The Impact of Scheduling on Edge Windowing

Transcription

1 The Impact of cheduling on Edge indowing Alphan ahin, tudent Member, IEEE, and Huseyin Arslan, enior Member, IEEE, University of outh Florida, Tampa, FL, Abstract The recently proposed windowing technique provides a new degree of freedom between spectral efficient sidelobe suppression and controllable inter-symbol-interference (II) for orthogonal frequency division multiplexing (OFDM) based systems. By combining the introduced degree of freedom of windowing and the dependency of the channel dispersive characteristics to the distance between transmitter and receiver, II can be eliminated. Therefore, scheduling strategies becomes critically important for windowing in multiple accessing environment. In this paper, windowing technique is investigated along with different scheduling strategies; random scheduling, ranging based scheduling, and root mean square (RM) delay spread based scheduling. Considering these scheduling strategies with the channel and windowing parameters, the performance metrics of sidelobe suppression, average error vector magnitude (EVM) on each subcarrier, and the worst case statistical characteristics of EVM are evaluated. Index Terms Edge windowing, OFDMA, scheduling strategies I. ITRODUCTIO Orthogonal frequency division multiplexing (OFDM) is a scheme suffering from the high sidelobes since rectangular windowed orthogonal subcarriers correspond to sinc functions in frequency domain. Therefore, OFDM signal transmission without any precautions causes severe adjacent channel interference (ACI). Even if several sidelobe suppression methods are available in the literature to prevent ACI (see i.e. [] [3]), almost all the successful techniques introduce a tradeoff between suppression of sidelobes, spectral efficiency, and computational complexity. Edge windowing is a unique technique that provides both spectral efficiency and sidelobe suppression at the same time without increasing complexity by allowing controllable interference-symbol interference (II) and inter-carrierinterference (ICI) on subcarriers [4]. ince the subcarriers located at the of the band build up the ACI more than the subcarriers located at the center of the OFDM band, windowing applies heavy windowing for the subcarriers. Also, it eliminates/reduces the additional windowing time [] by stealing the windowing time from the cyclic prefix duration of the subcarriers. Another critical aspect that the windowing can take the advantage of the dependency of the channel dispersion characteristics to the distance between the transmitter and the receiver. In multiple accessing environments, windowing along with the proper scheduling strategies can exploit this feature to avoid inter-symbol interference (II) on the subcarriers and to mitigate inter-carrier interference (ICI) on the subcarriers located at the middle of the band. In this paper, we analyze the windowing technique along with three scheduling strategies; random scheduling, ranging based scheduling, and root mean square (RM) delay spread based scheduling. By relating the windowing parameters to the distance between receiver and transmitter, and channel parameters, we investigate the scheduling strategies for windowing with the performance metrics of sidelobe suppression, average error vector magnitude (EVM) [5], and worst case EVM statistics. II. YTEM MODEL Consider the downlink of an orthogonal frequency division multiple accessing (OFDMA) based system with a coverage radius of R. The base station is located at center of the cell and the locations of mobile stations are distributed uniformly. The transmitted OFDMA symbol from the base station is given with the parameters of available subcarriers, cyclic prefix size, T s OFDMA symbol duration, and G guard subcarriers. e consider windowing for spectral shaping. Compared to the conventional windowing approach where all the subcarriers are equally windowed, in windowing approach, subcarriers are applied to heavy windowing by stealing the windowing time from the cyclic extension durations of the subcarriers as shown in Fig.. hile the sizes of the cyclic extensions of the subcarriers remain as, the sizes of the cyclic extensions of the subcarriers are reduced to. Then, light windowing with and heavy windowing with = + are applied for subcarriers and subcarriers, respectively. ote that since <, windowing reduces the additional windowing time of the conventional windowing to. For windowing operation, we consider the raised cosine windowing function [] with the characteristics (in samples) + πn cos(π + β T ) n β T g n = β T n T + πn cos(π β T ) T n (β + ) T () where β is the roll off factor ( β ) and T is the symbol length for the raised cosine function. Thus, while the parameters of raised cosine windowing function are T = + +, = β ( + ) for the subcarriers of the windowing, the same parameters are T = + +, = β ( + ) for the conventional windowing. e should note that windowing can introduce better sidelobe suppression performance than conventional windowing depending on the parameter of, A circular shape is considered rather than hexagonal shape in order to simplify the analysis.

2 Frequency Frequency Distance Time T RM ubcarriers ubcarriers (a) Random scheduling. G G Conventional indowing G Edge indowing G Fig. : Time-frequency representations of conventional windowing and windowing approaches. and, since heavier windowing is applied to the subcarriers. e assume the power delay profile of the channel between the base station and the mobile stations decaying exponentially. The model of the exponential decaying is given in [6] as Distance Distance T RM ubcarriers ubcarriers (b) Ranging based scheduling. T RM ubcarriers ubcarriers (c) T rms based scheduling. Fig. : cheduling trategies. P exp [k] = Be kα, α T s τ () where k is the index for the tap, B and τ are the constants to be obtained to adjust the desired average power and the desired RM delay spread (T rms ) of the channel. The summation of P [k] is set equal to. Hence, B is derived as P [k] = B = e α. (3) k= ince T rms of the channel can be obtained from the second order central moment of (), by calculating its inverse function, τ is derived in [6] as τ = ln ( T rms β β + + ), β T s. (4) ( ) T rms β Also, we consider that T rms depends on the distance between base station and mobile station. The mathematical expression which relates T rms and the distance is given [7] as T rms = T d ϵ y (5) where d is the distance between base station and mobile station in kilometers, ϵ is a distance coefficient lies between.5 ϵ, T is the median value of T rms at d = km, and y is a lognormal distributed random variable. The standard deviation of y lies as σ y 6 in db. Thus, the distribution of T rms is also lognormal. In [6], spike-plus-exponential model is proposed for channel power delay profile. e consider only the exponential part of this model for a pessimistic scenario. III. CHEDULIG TRATEGIE According to the equation given in (5), the nearby mobile stations to base station have less dispersive channels than the mobile stations located at further distances. Therefore, the required cyclic prefix size for the nearby mobile station is less than the one for the further mobile station. It is possible to exploit this feature to avoid II for windowing. The proper scheduling approach for windowing is to group the mobile stations with similar dispersion characteristics and to assign them to the proper subcarriers which do not generate II. In this section, we investigate three fundamental scheduling strategies for the windowing; random scheduling, ranging based scheduling and, T rms based scheduling. A. Random cheduling Random scheduling strategy is considered to observe the impact of ignoring scheduling on the windowing. In this scheduling strategy, all the spectrum resources are distributed randomly to the mobile stations as in Fig. (a). Thus, the channel dispersion characteristics and the distance between mobile stations and base station are not considered for scheduling decision. B. Ranging Based cheduling Ranging based scheduling exploits the relation between the distance and dispersion given in (5). Thus, it is performed after estimating the distances of the mobile stations relative to the base stations with ranging operations. In this scheduling approach, the nearby mobile stations are assigned to the subcarriers, and the further mobile

3 3 stations are assigned to subcarriers as shown in Fig. (b). hile the spectrum resources located at the center of the subcarriers are employed for the nearest mobile station, the spectrum resources located at the center of subcarriers are used for the furthest mobile station. It should be noted that ranging based scheduling does not guarantee to group the mobile stations considering their T rms. Therefore, the mobile stations scheduled to subcarriers at the s of the subcarriers (i.e. located at middle distances) can observe severe II because of the having probability of high T rms. Also, note that the distribution of the distance between the mobile stations and base station is obtained for uniformly distributed mobile stations in the cell area as f r (r) = r R, r R. (6) Thus, the expected number of the mobile stations at further distances is higher than the number of the closer ones. Therefore, increasing also increases the probability of having II on these subcarriers. C. T rms Based cheduling T rms based scheduling applies similar scheduling approach introduced in ranging based scheduling. However, it considers the T rms parameters of the each mobile stations channels instead of their distances to the base station. In T rms based scheduling, the mobile stations with low T rms values and mobile stations with high T rms values are scheduled to the subcarriers and subcarriers, respectively, as in Fig. (c). hile the spectrum resources located at the center of the subcarriers are utilized for the mobile station with lowest T rms, the spectrum resources located at the center of subcarriers are assigned for the mobile station with highest T rms. For T rms based scheduling, the base station requires the channel dispersion information of each mobile station. In most of the cases (i.e. i-fi, LTE), the base station has ability to extract the downlink channels of the mobile stations. Thus, it is reasonable to have T rms information of each mobile stations at the base station. Also, we should note that T rms is a random variable depending on the distance between mobile station and the base station as in (5). Thus, T rms scheduling approach does not guarantee that the mobile stations are ordered on the spectral resources considering their distances. IV. UMERICAL REULT The performance of windowing along with aforementioned scheduling strategies is investigated through computer simulations. e consider that = 4, = 8, T s = 66.7 µs, G = 8, = 6 for OFDMA symbol parameters and T = µs, ϵ =.5, and σ y = db for the channel parameters for the urban environments. Therefore, windowing parameters become 8 and 43 from this set of simulation parameters. Also, we consider subcarriers (one resource block) per mobile station and 7 mobile stations which are distributed uniformly in R = m cell radius. All results shown are obtained over uppression (db) Proposed ( = ) Proposed ( = 9) Proposed ( = 4) Conventional Frequency (khz) Fig. 3: ide lobe suppression performances of conventional windowing and windowing. ( = 64, = 6, = 7) Average T RM.5 x Random Based cheduling Ranging cheduling T RM Based cheduling Resource Block Fig. 4: Average T rms on each resource block ( = 9). 5 OFDMA symbols per channel and 3 different channels per mobile stations. e perform all simulations with the same set of parameters in order to obtain a reasonable set of windowing parameters. Therefore, firstly, we compare the sidelobe suppression and throughput performances of windowing and conventional windowing. Then, we investigate the impact of scheduling on the average EVM on subcarriers and other EVM statistics. A. The ide Lobe uppression and Throughput Performances The sidelobe suppression performance of windowing depends on the parameters of, and values. e select = 64 for conventional windowing and = 7 for windowing and plot the sidelobe suppression performances of both windowing techniques as in Fig. 3. Edge windowing can offers sharper sidelobe suppression than the conventional windowing depending on and β. ince heavy windowing is applied to only subcarriers, increasing helps to improve the sidelobe suppression performance of windowing. In Fig. 3, windowing performance approaches to the sidelobe suppression performance of the conventional windowing after = 9.

4 4 Edge windowing reduces the additional windowing time of the conventional windowing approach. Thus, the throughput of the system with windowing becomes higher than the system with the conventional windowing. The increment on the throughput ( R) is calculated in percent as ubcarrier Index B. cheduling and Trms. 5 (a) Random scheduling ubcarrier Index C. The Impact of the cheduling trategies on EVM performances 5 (b) Ranging based scheduling In order to investigate the impact of the scheduling, we simulate the average EVM on each subcarriers and average EVM at different distances for different values ( = 64, = 7) in Fig. 5 and Fig. 6, respectively. If the scheduling is performed randomly, the average EVM on the subcarriers become drastically high compared to the subcarriers as shown in Fig. 5(a). ince the cyclic extension size of the subcarriers are insufficient for the mobile stations which have high dispersive channels, II reduces the EVM performances of these subcarriers significantly. Especially, it impacts the mobile stations located at further distances. As shown in Fig. 6(a), the mobile stations located at the of the cell observe high average EVM of %. It indicates that the average EVM increases rapidly with the distance between the mobile station and base station increasing. Also, it shows the dependency of average EVM to the parameter of windowing. If the scheduling is performed considering the distance between the mobile stations and the base station, average EVM rises on the s of the subcarriers as in Fig. 5(b). It is clear that the nearby mobile stations which are assigned to the center of the subcarriers do not observe II since their channels are expected to be less dispersive. However, the mobile stations which are scheduled to the subcarriers of the subcarriers can observe severe II due to their distances. The equation given in (6) shows that the average number of the mobile station increases linearly with the distance. ince. Average Trms values of the channels on each resource block are provided in Fig. 4 ( = 9). ince random scheduling does not consider the channel dispersion characteristics and the distances, average Trms does not vary over the resource blocks. For ranging based scheduling, average Trms decreases on the resource blocks where the windowing is applied and it increases at the middle of the OFDMA band. ince Trms based scheduling exploits the knowl of Trms of each mobile station s channel, it provides a better grouping of the mobile station with the same Trms. Thus, the average Trms values with Trms based scheduling are less than the ones with ranging based scheduling at the center of the band of the subcarriers. Also, Trms based scheduling provides larger average Trms values at the middle of the OFDM band..3 5 Considering the simulation parameters, windowing provides 5% increment on throughput relative to the system with conventional windowing ubcarrier Index (7).7. R = (c) Trms based scheduling. Fig. 5: The impact of scheduling on average EVM of subcar riers ( = 64, = 7, = 6). more mobile stations are located at the large distances, more mobile station have the channels with high Trms as shown in Fig. 4. Therefore, the mobile stations scheduled to the subcarriers of the subcarriers can observe high EVM with ranging based scheduling. This issue is also given in Fig. 6(b). ince ranging based scheduling strategy assigns the subcarriers of the subcarriers to the mobile stations at middle distances, these mobile stations observe high EVM

5 Distance (m) (a) Random scheduling Distance (m) (b) Ranging based scheduling ing of the mobile stations with the same T rms than the ranging based scheduling, it offers better average EVM performance. However, using higher values (i.e. 3) impacts the EVM on the subcarriers of the subcarriers. Also, increasing degrades the average EVM of the further mobile stations because they have highly dispersive channels. The relation between the distance of the mobile station and average EVM is given for different values in Fig. 6(c). If we consider the = 9 for the system design, average EVM does not exceed the.6% in both Fig. 5(c) and Fig. 6(c). According to simulation results given in Fig. 5 and Fig. 6, the windowing along with T rms based scheduling is superior than the other scheduling strategies when = 64, = 7, = 6, = 9. ith these parameters, we analyze the statistical distributions of EVM on subcarriers in Fig. 7. The lower CDF bound of EVM on subcarriers is given in Fig. 7(a) by considering the worst case probability for a given EVM value on each subcarriers. Thus, the CDF curve of EVM for each subcarrier is always better than the curves given in Fig. 7(a). Also, the average of the all CDF curves of EVM on subcarriers is given in Fig. 7(b) in order to evaluate the impact of the scheduling. As shown in Fig. 7b, whereas the worst case probability of EVM below.5% is 8% for both random scheduling and ranging based scheduling, it is 96% for T rms based scheduling. Even if the worst case probabilities are the same for both ranging based scheduling and random scheduling, the probability values are different in average case. As shown in Fig. 7(b), while the probability is 9% for ranging based scheduling, it is 88% for random scheduling. Also, the probability of 98% is obtained for T rms based scheduling Distance (m) 3 (c) T rms based scheduling. Fig. 6: The impact of scheduling on average EVM of subcarriers ( = 64, = 7, = 6). particularly. For instance, the mobile stations at 6 m away from the base station have higher average EVM than the other distances when = 9 according to the simulation results shown in Fig. 6(b). If the base station schedules the mobile stations considering the T rms of the each mobile station s channels, the average EVM performances on subcarriers increase significantly as in Fig. 5(c). ince T rms based scheduling provides better group V. COCLUIO As a result of our analysis, windowing along with a proper scheduling provides both sidelobe suppression and increments on the throughput with tolerable EVM on subcarriers. Even if the ranging based scheduling provides improvement on EVM performance compared to the random scheduling, it is not reasonable for most the cases because ranging based scheduling does not guarantee to group the mobile stations with the same T rms. However, T rms based scheduling along with the windowing provides sufficient improvement on EVM performances by guarantying it. Considering our simulation parameters, the worst case probability of EVM below.5% on a subcarrier is 96% with T rms based scheduling when = 64, = 7, = 6, and = 9. Also, windowing provides 5% increment on throughput compared to the conventional windowing. REFERECE [] T. eiss, J. Hillenbrand, A. Krohn, and F. Jondral, Mutual interference in ofdm-based spectrum pooling systems, in Proc. IEEE VTC 4, vol. 4, May. 4, pp []. Brandes, I. Cosovic, and M. chnell, Reduction of Out-of-Band Radiation in OFDM ystems by Insertion of Cancellation Carriers, IEEE Communications Letters, vol., no. 6, pp. 4 4, 6. [3] H. Mahmoud and H. Arslan, idelobe uppression in OFDM-Based pectrum haring ystems Using Adaptive ymbol Transition, IEEE Communications Letters, vol., no., pp , Feb. 8. [4] A. ahin and H. Arslan, Edge indowing for OFDM Based ystems, IEEE Communications Letters,.

6 Random cheduling Ranging Based cheduling T RM Based cheduling Probability EVM (%) (a) The CDF bound for EVM Random cheduling Ranging Based cheduling T RM Based cheduling Probability EVM (%) (b) The average of the all CDF curves for EVM Fig. 7: The CDF curves related with EVM measurements = 64, = 7, = 6, = 9). ( [5] M.D. McKinley, K.A. Remley, M. Myslinski, J.. Kenney, D. chreurs, and B. auwelaers, EVM calculation for broadband modulated signals, in 64th ARFTG Conf. Dig, 4, pp [6] V. Erceg, D. Michelson,. Ghassemzadeh, L. Greenstein, J. Rustako, A.J., P. Guerlain, M. Dennison, R. Roman, D. Barnickel,. ang, and R. Miller, A model for the multipath delay profile of fixed wireless channels, elected Areas in Communications, IEEE Journal on, vol. 7, no. 3, pp , Mar [7] L. Greenstein, V. Erceg, Y. Yeh, and M. Clark, A new path-gain/delayspread propagation model for digital cellular channels, IEEE Transactions on Vehicular Technology, vol. 46, no., pp , May 997.