A New Ranging Technique for IEEE e Uplink

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1 I.J. Wireless and icrowave Technoloies, 011, 4, 19-6 Published Online Auust 011 in ECS ( DOI: /ijwmt Available online at A ew Ranin Technique for IEEE 80.16e Uplin Wan Shi a,*1, Wan Yinchun b,*, Guan Jianxin c,*3 a Office of Research & Development, aval University of Enineerin, Wuhan, China b Administrative Office of Trainin, aval University of Enineerin, Wuhan, China c Department of Comm. Enineerin, aval University of Enineerin, Wuhan, China Abstract Aimin at the shortcomins of the traditional ranin alorithm, this paper proposes a new ranin technique for 80.16e uplin in the frequency domain. The ranin technique eliminates the effect of the timin offset by computin the frequency difference of adjacent sub-carriers in the ranin channel, which reduces the search space from two dimensions to one dimension. When there is slot, the ranin code can be detected by adoptin a threshold. The ranin technique is implemented throuh one-dimension search in the frequency domain, and consequently the complexity can be reduced and without losin the performance of timin estimation. The simulation results show the ood ranin performance of this technique. Index Terms: 80.16e; Ranin; Uplin 011 Published by ECS Publisher. Selection and/or peer review under responsibility of the Research Association of odern Education and Computer Science 1. Introduction The multiple access scheme adopted in IEEE 80.16e uplin is Orthoonal Frequency Division ultiple Access (OFDA), in which different users possess correspondin sets of sub-carriers. When the user attempts to access the networ or the handover happens, the process of ranin is required. The ranin process performs two main tass: detectin all ranin codes in the current ranin slot and estimatin the correspondin Return Time Delay (RTD) of these ranin codes. For the OFDA system usin Time Division Duplex (TDD) mode, the ranin process requires the accurate timin synchronization between Base Station (BS) and obile Station (S). The problem is mainly discussed in this paper. The traditional ranin alorithm is implemented in the frequency domain[1]. In this alorithm the time domain sequences will firstly be transformed into frequency domain throuh Fast Fourier Transformation (FFT), and then the transformed sequences will correlate with the all ranin codes in the set of ranin codes. Because of the existence of time offset, the reversal of the phase in the frequency domain will happen. The time offsets need be taen into account and the cross-correlation process in the traditional alorithm is a twodimension and erodic one. In the IEEE 80.16e there are 56 ranin codes. If the RTD is considered in the This paper is sponsored by the nature science fund of aval University of Enineerin (o.hgdqjj0). * Correspondin author: address: *1 shi_wan@tom.com; * yc_wan@tom.com; *3 jx_uan@sina.com

2 0 A ew Ranin Technique for IEEE 80.16e Uplin rane of [0,/], the computation burden of the two-dimension erodic search is very hih, which enhances the difficulty to implement it. Besides the reat complexity, the performance of the traditional alorithm is limited by the frequency selective fadin channel[]. This is because the traditional technique can t eliminate the effect of the channel s phase variation on the correlation function. A new ranin technique which is implemented in the frequency domain is proposed. The proposed technique computes the difference in frequency domain between the adjacent sub-carriers in the ranin channel and eliminates the effect of the timin offset. Therefore the search space decreases to one-dimension from two-dimensions. At the same time a specific threshold is used to detect the ranin codes in the current ranin slot. The estimation of the correspondin ranin code s RTD is acquired from the phase of the correlation function. Accordinly a less search rane is defined based on the estimation and all the possible timin offsets can be searched in this one-dimension space.. Description of The Existin Alorithms The literature [1] divides the whole process of ranin into three steps: Firstly, compute the power in the frequency domain of the received sinals and compare this power with the predefined threshold to determine if the ranin code exists in the current FFT window. Secondly, determine the possible timin offset in the FFT window where the ranin code exists in. Finally, eliminate the effect of the timin offset and detect the ranin code throuh cross-correlation operation in the frequency domain. The method proposed in [1] wors well in the Additional White Gaussian oise (AWG) channel and has lower complexity. But this method can t wor effectively in the multi-path channel. Because the received power in the frequency domain has lare fluctuation which invalidates the method of threshold detection. We can t determine whether the ranin code exists in the current FFT windows throuh the predefined and invariable threshold. In order to overcome the shortcomins of the traditional ranin technique (whose performance is limited by the frequency selective fadin multi-path channel and the noise), the literature [] proposed another ranin technique which is based on differential detection combined with multiple lenth FFT computation. In this method the differential detection is used to counteract the effect of the frequency selective fadin in the multipath channel, and the multiple lenth FFT computation is used to eliminate the effect of the noise. But the leadin modulation sequence in the IEEE 80.16e standard doesn t adopt the scheme of differential code. The method proposed in [] can t be directly used in the 80.16e standard. The two literatures [3] and [4] both present the same idea of difference in the frequency domain as shown in the literature []. This idea reduces the number of dimension of the erodic search process from two to one and can counteract the effect of the frequency selective fadin in some extent. The RTD can be simultaneously estimated throuh the phase of the correlation function. This method can reatly reduce the complexity of the traditional technique, but it will incur some loss in the performance of detection and timin offset estimation. For the detection of the ranin code, the determination of the threshold is very difficult problem. Furthermore the method in [3] and [4] is infeasible when there are several ranin users. This is because the superposition of sinals from multiple users will larely impact the performance of timin offset estimation. oreover the difference computation in frequency domain will reduce the performance of the cross-correlation characteristic of the ranin codes (about 0.8 db). 3. The ew Ranin Technique 3.1. The Principle of The Technique We denote by n y the received sequences in the time domain. In the condition of the AWG channel, we may write

3 A ew Ranin Technique for IEEE 80.16e Uplin 1 / 1 j n / n n / y X H e w (1) where ε is the normalized carrier frequency offset, X is the BPSK-modulated ranin code, H is the c h a n n e l r e s p o n s e a n d wn i s t h e c o m p l e x G a u s s i a n n o i s e i n t h e t i m e d o m a i n. There are two schemes to implement the initial ranin. The first scheme uses two OFD symbols to transmit a ranin code, and the second one uses four OFD symbols to transmit two adjacent ranin codes. Here the first case is discussed and the other case can be processed usin the similar manner. The time domain structure of the ranin code defined in the 80.16e standard is shown in Fi. 1. CP GRD copied samples OFD sinal period copied samples OFD sinal period Fi. 1. The time domain structure of the ranin code As shown in the above Fi. 1, the continuity of the phase is preserved by the two consecutive ranin symbols. Supposin that the RTD is not larer than s,then we can obtain a whole ranin symbol from the time domain sequences whose lenth is equal to the lenth of two consecutive FFT windows. In this paper we suppose the RTD has the rane of [0, / ], where is the lenth of an OFD symbol. Supposin the ranin user s RTD is denoted by TO, in the ideal channel the two estimations of the timin offset obtained from the time domain sequences in the two FFT windows are iven as TO 1 TO () After we have obtained the two -point time domain sequences of the ranin sinal, we can transform them into the frequency domain throuh FFT. For a whole ranin symbol the frequency domain sequences Y can be expressed as sin Y X H e sin / j n / e I W j 1/ (3) where n is the RTD, I is inter-carrier interference (ICI) which is produced due to the carrier frequency offset and the return time delay, and W is the term of complex noise. Let I be the inter-carrier interference (ICI), then

4 A ew Ranin Technique for IEEE 80.16e Uplin / sin I X H sin m / m m m/ m j 1 / j m / j n / e e e (4) ˆ We express the cross-correlation in the frequency domain as Z Y X, where X ˆ is the candidate in the Xˆ satisfies the followin ranin code set. When the local ranin code is matched with the transmitted code, ˆ condition of X X 1. This is because the ranin code is modulated usin BPSK. The differential crosscorrelation function of the adjacent sub-carriers is iven by * * ˆ ˆ * ˆ ˆ * Z Z Y X Y X Y Y X X sin HH sin / noise _ terms * j n/ 1 e (5) Inorin the term of sin and the term of phase, the noise_terms in the above equation is written as follows: noise terms H I H W I H * * * _ I I I W W H * * * W I W W * * 1 1 (6) We usually suppose that the channel response is independent from the noise and the enery of ICI interference is much less than the power of the useful sinal. This hypothesis is reasonable in the actual case. However some correlation is liely to exist between W and W 1 in the specific noise environment. But this ind of correlation can t exist in the whole ranin channel. Superposin the frequency domain cross-correlation of all adjacent sub-carriers in the ranin channel, we can derive the correlation function as follows: 1 * j n/ P ZZ 1 e K 1 sin K sin / HH * 1 (7) where K is the number of the adjacent sub-carriers in the ranin channel. When the ranin channel occupies 6 adjacent sub-carriers, the number of sub-carriers is 144 and the number of the adjacent subcarriers K is 6 6 3=108. We use the manitude of the correlation function as the metric function and it can be written as

5 A ew Ranin Technique for IEEE 80.16e Uplin 3 1 sin P H H K sin / * 1 (8) Let 1 denote the metric function obtained from the time domain sequences in the first FTT window and denote the correspondin one in the second FFT window. Accordin to (), the estimation of the RTD is iven as round ar P1, if 1 round ar P, if 1 (9) If a metric function exceeds the predefined threshold, we can thin that the candidate code correspondin with this metric function is the current ranin code which is bein transmitted. When we set the threshold we need balance between the probability of losin detection and the probability of false detection. We should emphasize that the larer between 1 and is used to detect the ranin code and estimate the timin offset. 3.. The Rane of the Estimated Timin Offset and The Phase Reversal In the proposed technique the phase of the correlation function is used to estimate the RTD. The rane of estimation is limited by the periodic characteristic of the phase. As mentioned in the context the larer between 1 and is used to estimate the timin offset. Accordin to (), the rane of estimation of the timin offset is iven as, + (10) We must notice that the phenomenon of phase reversal may happen when the phase of the correlation function is used to estimate the timin offset. The phase reversal means that the phase of the correlation function turns to π from -π or vice versa. In the non-ideal channel the possible phase reversal will result in two inds of case. The first is that the estimated timin offset is close to the but not the when the actual timin offset is close to. The second is that the estimation is liely close to +, but the actual + timin offset is close to. After thorouh analysis we can find that phase reversal is liely to happen when the FFT window is lyin in the middle of initial ranin sinal whose lenth is equal to the lenth of the two symbols The Optimization of The Timin Offset Estimation 1) The technique eliminatin the effect of the phase reversal In the above section we have depicted the phenomenon of phase reversal and the condition when it maybe happens. ow we will research the technique to eliminate the effect of the phase reversal. When one metric function exceeds the threshold, the processin method is described as follows:

6 4 A ew Ranin Technique for IEEE 80.16e Uplin If is reater than 1 and the estimation of timin offset is neative, we thin that the phase reversal has happened and add to the estimated value of the timin offset. If 1 is reater than and the estimation of timin offset is positive, we thin that the phase reversal has happened and subtract from the estimated value of the timin offset. But there are some hidden troubles in the above method. For example, when the timin offset is reater than zero but less than, 1 is liely to be reater than. At this time if we only adopt the latter processin means, we will improperly process the estimated value of the timin offset. When the actual timin offset is close to the, the phase reversal brins a + offset to the estimation and as a result the final estimation is close to. But when the actual timin offset is really close to, it is impossible that 1 is reater than. Based on the above fact we can set a better threshold than zero. In this case the threshold can be set as ( + ). + When the actual timin offset is close to the, the phase reversal brins a offset to the estimation + and as a result the final estimation is close to. Similarly when the actual timin offset is really close + to, it is impossible that is reater than [ ( / )] / 1. In this case the threshold can be set as. In the IEEE 80.16e standard the maximal can be equal to 4 /, therefore the equation is fitly equal to. At this condition is liely to be reater than 1. But two facts prevent the appearance of this case. The first fact is that the WiAX forum selects 8 as the lenth of cyclic prefix (CP) of mobile WiAX. The second fact is that the actual timin offset is mainly concentrated on the positive section and the neative estimation with small absolute value only exists in the case of periodic ranin. After usin (9) to estimate the RTD, we can use the followin technique to eliminate the effect of phase reversal: 1, if and +/ /, if and /4 1 (11) ) The technique improvin the performance of timin offset estimation Except the effect of the noise, the method of estimatin the RTD in (9) will be influenced by the phase chane of the channel response of adjacent sub-carriers. In the case of multi-users ranin these users data will overlap on the same sub-carrier set in frequency domain. This will influence the estimation of phase and consequently will influence the estimation of RTD. The interference amon the multi-users has lare impact on the performance of estimatin the timin offset. So we can conclude that the technique usin the phase to estimate the timin offset is infeasible in the case of multiple users ranin. The traditional ranin technique estimatin the timin offset is mainly influenced by the multi-path channel. The pea values proportional with the channel coefficients will appear at the locations of each path [5]. The primary simulation result shows that the performance of the traditional ranin technique is much better than the performance of the technique usin the phase to estimate the timin offset in the case of multiple users ranin. We will combine these two techniques to improve the performance of the timin offset estimation. The complexity due to this combination is low and acceptable. The process of the alorithm is iven as follows: a) Use (7) to (9) to detect the ranin code in the current ranin slot and estimate the correspondin timin offset; b) Use (11) to eliminate the effect of phase reversal;

7 A ew Ranin Technique for IEEE 80.16e Uplin 5 c) Set a search rane at the both sides of the current timin offset estimation and compensate the phase for the timin offset candidates in this search rane; then compute the correlation function in the frequency domain; d) Select the timin offset candidate correspondin to the pea value of correlation function as the new timin offset estimation. Supposin the search lenth in sinle side is L, the search ran R can be determined accordin to the estimation in (11) as follows: R n L n L (1) If the above search rane exceeds the bound iven in (10), the search rane will be truncated. Compensatin the phase for every candidate of the timin offset and computin the correlation function in the frequency domain, we have P n Y X e, if * j n / t * j n / P n Y X e, if t t t n P n 1 1 (13) Then we select the timin offset candidate correspondin to the maximal metric function as the new timin offset estimation which is expressed as n ˆ ar max t n (14) 3.4. The Setup of The Threshold Based on the metric functions iven in (8) of all possible ranin codes at the location of first and second FFT windows, we can respectively compute the rms value. Settin the threshold used to detect the ranin code at the value which is m db larer than rms, we have T 10, s 1, s m /10 s, r ri (15) where I is the set of the ranin codes and the value of m is determined throuh simulation. The ranin code candidate correspondin to the metric function exceedin the threshold is detected as the ranin code in the current ranin slot. 4. Simulation Result and Performance Analysis In order to validate the performance of the ranin technique proposed in this paper, we simulate the proposed technique and compare the result with others in literature [3] and [4]. Fi. shows the performance of the technique proposed in this paper compared with which were iven in literature [3] and [4].

8 6 A ew Ranin Technique for IEEE 80.16e Uplin Fi.. The mean square error of ranin technique The simulation condition is the uplin PUSC. The size of FFT is 104. The adopted channel is the Vehicle A test channel with 100 Hz Doppler frequency offset. The modulation scheme is QPSK. The result in Fi. shows that the performance of the technique proposed in this paper is close to the techniques in reference [3] and [4] and is a little better than them. 5. Conclusion Aimin at the shortcomins of the traditional ranin alorithm, this paper proposes a new ranin technique for 80.16e uplin in the frequency domain. The ranin technique eliminates the effect of the timin offset by computin the frequency difference of adjacent sub-carriers in the ranin channel, which reduces the search space from two dimensions to one dimension. And the threshold is used to detect the ranin code existin in the current ranin slot. The simulation result shows the ood ranin performance of this technique. References [1] Hisham A. ahmound, Huseyin Arslan, and ehmet Kemal Ozdemir, Initial Ranin for WiAX (80.16e) OFDA. [] Doo Hwan Lee, Hui Won Je, and Kwan Bo Lee. Differential Detection Scheme with Combinin ultiple FFT Blocs for OFDA Ranin of IEEE 80.16e. [3] Altera, Application ote 430, WiAX OFDA Ranin. [4] Cory S. odlin, and Tari uharemovic, Patent, US 007/ A1, Orthoonal Frequency Division ultiplexin Access (OFDA) Ranin. [5] Jerry Krinoc, et al, Comments on OFDA Ranin Scheme Described in IEEE 80.16ab- 01/01r1, IEEE 80.16abc-01//4, Auust 001.