarriers with frequency spacing ∆f and indices in the set J = {0, 1, . . . , N − 1}. Following [5], we denote R the number of subchannels reserved for the IR process. Each subchannel is divided into Q subbands uniformly spaced over the signal bandwidth at a distance (N/Q)∆f from each other. A given subband is composed of a set of V adjacent subcarriers. The subcarrier indices within the qth subband (q = 0, 1, . . . , Q−1) of the rth ranging subchannel (r = 0, 1, . . . , R − 1) are (r) (r) collected into a set Jq = {iq,ν ; ν = 0, 1, . . . , V − 1} with entries rN qN + + ν. (1) i(r) q,ν = Q QR The rth subchannel is thus composed of subcarriers with Q−1 (r) indices taken from J (r) = ∪q=0 Jq . Hence, a total of NR = QV R ranging subcarriers are available in the system (r) with indices in the set JR = ∪R−1 . The remaining r=0 J N − NR subcarriers are used for data transmission and are assigned to data subscriber stations (DSSs) which have already completed their IR process and are assumed to be perfectly synchronized to the BS time and frequency scales [5]. We denote by M the number of consecutive OFDM blocks reserved for IR and assume that each ranging subchannel can be accessed at most by M −1 RSSs. The latter are separated by means of specific ranging codes selected in a pseudo-random fashion from a predefined set {c1 , c2 , . . . , cM−1 }, with ck = [ck (1), ck (2), . . . , ck (M )]T (the superscript T denotes the transpose operation). As in [5], we assume that different RSSs employ different codes. Without loss of generality, in what follows we concentrate on the rth ranging subchannel and denote by K (r) ≤ M − 1 the number of simultaneously active RSSs. Also, to simplify the notation, the subchannel index (r) is dropped in all subsequent derivations. The waveform transmitted by the kth RSS (1 ≤ k ≤ K) propagates through a multipath channel characterized by an impulse response hk = [hk (0), hk (1), . . . , hk (L − 1)]T of length L (in sampling periods). At the BS, the received samples are not synchronized with the local references. We denote by θk the timing error expressed in sampling periods while εk is the frequency offset normalized to the subcarrier spacing. As discussed in [8], subscriber stations that intend to start the ranging process compute initial frequency and timing estimates on the basis of a downlink control signal broadcast by the BS. The estimated parameters are then employed by each RSS as synchronization references for the uplink ranging transmission. This means that during IR the CFOs are only due to Doppler shifts and/or estimation errors and, in consequence, they are assumed to lie within a small fraction of the subcarrier spacing. Furthermore, in order to eliminate interblock interference (IBI), we assume that during the ranging process the CP length comprises NG ≥ θmax +L sampling periods, where θmax is the maximum expected timing error [9]. This assumption is not restrictive, since in many standardized OFDM systems the initialization blocks are usually preceded by long CPs. B. Signal model We denote by Ym the QV -dimensional vector that collects the DFT outputs corresponding to the considered subchannel during the mth OFDM block. Since the DSSs are assumed to be perfectly synchronized to the BS references, their signals will not contribute to Ym . In contrast, the presence of uncompensated CFOs destroys orthogonality among ranging signals, thereby leading to some interchannel interference (ICI). However, as the subchannels are well separated in the frequency domain, we can reasonably neglect interference on Ym arising from ranging signals of subchannels other than the considered one. Under this assumption, we may write Ym = K X ck (m)ejmωk NT A(ωk )Sk (θk ) + nm (2) k=1 where ωk = 2πεk /N , NT = N + NG is the duration of the cyclically extended block and nm is a Gaussian vector with zero mean and covariance matrix σ 2 IQV (we denote by IN the identity matrix of order N ). Also, we have defined A(ωk ) = FV(ωk )FH (3) where V(ωk ) accounts for the CFOs and is given by  V(ωk ) = diag ejnωk ; n = 0, 1, . . . , N − 1 (4)  H H  H while F = F0 , F1 , . . . , FH (the superscript H denotes Q−1 the Hermitian transposition) with Fq (q = 0, 1, . . . , Q − 1) denoting a V × N matrix with entries 1 [Fq ]ν,n = √ e−j2πniq,ν /N N 0 ≤ ν ≤ V −1, 0 ≤ n ≤ N −1. (5) Vector Sk (θk ) in (2) can be partitioned as Sk (θk ) =  T T Sk (θk , i1 ), STk (θk , i2 ), . . . , STk (θk , iQ−1 ) , where Sk (θk , iq ) is a V -dimensional vector with elements Sk (θk , iq,ν ) = e−j2πθk iq,ν /N Hk (iq,ν ), 0 ≤ ν ≤ V − 1 (6) while Hk (iq,ν ) denotes the channel frequency response over the iq,ν th subcarrier and is given by Hk (iq,ν ) = L−1 X hk (ℓ)e−j2πℓiq,ν /N . (7) ℓ=0 From (6) we see that θk simply appears as a phase shift across the DFT outputs. The reason is that the CP length is larger than the maximal expected propagation delay, thereby making the ranging signals quasi-synchronous. In the following sections we show how vectors {Ym }M−1 m=0 can be exploited to compute frequency and timing estimates for all active ranging codes. III. E STIMATION OF THE K X ck (m)ejmωk NT Sk (θk ) + nm . (8) This equation indicates that each CFO results only in a phase shift between contiguous OFDM blocks. Collecting the iq,ν th DFT output of all M ranging blocks into a vector Y(iq,ν ) = [Y0 (iq,ν ), Y1 (iq,ν ), . . . , YM−1 (iq,ν )]T , we may write K X Sk (θk , iq,ν )Γ(ωk )ck + n(iq,ν ) (9) k=1 where n(iq,ν ) is Gaussian distributed with zero-mean and covariance matrix σ 2 IM , while Γ(ωk ) = diag{ejmωk NT ; m = 0, 1, . . . , M − 1} is a diagonal matrix that accounts for the phase shifts induced by ωk . Inspection of (9) reveals that, apart from thermal noise, vector Y(iq,ν ) is a linear combination of the frequency-rotated codes {Γ(ωk )ck }. This means that the signal space is spanned by the K vectors {Γ(ωk )ck } that correspond to the active RSSs [10]. Then, if we temporarily assume that the number K of active codes is known at the receiver, an estimate of ωk (k = 1, 2, . . . , K) can be obtained by resorting to the MUSIC algorithm [7]. To see how this comes about, we use the observations {Y(iq,ν )} to obtain the following sample correlation matrix R̂Y = 1 QV V −1 Q−1 X X Y(iq,ν )YH (iq,ν ). (10) v=0 q=0 Next, based on the forward-backward (FB) approach [10], we compute e Y = 1 (R̂Y + JR̂TY J) R (11) 2 where J is the exchange matrix with 1’s on the anti-diagonal and 0’s elsewhere. We denote by λ1 ≥ λ2 ≥ · · · ≥ λM the e Y arranged in non-increasing order, and by eigenvalues of R {s1 , s2 , . . . , sM } the corresponding eigenvectors. The MUSIC algorithm relies on the fact that the eigenvectors associated (12) ω e with 1 Ψk (e ω ) = PM m=K+1 k=1 Y(iq,ν ) = ω̂k = arg max {Ψk (e ω)} , CFO S To simplify the derivation, we assume that the CFOs are adequately smaller than the subcarrier spacing, i.e., |ωk | ≪ 1. In such a case, matrices A(ωk ) in (3) can reasonably be replaced by IN to obtain [8] Ym ≈ with the M −K smallest eigenvalues are an estimated basis of the noise subspace and, accordingly, they are approximately orthogonal to all vectors in the signal space [7]. Hence, an estimate of ωk is obtained by minimizing the projection of Γ(e ω )ck onto the noise subspace, i.e., H ω )s cH m k Γ (e 2. (13) It is worth observing that CFO recovery must be accomplished for any active RSS. However, since the BS has no prior knowledge as to which codes have been transmitted in the considered subchannel, it must evaluate the quantities {ω̂1 , ω̂2 , . . . , ω̂M−1 } for the complete set {c1 , c2 , . . . , cM−1 }. At this stage the problem arises of identifying which codes are actually active. The identification algorithm looks for the K largest values in the set {Ψk (ω̂k )}M−1 k=1 , say {Ψuk (ω̂uk )}K , and declare as active the corresponding k=1 codes {cuk }K k=1 . The CFO estimates are eventually found as T ω̂u = [ω̂u1 , ω̂u2 , . . . , ω̂uK ] . At this stage we are left with the problem of estimating the parameter K to be used in (13). For this purpose, we adopt the MDL approach and obtain [6] n o (14) K̂ = arg min F (K̃) K̃ where F (K̃) is the following metric F (K̃) = 1 K̃(2M − K̃) ln(QV )−QV (M − K̃) ln ρ(K̃) (15) 2 with ρ(K̃) denoting the ratio between the geometric and arithmetic mean of {λK̃+1 , λK̃+2 , . . . , λM }. Finally, replacing K by K̂ in (13) leads to the proposed MUSIC-based frequency estimator (MFE) while the described identification algorithm is called the MUSIC-based code detector (MCD) IV. E STIMATION OF THE TIMING DELAYS After code detection and CFO recovery, the BS must acquire information about the timing delays of all ranging signals. This problem is now addressed by resorting to LS methods. In doing so we still assume that the number of active codes has been correctly estimated so that K̂ = K. Also, to simplify the notation, the indices {uk }K k=1 of the detected codes are relabeled following the map uk −→ k for k = 1, 2, . . . , K. We begin by reformulating (9) in a more compact form. For this purpose, we collect the CFOs and timing errors in two K-dimensional vectors ω = [ω1 , ω2 , . . . , ωK ]T and θ = [θ1 , θ2 , . . . , θK ]T . Then, after defining the matrix C(ω) = [Γ(ω1 )c1 Γ(ω2 )c2 · · · Γ(ωK )cK ] and the vector S(θ, iq,ν ) = [S1 (θ1 , iq,ν ), S2 (θ2 , iq,ν ), . . . , SK (θK , iq,ν )]T , we may rewrite (9) in the equivalent form Y(iq,ν ) = C(ω)S(θ, iq,ν ) + n(iq,ν ). (16) Omitting for simplicity the functional dependence of S(θ, iq,ν ) on θ and assuming ω̂ ≈ ω, from (16) the maximum likelihood estimate of S(iq,ν ) is found to be Ŝ(iq,ν ) = [CH (ω̂)C(ω̂)]−1 CH (ω̂)Y(iq,ν ). and we have denoted by ŝk (ν, ℓ) the Q-point IDFT of the sequence {Ŝk (iq,ν ); 0 ≤ q ≤ Q − 1}. In the sequel θ̂k is termed the LS-based timing estimator (LS-TE). Once θ̂k has been computed from (23), it is used in (22) to estimate the CIR of the kth RSS as ĥk = (17) Substituting (16) into (17) yields Ŝ(iq,ν ) = S(iq,ν ) + ξ(iq,ν ) (18) Ŝk (iq,ν ) = e 2πθk N iq,ν L−1 X hk (ℓ)e −j 2πn N iq,ν + ξk (iq,ν ). (19) ℓ=0 iT h On denoting Ŝk (ν) = Ŝk (i0,ν ), Ŝk (i1,ν ), . . . , Ŝk (iQ−1,ν ) , 2πθk and Φ(θk , ν) = diag{e−j N may rewrite (19) as follows iq,ν ; q = 0, 1, . . . , Q − 1}, we Ŝk (ν) = Φ(θk , ν)F(ν)hk + ξ k (ν) (20) where ξ k (ν) = [ξk (i0,ν ), ξk (i1,ν ), . . . , ξk (iQ−1,ν )]T while F(ν) is a matrix of dimension Q × L with entries [F(ν)]q,ℓ = 2πℓ e−j N iq,ν for 0 ≤ q ≤ Q − 1 and 0 ≤ ℓ ≤ L − 1 Equation (20) indicates that, apart from the disturbance term ξ k (ν), Ŝk (ν) is only contributed by the kth RSS, meaning that ranging signals have been successfully decoupled at the BS. We may thus exploit vectors {Ŝk (ν) ; ν = 0, 1, . . . , V − 1} to get LS estimates of (θk , hk ) separately for each RSS. This amounts to minimizing the following objective function with respect to (θ̃k , h̃k ) Λk (θ̃k , h̃k ) = V −1 X ν=0 2 Ŝk (ν) − Φ(θ̃k , ν)F(ν)h̃k . (21) V −1 1 X H ĥk = F (ν)ΦH (θ̃k , ν)Ŝk (ν) QV ν=0 (22) 0≤θ̃k ≤θmax where Υ(θ̃k ) is given by θ̃kX +L−1 ℓ=θ̃k |ŝk (0, ℓ)|2 (26) and becomes periodic in θ̃k with period Q. In such a case, the estimate θ̂k is affected by an ambiguity of multiples of Q. This ambiguity does not represent a serious problem as long as Q can be chosen to be greater than θmax . Unfortunately, in some applications this may not be the case. For example, in [5] we have Q = 8 while θmax = 102. A. Reduced-complexity timing estimation Although separating the RSS signals at the BS considerably reduces the system complexity, evaluating Υ(θ̃k ) for θ̃k = 0, 1, . . . , θmax may still be computationally demanding, especially in applications where θmax is large. For this reason, we now develop an ad-hoc reduced complexity timing estimator (RC-TE). We begin by decomposing the timing error θk into a fractional part βk , less than Q, plus an integer part which is multiple of Q, i.e., θ k = βk + p k Q (27) where βk ∈ {0, 1, . . . , Q− 1} while pk is an integer parameter taken from {0, 1, . . . , P − 1} with P = ⌊θmax /Q⌋. Omitting the details, it is possible to rewrite Υ(θ̃k ) as (28) where Υ1 (β̃k ) = β̃kX +L−1 V −1 X ν=0 2 |ŝk (ν, ℓ)| (29) while Υ2 (β̃k , p̃k ) is shown in (30) at the top of the next page. The RC-TE is a suboptimal scheme which, starting from (28), estimates βk and pk in a decoupled fashion. More precisely, an estimate of βk is first obtained looking for the maximum of Υ1 (β̃k ), i.e., n o Υ1 (β̃k ) . (31) β̂k = arg max 0≤β̃k ≤Q−1 θ̃kX +L−1 V −1 X ℓ=θ̃k V =1 = ℓ=β̃k where we have used the identity FH (ν)F(ν) = Q · IL . Then, substituting (22) into (21) and minimizing with respect to θ̃k yields the timing estimate in the form n o Υ(θ̃k ) (23) θ̂k = arg max Υ(θ̃k ) = Υ(θ̃k ) Υ(θ̃k ) = Υ1 (β̃k ) + Υ2 (β̃k , p̃k ) For a fixed θ̃k , the minimum of Λk (θ̃k , h̃k ) is achieved at (25) It is worth noting that for V = 1 the timing metric (24) reduces to where ξ(iq,ν ) is a zero-mean disturbance term. From (6) and (7) it follows that −j V −1 1 X H F (ν)ΦH (θ̂k , ν)Ŝk (ν). QV ν=0 ν=0 2 ŝk (ν, ℓ)ej2πℓν/N (24) Next, replacing βk with β̂k in the right-hand-side of (28) and maximizing with respect to p̃k , provides an estimate of pk in the form Υ2 (β̃k , p̃k ) = 2ℜe  +L−1 V −2 V −ν−1 β̃kX X X  ℓ=β̃k ν=0 ŝk (ν, ℓ)ŝ∗k (ν + n, ℓ)e−j2πn(ℓ+p̃k Q)/N n=1   (30)  0 max 0≤p̃k ≤P −1 (32) FLM A further reduction of complexity is possible when V = 2. Actually, in this case it can be shown that maximizing Υ2 (β̂k , p̃k ) is equivalent to maximizing cos(ϕk − 2π p̃k Q/N ), where ϕk = arg  +L−1 β̂kX  ŝk (0, ℓ)ŝ∗k (1, ℓ)e−j2πℓ/N ℓ=β̂k    . (33) 10 -1 MCD Pf p̂k = arg 10 n o Υ2 (β̂k , p̃k ) . 10 10 -2 -3 Ω = 0.05 Ω = 0.075 K=2 K=3 The estimate of pk is thus obtained in closed-form as N ϕk . p̂k = 2πQ V. S IMULATION 10 -4 -2 (34) 0 2 4 6 8 10 12 14 16 18 20 22 SNR, dB RESULTS A. System parameters The simulated system is inspired by [5]. The total number of subcarriers is N = 1024 while the number of ranging subchannels is R = 8. Each subchannel is composed by Q = 16 subbands uniformly spaced at a distance N/Q = 64. Any subband comprises V = 2 adjacent subcarriers while the ranging time-slot includes M = 4 OFDM blocks. The ranging codes are taken from a Fourier set of length 4 and are randomly selected by the RSSs at each simulation run T (expect for the sequence [1, 1, 1, 1] ). The discrete-time CIRs have L = 12 channel coefficients. The latter are modeled as circularly symmetric and independent Gaussian random variables with zero means (Rayleigh fading) and exponential power delay profiles, i.e., E{|hk (ℓ)|2 } = σh2 ·exp(−ℓ/12) with 2 ℓ = 0, 1, . . . , 11 and σh2 chosen such that E{khk k } = 1. Channels of different users are assumed to be statistically independent. They are generated at each new simulation run and kept fixed over an entire time-slot. The normalized CFOs are uniformly distributed within the interval [−Ω, Ω] and vary at each simulation run. We consider a cell radius of 10 km, corresponding to a maximum transmission delay θmax = 204. A CP of length NG = 256 is chosen to avoid IBI. B. Performance evaluation We begin by investigating the performance of MCD in terms of probability of making an incorrect detection, say Pf . This parameter is illustrated in Fig. 1 as a function of SNR = 1/σ 2 under different operating conditions. The number of active RSSs varies from 2 to 3 while the maximal frequency offset is either Ω = 0.05 or 0.075. Comparisons are made with the ranging scheme discussed by Fu, Li and Minn (FLM) in [5], where the kth ranging code is declared active provided that the quantity Fig. 1. Pf vs. SNR for K = 2 or 3 when Ω is 0.05 or 0.075. Q−1 V −1 1 XX H c Y(iq,ν ) Zk = 2 M q=0 ν=0 k 2 (35) exceeds a suitable threshold η which is proportional to the estimated noise power σ̂ 2 . The results of Fig. 1 indicates that the proposed scheme performs remarkably better than FLM because of its intrinsic robustness against CFOs. As expected, the system performance deteriorates for large values of K and Ω. The reason is that increasing K reduces the dimensionality of the noise subspace, which degrades the accuracy of the MUSIC estimator. Furthermore, large CFO values result into significant ICI which is not accounted for in the signal model (8), where A(ωk ) has been replaced by IN . Fig. 2 illustrates the root mean-square-error (RMSE) of the frequency estimates obtained with MFE vs. SNR. Again, we see that the system performance deteriorates when K and Ω are relatively large. Nevertheless, the accuracy of MFE is satisfactory under all investigated conditions. The performance of the timing estimators is measured in terms of probability of making a timing error, say P (ǫ), as defined in [8]. More precisely, an error event is declared to occur whenever the estimate θ̂k gives rise to IBI during the data section of the frame. In such a case, the quantity θ̂k − θk + (−NG,D + L)/2 is larger than zero or smaller than −NG,D + L − 1, where NG,D is the CP length during the data transmission phase. Fig. 3 illustrates P (ǫ) vs. SNR as obtained with RC-TE and FLM when NG,D = 64. The operating conditions are the same of the previous figures. Since the performance of LS-TE is virtually identical to that of RCTE, it is not reported in order not to overcrowd the figure. We 10 0 MFE Frequency RMSE 10 10 10 10 -1 [2] [3] -2 [4] -3 Ω = 0.05 Ω = 0.075 K=2 K=3 [5] -4 -2 0 2 4 6 8 10 12 14 16 18 20 22 [6] SNR, dB Fig. 2. Accuracy of the frequency estimates vs. SNR for K = 2 or 3 when Ω is 0.05 or 0.075. [7] [8] 0 10 [9] -1 10 P(ε ) FLM [10] -2 10 -3 10 Ω = 0.05 Ω = 0.075 K=2 K=3 -4 RC-TE 10 -2 0 2 4 6 8 10 12 14 16 18 20 22 SNR, dB Fig. 3. P (ǫ) vs. SNR for K = 2 or 3 when Ω is 0.05 or 0.075. see that for SNR values larger than 6 dB the proposed scheme provides much better results than FLM. VI. C ONCLUSIONS We have derived a novel timing and frequency synchronization scheme for initial ranging in OFDMA-based networks. The proposed solution aims at detecting which codes are actually being employed and provides timing and CFO estimates for all active RSSs. CFO estimation is accomplished by resorting to the MUSIC algorithm while a LS approach is employed for timing recovery. 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