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Int. J. Communications, Network and System Sciences, 2009, 2, 775-785 doi:10.4236/ijcns.2009.28090 blished Online November 2009 (http://www.SciRP.org/journal/ijcns/). Copyright © 2009 SciRes. IJCNS Pu Subcarrier Availability in Downlink OFDM Systems with Imperfect Carrier Synchronization in Deep Fading Noisy Doppler Channels Litifa NOOR1, Alagan ANPALAGAN1, Sithamparanathan KANDEEPAN2 1WINCORE Research Lab, Ryerson University, Toronto, Canada 2Wireless Signal Processing Group, National ICT, Australia Email: alagan@ee.ryerson.ca, lnoor@ee.ryerson.ca Received July 11, 2009; revised August 30, 2009; accepted September 19, 2009 Abstract Multicarrier systems such as orthogonal frequency division (OFDM) are considered as a promising candidate for wireless networks that support high data rate communication. In this article, we investigate the perform- ance of a multiuser OFDM system under imperfect synchronization. Analytical results indicate that the SNR degrades as the average power of the channel impairments such as AWGN, carrier frequency offset due to Doppler frequency and fading gain is increased. The SNR degradation leads to imperfect synchronization and hence decreases the total number of subcarriers available for allocation. Monte Carlo analysis shows up to 22% loss in the number of allocatable subcarriers can be expected under a specific imperfect synchroniza- tion condition as compared to perfect synchronization. We utilize empirical modelling to characterize the available number of subcarriers as a Poisson random variable. In addition, we determine the percentage de- crease in the total number of allocatable subcarriers under varying channel parameters. The results indicate 19% decrease in the number of available subcarriers as average AWGN power is increased by 10dB; 44% decrease as the Doppler frequency is varied from 10Hz to 100Hz; and 56% decrease as the fading gain is varied from 0dB to -30dB. Keywords: OFDM, Subcarrier Availability, Synchronization 1. Introduction The growing demand for high-speed wireless communi- cations has led to the investigation of spectrally effcient systems for downlink transmission in multicarrier sys- tems [1]. Multicarrier systems such as Orthogonal Fre- quency Division Multiplexing (OFDM) enable the net- work to provide high data rate communication by using adaptive subcarrier allocation. Although high data rate communication is subject to inter-symbol interference (ISI) due to dispersive nature of wireless channels, OFDM enables the radio network to support high data rates while reducing the effect of ISI [2,3]. However, OFDM based systems are sensitive to car- rier frequency offset (CFO), which leads to the loss of orthogonality between the subcarriers and thus introduc- tion of inter-channel interference (ICI) [4]. CFO is caused by differences in transmitter and receiver oscilla- tor frequencies, Doppler frequency due to relative mobil- ity between transceivers and phase noise introduced by non-linear channels. Since accurate frequency synchro- nization is very important for reliable signal reception [5], OFDM systems utilize different synchronization schemes to facilitate acquisition and tracking of carrier frequency. However, the distortion inherent in wireless channels requires special design techniques and rather sophisti- cated adaptive coding and modulation algorithms to achieve accurate synchronization. Different methods have been suggested to reduce the effect of CFO [6–8], but obtaining perfect synchronization in wireless chan- nels remains a challenging task. Hence, in this article we investigate the performance of multiuser OFDM under imperfect synchronization. In the literature, various subcarrier allocation algo- rithms have been presented for multiuser OFDM systems. Many of these algorithms support high aggregate data *This work was supported in part by a grant from National Science and Engineering Research Council of Canada.. L. NOOR ET AL. 776 rate and maximize system capacity [9–14]. However, the performance improvement is achieved when the system is based on perfect synchronization and the utilization of instantaneous channel information to adaptively allocate subcarriers. Assuming that the channel variation in a frequency selective fading environment is independent of each other, adaptive subcarrier allocation based on in- stantaneous channel information is an effective method to resource allocation in multiuser OFDM systems. However, obtaining the instantaneous channel condition under hostile wireless channels is not attainable in prac- tical systems. Hence identifying the subcarriers with rela- tively low SNR and avoiding allocation of such subcarri- ers is a more practical approach to subcarrier allocation. In this article, we determine the percentage loss in the available number of subcarriers under imperfect syn- chronization in comparison to perfect synchronization. The frequency synchronization scheme used is the open-loop maximum likelihood (ML) estimator. The performance of synchronization depends on noise, Dop- pler frequency and deep-fades in the channel that reduce the effective SNR associated with the subcarrier, which in turn degrades the allocatability of the subcarrier. The purpose of evaluating the system performance under im- perfect synchronization is to restrict allocation of the subcarriers that are not suitable for transmission. Al- though the number of allocatable subcarriers as com- pared to perfect synchronization decreases which trans- lates to a decrease in the aggregate data rate for a given number of users, the BER performance of the system could be improved by avoiding allocation on subcarrriers that are not suitable for transmission. Hence, any subcar- rier allocation algorithm can be utilized while consider- ing the variations in the total number of subcarriers. To the best of our knowledge, this is the first paper to char- acterize the subcarrier availability in deep fading noisy Doppler channels. The organization of this article is as follows. In Sec- tion 2, the OFDM system model is discussed. In Section 3, we discuss the frequency synchronization utilized for the OFDM system. Following, a detailed analysis of SNR is provided in Section 4. In Section 5, we discuss the number of available subcarriers under imperfect syn- chronization and model the statistical characteristics of allocatable subcarriers. Following, in Section 6 we evaluate the number of available subcarriers under vari- able SNR. In Section 7, the paper is concluded. 2. System Model Figure 1 shows the baseband equivalent model of the OFDM system that is being considered in this paper. This analysis is independent of mapping of the transmit- ted data as complex values a0,i . . . aN −1,i , and is there- fore applicable to all forms of modulation which is util- ized in OFDM systems. As indicated in Figure 1, the IFFT is performed on the complex data symbols ak,i for k = 0, 1, . . . , N − 1, to produce the time-domain samples bn,i for n = 0, 1, . . . , N − 1 as follows: 12( ) ,, 0 1n N j k N ni ki k bae N (1) where N is the number of data samples. The OFDM symbol bn,i is transmitted through the frequency selective Doppler channel. The frequency response of the channel is indicated by: 2() = k jfT N K K He k (2) where αk is the (Rayleigh) fading gain for the kth subcar- rier, ej2π∆fT is the CFO due to Doppler frequency with ∆f indicating the Doppler frequency and T indicating the symbol period, and ηk is the Additive White Gaussian Noise (AWGN) component on the kth subcarrier. The system is based on the characteristics of multiuser frequency-selective fading channels where different sub- carriers are subject to different fading levels and the cha- nnel variations in a multiuser environment are indepen- dent of each other. To ensure frequency selectivity, the coherence bandwidth of the channel, which is the recip- rocal of the multi-path spread, is assumed to be smaller in comparison to the bandwidth of the transmitted signal. Figure 1. Baseband Equivalent OFDM System Model. Copyright © 2009 SciRes. IJCNS L. NOOR ET AL. 777 Under the assumption of AWGN channel, the received signal with the frequency offset and the fading gain is given as: 12( )2() 0 12( ) 0 nfT Njkj k NN kkk n nfT Njk NN kk k n yaee ae C opyright © 2009 SciRes. IJCNS k (3) The received signal on the kth subcarrier and in the ith symbol period can be written as: yk,i = ak,iαk,iej2πN(∆fT)+ηk , (4) where ak,i is the transmitted data on the kth subcarrier in the ith symbol period, and ∆f T is the normalized fre- quency offset. The received signal after FFT is expressed as: 12 ,, 11 2( ) ,, 0 1 km NjN mi kim ko k NN jlmfT N li lim lo k zye ae N (5) Using the properties of geometric series, zm,i can be expressed as: 1 1() ,,, 0 1sin() sin () N NjlmfT N mili lim l lm fT za e Nlm fT N (6) The analysis of ICI can be simplified by defining N complex weighting coefficients, c0, ...., cN −1, which give the contribution of each of the N point values a0,I , ....aN −1,i to the output value. Based on this, zm,i is written as: 1 ,,, ,, 0, N miomimil mlilim llm zcac a (7) where the first term is the desired signal and second term is the ICI. co is the attenuation factor, am,i is the transmit- ted data on the mth subcarrier in the ith symbol period, and αm,i is the (Rayleigh) fading gain on the mth subcar- rier during ith symbol period. Using geometric series expansion, zm,i can be written as: 1 1 ()()()() ,,, ,, 0, 1sin ()1sin () sin ()sin () N N NI jfT jlmfT N N mimi mili lim llm fTl mfT zea ae NN fTl mfT NN (8) For noiseless case, when ∆f T = 0, zm,i = am,i + ηm which indicates the transmitted data plus noise. In the case where ∆f 0, the transmitted data is subject to attenuation and ICI. In addition, the relationship between the attenuation component c0 and ∆f T indicates that attenuation in the desired signal component increases as the ∆f T is in- creased. Given that an increase in CFO is caused by an increase in the Doppler frequency, it can be seen that as the Doppler frequency is increased the attenuation in the desired signal increases leading to a decrease in the SNR. The αm,i is the (Rayleigh) fading gain for the mth sub- carrier in the ith symbol period which attenuates the de- sired signal, which in turn reduces the SNR. Each sub- carrier experiences a different level of fading and the maximum number of subcarriers that are in deep fade are dependent on the channel condition and vary every transmission time. The deep-fading in the channel de- grades the corresponding subcarriers by reducing the effective SNR associated with the subcarrier. 3. Frequency Synchronization To emulate imperfect synchronization, the system is considered under channel impairments such as Doppler frequency and frequency selective fading. The Doppler frequency leads to substantial CFO and the frequency selective fading subjects the subcarriers to independent fading gains. The CFO and the deep-fades in the channel degrade the corresponding subcarriers which reduces the effective SNR associated with the subcarrier. This makes the synchronization system at the receiver to perform poorly, and eventually lose lock with the corresponding subcarriers. Hence, the system experiences imperfect synchronization. The frequency synchronization scheme utilized for the OFDM system is the well-known open-loop maximum likelihood (ML) estimator [15–17]. The frequency esti- mator gives rise to some jitter in the estimated frequency, increasing with decreasing SNR, due to the input noise. Correspondingly, the symbol error probability perform- ance also degrades due to imperfect carrier recovery at low SNR. To avoid this, we set a threshold limit on the synchronizer, making sure that the frequency jitter does not exceed a certain limit. The frequency jitter has to be less or equal to the threshold frequency for the subcarrier to be declared as available for allocation. In this work, the threshold frequency is set as 10Hz. If the synchro- nizer is unable to lock to the carrier with this threshold limit, due to noise, Doppler frequency or deep fades, then we declare the subcarrier to be un-lockable during the given transmission time. Hence, the subcarrier is de- clared as not suitable for allocation. Under the assumption of constant received signal power, as the noise power increases the number of sub- L. NOOR ET AL. 778 carriers available for transmission decreases. The de- crease in the total number of subcarriers available for reliable transmission imposes limitation on the total achievable data rate by the system. Hence, determining the decrease in the number of available subcarriers under imperfect synchronization which is the case in practical systems is important in assessing the accurate system performance. 4. SNR Analysis In this section, we derive the expression for the SNR on the mth subcarrier as: m mm D m IN p SNR PP (9) where PDm is the average power of the desired signal, PIm is the average interference power and PNm is the average noise power on the mth subcarrier. The average power of the desired, interference and noise on the mth subcarrier is defined as 22 , Mm DmIm PED PEN , and 2 m Nm PEN respectively. Hence, the average SNR on the mth subcar- rier is formulated as: 2 2 m m mm ED SNR EI EN 2 (10) where the average power of the desired signal is calcu- lated as: 2 2 ,,momi mi EDEc a (11) Assuming that the transmitted data and the fading gain are independent, the average power of the desired signal can be written as: 22 2 , () () mo mimi EDc EE 2 , (12) The ICI power is expressed as: 2 1 2 ,, 0, 2 122 ,, 0, N mlmlili llm N l mlili llm EIEc a cE Ea (13) The above equation can be simplified as [4]: 2 22 ,, 1 molim EIcEE a 2 i (14) The power of the noise is expressed as : 2 m EN No (15) Hence, the SNR on the mth subcarrier is written as: 222 ,, 222 ,, () () (1) ()() omi mi m oli mi cE Ea SNR cEEa N o (16) The above equation indicates the dependence of the SNR on the noise, frequency offset due to Doppler fre- quency and fading gain. Hence, as the average noise power increase the SNR decreases. In addition, to show the dependence of SNR on the CFO due to Doppler fre- quency, we express co as a function of ∆f T. Hence, the SNR is written as: 22 ,, 22 ,, ()()() (1()) ()() mi mi m limi o fT EEa SNR f TEE aN (17) Figure 2. SNR versus Fading gain with different Doppler Frequency and constant average noise power of -10dB. Copyright © 2009 SciRes. IJCNS L. NOOR ET AL. 779 Figure 3. SNR versus Fading gain with different AWGN power and constant Doppler Frequency of 10Hz. This expression clearly indicates that the desired signal and interfering power decrease due to CFO which in turn causes the SNR to decrease. Analysis is performed to study the changes in the SNR as the average power of channel parameters such as av- erage noise power, Doppler frequency and fading gain are varied. Figure 2 indicates the changes in the SNR as the av- erage fading gain is varied between -30dB to 0dB when average noise power is kept constant at -10dB. The SNR performance is evaluated under Doppler frequency of 10Hz, 30Hz, and 50Hz. As evident from (17), the aver- age power of the fading gain degrades the signal power as well as the interference power. Hence, the increase in the average power of the fading gain degrades the SNR as indicated in Figure 2. Also, the increase in the Dop- pler frequency causes the interference power to increase. It is evident from this figure that as the Doppler fre- quency increases, the SNR decreases. The increase in the Doppler frequency from 10Hz to 50Hz results in 12dB decrease in the SNR for an average fading gain of 0dB. Figure 3 indicates the changes in the SNR as the av- erage fading gain is varied between -30dB to 0dB and the Doppler frequency is kept at 10Hz. The SNR per- formance is evaluated under average noise power of -10dB, -3dB and -0.5dB. As evident from (17), the in- crease in the average noise power increases the noise power and hence degrades the SNR. As illustrated in Fig. 3, when the average noise power is increased by 9.5dB, the SNR decreases by 9dB for an average fading gain of 0dB. To maintain the adaptivity of the system further sim- plifying of (17) is avoided. Instead, Monte Carlo analysis is performed with values generated from Rayleigh dis- tributions. Due to random nature of time variant multi- path channels, it is reasonable to characterize such chan- nels statistically. The random variable αm is usually modelled using Rayleigh distribution and the subcarriers that are in deep-fade are not utilized during any trans- mission time interval in our case. To analyze the random effect, Monte Carlo analysis is performed to obtain the characteristics of the channel. Although the fading gains follow Rayleigh distribution, only the subcarriers that are identified as allocatable by the ML threshold limit are declared as allocatable. 5. Available Subcarriers with Imperfect Synchronization In this section, an analysis is performed to quantify the variations in the number of available subcarriers under imperfect synchronization which results from noise, Do- ppler shift and frequency selective fades in the channel. To emulate the effect of imperfect synchronization in a multiuser OFDM system, the average noise power, Doppler frequency and average fading level are selected as −3dB, 25Hz and −4dB respectively. The threshold frequency is set as 10Hz. The carrier frequency of the system is selected to be 4GHz and the forward link channel bandwidth is 20MHz. The total number of sub- carriers, N, is 64 and the subcarrier bandwidth is 312.5kHz. The objective of the simulation is to obtain the average number of subcarriers for each user under imperfect synchronization and the variations in the total available subcarriers as the number of users is varied. 5.1. Number of Available Subcarriers under Constant SNR The simulation results indicate that the number of sub- carriers available for users varies in each transmission C opyright © 2009 SciRes. IJCNS L. NOOR ET AL. 780 time slot and under imperfect synchronization the total number of subcarriers available for reliable transmission is smaller compared to perfect synchronization. The availability of subcarriers for a certain user can be de- fined as follows: kK aT NNN k a (18) where is the number of available subcarriers, k a N K T N is the total number of subcarriers and k a N is the number of subcarriers that are not suitable for allocation for the kth user. The k a N varies for different users supporting the fact that the channel conditions in a multipath envi- ronment is random and changes for each user. Under the specified channel conditions, in a multiuser environment the average number of subcarriers available for User-1 is 49 and for User-2 is 48. This translates to 77% and 75% available subcarriers for User-1 and User- 2 respectively in comparison to perfect synchronization. To ensure reliable data trans mission, subcarrier alloca- tion algorithms should consider the variations in the total available subcarriers for each user and avoid allocating subcarriers from k a N . In addition, we determine the maximum and minimum number of available subcarriers under a given SNR in a multiuser environment. As indicated in Figure 4, as the number of users increase, the minimum number of available subcarriers for transmission decreases while the maximum number of subcarriers available for transmis- sion increases. This indicates that over a large number of trials the average number of allocatable subcarrier is 46. Figure 4. Number of available subcarriers versus number of users. (a) User-1 (b) User-2 Figure 5. Probability mass function of the available subcarriers. Copyright © 2009 SciRes. IJCNS L. NOOR ET AL. 781 (a) User-1 (b) User-2 n addition, the maximum and minimum available sub- .2. Statistical Model of the Subcarrier this section, empirical analysis is used to determine number of available subcar- rie -1 and U The DRV is identified as a PRV because it has the xplained bellow: od of Nt th s are statistically independent because th for trans- mission can be ean, λ = 0. transmission, perfect synchronization is Figure 6. Cumulative distribution function of the available subcarriers. I carriers indicate the upper and lower bound of the achievable data rate for the users since the data rate is directly proportional to available subcarriers. It can be stated that while the average available subcarriers does not vary significantly with the increase in the number of users, the minimum and maximum available subcarriers indicate noticeable variations. As the number of users increases, the difference between the maximum and minimum available subcarrier increases, which provides flexibility in the total number of allocatable subcarriers. This system characteristic supports multiplexing gain which in turn increases the aggregate data rate. 5 Availability In the statistical characteristics of the number of available subcarriers. Given that the number of available subcarri- ers for transmission is a random variable that takes countable values, it is modelled as a discrete random variable (DRV) [18]. The obtained results are used to develop the probability mass function (PMF) of the available subcarriers for User-1 and User-2, which is indicated in Figure 5. The PMFs are used to obtain the cumulative distribution function (CDF) for both users which is given in Figure 6. Based on the PMF of the rs, it is identified as a Poisson random variable (PRV) with the parameter λ that defines the average number of available subcarriers in a given time interval. In our simulation, it is observed that λ for User ser-2 are 51 and 49 respectively. In general, for all us- ers λ is the same on average and hence the number of allocatable subcarriers is a PRV. characteristics of a PRV which are e 1) The number of available subcarriers is determined in transmission time slot with a fixed length, ts. 2) The number of available subcarriers for each user varies in the time interval ts but over a time peris e number of available subcarriers for each user has a constant average. 3) The number of subcarriers that are available in dis- joint time interval e fading gains are uncorrelated. Although the number of available subcarriers is a PRV, the availability of each subcarrier modelled as a Bernoulli random variable (BRV) where the availability of the each is indicated by a 0 in- dicating not available for allocation and 1 available for allocation. Each subcarrier availability can be viewed as a Bernoulli trial because the number of available subcar- rier in each trial is independent, and at most a certain number of subcarriers is determined in each trial. This further supports modelling of the total number of avail- able subcarrier as a PRV since a sequence of Bernoulli trials occurring in time is modelled as a PRV. Based on the above observations, the number of avail- able subcarriers is identified as a PRV with m 78N, where N is the total number of subcarriers. Hence, the average percentage loss of the subcarriers under im- perfect synchronization is 22% under the specified channel condition. To avoid performance degradation in terms of subcar- rier availability for required. Since practical systems are subject to imper- fect synchronization, the analysis indicates that deter- mining the availability of subcarriers for transmission is essential in the optimization process of radio resource allocation for multiuser systems. C opyright © 2009 SciRes. IJCNS L. NOOR ET AL. 782 Figure 7. Number of available subcarriers versus AWGN power. Figure 8. Number of available subcarriers versus Doppler Frequenc. 6. Number of Availa In estigate the variations in the total umber of subcarriers as the factors such as, average the changes in the number of available bcarriers, the AWGN power is varied while the Dop- carriers under different AWGN power. Based on the results, as the AWGN ber of available requency is changed while ading gain are kept constant values of −3dB and −4dB respectively. As illustrated y ble Subcarriers under the number of available sub Variable SNR this section, we inv n noise power, which is modelled as AWGN, Doppler fre- quency, and fading gain are changed. 6.1. AWGN To determine su pler frequency and the fading gain are kept constant at values of 25Hz and −4dB respectively. Figure 7 shows power is varied between −10dB to 0dB, the number of available subcarriers decreases by 19%. 6.2. Doppler Frequency To investigate the variations in the num subcarriers as the Doppler f the AWGN power and the f at in Figure 8, as the Doppler frequency is varied between 10Hz to 100Hz the number of available subcarriers de- creases by 44%. Copyright © 2009 SciRes. IJCNS L. NOOR ET AL. 783 Figure 9. Number of available subcarriers versus fading level. Figure 10. Number of available subcarriers versus AWGN power for different Doppler Frequency. 6.3. Freque ber of available aried, the AWGN ower and the Doppler frequency are kept constant at available subcarriers is de ng gain ailable sub- carriers with the variations in AWGN power and Dop- able s ncy Selective Fading and the Doppler frequency under a constant fadi of −4dB. Figure 10 shows the number of av To determine the changes in the num subcarriers as the fading level is v p −3dB and 25Hz respectively. Figure 9 depicts the corre- sponding number of subcarriers as the fading level is varied between −30 to 0dB. Hence, as the fading level is varied between 0dB to −30dB the number of available subcarries decreases by 56%. To further analyze the effect of the hostile channel conditions such as AWGN power, deep-fading and Dop- pler frequency, the number of termined with the variation in both the AWGN power pler frequency. Based on the results, it can be stated that 40Hz increase in the Doppler frequency leads to 20% decrease in the number of available subcarriers for an AWGN power of 0dB. In addition, the number of available subcarriers is de- termined with the variation in both the AWGN power and the fading level under a constant Doppler frequency of 25Hz. Figure 11 shows the number of available sub- carriers with the variations in AWGN power and fading levels. As evident from this figure, 20dB increase in fad- ing gain results in 12% decrease in the number of avail- ubcarriers for an AWGN power of 0dB. C opyright © 2009 SciRes. IJCNS L. NOOR ET AL. 784 Figure 11. Number of available subcarriers versus AWGN power for different fading gain. Hence, channel constraints such as AWGN, Doppler effect and frequ implication on sy vailable subcarriers changes with the variation in the A adation in terms of subcarrier smission, perfect synchronization is tical systems are subject to imperfect nchronization, the analysis indicates that determining 10Hz to 100Hz in Dopplefrequency causes 44% de- ubcarriers, and o −30dB result in 56% decrease in the number of allocatable subcarriers. ncy division multiplex- ansaction on Communications, pp. 665–675, ] J. A. C. Bingham, “Multicarrier modulation for data er sensitivity of d R. Reggiannini, “Carrier frequency acquisi- tion and tracking for OFDM systems,” IEEE Transaction ency selective fading impose noticeable stem performance. The total number of crease in the number of allocatable s changes in the fading level between 0dB t a WGN power, Doppler shift and fading level. Thus, under imperfect synchronization, which is the case in most communication systems, not all the subcarriers are available for transmission. 7. Conclusions o avoid performance degrT availability for tran required. Since prac sy the availability of subcarriers for transmission is essential in the optimization process of radio resource allocation. In this paper, we perform an analysis to determine the SNR degrades as the average power of the channel im- pairments such as AWGN, CFO due to Doppler fre- quency and fading gain are increased. The decrease in SNR causes imperfect synchronization and hence re- duces the total number of available subcarriers for allo- cation. We use empirical modelling to characterize the number of available subcarriers as Poisson random vari- able and it is determined that under imperfect synchro- nization up to 22% of the subcarriers are not suitable for transmission as compared to perfect synchronization under certain channel conditions. We have determined the variations in the number of available subcarriers with the changes in the parameters such as AWGN, Doppler frequency and deep fades that introduce imperfect syn- chronization. It has been illustrated that a 10dB increase in the average AWGN power leads to 19% decrease in the total number of allocatable subcarriers; a variation of Thus, under imperfect synchronization all the subcarriers are not available for transmission. Given that the data rate is directly proportional to the total number of avail- able subcarriers for transmission, to provide a realistic measure of the system capacity subcarrier allocation al- gorithms should be based on the number of avail- able subcarriers under imperfect synchronization. Although subcarrier allocation under the constraint of imperfect synchronization does not support more users or higher data rates, it improves system reliability by eliminating allocation on unavailable subcarriers and hence improv- ing the system BER performance. 8. References [1] D. H. J. Sun and J. SauVola, “Features in future: 4g vi- sions from a technical perspective,” IEEE GLOCOM, Vol. 6, pp. 3533–3537, November 2001. [2] L. J. Cimini, “Analysis and simulation of a digital mobile channel using orthogonal freque r ing,” IEEE Tr July 1995. [3 transmission: An idea whose time has come,” IEEE Com- munication Magazine, pp. 5–14, 1990. [4] M. v. B. T. Pollet and M. Moeneclaey, “B ofdm systems to carrier frequency offset and wiener phase noise,” IEEE Transaction on Communications, Vol. 43, pp. 191–193, 1995. [5] M. Luise an Copyright © 2009 SciRes. IJCNS L. NOOR ET AL. 785 correction,” IEEE offset in ofdm systems,” I um ml estimation of . M. C. Y. Wong, and R. S. Cheng, “Multiuser K. B. Lee, “Transmit power adaptation FDM systems,” IEEE Global Tele- ol. 2, 2000. ectrum Tech- t trans- Transaction on Communications, Vol. 44, 1996. [6] P. H. Moose, “A technique for orthogonal frequency division multiplexing frequency offset Transaction on Communications, Vol. 42, pp. 2908–2913, 1994. [7] P. B. J. van de Beek and M. Sandell, “Ml estimation of timing and frequency EEE n Transaction on Signal Procesings, Vol. 45, pp. 1800– 1805, 1997. [8] S. K. N. Lashkarian, “Globally optim miss timing and frequency offset in ofdm systems,” IEEE In- ternational Conference on Communications, Vol. 2, pp. 1044–1048, 2000. [9] K. L. R on In OFDM with adaptive subcarrier, bit, and power alloca- tion,” IEEE Journal, Selected Areas in Communications, Vol. 17, 1999. [10] J. Jang and for [17] S. Kandeepan and S. Reisenfeld, “Performance analysis of a correlator based maximum likelihood frequency es- timator,” SPCOM, pp. 169–173, 2004. multiuser OFDM systems,” IEEE Journal, Selected Areas in Communications, Vol. 21, 2003. [11] B. E. Z. Shen and J. G. Andrews, “Optimal power alloca- tion in multiuser O communications Conference, Vol. 1, 2003. [12] J. C. W. Rhee, “Increased in capacity of multiuser ofdm system using dynamic subchannel allocation,” IEEE 51st, Vehicular Technology Conference, V [13] S. Y. C. Suh and Y. Cho, “Dynamic subchannel and bit allocation in multiuser OFDM with a priority user,” IEEE Eighth International Symposium, Spread Sp iques and Applications, pp. 919–923, 2004. [14] P. Song and L. Cai, “Multi-user subcarrier allocation with minimum rate request for downlink OFDM packe ion,” IEEE 59th Vehicular Technology Conference, Vol. 4, 2004. [15] D. Rife and R. Boostyn, “Single-tone parameter estima- tion from discrete-time observations,” IEEE formation Theory, Vol. 5, 1974. [16] S. Kandeepan, “Synchronisation techniques for digital modems,” PhD thesis, University of Technology, Sydney, July 2003. [18] S. Ross, “Introduction to probability models,” Academic Press, 2003. C opyright © 2009 SciRes. IJCNS |