On Effectively Determining the Downlink-to-uplink Sub-frame With Ratio for Mobile WiMAX Networks Using Spline Extrapolation Panagiotis Sarigianniis, Member, IEEE, Member Malamati Louta, Member, IEEE, Member Department of Informatics an Telecommunications Engineering University of Western Maceonia Kozani, 000, Greece {psarigianniis, louta}@uowm.gr Abstract One of the most valuable esign issues of the Worlwie Interoperability for Microwave Access (WiMAX) stanar is its flexibility. It allows multiple ownlink-to-uplink uration efinitions concerning the with of the corresponing sub-frames, thus, the telecommunication companies an businesses are able to efine the ownlink-to-uplink with from : to : respectively to meet the traffic emans of the connecte subscribers. However, the ecision on efining the most appropriate ratio is not yet solve, since current efforts on eveloping scheuling an mapping schemes consier it as fixe. In this work, a novel aaptive mapping approach base on cubic spline extrapolation - is propose in orer to ynamically etermine the most appropriate ownlink-touplink with ratio in accorance to the ownlink an uplink traffic emans. The metho propose is evaluate through realistic simulation scenarios, whereas its performance is compare with static approaches maintaining a fixe ratio. The results inicate that the approach suggeste succees noticeable improvements in terms of network service capabilities an banwith utilization. Keywors-Extrapolation, IEEE 0., mapping, OFDMA, splines, WiMAX I. INTRODUCTION Wireless broaban communications have attracte the attention of inustry an acaemic community in the recent years. The Worlwie Interoperability for Microwave Access (WiMAX) solution efine by the IEEE 0. group in has been a promising technology for point to multipoint broaban wireless access. The current 0.e stanar known as mobile WiMAX supports subscribers mobility exploiting the Orthogonal Frequency Division Meium Access (OFDMA) multi-carrier moulation scheme for communication. Communication in an 0.e access network is carrie out between a Base Station (BS) an a number of connecte Mobile Stations (MS). The BS establishes a full-uplex communication link with each MS. Information is transmitte in frames incorporating ata exchange from the BS to MSs (ownlink irection) an from MSs to BS (uplink irection). Respectively, each frame consists of an uplink an a ownlink sub-frame, the with of which varies from : to :. WIMAX supports both Time Division Duplexing Angelos Michalas Department of Informatics an Computer Technology Technological Eucational Institute of Western Maceonia Kastoria, 00, Greece amichalas@kastoria.teikoz.gr (TDD) an Frequency Division Duplexing (FDD) to provie biirectional communication. In TDD the ownlink subframe precees the uplink sub frame in the time omain with a small guar interval in between whereas in the FDD both sub frames are transmitte in parallel over ifferent carriers. The majority of WIMAX implementations use TDD ue to its simple esign an flexible frame partitioning []. TDD technique is also aopte in this work. The BS allocates MS requests in the uplink an ownlink sub-frames. Banwith requests are structure in a rectangular shape of two imensions. The vertical imension associates with frequency whereas the horizontal associates with time. OFDMA allows subscribers to use ifferent banwith regions in both time an frequency omains consisting of contiguous series of slots. A slot is the minimum timefrequency resource allocate to a single subscriber. Moreover, each ownlink request (or a set of requests that share common PHY characteristics referre to as a burst) must follow the rectangular shape. This rule oes not apply for uplink requests, simplifying, thus, the uplink allocations. Recent scheuling an mapping approaches presente by the research community try to allocate bursts of various sizes to ownlink an uplink sub frames. However, they consier a fixe banwith size in each sub frame without taking avantage of the ynamic aaptation scheme propose by the stanar. In this work, a novel approach is propose that ajusts the capacity of the ownlink an uplink sub frames of the OFDMA framework to accommoate emaning traffic loa an new incoming requests. The etermination of the most suitable ownlink-touplink with ratio is aresse by applying an extrapolation metho. In this way the well-known cubic spline interpolation technique is applie in a set of scattere ata, obtaine by previous transmissions. More specifically, the applie extrapolation metho, calle Extrapolate Ratio Determination (), attempts to estimate the most appropriate ratio base on the most recent previous observations. The estimate ratio is given as an input for the next transmission, hence efining the with of the ownlink an the uplink sub-frames. The rest of the paper is structure as follows. Section II escribes briefly the OFDMA technique while Section III outlines recent allocation proposals from the relate research literature. In section IV the propose mapping approach is
Frequency Domain (Subcarriers) Preamble FCH UL-MAP DL-MAP DL-Burst # Allocation DL-Burst # Allocation DL-Burst # Allocation DL-Burst # Allocation DL-Burst # Allocation Downlink Sub-Frame Guar Time Domain (Symbols) Figure. A Mobile WiMAX TDD frame. UL-Burst # Allocation UL-Burst # Allocation UL-Burst # Allocation UL-Burst # Allocation UL-Burst # Allocation Ranging Uplink Sub-Frame presente. Section V provies a set of inicative results of the efficiency of the propose moel. Finally, conclusions are given in Section VI. II. BACKGROUND The IEEE 0. OFDMA technique provies a multiple access mechanism to subscribers. Its TDD frame is epicte in Fig.. The TDD frame is structure in time an frequency omains compose by a ownlink sub frame an an uplink sub frame with a small guar interval between them. Subframes with uration coul be configure varying from : to :. This functionality reners the stanar ajustable to ynamic traffic profiles allowing the moification of the ownlink-to-uplink ratio even on a frame-by-frame basis. The ownlink sub-frame begins with a preamble that is use to achieve time an frequency synchronization, followe by a frame control heaer (FCH) an two MAP messages. The FCH inclues information concerning the MAP fiels such as message length, coing an moulation information. Downlink an uplink MAP fiels efine transmission instructions for each MS, incluing burst allocations in each sub frame. III. RECENT MAPPING SCHEMES In this section, we briefly present the most recent mapping schemes for Mobile WiMAX. Most research efforts [-] concentrate on ownlink mapping ue to the restriction for rectangular allocation in the ownlink sub frames. The authors in [] formalize the two imensional mapping problem an propose heuristic algorithms which coul also support QoS constraints. In [] a binary-tree full search approach is use for optimal placement of rectangular bursts in a time-frequency frame. Accoringly, the authors limit the user requests to eight per frame ue to the high search complexity. Efforts in [-] inclue an initial sorting of the incoming requests in escening orer followe by the mapping proceure. The authors in [, ] follow an approach where the requests with common transmission characteristics are groupe into buckets. In the sequel, buckets are mappe in a column by column basis of the rectangular bin. The Guar mapping proceure in [] involves allocation of resources from right to left an from bottom to top. In our previous work, the AHBM algorithm was propose for accommoating ownlink requests []. The iea introuce applies an initial creation of horizons, which constitutes the basis of the forthcoming requests. Hence, initial requests efine horizons an then the forthcoming requests are mappe accoring to horizons. Large requests are accommoate first, leaving minimum remaining ile space, while horizons are forme in a right to left an bottom to top manner. In the sequel, the remaining requests are mappe base on the horizons. Accoring to the performance evaluation results, the AHBM scheme seems to present consierable improvements compare to other leaing schemes [, ]. Therefore, we employ the AHBM scheme as the main ownlink mapping tool for our stuy. The uplink mapping is straightforwar since there is no restriction on the allocation of bursts in the uplink sub-frame. The simplest scheme use for resource allocation in the uplink sub-frame is the horizontal mapping of sub-channels in the frequency omain. Each request occupies horizontal strips of the allocation bin one after the other without leaving ile slots in between. This metho allows contiguous slots to be accommoate on a row-by-row basis until all requests are mappe or the allocation is fully fille. We also aopt this technique as the main uplink mapping scheme for our stuy ue to its simplicity. Several scheuling an mapping approaches on resource allocation in Mobile WiMAX employ sub-frames of fixe size, ignoring that ownlink-to-uplink ratio coul be ynamically moifie as specifie by the stanar. It is worth mentione that our previous work [] limits its focus on the ownlink sub-frame, since it examines only the feeback provie from the ownlink mapping process in contrary to this stuy that consiers both the performance of ownlink an uplink mapping processes in orer to ynamically ajust the ownlink-to-uplink ratio. IV. DOWNLINK-TO-UPLINK RATIO DETERMINATION A. Scope an Motivation Static scheuling an mapping schemes may limit network performance by keeping the sub-frames length fixe, particularly in a ynamically environment of a WiMAX access network. A fixe ownlink-to-uplink ratio of the OFDMA framework coul result in failure to map a portion of subscribers requests, even though there are available resources in the whole frame. This weakness is aresse in the current stuy by proposing a novel mechanism that ynamically ajusts the capacity of ownlink an uplink sub-frames with in orer to accommoate existing traffic requests. The aaptation scheme use employs an effective technique, stemming from the numerical analysis fiel, calle extrapolation spline. B. Cubic Splines The interpolation an extrapolation techniques are wiely use to fit smooth continuous function through iscrete ata. Among other interesting interpolation techniques, spline
metho seems to be one of the most attractive one, since it infers piecewise cubic polynomials to interpolate the ata points. One of the most interesting avantages of low-orer polynomials is the low complexity, since they keep the computational requirements low compare to other interpolation techniques that inclue complex numerical calculations, involving higher egree curves []. C. Algorithm The ownlink-to-uplink with ratio ajustment is the main objective of the algorithm propose. In orer to efficiently operate, the algorithm nees recent scattere ata. This set of collecte ata will be the basis of the extrapolation, applie by the scheme so as to estimate the next - most suitable - ratio. The set of collecte scattere ata is obtaine by the execution of the ownlink an uplink mapping processes. The algorithm receives the feeback obtaine by each mapping process an estimates the most appropriate ratio with respect to the banwith nees of both sub-frames. In other wors, the scheme etermines the grante symbols per irection, which means it is able to offer more symbols to the irection that nees more banwith. Furthermore, the mapping approach propose shoul be capable of balancing the banwith sharing between the two sub-frames. The current status of each mapping process is avertise by the feeback info. The feeback is forme with respect to two basic performance metrics. The first one is calle unserve_slots an enotes the cumulative number of requests that fail to fin accommoation space, measure in slots. The secon one is calle ile_slots an refers to the total number of waste slots within the examine sub-frame (ownlink or uplink sub-frame): unserve _ slots ile _ slots ownlink _ feeback = H u u unserve _ slots ile _ slots uplink _ feeback = H where unserve_slots (unserve_slots u ) stans for the unserve_slots, prouce from the ownlink (uplink) mapping process. In the same manner, ile_slots (ile_slots u ) enotes the number of ile_slots, efine by the ownlink (uplink) mapping process. The parameter H symbolizes the allocation bin s height. Positive feeback implies that there is no sufficient allocation space ( unserve _ slots > ile _ slots ), while a negative one affirm banwith wastage, since one or more columns are in excess. Lastly, zero feeback stans for a consummate mapping. The scheme is escribe in Algorithm. Two states, the current an the ieal, obliquely show the ownlink-touplink ratio. The set of all possible states shows all possible with values that the ownlink (or the uplink) may receive in relation to the uplink (or the ownlink) sub-frame. For example, if the frame with is set to slots an the initial ownlink-to-uplink ratio is : then the with of the ownlink sub-frame is, the same as the uplink sub-frame. The couple of values (, ) enotes the first possible state of the pool, so in this case current =. The next possible state, giving current =, gives the set (, 0), while the final possible state of the set is given by current =, enoting the set (, ). Beyon the current state, the ieal state points out the state that coul return the most efficient feeback if was applie an of course it is known only after the completion of both mapping processes. In the light of the aforementione remarks, the algorithm consists of a IF- ELSE_IF central loop, in which the ieal state is etermine base on the feeback obtaine by the mapping proceures. The latest V ieal states are recore into an array, calle history, which is use in orer to provie the y-axis scattere ata for the extrapolation technique. Specifically, the history vector continuously upates its values an upon the completion of the mapping processes provies its values to the applie extrapolation technique in orer to estimate the history[v+] ieal state for the next frame. Hence, the algorithm provies an estimate ownlink-to-uplink with ratio base on the previous most appropriate V ratios an the forthcoming frame begins with this value ( current = history[ V + ] ). It shoul be note that the estimate state is not allowe to surpass the upper an lower limits in accorance with the stanar ratio limits, i.e., from : to :. Finally, it is worth mentioning that the extrapolation process may be erroneous, returning state values out of the bouns. For this purpose, it is consiere that if the extrapolation technique estimates a value out of the bouns (e.g., enoting a ratio :) then the ieal state is aopte ( current = ieal ). Algorithm: mapping algorithm - Set the initial ownlink-to-uplink with ratio :, i.e., current = - FOR each frame - Apply the ownlink mapping algorithm aopte by []. - Apply the fixe uplink mapping algorithm. - Calculate ownlink_feeback an uplink_feeback. - IF ownlink_feeback > 0 uplink_feeback < 0 THEN ieal = current - + min( ownlink _ feeback, uplink _ feeback ) - ELSE_IF ownlink_feeback < 0 uplink_feeback > 0 THEN ieal = current - min( ownlink _ feeback, uplink _ feeback ) - ELSE_IF ownlink_feeback > uplink_feeback THEN ieal = current - ownlink _ feeback uplink _ feeback + - ELSE_IF ownlink_feeback < uplink_feeback THEN ieal = current - uplink _ feeback ownlink _ feeback - END_IF - FOR counter = :V- - history[ V counter + ] = history[ V counter] - END_FOR - history[] = ieal
0 0 Mean number of unserve MSs Mean number of unserve MSs 0 0 Number of connecte MSs 0 0 Number of connecte MSs Figure. Scenario: Mean number of unserve MSs. - Apply Cubic Spline Extrapolation with x =,,..., V an y = history[], history[],..., history[ V ] an calculate history[ V + ] - Set current = history[ V + ] - END_FOR V. PERFORMANCE EVALUATION The performance of the is evaluate in this section in a custom Matlab environment. Apart from, three static mapping schemes, maintaining static an preefine ownlink-to-uplink ratio, are evelope also in orer to be compare with the approach. All schemes aopt the AHBM algorithm [] as the main mapping process regaring the ownlink mapping an the fixe uplink mapping scheme as the algorithm for the uplink sub-frame. It is assume that for each frame MSs may request only a single burst for each irection. For each simulation conucte, a single BS is consiere along with multiple MSs that have been establishe communication to the BS. Both ownlink an uplink irections are consiere. Regaring the simulation parameters, the partially use sub-channelization (PUSC) moe is aopte ue to its common frequency iversity for mobile communication environments efining 0 istinct channels. The frame length is fixe an it is consiere as 0 ms. In aition, three symbols are eicate to control information (one symbol for Preamble, an two symbols for MAP an FCH fiels). As previously mentione, the scheme is able to efine the ownlink-to-uplink ratio on a frame-by-frame basis. The three fixe schemes maintain a fixe ratio in the context of all simulation scenarios conucte in this work. Therefore, the so-calle mapping scheme efines the ownlink-to-uplink ratio stable an equal to :, allowing symbols for each sub-frame. Similarly, the scheme maintains the ratio to : offering available symbols to TABLE I. POISSON REQUEST VALUES # of Frame 00 000 00 0 000 iteration λ (slots) 0 0 0 λ u (slots) 0 0 0 Figure. Scenario: Mean number of unserve slots. ownlink sub-frame an to the uplink one. Lastly, the thir stanar mapping scheme, calle keeps the ratio equal to :, allowing symbols for ownlink an for uplink. The scheme ajusts the ratio from : to :, allowing to available symbols to be exploite in the context of the ownlink sub-frame an to available symbols eicate to uplink sub-frame, respectively. Three performance metrics are consiere. First, the mean number of unserve MSs is consiere, which expresses the portion of MSs that fail to be accommoate in both ownlink an uplink sub-frame ue to lack of resources, secon the mean number of unserve slots is measure, which enotes the total number of slots that fail to fin allocation space in both sub-frames ue to lack of resources, an three the mean number of ile slots, which inicates the utilization of the available allocation bin. The performance evaluation is subivie in two scenarios. In the former one, the performance of the four mapping approaches is evaluate as the number of the connecte MSs to the BS increases. In the latter one, the mapping performance is evaluate as the ownlink traffic loa increases keeping the uplink traffic loa stable. Each simulation experiment elapses after 000 contiguous transmission frames. The generate traffic follows a Poisson process, consiering ifferent λ for each irection. In the first evaluation scenario the number of the connecte MSs varies from to 0, while the Poisson mean values vary as time passes, inicating an unpreictable, realistic, an alterable behavior. In the secon scenario the number of the connecte MSs is consiere stable an equal to 0 for each irection, altering, however, the Poisson mean value of the ownlink requests, enote by λ. Mean number of ile slots 00 000 00 00 00 0 0 Number of connecte MSs Figure. Scenario: Mean number of ile slots.
0 00 00 Mean number of unserve MSs Mean number of ile slots 00 00 00 00 00 0 0 0 0 0 lamba (ownlink) 00 0 0 0 0 0 lamba (ownlink) Figure. Scenario: Mean number of unserve MSs. Specifically, the Poisson mean value of the uplink requests remains fixe an equal to 0, while λ is increase from 0 to 0. Table I summarizes the exact number of Poisson values for the first evaluation scenario. The evaluation results are expresse in Figs -, where Fig. shows the performance of the four schemes, in terms of the mean number of unserve MSs, Fig. epicts the mean number of unserve slots, an Fig. illustrates the mean number of ile slots, as the number of MSs increases. It is clear that the role of the approach propose is beneficial, since it achieves a) to reuce the number of subscribers that fail to be mappe, b) to ecrease the portion of waste banwith, an c) to limit the number of slots that shoul be returne to the scheuler in orer to be re-allocate in the following frames. In essence, the senses the banwith nees of both irections an assign the waste portion of allocation space, if any, to the sub-frame that coul really exploit it. This ability is cause by the appropriate ownlink-to-uplink ratio estimation, which provies more allocation opportunities to the sub-frame that nees it mostly. In the secon set of experiments (Fig. -), the obtaine results with respect to the aforementione performance metrics are acquire keeping the number of the connecte MSs stable an equal to 0 for each irection, altering, however, the λ. Specifically, the Poisson mean value of the uplink requests remains fixe an equal to 0, while λ is increase from 0 to 0. Fig. shows the mean number of unserve MSs, Fig. presents the mean number of unserve slots, an Fig. epicts the mean number of ile slots. Mean number of unserve slots 00 00 00 00 0 0 0 0 0 lamba (ownlink) Figure. Scenario: Mean number of unserve slots. Figure. Scenario: Mean number of ile slots. Once again the approach presents better network performance compare to the fixe schemes. Its ability to aequately ajust the ownlink-to-uplink with ratio leas to consierable improvements, since the effectively exploits the available banwith, re-efining the sub-frame s bounaries base on the traffic nees. VI. CONCLUSIONS Recent scheuling an mapping approaches presente in the literature assume a fixe ownlink-to-uplink with ratio, resulting in limite network performance. A novel approach was presente in this paper, by ajusting the capacity of the ownlink an uplink sub frames of the OFDMA framework so as to accommoate emaning traffic loa an new incoming requests. The iea beyon this approach lies in the cubic spline extrapolation technique, which is applie in orer to estimate the most suitable ratio. The approach presente is evaluate in realistic scenarios, whereas the performance results inicate consierable performance improvements. REFERENCES [] J. Anrews, A. Ghosh, R. Muhame, Funamentals of WiMAX, Unerstaning Broaban Wireless Networking, Prentice Hall,. [] Y. Ben-Shimol, I. Kitroser, an Y. Dinitz, Two-Dimensional Mapping for Wireless OFDMA Systems, IEEE Trans. Broacasting, vol., no., pp.-, September. [] C. Desset, E. B. e Lima Filho, an G. Lenoir, WiMAX Downlink OFDMA Burst Placement for Otimize Receiver Duty-Cycling, in Proc. IEEE Int. Conf. Comm., pp. -,. [] T. Ohseki, M. Morita, an T. Inoue, Burst Construction an Packet Mapping Scheme for OFDMA Downlinks in IEEE 0. Systems, in Proc. IEEE Global telecom Conf., pp. 0-,. [] T. Wang; H. Feng; B. Hu;, "Two-Dimensional Resource Allocation for OFDMA System," in Proc. IEEE International Conference on Communications Workshops, pp.-, - May. [] C. So-In, R. Jain, an A. Al-Tamimi, eocsa: An Algorithm for Burst Mapping with Strict QoS requirements in IEEE 0.e Mobile WiMAX Networks To appear in the n Inter. Conf. on Comp. an Automation Engin. (ICCAE 00), Feb. 00. [] P. G. Sarigianniis, G. I. Papaimitriou, P. Nikopolitiis, M. S. Obaiat, an A. Pomportsis, A Novel Aaptive Mapping Scheme for IEEE 0. Mobile Downlink Framing, Globecom 00, to appear. C. Geral, P. Wheatley, "Applie Numerical Analysis", Aison-Wesley Publishing Company,.