Effect of Carrier Frequency Offset on the BER Performance of Variable Spreading Factor OFCDM Systems

Transcription

1 This full text paper was peer reviewe at the irection of IEEE Communications Society subject matter experts for publication in the ICC 008 proceeings. Effect of Carrier Frequency Offset on the erformance of Variable Spreaing Factor OFCDM Systems Lamiaa Khali an Alagan Anpalagan WINCORE Laboratory Ryerson University, Toronto, Canaa Abstract In this paper, the effect of frequency offset on the performance of ownlink OFCDM systems with variable spreaing factors is investigate. The bit error rate of ownlink VSF-OFCDM is analyze taking into account the effect of carrier frequency offset when subcarrier grouping is use. An analytic expression of the SINR for ownlink OFCDM with frequency offset ug BSK moulation is erive for the case of maximal ratio combining receiver. Numerical results show that, when the total spreaing factor is fixe to 3, the VSF-OFCDM system with higher frequency omain spreaing factor is more sensitive to frequency offset than that with lower frequency omain spreaing factor. Our results also show that, as the number of users increases, the egraation of the performance is more pronounce with the higher frequency omain spreaing factor ce more subcarriers are present in each group. Inex Terms OFCDM, spreaing factors, frequency offset, Doppler,. I. INTRODUCTION Orthogonal Frequency an Coe Division Multiplexing OFCDM system has been propose for future broaban wireless communications 1]. OFCDM uses ata spreaing in both time an frequency omain, where each ata stream is segmente into multiple substreams an sprea over multiple subcarriers an several OFCDM symbols, exploiting aitional frequency an time iversity. Introucing the Variable Spreaing Factor VSF concept in OFCDM, which changes the Spreaing Factor SF in both the time an frequency omain, was propose in ]. The total spreaing factor SF is the prouct of time omain spreaing factor SF time an frequency omain spreaing factor SF freq. One of the main characteristics of VSF-OFCDM is that it can aaptively control SF time an SF freq accoring to the propagation conitions, channel loa an raio parameters. One of the main rawbacks of multicarrier systems is that they suffer from performance egraation ue to Carrier Frequency Offset CFO. CFO causes a reuction in the esire signal amplitue as well as a loss of orthogonality between subcarriers which results in Intercarrier Interference ICI. The impact of frequency offset on multicarrier systems was investigate in 3] an 4] for MC-CDMA an grouporthogonal MC-CDMA respectively an in 5] for both uplink an ownlink MC-DS-CDMA systems. Recently, there are some papers investigating the effect of frequency offset on OFCDM systems. In 6], the performance of multiple antenna OFCDM systems with imperfections was stuie. In 7], the sensitivity of OFDM-CDMA systems to carrier frequency offset was investigate for zero forcing an minimum mean square error equalizers. However, no subcarrier grouping was consiere in their analysis, although this strategy has an impact on the ifferent types an amount of interference introuce with frequency offset. Also, the effect of ug variable spreaing factors on the performance of OFCDM systems was not investigate in their work. Two major factors that cause CFO are the Doppler sprea cause in the channel for a high spee mobile an the ifferences between the oscillators in the transmitter an the receiver. In this paper, the effect of the frequency offset is analyze by investigating the type an the amount of interference cause by CFO in VSF-OFCDM systems with ifferent spreaing factors. An analytic expression of the SINR for ownlink VSF-OFCDM with frequency offset ug BSK moulation is erive for the case of Maximal Ratio Combining MRC receiver. In our analysis, the stanar Gaussian approximation 8] is applie to the interference an noise terms. The paper is organize as follows: section II gives a brief escription of the OFCDM system. In section III, the of VSF-OFCDM is erive in the presence of frequency offset for MRC receiver. In section IV, numerical results are presente base on the erivation in section III. Finally, the paper is conclue in section V. II. SYSTEM MODEL An OFCDM system with K simultaneous users is consiere. The total spectrum is ivie into G groups, each group has M non-contiguous subcarriers that are equally space throughout the spectrum. The subcarrier grouping is use to maximize frequency iversity gains an minimize Multiple Access Interference MAI 9]. The impulse response of the channel for the k th user an the m th subcarrier of the g th group can be escribe as 10]: h k m,gt =α k m,gte iπfk t+φk m,g, /08/$ IEEE

2 This full text paper was peer reviewe at the irection of IEEE Communications Society subject matter experts for publication in the ICC 008 proceeings. where α m,g k are inepenent ientically istribute i.i.. Rayleigh ranom variables an k = 1,,K g ; m = 1,,M; g =1,,G. The phase, φ k m,g, is a uniformly istribute ranom variable over the interval 0, π, which is inepenent for each bit, subcarrier an user. The Doppler shift cause in the channel for a high spee mobile user results in frequency offset which is ifferent for each subcarrier accoring to where it is locate in the spectrum. However, if the maximum Doppler sprea is very small with respect to the subcarrier spacing, we can consier the CFO cause by the Doppler shift a common phenomenon in all the subcarriers 3]. We also assume that each subcarrier experiences inepenent, frequency nonselective faing. Furthermore, the channel faing an phase shift variables are consiere to be constant over a chip uration T c. The receive signal with CFO, assuming BSK moulation, for the users in group g can be erive as rt = j n=1 K G g g=1 k=1 b k j,g l=1 α k l,g k j,l cos l,g t + φ k l,g + k t c T k pt jn + n+nt, where S is the esire signal term; η is the noise term; MAI represents the multiple access interference impose by the interfering users in the same group as the esire user from the same subcarriers, where the consiere subcarriers are m =1,,M; ICI 1 is the self-intercarrier interference from the other subcarriers of the same group; ICI is the multiple access intercarrier interference impose by the interfering users in the same group of the esire user, but associate with subcarriers ifferent from the consiere subcarrier an ICI g is the intergroup intercarrier interference which represents the intercarrier interference from other subcarriers in other groups. These parameters are consiere for user 1 in group 1 at the j th transmitte bit. The esire signal term can be written as S = 1 b1 j,1 α 1 1 cos jn + n +1/ 1 + φ1 n=1 1 ˆφ The interference term MAI is obtaine from 3 with the conition g =1an l = m for k = 1. It can be expresse as 5 where is the transmitte power on one subcarrier; K g is the total number of users in group g; N is the length of the time omain N coe an it is assume to be equal to the spreaing factor in the time omain SF time. The number of subcarriers M in each group g is assume to be equal to the spreaing factor in the frequency omain SF freq. b k j,g is the BSK signal for the k th user in the g th group uring the j th transmitte bit. For the k th user, c F k j,l is the l th chip in the frequency omain spreaing sequence of length M an c T k is the n th chip in the time omain spreaing coe on the l th subcarrier uring the j th transmitte bit. Each chip belongs to the set {1, 1}. pt is the rectangular pulse efine on the interval 0, T c ]. l,g = c + πg+l 1G T c is the l th subcarrier frequency on the g th group an c is the carrier frequency. nt is an Aitive White Gaussian Noise AWGN with zero mean an ouble-sie power spectral ensity N 0 /. III. BIT ERROR RATE ANALYSIS Maximal Ratio Combining MRC is consiere in this analysis. Without loss of generality, if we aim to recover the ata transmitte to user 1 in group 1, the ecision variable of user 1 in group 1 uring the j th transmitte bit is given by v 1 j,1 = 1 T c ˆφ 1 n=1 jn+n+1 jn+nt c α 1 pt jn + nt crt cos t ct,n 1 ˆφ t, 3 where enotes the estimate phase of the mth subcarrier in group 1 uring the j th transmitte bit to user 1. For simplicity of further calculations, the ecision variable can be written as v 1 j,1 = S + MAI + ICI1 + ICI + ICIg + η, 4 MAI = K 1 k= n=1 b k j,1 k k α 1 αk c T 1 k,nct,n cos jn + n +1/ k + φk 1 k 1 ˆφ, where K 1 are the total number of users in group 1. Accoring to the central limit theorem, the MAI can be approximate by a Gaussian ranom variable with zero mean an variance given by σ MAI = N 4 K 1 1 E k α k k 6 ] M α 1, 7 where φ k 1 an ˆφ are i.i.. ranom variables uniformly istribute over 0, π. The term jn + n +1/ k T c] only rotates the phase φ k 1 ˆφ ]; therefore, Ecos jn + n +1/ k T c + φ k 1 ˆφ ] = 1. The self-intercarrier interference term ICI 1 can be obtaine from 3 by letting k =1, g =1an l =m. It can be written as 1 ICI 1 = b1 j,1 1 l=1 n=1 + T c α 1 α1 1 1 j,l c T 1 1,ncT cos jn + n +1/ 1 + T c + φ k 1 ˆφ 8

3 This full text paper was peer reviewe at the irection of IEEE Communications Society subject matter experts for publication in the ICC 008 proceeings. The ICI 1 can be approximate by a Gaussian ranom variable with zero mean an variance given by σici 1 = N 1 α 1 4 α 1 9 l=1 1 + T c The multiple access intercarrier interference from users in the same group as the esire user, but associate with the subcarriers ifferent from the consiere subcarrier, ICI,is obtaine by setting k = 1, g =1an l =m in 3. It can be written as ICI = K 1 b k j,1 k k= l=1 n=1 α 1 αk 1 1 k ct,n j,l c T k cos jn + n +1/ k k + T c + T c + φ k 1 ˆφ 10 The ICI can be approximate by a Gaussian ranom variable with zero mean an variance given by σ ICI = NK α 1 E α k k k + T c ] 11 The interference from other groups ICI g can be obtaine from 3 by letting g = 1an can be expresse as k K G g ICI g = b k j,g g= k=1 l=1 n=1 k + l,g T c α 1 αk 1 1 k l,g ct,n j,l c T k cos jn + n +1/ k + l,g T c + φ k 1 l,g ˆφ 1 The ICI g can be approximate by a Gaussian ranom variable with zero mean an variance given by σici g = N G M K g α 1 4 g= k ] 13 E α k l,g k + l,g T c The noise term η is a Gaussian ranom variable with zero mean an variance given by σ η = Eη ]= NN 0 4T c α If we assume the frequency offset is equal an constant for all users 3], 4], then, k =. Also, we can assume the estimate phase for user 1 in group 1 in 5 to be ˆφ 1 =jn + n +1/ T c + φ 1. This means that the subcarrier phase estimator etermines the value of the phase rotation at time n +1/T c which is the mile of the n th chip integration interval. The esire signal term becomes S = N b1 j,1 1 1 α 1 15 In our analysis, we consier ownlink transmission; therefore, we can assume that all the users suffer equal faing gain an phase shift on each subcarrier 4], which means that α m,g k = α m,g, an we can further simplify 7, 9, 11, 13 an 14 as follows σ MAI = N 4 K 1 1 πf T c πf T c α 4, 16 σici 1 = N 4π πf T c M α α f l=1 T c +l mg, 17 σici = NK 1 1 4π πf T c M α α f l=1 T c +l mg, 18 σici g = N 4π πf T c G K gα l,g α, g= l=1 f T c +g 1 + l mg σ η = NN 0 4T c 19 α. 0 The Signal to Interference an Noise Ratio SINR of user 1 in group 1 uring the j th bit can be expresse as where γ 1 j,1 = E S] σmai + σ ICI 1 + σici + σici g + ση, 1 E S] = N πf T c M ] πf T c α. The probability of error for MRC base on the Gaussian assumption for BSK moulation can be expresse as e = 1 erfc γ 1 j,1 3

4 This full text paper was peer reviewe at the irection of IEEE Communications Society subject matter experts for publication in the ICC 008 proceeings. IV. NUMERICAL RESULTS In this section, the effect of frequency offset on the performance of VSF-OFCDM system with ifferent spreaing factors is investigate by numerical evaluation ug Monte- Carlo simulation. The ifferent spreaing factors can be use to provie ifferent levels of frequency iversity, or to minimize MAI in the event of high channel loas. We consier a VSF-OFCDM system with 18 subcarriers an 16 users, having carrier frequency offsets of 0, 10, 0 an 30% of the frequency spacing between ajacent subcarriers. Each of the configurations uses a total spreaing factor SF = SF time SF freq of 3 to provie a suitable performance comparison. We use an ientical ata rate for each user in each analysis by transmitting a number of substreams equal to a multiple of the number of chips in the time omain spreaing coe N. In this evaluation, we transmit N substreams simultaneously for each user. Fig. 3. SF. 10 SF=16x SF=8x4 SF=4x8 SF=x16 10 Normalize frequency offset vs. normalize frequency offset at E b /N o = 0B for ifferent Fig. 1. offsets. 10 offset=0 offset=10% offset=0% offset=30% Eb/NoB 10 Fig.. offsets. vs. E b /N o with SF=x16 at ifferent normalize frequency offset=0 offset=10% offset=0% offset=30% Eb/NoB vs. E b /N o with SF=16x at ifferent normalize frequency Figs. 1 an show the vs. E b /N o with total SF of x16 to represent a case with higher SF freq with respect to SF time an 16x to represent a case with higher SF time respectively. It can be observe from these figures that the egraation in cause by CFO is insignificant at low E b /N o. However, as E b /N o increases the OFCDM system makes a transition from being noise-limite to being interference-limite, an the egree of egraation increases as well. It can also be seen from the figures that the egraation in cause by the CFO increases with higher SF freq because more subcarriers are present in each group which increases the intercarrier interference. As shown in Fig. 1, a egraation of the performance from approximately 0.1 to 3 occurs when the frequency offset increases from 0 to 30%. From Fig., we can see that, at low SF freq,maiis the main factor that causes the performance egraation ce there are fewer subcarriers in each group which ecreases the effect of the intercarrier interference ue to frequency offset than the case with higher SF freq. Fig. 3 shows the vs. the normalize frequency offset with respect to the subcarrier spacing for ifferent spreaing factors with E b /N o = 0B. From Fig. 3, it can be observe that at high E b /N o, higher SF freq performs better than higher SF time for a fixe SF of 3 when there is no frequency offset ce the frequency iversity allows the system to achieve higher absolute performance. However, as the frequency offset increases, higher SF time gives better performance as the effect of the intercarrier interference becomes ominant. From Fig. 3, we can also see that, when the frequency offset is higher than 10%, the performance starts to eteriorate for the higher SF freq, while the lower SF freq tolerates a frequency offset up to 0% of the frequency spacing between ajacent subcarriers. These results suggest that for a fixe total SF of 3, increag SF time with respect to SF freq will ecrease the sensitivity of the VSF-OFCDM system to the effect of the frequency offset which will result in an overall better performance of the OFCDM system in the presence of consierable frequency

5 This full text paper was peer reviewe at the irection of IEEE Communications Society subject matter experts for publication in the ICC 008 proceeings. 10 soli: offset=0 ashe: offset=30% 48 users 3 users 16 users Eb/NoB Fig. 4. vs. E b /N o with 18 subcarriers an SF=x16 for ifferent number of users at frequency offsets of 0 an 30% users 3 users soli: offset=0 16 users ashe: offset=30% Eb/NoB Fig. 5. vs. E b /N o with 18 subcarriers an SF=16x for ifferent number of users at frequency offsets of 0 an 30%. offset. Figs. 4 an 5 show the vs. E b /N o with 18 subcarriers having carrier frequency offsets of 0 an 30% for ifferent number of users with total SF of x16 an 16x respectively. It can be observe from these figures that as the number of users increases, the egraation in performance increases as well for both spreaing factors. This is to be expecte ce the intercarrier interference terms ICI an ICI g are proportional to the number of users. From Fig. 4, we can see that, for SF=x16, the effect of increag the frequency offset from 0 to 30% for 16 users is almost similar to oubling the number of users from 16 users to 3 users in terms of the egraation of the performance. From Fig. 4, we can also see that, as the number of users increases from 16 to 48 users, the egraation of the performance ue to the increase of frequency offset from 0 to 30% increases from approximately to InFig.5,forSF=16x, as the number of users increases from 16 to 48 users, the egraation of the performance ue to the increase of frequency offset from 0 to 30% increases from approximately 0.5 to 10. From these results, we can see that for a fixe SF of 3, the egraation ue to increag the number of users is more pronounce with the higher SF freq ce we have more subcarriers in each group as mentione earlier. V. CONCLUSIONS In this paper, the performance of ownlink VSF- OFCDM system ug BSK moulation has been analyze in the presence of frequency offset. From the numerical results we conclue that, when the total spreaing factor is fixe to 3, the OFCDM system with higher SF freq is more sensitive to frequency offset than that with lower SF freq. Also, the effect of the normalize frequency offset on performance is small when the normalize frequency offset is less than 10% of the frequency spacing between ajacent subcarriers for the higher SF freq with respect to SF time an less than 0% for the lower SF freq. In aition, results show that the egree of egraation ue to CFO in the VSF-OFCDM system is a function of the number of users. In our future work, we will investigate ifferent techniques for the estimation an correction of the carrier frequency offset in orer to enhance the performance of ownlink VSF-OFCDM systems. REFERENCES 1] L. Xiao an Q. Liang, A Novel MC-D-CDMA Communication System an Its Detection Methos, in IEEE International Conference on Communications, vol. 3, pp , June 000. ] H. Atarashi, S. Abeta, an M. Sawahashi, Variable Spreaing Factor Orthogonal Frequency an Coe Division Multiplexing VSF-OFCDM for Broaban acket Wireless Access, IEICE Transactions on Communications, vol. E86-B, pp , January ] Y. Kim, S. Choi, C. You, an D. Hong, Effect of Carrier Frequency Offset on the erformance of an MC-CDMA System an its Countermeasure Ug ulse Shaping, in IEEE International Conference on Communications, vol. 1, pp , June ] W. Yang, J.-Y. Liu, an S.-X. Cheng, Effect of carrier-frequency offset on the performance of group-orthogonal multicarrier CDMA systems, in Elsevier Signal rocesg, vol. 86, pp , December ] H. Steenam an M. Moeneclaey, The Effect of Carrier Frequency Offsets on Downlink an Uplink MC-DS-CDMA, IEEE Journal on Selecte Areas in Communications, vol. 19, pp , December ] J.-H. Moon, Y.-H. You, W.-G. Jeon, an J.-H. aik, erformance of Multiple-Antenna OFCDM With Imperfections, IEEE Communications Letters, vol. 8, pp. 1 14, January ] Y. Nasser, M. es Noes, L. Ros, an G. Jourain, Sensitivity of OFDM- CDMA Systems to Carrier Frequency Offset, in IEEE International Conference on Communications, vol. 10, pp , June ] M. ursley, erformance Evaluation for hase Coe Sprea Spectrum Multiple Access Communication-art I: System Analysis, IEEE Transactions on Communications, vol. COM-5, pp , August ] R. Calwell an A. Anpalagan, erformance Analysis of Subcarrier Allocation in Two Dimensionally Sprea OFCDM Systems, in IEEE Vehicular Technology Conference, pp. 1 5, September ] C. J. Jakes, Microwave Mobile Communications. IEEE ress, New Jersy, 1994.