Initial Ranging for WiMAX (802.16e) OFDMA

Transcription

1 Initial Ranging for WiMAX (80.16e) OFDMA Hisham A. Mahmoud, Huseyin Arslan Mehmet Kemal Ozdemir Electrical Engineering Det., Univ. of South Florida Logus Broadband Wireless Solutions 40 E. Fowler Ave., ENB-118, Tama, FL, Cororex Park Pl. Suite 700, Tama, FL Abstract Ranging is one of the most imortant rocesses in the new mobile WiMAX standard. Power adjustment, timing offset estimation, and synchronization between a Base Station (BS) and all users within a cell are done through the ranging rocess or more secifically initial ranging. In this aer we discuss the details of initial ranging and some of the roosed algorithms as well as a novel algorithm to carry out a successful ranging rocess. Performance curves and comutational comlexity comarisons will be resented. It is observed that the roosed algorithm offers a better trade-off between comutational comlexity and erformance. I. INTRODUCTION WiMAX as a new technology has got the attention of researchers and wireless comanies. This new wireless technology romises to deliver both high data rates and longrange coverage. With the aroval of the new mobile WiMAX standard (IEEE80.16e-005) at the beginning of the year 006, this technology has become even more exciting. Unlike WiFi, which was originally designed for indoor alications and local area networks (LAN), WiMAX is otimized for outdoor alications and Metroolitan area networks (MAN). It has been even anticiated that WiMAX will relace citywide WiFi rojects and 3G cellular networks, making it even more attractive. One of the exciting asects of WiMAX is that its Medium Access Control (MAC) layer suorts more than one hysical layer (PHY) mode. This feature not only enables comanies to differentiate their roducts from each other, but also makes WiMAX an adative technology that can satisfy different needs deending on the alication. One of the most interesting PHY modes suorted by WiMAX standard is Orthogonal Frequency Division Multile Access (OFDMA) PHY mode. OFDMA PHY mode enables a WiMAX Base Station (BS) to suort multile users at the same time. In this mode, a BS system utilizes the available channel by dividing the available subcarriers into subchannels that can be assigned to multile users in a sohisticated and adative way. As a matter of fact, users can be assigned to different bandwidths, different time durations, and different modulation orders based on various arameters such as user Carrier-to-Interference-and-Noise Ratio (CINR) and the available bandwidth. In addition, mobility suort of WiMAX is mainly imlemented in OFDMA PHY. Although WiMAX has these advantages, its system comlexity increases and new roblems arise. One of these roblems is timing and synchronization between a BS and subscriber stations (SS s). While other Orthogonal Frequency Division Multilexing (OFDM) receivers can easily synchronize to the received signal, this is not the case for the OFDMA receiver. At an OFDMA receiver, where multile users arrive at the same time, if the users are not synchronized with the receiver, they will interfere with each other and the BS will not be able to recover the individual signal of each user. Hence for OFDMA PHY mode to work roerly, all users should arrive at the BS at the same time with a considerably high timing accuracy. This can be achieved if all users are synchronized with the BS before the communication link is established. The standard states that for a user to join the channel, first, the Round Tri Delay (RTD) between the user and the BS must be known to the user. This delay estimation is used by the user to synchronize its signal such that it arrives at the BS in its designated time. The rocess in which this delay is estimated is called Initial Ranging, and this is mandated for all SS s that desire to synchronize to the channel initially. Other tyes of ranging rocesses (e.g. eriodic ranging and bandwidth request) exist but we will consider initial ranging in this aer. As stated in the IEEE80.16e-005 standard [1], the MAC layer at the BS defines a ranging channel as a grou (or more) of six subchannels, where a subchannel is a grou of subcarriers that are chosen according to a randomization formula. In addition, users are allowed to collide in this ranging channel. Any SS that attemts to establish a communication link is required to carry out a successful initial ranging rocess with the BS. Once a SS senses a BS, for network entry it first scans for a Down Link (DL) channel and synchronizes itself with the BS. Then, the SS shall acquire transmit arameters, which are included in the Ulink Channel Descritor (UCD), U Link (UL)-MAP, and DL-MAP. The last ste would be to erform initial ranging. At the receiver side, the BS is required to detect different received ranging codes, estimate the timing offset and the ower for each user that bears an initial ranging code. The BS then broadcasts the detected ranging codes with adjustment instructions for the timing and ower level. The status notifications of either ranging successful or retransmission are also broadcasted. In initial ranging, the SS chooses one of the available ranging codes randomly and transmits it twice over two consecutive OFDM symbols with BPSK modulation. The SS should transmit the ranging code at a random time during the ULink (UL) frame as long as there is a ranging oortunity. UL-MAP will show if a ranging oortunity is available through the next

2 UL frame. Another otion is to send two consecutive ranging codes over four OFDM symbols to increase the robability of code detection [1]. However, we will consider the first method as the same alies to the second one. Synchronization for multiuser OFDM systems has been discussed in the literature. One method is to use filters matched to the intended user s subcarriers (in our case, the ranging channel subcarriers) and then use the Cyclic Prefix (CP) redundancy to estimate the timing offset []. However, this method will not work with OFDMA since multile users collide in the same channel. In addition, the ranging subcarriers are not necessarily adjacent, which makes the filtering rocess inalicable. In [3] it was roosed to synchronize the users to the BS one at a time, with the assumtion that other users are already synchronized. Again, we will have the same roblem with multile users colliding in the ranging channel. Finally, in [4] it was roosed to use a bank of correlators (corresonding to number of ranging codes) in the frequency domain to detect received ranging codes. However, this method comlexity increases as the number of codes increases. In this aer, we roose a new ranging detection algorithm for OFDMA PHY. A erformance and comlexity comarison between the roosed algorithm and the current algorithms will be resented. It is observed that the roosed algorithm offers a better trade-off between the accuracy and comlexity of the initial ranging rocess. II. SYSTEM MODEL Our system model is mainly based on the IEEE80.16e- 005 standard [1]. We consider the UL of an OFDMA system with N t subcarriers. After assigning the DC and guard subcarriers, the remaining subcarriers, N d, are groued into Q subchannels. Each subchannel has N Q = N d /Q subcarriers. Each user in the UL is assigned to one or more subchannels. The BS defines a grou of six subchannels (or more) for ranging. Note that the subcarriers assigned to each subchannel are chosen randomly and thus they are not necessarily adjacent. The BS broadcasts all the ranging information (i.e. ranging oortunities, ranging subchannels, ranging codes...etc) in the UL-MAP. One ranging time slot sans two OFDMA symbol duration. The kth user signal in frequency domain is denoted c (k) = [c (k) (0), c (k) (1),..., c (k) (L 1)] T, where is the index of the randomly chosen ranging code and L is the length of the ranging code. The signal is then extended to the length of N t by inserting N t L zeros which results in X (k) = (0), X (k) (1),..., X (k) (N t 1)] T. Note that [X (k) X (k) (m) = { c (k) (n), if m = i r (n); 0, otherwise, where i r (n) is the index of the nth ranging subcarrier. The vector X (k) is then fed to an N t -oint Inverse Discrete Fourier Transform (IDFT). The resulting signal in time domain is extended over two OFDMA symbols by reeating x (k) twice and adding the cyclic refix and ostfix as shown in Fig. 1. This (1) One OFDMA symbol duration including CP x N-CP... x N-1 x 0 x 1... x N-1 x 0 x 1... x N-1 x 0... x CP-1 Fig. 1. coy { { coy Initial ranging transmission over two OFDMA symbols. method of adding the cyclic redundancy is to avoid hase discontinuity over the whole ranging time slot. Hence, by using an observation window of (N t + CP) at the receiver, we can guarantee that a comlete coy of the time-domain signal x (k) will be received. Finally, the transmitted signal will be noted as S (k) = [S (k) (0), S (k) (1),..., S (k) (N t +CP 1)] T, where = [x (k) (N t CP),..., x (k) (N t 1), x (k) (0),..., x (k) (N t S (k) 1), x (k) (0),..., x (k) (N t 1), x (k) (0),..., x (k) (CP 1)] T. The transmitted signal (S (k) ) goes through an additive white Gaussian channel with noise ower sectral density N 0. To simlify our analysis, we assume that the channel is flat and has a constant gain of one. The derivation for other channel tyes is straightforward. The receive signal in the frequency domain will be, Y = S (k) + W, () where W is a vector of comlex white Gaussian noise samles with zero mean and N 0 / variance, and N 0 is the noise ower sectral density. We assume that all users other than users erforming initial ranging are synchronized to the BS. This is a valid assumtion as synchronizing to the BS is mandatory before a SS can establish the communication link. With this assumtion it is guaranteed that there will not be interference from other users signal to the ranging channel. Unfortunately, we cannot say the same for initial users as their unsynchronized signal will interfere with synchronized users. However, as this situation is unavoidable, initial users are required by the standard to start the ranging rocess with minimum ower level ossible. Then, as the user fails to get a resonse from the BS, the ower is increased incrementally until a resonse is detected. If the maximum ower level is reached and still the user cannot get a resonse from the BS, the user starts from the minimum ower level and the rocess is reeated. This shows how imortant it is for a BS to detect initial ranging users with the lowest signal levels ossible. III. CURRENT RANGING ALGORITHMS One way of detecting ranging codes at the BS would be correlating the received signal in time domain. We can cross correlate the received signal with all ossible ranging codes. However, this would be comutationally heavy. With less comutation, we can also auto-correlate the received signal with its delayed relica by exloiting the reetition in the ranging code. Unfortunately, to accomlish that, we need

3 to get rid of other users signal as the ranging users are frequency-multilexed with synchronized users. This will not only increase the comlexity and delay of the algorithm, but it will also be affected by the quality of other users estimation. In addition, the ranging codes are Pseudo Noise (PN) codes roduced by seudo-random binary sequence (PRBS). These PN codes are modulated in the frequency domain, which means that in time domain the cross correlation between different codes is much weaker. In [4] an observation window of N t +CP was used and then the cross correlation with all ossible codes was erformed. Using this window size ensures that at least one comlete OFDMA symbol will fill the observation window. Another aroach is to erform the cross correlation over frequency domain signal at the outut of the Discrete Fourier Transform (DFT) [5]. In this case, a comlete OFDMA ranging symbol in the observation window will result in a correct ranging code in the frequency domain even with a timing offset. The effect of the timing offset will be translated into a linear hase shift in the frequency domain. To estimate the timing offset of the ranging code, it is needed to correlate with all ossible hase shifts (corresonding to timing offsets). So, the received signal is correlated with all ossible codes and all ossible linear hase shifts and a threshold is set to detect the existence of a ranging code in the current observation window and its timing offset. One advantage of taking the cross correlation rocess into the frequency domain is that there will be no interference from synchronized users signal to the ranging channel. This would reduce the robability of a misdetection or a false alarm due to the ower difference between the ranging users signal and the synchronized users signal. Another advantage would be that the PN codes were originally sent over frequency and thus correlating in time domain will imair the cross correlation roerties between different codes. The main disadvantage of reviously mentioned algorithms is the high comutational comlexity. If the total number of codes is K and the maximum timing offset considered is τ max samles, then Kτ max cross correlation oerations are needed every OFDMA symbol. In the wireless IEEE standard 80.16a [6] and 80.16ab [7] considered in [4] and in [5] resectively, the long ranging codes used for initial ranging are only 16 codes. However, for IEEE80.16e [1], the number of ranging codes is 56 codes. These codes will be divided into three categories: initial ranging codes, eriodic ranging codes, and bandwidth-requests codes. Initially, the BS would assign more codes for initial ranging as users within the cell start entering the network. If we assume that 18 codes would be assigned for initial ranging, then for OFDMA systems based on IEEE80.16e-005, the comutational comlexity for the ranging rocess would be eight times as much as the comlexity of 80.16a/b. IV. PROPOSED ALGORITHM In our algorithm we will concentrate more on the trade off between comutational comlexity and erformance of the ranging rocess. We choose to use an observation window with one OFDMA symbol size and aly the algorithm in frequency domain for the advantages of this method that was mentioned earlier in section III. However, instead of directly crosscorrelating with every ossible code and every ossible hase offset for every OFDMA symbol, we break the initial ranging rocess into three main tasks. Our first task would be to find OFDMA symbols containing ranging codes. This ste will allow us to find out which symbols we should work on further and which ones we should just dro so that the comutational comlexity wasted on emty OFDMA symbols is reduced. Energy detector will be used to detect OFDMA symbols containing ranging codes in the ranging channel, which will be discussed in more details in section IV-A. Next, we will find how many codes are there within detected OFDMA symbols from ste one and determine the timing offset (linear hase shift) for each code. Again, in this ste we further reduce the comutational comlexity by first finding the timing offset of the codes before erforming the cross correlation with all ossible codes for every ossible linear hase shift. Section IV- B discusses the details of this ste. The last ste in the algorithm is detection of multiuser codes by cross correlating detected codes with all ossible ranging codes after removal of any timing offsets. This will be covered in section IV-C. Using this aroach, the comutational comlexity is greatly reduced while the erformance is still accetable as will be shown in sections V and VI A. Energy Detector If there is a ranging oortunity in the next UL frame, the ranging channel will be available through the entire UL subframe duration. The BS samles the received signal and grous it into N t + CP samles. The CP is removed and the remaining N t samles are fed to the DFT unit. The ranging channel will contain noise and energy from ranging users. Fig. shows the received signal of a ranging user. There are three ossible OFDMA symbols: a) emty symbols containing only noise, b) symbols containing incomlete arts of a ranging code which will cause interference to subcarriers other than the ranging subcarriers and thus affecting other users, and c) a comlete ranging code. We are more interested in detecting the third kind, as it contains the required information to detect the user ranging code. Emty symbols should be ignored since they contain no information. OFDMA symbols with incomlete ranging codes are easy to tackle since the information included in them (i.e. the ranging code, its timing offset, and signal ower) can be extracted from the symbols with comlete ranging code. In order to detect symbols with a comlete ranging code we use a simle energy detector in frequency domain. The energy detector measures the energy within the ranging subcarriers. This method has two advantages: a) since the energy is measured in the frequency domain and since the ranging subcarriers are not adjacent, the robability of a ulse of noise triggering the energy detector by mistake is low, b) the measured energy is already done to measure the noise variance

4 Frequency domain signal DFT Time domain signal Interference Code X k Interference Code x k Code x k S n S n+1 S n+ S n+3 t Fig.. Initial ranging codes at the receiver. of the channel and can also be used later to measure the ower of the ranging user signal. So, no additional comutational comlexity is required for this ste. The measured energy in the ranging channel will be, E g = Y (m), (3) where m = i r (n) and Y is the N t vector at the outut of the DFT unit at the receiver side. After measuring the energy within the ranging channel, a threshold (η 1 ) is used to decide if the OFDMA symbol contains a ranging code or not. To find the best value for (η 1 ) we calculate the robability of a false alarm (P fa ) and the robability of misdetection (P md ). We define the robability of a false alarm as the robability of a noise only symbol s energy exceeding (η 1 ). In the same manner, the robability of misdetection is defined as the robability of the energy of an OFDMA symbol not exceeding (η 1 ) while containing a comlete ranging code. Note that we ignore the case of an OFDMA symbol containing incomlete ranging code as missing this symbol will not affect us. In addition, detecting an incomlete ranging code can also rovide correct ranging information if the timing offset is relatively small. If the current OFDMA symbol contains no ranging code, then Y (m) = W (m), and, E g = W(m), = W R (m) + W I (m), (4) where W R (m) and W I (m) are the real and imaginary arts of W(m), resectively. The energy in this case is the sum of L samles of the square of Gaussian random variables with zero mean and N o / variance. Hence, the measured energy can be described as a random variable with Chi-square distribution having a mean µ 1 = LN 0 and variance σ 1 = LN 0. Using the central limit theorem, if L is large is enough, the energy distribution can be aroximated as a normally distributed variable with the same mean and variance. In our case, L or the ranging code length is 144 bits which is large enough to validate this aroximation. t The robability of false alarm then becomes, ( ) η 1 µ 1 P fa = 0.5erfc. (5) πσ 1 For an OFDMA symbol containing a comlete ranging code, if the user has a timing offset of τ k samles then the OFDMA symbol containing the comlete ranging code will be cyclically shifted by τ k samles as shown in Fig.. The OFDMA symbol in the frequency domain will have a linear hase shift of πnτ k /N t where n is the subcarrier index. In this case, E g = c (k) (m)e jφm(τk) + W(m), (6) where φ m (τ k ) = πmτ k /N t. Since BPSK modulation is used, then c (k) (m) = ±1. Then it can be shown that, E g = 1 + W R (m) + W I (m) + c (k) (m)cos[φ m (τ k )] W R (m)+ c (k) (m)sin [φ m (τ k )] W I (m). (7) Note that the exected value for the last two terms in (7) goes to zero for large L. Again, using the central limit theorem, the distribution of this energy can be aroximated as a normally distributed random variable with mean µ = L + LN 0 and variance σ = LN 0 + LN 0. Hence, the robability of a misdetection becomes, ( ) η 1 µ P md = 1 0.5erfc. (8) πσ Fig. 3 shows P fa and P md against η 1 normalized by L and N 0 for different Signal-to-Noise Ratio (SNR) levels. As we can see P fa does not change as the SNR changes since η 1 is normalized and since P fa deends only on N 0. Here we assume that N 0 knowledge is required to choose the best value of η 1 which is a valid assumtion since the BS needs to estimate N 0 to calculate different users SNR. B. Timing Offset Estimation In the revious ste, we detected OFDMA symbols containing one or more comlete ranging codes. The next ste is to estimate the timing offset for each of these codes. Since we are erforming our algorithm in frequency domain, timing offset would be directly translated into linear hase shift. In this case, what we are estimating is actually the linear hase shift for each code in the current OFDMA symbol. A straightforward way of doing this is to cross-correlate the ranging channel of the current OFDMA symbol with all ossible codes and all ossible linear hase shifts. This rocess can be followed by using a threshold to detect different ranging codes and their hase shifts within the current symbol. However, this is comutationally heavy. We intended to reduce the comlexity of this oeration by exloiting the fact that timing offsets only

5 Probability P fa P ms, SNR = 0dB P ms, SNR = 5dB P ms, SNR = 10dB Normalized energy level µ 3 µ Normalized Threshold η.( / L N ) 1 0 Fig. 3. P fa and P md for different noise levels Ranging codes er OFDMA symbol Fig. 4. µ 3 and µ 4 for different numbers of ranging users. affect the hase of the frequency domain signal. Since BPSK modulation is used, the signal does not have an imaginary art. If there are K ranging users within the current OFDMA symbol, each user has a timing offset τ k samles, where 0 < τ k < τ max and τ max is the maximum delay between the SS and the BS within the current cell. Then, Y (m) = K 1 i=0 c (i) (m)e jφm(τi) + W(m), (9) where m = i r (0), i r (1),..., i r (L 1). As can be seen in (9), if there was no timing offset (τ i = 0), the whole energy of the ranging user will be only in the real art of the signal and the imaginary art will contain only noise. Hence, by alying all ossible linear hase shifts and taking the energy of the real art of the signal, we have, { E r (u) = R Y (m)e jφm(τi)} { K 1 = i=0 c (i) (m)cos[φ m (τ i τ u )] + W R (m)cos[φ m (τ u )]}, (10) where u = 0, 1,..., τ max. We assume that τ i is a uniformlydistributed random variable between 0 and τ max. In addition, m is chosen randomly from the available subcarriers. Hence, we aroximate the hase [πm(τ i τ u )/N t ] as a uniformlydistributed random variable between 0 and π. Clearly, for τ i = τ u, cos[φ m (τ i τ u )] = 1 and we will have a eak in the measured energy, E r (u). So, we set a threshold to detect those eaks and thus obtain an estimate of τ i for all values of i. We will set the threshold, η, as a function of Ēr where, Ē r = 1 K K 1 u=0 E r (u). (11) There are two cases here for any u: when τ i τ u, E r (u) will have an aroximate mean of µ 3 = L (K + N 0 )/. On the other hand, when τ i = τ u, E r (u) will have an aroximate mean of µ 4 = L (K N 0 )/. Then, Ē r = Kµ 4 + (τ max K)µ 3 τ max. (1) This equation is valid only with the assumtion of K < τ max, which is a reasonable assumtion since deending on the cell radius τ max can go u to N t / while the number of ranging users within the same OFDMA symbol is usually much lower than that. Fig. 4 shows µ 3 and µ 4 for different values of K, where µ i = µ i /Ēr is the normalized mean. As we can see from Fig. 4, as the number of ranging users increases, the robability of a misdetection increases since the difference between the two levels ( µ 3, µ 4 ) decreases. In addition, the variance of the measured energy also increases with the number of ranging users, since they act as interference source for τ i τ u as we can see from (10). C. Code Detector In the revious two stes of the algorithm, we detected OFDMA symbols containing ranging codes and we detected their timing offset. The last stage is to detect which code was transmitted out of the available ranging codes, P, where P is the number of codes assigned by the BS for initial ranging. In this ste, we remove the linear hase shift corresonding to each ranging code and then we cross-correlate with all ossible ranging codes. The correlator outut is then, E c (v) (i) = { R Y (m)e jφm(ˆτi)} c (i) (n), (13) where i = 0, 1,..., P 1, and ˆτ i is the estimated timing offset of the ith user. The vector E c (v) is calculated for every detected ranging code, v, where v = 0, 1,..., K 1, and K

6 is the total number of detected ranging codes. E c (v) is then comared to a threshold, η 3, to detect the ranging codes within the current OFDMA symbol and with this timing offset, η 3 is chosen as a function of the root mean square value of E c (v). We could have just chosen the code with maximum correlation since we are not suosed to reach this ste unless there is a ranging code in the current OFDMA symbol. However, we choose to use a threshold so that we can detect users with the same timing offset in the current OFDMA symbol. V. COMPUTATIONAL COMPLEXITY For ractical alications, the comutational comlexity of an algorithm is of a great imortance. In this section we evaluate the comlexity of the roosed algorithm and comare it to other algorithms. The two algorithms we comare the roosed algorithm are the ones used in [4], [5]. We are going to name them: algorithm 1 and algorithm, resectively. For algorithm 1, an observation window with the OFDMA symbol size is used. A bank of correlators equal to the number of available ranging codes P is used to searate ranging codes in the received signal. If the maximum ossible delay is τ max, then (τ max +1)P cross-correlation oerations are erformed for every OFDMA symbol with ranging oortunity. Assuming the current UL is N UL OFDMA symbols, where N UL is required by the standard to be multile of 3, then the total number of correlation oerations erformed would be N UL (τ max + 1)P and the same number for threshold comarison oerations. Algorithm differs from algorithm 1 in that algorithm erforms the cross correlation in frequency domain. Thus, to erform the cross correlation for every ossible timing offset, a linear hase shift of φ m (τ u ) and u = 0, 1,..., τ max is alied to the signal in frequency domain. Then the cross correlation is erformed. Hence, algorithm has an addition of τ max + 1 linear hase shifts added to its comutational comlexity. However, since the correlation is erformed in the frequency domain and since BPSK modulation is used, then the correlation will be done using real-signals unlike algorithm 1 which will have to erform comlex-signal correlation. In the roosed algorithm, the energy of the ranging channel for every OFDMA symbol is calculated, so we have N UL energy calculation oerations and threshold comarisons. The energy calculation is erformed anyway for N 0 estimation. Assuming that every ranging symbol triggers the energy detector over two OFDMA symbols, then at most K OFDMA symbols will make it to the next stage of the algorithm, where K is the total number of ranging users within the current UL frame. Of course, if one or more codes collide, then less OFDMA symbols will make it to the next stage. In the second stage, all ossible linear hase shifts are alied to the OFDMA symbol (i.e. from 0 to τ max ). Then the energy of the real art of the signal is measured and comared to a threshold. Hence, (1 + τ max ) linear hase shifts, real energy calculation, and comarison oerations are erformed. For the last stage, only the K ranging codes, with at K ranging OFDMA symbols, will make it. A cross-correlation TABLE I PROPOSED ALGORITHM S COMPUTATIONAL COMPLEXITY. Oeration ADD MUL Correlation, comlex (L-1)+L 4L Correlation, real L-1 L Energy Cal., comlex (L-1)+L 4L Energy Cal., real L-1 L Phase shift L 4L with all ossible codes is erformed. Then KP correlations and comarison oerations (CMP) are erformed at this stage. Table I shows the number of additions (ADDs) and multilications (MULs) needed for each oeration. Using Table I, the comutational comlexity of the algorithms under investigation becomes, Algorithm 1: Algorithm : N UL P(τ max + 1)(4L ) ADD + 4LN UL P(τ max + 1) MUL + N UL P(τ max + 1) CMP (τ max + 1)(L + N UL PL N UL P) ADD + Proosed Algorithm: L(τ max + 1)(4 + N UL P) MUL + N UL P(τ max + 1) CMP [ NUL (4L ) + K(τ max + 1)(3L 1) + KP(L 1) ] ADD + [ L(KP + ) + 10KL(τmax + 1) ] MUL + [ NUL + K(τ max + P + 1) ] CMP Finally, using Table II we calculate the comlexity of all three algorithms. We assume N UL = 1 OFDMA symbols, P = 56 codes(maximum), L = 144 bits(standard [1]), and τ max = 51 samles for N t = 104. The number of cycles needed by each algorithm is as follows, Algorithm 1: cycles, Algorithm : cycles, Proosed Algorithm : cycles for K = 1, cycles for K = 0. The difference in comutational comlexity is evident. The comlexity of the roosed algorithm is a few orders of magnitude lower than the comlexity of algorithms 1 and. While both algorithm 1 and maintain fixed comlexity regardless of the number of ranging users K, the roosed algorithm can udate to K which gives it the lowest limit in comutational comlexity.

7 TABLE II CPU CYCLE COUNT BASED ON XILINX VIRTEX-4 FPGA. Oeration CPU cycles ADD 1 float oint MUL 34 CMP 1 VI. SIMULATION RESULTS An OFDMA system model based on [1] is used with arameters, N t = 104, CP = 18 samles, N UL = 1 OFDMA symbols, L = 144 bits, and τ max = 51 samles. The total number of ranging codes is 56 codes. In the simulations, all codes are assigned to initial ranging, i.e. P = 56. The ranging channel is made u of six subchannels and sanning 144 subcarriers er OFDMA symbol. The channel is an additive white Gaussian noise channel and the SNR=10dB at the BS for all ranging users signal. Ranging users choose two consecutive symbols randomly to send their ranging code during the UL frame with equal robability. For every number of ranging users, K, the erformance is obtained after 1000 (1 OFDMA symbols) simulation runs. The thresholds where chosen to be η 1 = 15, η = 1., and η 3 = 6. Fig. 5 shows the erformance of the roosed algorithm for different numbers of ranging users, K. The robability of misdetection, P md, is the robability of missing one of the received ranging codes. The robability of timing error, P te, is the robability of making an error in the timing offset estimation for detected ranging codes. Even for as high as 10 ranging users er UL frame, still the robability of misdetection is below 8%. This shows that even with the reduced comutational comlexity of the roosed algorithm, the erformance is still at a high level. In addition, the robability of a false alarm was found to be zero in our simulation. However, this would not be the case if other imarments, such as multiath fading and intercarrier interference, were introduced. Fig. 6 shows the robability of collisions between ranging codes within the simulated UL frame. For every OFDMA symbol in the UL frame, the number of ranging codes in the symbol is determined. Next, we calculate the number of symbols with collisions (i.e. containing two or more ranging codes). The final number is normalized by the total number of ranging codes that was transmitted. We can see that as the number of ranging codes within the UL frame increases, the robability of more codes colliding within the same OFDMA symbol increases and thus increasing the robability of a misdetection. VII. CONCLUSIONS We resented a novel algorithm for OFDMA initial ranging rocess based on IEEE80.16e-005 standard. The roosed algorithm erforms multiuser code detection and timing offset estimation for ranging users. The algorithm is divided into three arts. The first art detects OFDMA symbols with Probability Probability Probability of misdetection P md Probability of timing error P te Ranging codes er UL frame Fig. 5. Colliding codes er OFDMA symbol Fig. 6. Performance of the roosed algorithm Ranging codes er UL frame Probability of ranging code collisions. ranging users. The second art estimates the timing offset for each user with the current OFDMA symbol. Finally, the last art detects the multiuser code. A comlexity comarison between the roosed algorithm and other existing algorithms shows a sueriority of the roosed algorithm. Simulation results showed that the roosed algorithm erforms well with as high as 10 ranging users er UL frame. Hence, it is believed that the roosed algorithm can be realized in ractical mobile WiMAX BS s. REFERENCES [1] IEEE Standard for Local and metroolitan area networks Part 16: Air Interface for Fixed and Mobile Broadband Wireless Access Systems Amendment : Physical and Medium Access Control Layers for Combined Fixed and Mobile Oeration in Licensed Bands and Corrigendum 1, IEEE Std 80.16e-005 and IEEE Std /Cor (Amendment and Corrigendum to IEEE Std ) Std.,

8 [] J. J. van de Beek, P. Borjesson, M.-L. Boucheret, D. Landstrom, J. Arenas, P. Odling, C. Ostberg, M. Wahlqvist, and S. K. Wilson, A time and frequency synchronization scheme for multiuser OFDM, IEEE J. Select. Areas Commun., vol. 17, no. 11, , Nov [3] M. Morelli, Timing and frequency synchronization for the ulink of an OFDMA system, IEEE Trans. Commun., vol. 5, no., , Feb [4] X. Fu and H. Minn, Initial ulink synchronization and ower control (ranging rocess) for OFDMA systems, in Proc. IEEE Global Telecommun. Conf. (GLOBECOM), vol. 6, Nov. 9- Dec. 3, 004, [5] J. Krinock, M. Singh, M. Paff, V. Tien, A. Lonkar, L. Fung, and C.-C. Lee, Comments on OFDMA ranging scheme described in IEEE 80.16ab- 01/01r1, IEEE 80.16abc-01/4, Aug [6] Broadband Wireless Access: IEEE MAN standard, IEEE LAN/MAN standards committee 80.16a, 003. [7] Air Interface for Fixed Broadband Wireless Access Systems, IEEE LAN/MAN standards committee IEEE 80.16ab-01/01r1, July 001.