RANGING SIGNAL DESIGN AND ITS DETECTION FOR OFDMA SYSTEMS

RANGING SIGNAL DESIGN AND ITS DETECTION FOR OFDMA SYSTEMS

Kuhn Chang Lin and Yu T. Su

Department of Communications Engineering

National Chiao Tung University, Hsinchu, 30056 TAIWAN

Email addresses: tony.cm95g@nctu.edu.tw, ytsu@mail.nctu.edu.tw

ABSTRACT

A single-symbol based initial ranging signal structure and the associated signal detection and timing synchronization methods for OFDMA systems are presented. The proposed structure makes it feasible and flexible for a receiver to de-tect single and multiple ranging codes and estimate the cor-responding timing offsets. Our approach offers improved performance and enhanced robustness against multi-user in-terference and multi-path fading. Numerical results verify the effectiveness of the proposed method and its advantages over existing alternatives.

Index Terms— OFDMA, ranging process, multi-user

ranging code detection, timing estimation, and MUSIC 1. INTRODUCTION

Several studies on the initial ranging for an OFDMA system like that specified by the IEEE 802.16e standard [1] have been reported [2]-[6]. These works fall into two major categories. The first category [2] is based on the ranging codes given in [1]. The second category [3]-[6] proposes new ranging code structures. [4] suggested an interleaved channel assignment scheme to overcome the major draw-backs of the above approaches. However, multiple OFDMA symbols are needed and the carrier frequency offsets (CFOs) between the received signals and the BS local reference is not taken into account and perfect frequency alignment among all ranging subscriber stations (RSSs) and the BS is assumed instead. Such an assumption is not realistic and ignores the fact that the residual CFOs cause the loss of orthogonality among ranging codes and are likely to induce severe perfor-mance degradation. Lin [5] and Sanguinetti [6] employed a MUSIC-like algorithm to overcome this difficulty. The lat-ter, however, requires a longer ranging signal duration (and therefore lower system throughput). Guard bands between neighboring subbands of different ranging channels are also needed to prevent interference from other groups. We pro-pose a specific ranging channel assignment and a new class of frequency domain ranging codes which enables the BS

This work is an extension of the IEEE 802.16m technical con-tribution [5] and was supported in part by the NCTU-MediaTek Re-search Center at the National Chiao Tung University.

to employ a MUSIC-like algorithm to detect multiple RSSs and estimate their timing offsets. Our design uses only one OFDM symbol; guard bands between ranging channels are not needed and the associated receive algorithm gives robust, excellent multi-user detection and timing estimation perfor-mance. Compared with the existing solutions, our proposal is more spectral efficient, yields improved performance and offers greater immunity against the multiuser interference and frequency selective fading.

Notation: [ ] and j denote the floor operation and √−1. (.)T_and(.)H_{denote transpose and Hermitian operations.}

2. CHANNEL ASSIGNMENT SCHEME Subcarriers assigned for RSSs are divided into Ngp groups with each group having Nb subbands and each sub-band consisting of Nc consecutive subcarriers such that each group can support a maximum of M RSSs. Let Sp be the set of indices of the subcarriers allocated to the pth group and denote by Rip the ith RSS in the pth group which employs the frequency domain ranging code {Cip(u) : u = 1, · · · , NbNc}. Let fsbe the lowest subcar-rier index allocated for RSSs. For0 ≤ p ≤ Ngp− 1, Sp is Sp= {fs+pNc+ιDb+ν : 0 ≤ ι ≤ Nb−1, 0 ≤ ν ≤ Nc−1}, (1) whereDbis the frequency spacing between two neighboring subbands. The frequency domain ranging signalXip(k) for Ripis defined as Xip(k) =  AipCip(u), k ∈ Sp, u = 1, 2, · · · NbNc 0, otherwise, (2) where|Cip(u)| = 1 and Aipis the relative amplitude ofRip. The maximum transmission delayDmax(samples) equals to the round-trip propagation delay between the BS and a RSS at the boundary of the cell. To avoid inter subcarrier inter-ference (ICI) and inter symbol interinter-ference (ISI), the length of the cyclic prefix (CP), Ng, must be larger than the sum of Dmax and the maximum delay spread among all uplink ranging channelsL (samples) [7]. This assumption is not re-strictive, since in many standardized OFDM systems the ini-tialization blocks are usually preceded by long CPs. With the CP inserted, the time domain ranging signal for Rip is xip(n), n = −Ng, −Ng+ 1, ..., N, where N is the FFT size.

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Assuming the uplink channels remain static within a sym-bol duration and ignoring the presence of noise for the mo-ment, we express the received ranging waveformyipR(n) for Ripas

yRip(n) = L−1_

l=0

hip(l)xip(n − l) (3) where hip(l), l = 0 , · · · , L − 1 are the associated chan-nel tap weights. The remaining N − NgpNcNb subcarriers are assigned toNDSS data subscriber stations (DSSs) which have already completed their initial ranging process and are assumed to be perfectly synchronized with the BS’ time and frequency scales. yiD(n) denotes the signal of the ith DSS. The received signal at the BS thus becomes

y(n) = Ngp−1 p=0 M−1_ i=0 yipR(n − dip)ej2πεipn/N + NDSS−1 i=0 yiD(n) + w(n) (4)

where {w(n)} are independent and identical distributed (i.i.d.) complex circular symmetric Gaussian random vari-ables with mean zero and variance σ2w = E[|w(n)|2] and dip,εiprepresent the timing offset and normalized frequency offset ofRip.

3. RANGING SIGNAL STRUCTURE

The maximum number of RSSs supported by one group, M , is M = min{[N /Ng], min{Nb, Nc} − 1 }. In practice, [N /Ng] is usually larger than 2, hence a judicial choice of {Nb, Nc} is needed to ensure M > 2.

The ranging code in theιth subband, Cι

ip, for theRipis given by

Cipι (ν) = e−j2πiν/M, ν = 0, 1, · · · , Nc− 1. (5) The same ranging code can be transmitted using different subcarrier group without causing any interference for the subcarriers allocated are disjoint. Our design does not ensure orthogonality among codes in the same group. When choos-ing the ith ranging code, the phase difference between two consecutive assigned subcarriers are rotated by −2πi/M. The phase rotation caused by round-trip delay and channel delay spread is between 0 and −2π/M. This implies that the overall frequency-domain phase shifts of all RSSs in the same group are non-overlapping over

 −2iπ M , −2(i+1)π M  , wherei = 0, 1, · · · , M − 1. By using the MUSIC algorithm [?], we perform one-to-one mapping from the overall phase shifts of RSSs in the same group into the corresponding RSSs associated with the detected peak positions. We can simulta-neously obtain the delay information ofRipfrom the overall phase shift without additional complicated computations. The RSSs in the same group can thus be easily detected and decoupled without using multiple OFDMA symbols.

4. RANGING METHOD

Our estimate assume that the timing offsetdipforRipis equal to the sum of the round-trip transmission delay and the

channel group delay. When a RSS receives the timing offset estimate from the BS, it adjusts its timing accordingly and retransmit its ranging code with both cyclic prefix and postfix to avoid inter carrier interference (ICI).

The code structure of (5) and the assumption that the sub-band sub-bandwidth is smaller than the uplink channel’s coherent bandwidth implies that the equivalent channel gains within a theιth subband of Ripare related by

Hipι (ν) ≈ Hipι(0)e−j2πν( i M+ dip N ), ν = 1, · · · , N_c− 1 (6) LetYι

pbe the Nc-dimensional vector that collects the com-ponents of the DFT output vector corresponding to the ιth subband of thepth group. Since the DSSs are assumed to be perfectly synchronized to the BS time reference, their signals will not contribute toYpι, we have

Yιp= M−1_

i=0

F(εip)vipHipι (0) + nιp (7) wherenι

pis the sum of white Gaussian noise and the interfer-ence from the nearby groups andvipis given by

vip=  1, e−j2π(i M+ dip N ), · · · , e−j2π(Nc−1)(Mi+ dip N ) T . (8) Furthermore,F(εip) is a Nc× NcToeplitz matrix with the element inath row and the bth column given by [7]

fa,b(εip) = sin(π(a − b + εip)) N sin(π(b − a + εip)/N)e

jπ(b−a+εip)(N−1)/N

(9) A RSS intending to start initial ranging should first derive its initial frequency and timing estimates from a downlink con-trol signal broadcasted by the BS. This means the CFOs are only due to Doppler shifts and/or estimation errors whence are assumed to lie within a small fraction of the subcarrier spacing, i.e., |εip| ≈ 0, and F(εip) in (7) can be replaced withINc, whereINcis an identity matrix of orderNc. When

|εip|  1, F(εip) can be viewed as a tri-diagonal matrix. In this case,F(εip)vipHipι(0) ≈ vipH˜ipι (0) with the exceptions of the highest and lowest indexed terms. By combing these small deviation terms withnιpto formn˜ιp, we rewrite (7) as

Yιp= M−1_

i=0

vipH˜ipι + ˜nιp, ι = 0, 1, · · · , Nb− 1 (10) which can be expressed in a more compact form

Yp=Yp0Y1p · · · YpNb−1 = VpH˜p+ ˜Np (11)

whereYpis the matrix obtained by stacking up the received samples from subbands within thepth group, Vp= (v0pv1p · · · v(M−1)p), ˜Np=˜np0˜n1p · · · , ˜nNpb−1 , and ˜ Hp= ⎛ ⎜ ⎝ ˜ H0p0 H˜0p1 · · · H˜0pNb−1 .. . ... . .. ... ˜ H(M−1)p0 H˜(M−1)p1 · · · H˜(M−1)pNb−1 ⎞ ⎟ ⎠ . (12) 2602

4.1. Multi-user Ranging Signal Detection and Timing Offset Estimation

The fractional frequency offset results in inter-carrier in-terference (ICI) to subbands in the nearby group. LetEpbe the energy (i.e., the magnitude square of the DFT output) of thepth subcarrier group excluding the highest and lowest in-dexed subcarriers of each subband. In the absence of signal, Ep is a chi-square distributed with2Nb(Nc− 2) degrees of freedom. When the noise variance is known, the desired false alarm probability can be achieved by selecting a properη0. We checkEp > η0 first to see if subsequent operations are needed.

The covariance matrix of Yp is defined by Φp = 1

NbYpYp

H

. When there are κp RSSs in the pth group, κp ≤ M , we have Nc − κp basis vectors which span the null spaceUwpand can be obtained by performing singular

value decomposition (SVD) onΦp. Assumingˆκp = M we compute

Υ(d) = _αH(d)UαH(d)α(d) wpUHwpα(d)

, d = 0, · · · , N − 1. (13) whereα(d) = (1, e−j2πd/N, · · · , e−j2πd(Nc−1)/N)T_{, and}

find the local maximums. These peak values correspond to the ratio of the total energy to the energy projecting onto the null space. There is an one-to-one correspondence between the local peaks and the active RSS’s delays. Therefore, we make a decision aboutRip according to whether there is a peak located within{Ni/M, N(i + 1)/M}.

The vector ˆdp = ( ˆd0p, ˆd1p, · · · , ˆd(M−1)p)T, which in-cludes information about the number of the active RSSs in thepth group and their delays, is obtained by the following algorithm.

1. ComputeEp based on the received frequency domain samples. IfEp < η0, “no signal” is declared and the algorithm terminates.

2. Arrange the frequency domain samples in matrix form Ypand setˆκp= M .

3. Apply SVD to Φp, find the Nc× (Nc − ˆκp) matrix ˆ

Uwpand thenΥ(d).

4. Find the largestˆκp peaks ofΥ(d) and compare these local peak values with the threshold,η1(Nc, Nb, ˆκp), which is determined by numerical optimization. If there existl peaks below the threshold then ˆκp← ˆκp−l and go back to Step 3.

5. Based on the local peak positions, we determine if an RSSRip is active and its timing offset ˆdip is obtained by subtractingN i/M from the peak position.

5. SIMULATION RESULT AND DISCUSSION 5.1. Simulation Setup

The OFDMA system parameters used in the simulations reported in this section are selected from [1] and [8]. The

uplink bandwidth is 10 MHz, and the subcarrier spacing is 10.9375 KHz. The FFT size, N , is 1024. ITU Vehicular A channel model is used and the sampling interval, Ts, is 89.285 ns. We consider a cell size of radius 5 km so that the round-trip delaydmax=33.34μs = 373 samples. Ng is assumed to be 512 samples to satisfy the condition Ng > dmax+ L and each group supports M = 2 RSSs. The sub-carriers numbers and OFDM symbols used by one group for our proposal (Nc= 6,Nb= 6,Ngp= 4 andDb= 140) and two earlier schemes are summarized in Table 1 where FLM refers to the scheme proposed by Fu, Li and Minn [4] while SMP is an abbreviation for the method proposed by Sanguinetti, Morelli, and Poor [6].

Table 1. System Parameter

Proposed FLM SMP

Supported RSS number

per group,M 2 2 2

Subcarriers

per OFDM symbol 36 36 32

(Nc× Nb) Ranging signal duration

(in OFDM symbols) 1 2 3

The supported maximum speed of RSS is 120 Km/hr and carrier frequency is 2.5 GHz. The normalized residual CFOs of RSSs thus lie within the range [-0.05,0.05] and are assumed to be i.i.d. for different RSSs. Because our proposed algorithm utilizes the FFT ouput data, the interference mainly come from RSSs in same group and RSSs in the nearby groups. We assume there areK active RSSs in the group and I RSSs in the nearby groups. Some or all of the following RSS distributions are considered: (i) K = 1, I = 0, (ii) K = 1, I = 1, (iii) K = 1, I = 2, (iv) K = 2, I = 0, and (v)K = 2, I = 2, within one ranging time-slot.

5.2. Multi-User Detection Performance

SNR is defined as the ratio of signal variance to noise vari-ance in time domain. Comparisons are made with FLM and SMP ranging schemes. The results of Fig. 1 indicates that the proposed scheme performs remarkably better than FLM and SMP because of its intrinsic robustness against CFOs. In FLM scheme, theith ranging code is declared active pro-vided that the quantity exceeds a suitable thresholdη which is proportional to the estimated noise powerσ2. The fractional RSSs’ CFOs destroy the orthogonality in the same group. When a RSS power becomes larger, so are the interference and the false alarm probability. Hence, the performance is dominated by the interference from the same group.

In the SMP scheme, the interference from the same group is mitigated by employing MUSIC algorithm with extending one more OFDM symbol. However, the interference from nearby groups degrades the performance when the subbands assigned for different groups are adjacent. For alleviating this effect, the guard bands are required. On the other hand, our scheme can find that the RSSs in the different group do not

−6 −4 −2 0 2 4 6 8 10 12 14 0 0.05 0.1 0.15 Average SNR (dB)

Probability of false alarm

(K,I)=(1,0) (K,I)=(1,1) (K,I)=(1,2) our scheme FLM SMP FLM SMP Our scheme

Fig. 1. Probability of false alarm as a function of average SNR. −10 −5 0 5 0.965 0.97 0.975 0.98 0.985 0.99 0.995 1

Probability of correct detection

Average SNR (dB) (K,I)=(1,0) (K,I)=(2,0) (K,I)=(2,2) our scheme FLM SMP Our scheme SMP FLM

Fig. 2. Detection probability performance as a function of average SNR.

cause increase of false alarm probability even if the residual frequency offset exists. When SNR is lower, both signal and null spaces are influenced by relative large noise. When the SNR> 5 dB, the noise effect becomes insignificant. How-ever, even for SNR< −6 dB, the false alarm probability is still less than 0.02. Fig. 2 shows the probability of cor-rect detection (PD) performance versus average SNR. As our ranging signal needs only one OFDM symbol the required transmission energy is less than the existing approaches that employ two or more symbols. Our proposal gives near perfect PD(≈ 1) even if SNR is as small as -10 dB. The performance degrades slightly if there are two RSSs in the same group. The reason is that the increased active RSS number reduces the di-mensionality of the noise subspace. When SNR is larger than -7 dB, the detection performance loss of is less than 0.005. 5.3. Performance of Timing Estimator

Fig. 3 plots the the timing estimation jitter, i.e., the root mean squared timing offset estimation error, as a function of the average SNR for the various RSS distributions. In each simulation run, the true transmission delays are taken ran-domly from the interval[0, dmax]. In simulating the FLM scheme, we employ the SEGA algorithm with two iterations. It is observed that one RSS in one group yields better per-formance than two RSSs in one group. But the perper-formance difference is just one sampling interval. We can see that for SNR larger than 1 dB the proposed and the FLM schemes give almost identical performance. After each RSS has

suc-−10 −5 0 5 10 15 0 2 4 6 8 10 12 14 16 18 20 Average SNR (dB)

Time offset estimation standard deviation (T

S ) (K,I)=(1,0) (K,I)=(2,0) (K,I)=(2,2) Our scheme FLM SMP SMP Our scheme FLM

Fig. 3. Timing jitter behavior as a function of average SNR. cessfully finished initial ranging, adjusted its timing offset, the BS will be able to support more RSSs in one group for subsequent periodic ranging since most of the round-trip de-lay uncertainty has been removed and the CP length can be reduced accordingly; see (5).

6. CONCLUSION

A single OFDMA symbol based ranging signal design for initial ranging in a wireless mobile OFDMA system is proposed. A ranging scheme that provides accurate multiple RSS’ timing estimate is presented as well. Our approach is based on the idea of projecting the received multiple ranging signals onto the null (noise) space. No information about the active RSSs’ strengths are needed in our proposal. Numer-ical results have demonstrated that the proposed solution is capable of offering excellent detection and false alarm proba-bilities performance and provides a good timing estimate for multiple active RSSs.

7. REFERENCES

[1] IEEE LAN/MAN Standard Committee, “Air interface for fixed and mobile broadband wireless access systems,” IEEE 802.16e-2005.

[2] J. Krinock, et al. “Comments on OFDMA ranging scheme described in IEEE 802.16ab01/01r1,” document IEEE 802.abs-01/24.

[3] X. Zhuang, et al., “Ranging improvement for 802.16e OFDMA PHY,” document IEEE 802.16e-04/143r1. [4] X. Fu,et al. “A new ranging method for OFDMA

sys-tems,”IEEE Trans. Wireless Commun, vol. 6, no. 2, pp. 659-669, Feb. 2007.

[5] K. C. Lin, et al., “Ranging Code Design for IEEE 802.16m,” IEEE C802.16m-08 329, May 5, 2008. [6] L. Sanguinetti, et al., “An improved scheme for initial

ranging in OFDMA-based networks,” inProc., ICC2008, Beijing, China, pp. 3469-3474, May 2008.

[7] M. Morelli, et al. “Synchronization techniques for or-thogonal frequency division multiple access (OFDMA): A tutorial review,”Pro. IEEE, vol. 95, no. 7, pp. 1394-1427, Jul. 2007.

[8] IEEE 802.16 Broadband Wireless Access Working Group, “Draft IEEE 802.16m evaluation methodology,” IEEE 802.16m-07/037r1.