The Potential of Dynamic Power and Sub-carrier Assignments in Multi-User OFDM-FDMA Cells

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1 The Potetial of Dyamic Power ad Sub-carrier Assigmets i Multi-User OFDM-FDMA Cells Mathias Bohge, James Gross, Adam Wolisz Telecommuicatio Networks Group, TU Berli Eisteiufer 5, 1587 Berli, Germay {bohge gross wolisz}@tk.tu-berli.de Abstract OFDM systems are kow to overcome the impairmet of the wireless chael by splittig the give system badwidth ito parallel sub-carriers, o which data symbols ca be trasmitted simultaeously. This eables the possibility of ehacig the system s performace by deployig adaptive (dyamic) mechaisms, amely power ad modulatio adaptio ad dyamic sub-carrier assigmets. I multi-user commuicatio systems (OFDM-FDMA), these mechaisms ca be used to achieve a level of system fairess esurig that each termial receives at least a eviromet-specific miimum amout of data per dow-lik phase. However, it has bee doubted by multiple previous ivestigatios that dyamic power adaptio provides eough performace gai i order to be applied i such systems, as it icreases the computatioal load sigificatly. I this study we discuss the performace gai due to the differet approaches ad show that i specific commuicatio scearios eablig a dyamic power distributio provides a sigificat performace icrease compared to dyamic schemes without power adaptio. 1 I. INTRODUCTION Future wireless commuicatio systems are expected to deliver high data rates to multiple wireless termials simultaeously. Due to the impairmets of the wireless chael such system will o loger be based o Siglecarrier Modulatio (SCM) schemes as the multi-path propagatio eviromet causes wireless chaels to be highly frequecyad time selective. Therefore, Orthogoal Frequecy Divisio Multiplexig (OFDM) appears as quite attractive trasmissio scheme for such future wireless systems: I a OFDM system, the total badwidth is split ito N parallel sub-chaels, kow as sub-carriers [1], where each sub-carrier ca be assumed to experiece flat fadig. However, differet sub-carriers of a broadbad wireless system have a strogly varyig atteuatio, i.e. the system provides frequecy diversity. This diversity ca be exploited by dyamically adaptig the modulatio type ad trasmit power per sub-carrier at the trasmitter, if the sub-carrier atteuatios are kow. Such dyamic schemes are kow as bit loadig algorithms [] [4] ad they provide a sigificat performace gai (e.g. i terms of throughput) compared to static setups. I case of a multi-user commuicatio sceario the degree of diversity icreases further, as the atteuatio of a wireless chael for differet termials is statistically idepedet. 1 This work has bee partially supported by the Germa research fudig agecy Deutsche Forschugsgemeischaft (DFG) uder the graduate program Graduiertekolleg 61 (MAGSI/Berli). Thus, i additio to the frequecy diversity per termial a additioal multi-user diversity per sub-carrier is preset. This fact has lead to the proposal of dyamic resource assigmet algorithms i a FDMA fashio. Differet termials are assiged periodically differet sets of sub-carriers. Per sub-carrier (agai) a differet modulatio type ad a varyig amout of power ca be employed. Today, may such dyamic sub-carrier assigmet algorithms have bee proposed [5], [6]. Compared to static schemes these dyamic assigmet algorithms ca provide a performace icrease of 1% per termial, simply by utilizig the give badwidth ad trasmit power much better. However, it is much more difficult to optimally assig sets of sub-carriers varyig i modulatio types ad trasmit power to the termials tha optimally assigig sets varyig i modulatio types oly. I the latter case each sub-carrier receives a equal amout of trasmit power. Together with a target bit error probability the suitable modulatio type ca be obtaied at oce. Not so i the case of dyamic power assigmets: Here, per sub-carrier multiple differet assigmet amouts of trasmit power (for each modulatio type oe power value) are possible ad the dyamic algorithm has to assig sub-carriers to termials keepig this additioal flexibility i mid. I additio, the total trasmit power is limited. Cosiderig the related work, it is kow that i the case of bit loadig algorithms for wireless poit-to-poit coectios the additioal performace obtaied from varyig the trasmit power compared to oly applyig adaptive modulatio is quite small [7], [8], such that it is ot recommeded to perform dyamic power assigmets. I the case of multiuser commuicatios it is a ope questio if the additioal computatioal burde pays off i terms of performace icrease. Several papers claim that adaptive power assigmets do ot achieve eough additioal performace to justify the additioal computatioal cost [9]. I cotrast, we show i this paper that the gai obtaied from dyamic power assigmets is quite sigificat i certai cases, amely whe the average atteuatio spread betwee differet termials i the cell is large eough. The remaider of this paper is structured as follows: I Sectio II, we describe our system model. The, i Sectio III, we discuss the optimizatio objective alog with the resultig optimizatio problems. I Sectio IV, we explai our simulatio setup ad aalysis methodology ad the preset our IEEE Globecom /5/$. 5 IEEE

2 results. Fially, i Sectio V, we coclude the paper. II. SYSTEM MODEL We cosider a sigle cell of a wireless system with radius r cell. Withi this cell, oe access poit coordiates all data trasmissios. J termials are located withi the cell. Each termial cotiuously dowloads data from the access poit through the dow-lik. The termials are uiformly distributed over the area of the cell. Oly the dow-lik data trasmissio directio is cosidered here, usig OFDM as trasmissio scheme. Time is divided ito uits (frames) of duratio T f. A. Physical layer The system features a total badwidth of B [Hz] at ceter frequecy f c. The give badwidth is split ito N subcarriers with a badwidth of B [Hz] N each [1]. I order to guaratee orthogoality betwee the sub-carriers, the symbol legth is idetical for all sub-carriers ad it is related to the N badwidth of each sub-carrier by B [Hz] = T s. Although each sub-carrier employs the same symbol rate, the amout of bits represeted by oe symbol might be differet o each subcarrier. This is due to the deploymet of differet modulatio types (out of a set of M available oes). I additio, a maximum trasmit power of P max is allowed to be radiated by ay trasmitter of the system. P max ca be arbitrarily split betwee the sub-carriers. B. Wireless chael model We cosider the termials to be quasi-static ad uiformly distributed over the cell. Still, due to the movemet of reflectig ad scatterig objects withi the cell, the perceived sigal quality per sub-carrier ad termial, i.e., their SNR, varies permaetly. The istat SNR of sub-carrier for termial σ j at time t is give by v (t) = p(t) the trasmissio power, h (t) carrier ad σ h (t), where p (t) deotes deotes the atteuatio of sub- deotes the oise power. The atteuatio is primarily resposible for the variatio of the perceived SNR; it varies due to path loss, shadowig ad fadig. Thus, h (t) ca be decomposed ito three factors reflectig these three effects. The atteuatio of each sub-carrier is assumed to be costat over the time uit T f. Note that this time uit is cosidered to be smaller tha the coherece time of the wireless chael, usig the defiitio from [1]. C. Medium access cotrol layer We assume a system where time is divided ito frames of legth T f. Durig each frame, a fixed time spa is reserved for dow-lik ad up-lik trasmissios. OFDM-FDMA is applied to the dow-lik trasmissios. Besides reservig a time spa for every frame, we do ot cosider the up-lik ay further. The duratio of oe dow-lik phase is deoted by T d. Prior to each dow-lik phase, the access poit geerates ew assigmets of sub-carrier subsets for each termial i the cell ad/or power assigmets for each sub-carrier. Delay effects owig to a iadequate processig power at the access poit are ot cosidered. The geeratio of the Fig. 1. The four combiatio possibilities. ew assigmets per frame is based o the kowledge of the sub-carrier ( states towards each termial deoted by the matrix H (t) = h (t) ). j, It is assumed that this kowledge is available. Note that i a real system this perfect chael kowledge will ot be available. Istead, the assigmets will be based o sub-carrier state estimates with some form of feedback from the termials to the access poit (durig the up-lik phase). If the legth of a frame is chose sufficietly smaller tha the coherece time of the sub-carriers, this chael kowledge will be quite close to the real values durig the followig frame, i.e. the estimate error will be rather small. As the access poit periodically geerates ew assigmets, the termials have to be iformed about these chages by a sigalig system to each payload data trasmissio. I this work we do ot cosider the loss due to sigalig thus, we assume the termials to acquire the kowledge without ay performace impact. III. STUDIED APPROACHES The system described i Sectio II features both dyamic assigmet mechaisms that were itroduced i I: bit loadig, ad dyamic sub-carrier assigmet. Compared to a static assigmet scheme, each of the possible combiatios of the two schemes (show i Figure 1) improves the system performace while causig some additioal computatioal effort at the access poit. I this sectio, we precisely characterize each combiatio by a iteger programmig problem [11]. The goal of this study is to highlight the performace differeces of the optimally solved dyamic combiatios, while also cosiderig a static approach. As described i Sectio II, each termial cotiuously receives a stream of data from the access poit (without further specifyig the type of data stream). A priori we assume that there is o motivatio to give some termials a higher throughput tha others. Therefore, the primary objective is to maximize the miimum throughput of all termials i the cell, gratig each termial i the cell a miimum average throughput (this approach is sometimes referred to as rate adaptive OFDM-FDMA approach [1]). Obviously, the miimum throughput is determied by termials with the worst atteuatio per sub-carrier (referred to as the weakest termials). The dyamic algorithm operates from dow-lik phase to dow-lik phase, such that this miimum throughput IEEE Globecom /5/$. 5 IEEE

3 varies from frame to frame, depedig o the curret subcarrier atteuatios. A. Approach I - Adaptive Modulatio with Static Assigmets We use this case as compariso scheme. For a static FDMA system, each sub-carrier is always assiged to exactly the same termial j. No reassigmet is doe. Each termial gets assiged the same umber of sub-carriers N J. The total power P max that is radiated by the access poit is equally distributed amog all sub-carriers. Depedig o the resultig istat SNR v (t) ad a target symbol error probability (SEP), for the termial j o sub-carrier at the time t, the access poit chooses the modulatio type with the highest possible throughput to be applied (adaptive modulatio). Note that this approach equals a static TDMA scheme with adaptive modulatio. Cosider [13] for details. B. - Equal Power Distributio ad Dyamic Subcarrier Assigmet I the secod approach, we deal with a system that features dyamic sub-carrier assigmet i combiatio with a equal power distributio per sub-carrier. As described i Sectio II, each sub-carrier is assiged to at most oe termial j at time t, idicated by a biary variable x (t),j set to oe ( x(t),j is set to zero if is ot assiged to j at t ). Each sub-carrier is employed with equal trasmit power. As i approach I, the adaptive modulatio scheme is applied o top of the dyamic sub-carrier assigmet ad fixed power distributio. For the chose objective, this results i a iteger programmig problem: max ɛ (1) s.t. x (t) 1 (ALLOC) j F p(t) h (t) x (t) ɛ j, (FAIR) σ ( p where F (t) h(t) describes the umber of bits per dowlik phase that ca be trasmitted o sub-carrier for termial j at time t with a trasmit power of p (t) (thus, this fuctio models the adaptive modulatio system, depedig also o the target SEP). The first costrait (ALLOC) guaratees the assigmet of at most oe termial to oe sub-carrier at a time. The secod costrait (FAIR) implemets the discussed objective: Maximizig the miimum throughput ɛ per termial per dow-lik phase. Note that o additioal costrait for the trasmit power is required as the power is statically distributed. σ ) C. I - Dyamic Power Distributio ad Static Assigmets I equals approach I i the static subcarrier/termial-mappig, yet istead of distributig the power statically over the sub-carriers, it is distributed dyamically with the same objective of maximizig the miimum throughput. The correspodig optimizatio problem results as follows: max ɛ () s.t. y (t) P max (POWER) F y(t) h (t) ɛ j, (FAIR) j σ where j describes a sub-carrier that is statically assiged to termial j. To poit up that the amout of power that is assiged to a termial j is ot a parameter, but the variable of the optimizatio problem, it is deoted by y (t). Agai, the parameter h (t) is the atteuatio that is experieced by termial j o sub-carrier at time t, σ is the oise power experieced by each sub-carrier. Hece, the term y (t) h (t) /σ = v (t),j describes the istat SNR of termial j for sub-chael. F (...) is the fuctioal mappig betwee the SNR ad the amout of bits coveyable per dow-lik phase. The first costrait (POWER) esures that the sum of allocated power to the sub-carriers equals or is smaller tha the maximum trasmissio power P max. As i, the secod costrait (FAIR) esures the maximizatio of the miimum throughput per frame. Sice the sub-carrier assigmet is static, there is o eed for the sub-carrier allocatio costrait (ALLOC) of approach II. D. - Dyamic Power ad Sub-carrier Assigmet The fourth approach combies both dyamic mechaisms. Hece, both optimizatio variables x (t) ad y(t) are combied i the optimizatio problem equatio. It is subject to all three costraits that were itroduced before: max ɛ (3) s.t. y (t) P max (POWER) x (t) 1 (ALLOC) j ( ) y (t) h (t) F x (t) ɛ j. (FAIR) σ Agai, F (...) is the fuctioal mappig betwee the SNR ad the amout of bits coveyable per dow-lik phase, depedig o the target SEP. IV. PERFORMANCE ANALYSIS I this sectio, we describe the methodology ad the sceario setup we assumed whe evaluatig the four approaches of Sectio III. We also metio the tools we used to solve the iteger programmig problems. Fially, we preset the results we derived from the simulatios. IEEE Globecom /5/$. 5 IEEE

4 A. Methodology ad Simulatio Sceario I order to obtai the system level results, we took the followig steps: Iitially we geerated chael trace files of the atteuatio values for each sub-carrier regardig each termial. Oe sample was geerated for every dow-lik phase ad sub-carrier per termial. Theses atteuatio values were used to geerate ad solve appropriate istaces of the liear programs described i Sectio III (usig the tools ZIMPL ad CPLEX). Whe cofigurig the chael model, we assumed the followig sceario. We chose a system with a badwidth equivalet to IEEE 8.11a, thus the available badwidth was B = 16.5 MHz, split ito 48 sub-carriers. As ceter frequecy we chose a chael from the U-NII lower bad, located at 5. GHz. Therefore, the maximum trasmit power for this bad was P max =1mW. J =16wireless termials were located withi the cell, uiformly distributed ad fixed at their positio. The sub-carrier s atteuatio chaged costatly due to the movemet of reflectig objects i the multi-path propagatio eviromet with a maximum speed of v max = 1 m/s. The effects ifluecig the sub-carrier atteuatio states were path loss, shadowig ad fadig. Path loss was determied by the formula P 1 P tx = K d, where α P P tx deotes the ratio betwee received ad trasmitted power, d deotes the distace betwee trasmitter ad receiver, K deotes the referece loss for the distace uit d is measured i ad α is the path loss expoet. We parameterized the referece loss with 1 log(k) = 46.7 db ad the path loss expoet with α =.4. The shadowig was assumed to be log-ormal distributed with a stadard deviatio of σ = 5.8 db ad a mea of db while o correlatioal behavior was icorporated i the model. For the fadig the power spectral desity was chose to have a Jakes-like shape [1] with the Doppler frequecy depedig o v max ad the ceter frequecy. The multi-path propagatio eviromet was characterized by a delay spread, iitially set to σ =.15 µs, with a expoetial power delay profile accordig to the large ope space model of ETSI C [14]. A example eviromet would be a large airport or expositio hall. For the adaptive modulatio, five modulatio types were chose: BPSK, QPSK, 16-QAM, 64-QAM ad 56-QAM. I cases of a static power distributio for the resultig SNR the modulatio type was chose which had the highest throughput while still providig a symbol error probability lower tha 1. I cases where the power was distributed dyamically, the same symbol error target was applied. B. Results As performace metric we cosidered the miimum average throughput per cell that could be achieved by solvig the optimizatio problem. The miimum average throughput represets the throughput of the cell that ca be guarateed We gratefully thak Torste Koch from the Zuse-Istitute Berli (ZIB) for eablig the usage of ZIMPL. by a system provider (or by a system s stadard). Thus, it is quite a importat metric. Two differet cases were cosidered. I the first case the radius of the cell was icreased (from 1 m to m), leadig to a larger differece i the distace betwee the termial closest to the access poit ad the oe farest away. Thus, the average atteuatio spread (due to the icreasig path loss differece of termials i the cell) of the sub-carriers icreased. As the optimizatio objective is to maximize the miimum throughput for all termials, the atteuatio spread is preset i the assiged sub-carriers 3. I the secod case cosidered, the cell radius was kept fixed (at 1 m) butthe trasmit power was varied (betwee dbmad dbm). All results are give i Figure. I the first case (icreasig the cell radius) i geeral the miimum throughput achieved decreases for each approach. The lowest throughput yields the static approach. The best performace is achieved i case of the fully dyamic approach, which is obviously also the case for varyig the trasmit power. The differece betwee a fully static approach ad the pure power adaptio case is rather small (about 3 kbit/s), correspodig to results regardig a compariso of adaptive modulatio ad bit loadig i poit-to-poit coectios [7]. For example, spedig the computatioal power i order to perform bit loadig at the access poit would eable a icrease of the cell s radius by about 1 m for a average miimum throughput of 4MBit/s while for a average miimum throughput of MBit/s the cell could be icreased by about 5 m. Switchig from the static approach to the dyamic sub-carrier assigmet approach yields a larger possible icrease: 3 m i case of the higher miimum throughput ad 6 m i case of the lower oe. Notice i particular that the radius gai for switchig from the pure dyamic sub-carrier approach to the fully dyamic approach is about 3 m i case of the higher miimum throughput ad 5 m i case of the lower oe. Thus, i particular i the case of the dyamic sub-carrier assigmet approach a adaptive power distributio pays off quite well. For a radius of 15 m switchig from the dyamic sub-carrier approach to the fully dyamic approach yields a 7 kbit/s higher throughput (a gai of 35%). Hece, especially for cells with a larger radius the fully dyamic approach yields a valuable further performace icrease. This ca also be observed from the throughput ratio plot i Figure for a icreasig cell radius. I this graph especially the completely differet performace gai whe switchig from a static to a dyamic power distributio for a static subcarrier assigmet or for a dyamic sub-carrier assigmet is give. While switchig from approach 1 to 3 oly yields a moderate icrease, switchig from approach to 4 yields quite a large icrease, especially for a large radius. Also, Figure holds the results for varyig the trasmit power. I geeral, as the trasmit power icreases so does the miimum average throughput for all schemes. As metioed 3 This is very differet to a pure rate maximizatio approach, where a subcarrier is assiged to the termial with the lowest atteuatio. Thus, distat termials suffer from starvatio. IEEE Globecom /5/$. 5 IEEE

5 Miimum average throughput / [Kbits/s] Miimum Throughput Approach I I Radius / [m] Throughput Ratio Miimum average throughput / [Kbits/s] Approach I I Miimum Throughput Trasmissio power costrait / [dbm] Throughput Ratio 5 I 8 I Ratio to static approach 4 3 Ratio to static approach Radius / [m] Trasmissio power costrait / [dbm] Fig.. Compariso of the 4 approaches (I: static system, II: dyamic sub-chael assigmet fixed power, III: pure bit loadig, IV: fully dyamic system) regardig the miimum average throughput for a icreasig radius (upper left) ad trasmit power (upper right), ad regardig the respective throughput ratios compared to the performace of the static approach (lower left ad right) above, the fully static approach achieves the worst performace ad the fully dyamic scheme achieves the best oe, while switchig from approach 1 to 3 ever provides as much additioal capacity as switchig from approach to 4. V. CONCLUSIONS I this study, we compared the most popular adaptive mechaisms that are used to ehace OFDM-FDMA systems, power adaptio ad dyamic sub-carrier assigmet, i terms of the achieved miimum throughput. I cotrast to previous ivestigatios we foud that the dyamic distributio of power does provide a sigificat performace icrease. This icrease is much higher if the sub-carriers are already assiged dyamically. The, if the trasmit power is low or the atteuatio spread i the cell is high (thus, a rather large cell is cosidered) we propose to cosider a fully dyamic approach due to the quite high additioal performace achieved. I cotrast, if oly the trasmit power is distributed dyamically for a static subcarrier assigmet (i FDMA but also i TDMA), the gai is rather small, such that this optio is ot recommeded (i accordace with previous publicatios). Regardig the complexity, it is geerally suspected that the optimal dyamic sub-carrier assigmet followig the here preseted approach is NP-hard. I cotrast, the pure dyamic power distributio ca be solved efficietly. Thus, as future work, efficiet sub-optimal solutio strategies especially for the fully dyamic approach are of iterest, sice sigificatly more performace is provided by this approach. REFERENCES [1] R. va Nee ad R. Prasad, OFDM Wireless Multimedia Commuicatios, chapter 9, Artech House,. [] I. Kalet, The multitoe chael, IEEE Trasactios o Commuicatios, vol. 37, o., pp , February [3] P. Chow, J. Cioffi, ad J. Bigham, A practical discrete multitoe trasceiver loadig algorithm for data trasmissio over spectrally shaped chaels, IEEE Trasactios o Commuicatios, vol. 43, o., February [4] R. Fischer ad J. Huber, A ew loadig algorithm for discrete multitoe trasmissio, i IEEE Proc. GLOBECOM, Nov 1996, pp [5] C.Y. Wog, R.S. Cheg, K.B. Letaief, ad R. Murch, Multiuser OFDM with adaptive subcarrier, bit ad power allocatio, IEEE Joural o Selected Areas of Comm., vol. 17, o. 1, pp , Oct [6] D. Kivac ad H. Liu, Subcarrier allocatio ad power cotrol for OFDMA, i Proc. Coferece o Sigals, Systems ad Computers,, vol. 1, pp [7] A. Czylwik, Adaptive OFDM for widebad radio chaels, i Proc. of the Global Telecommuicatios Cof., 1996, vol., pp [8] T. Huziker ad D. Dahlhaus, Optimal Power Adaptatio for OFDM Systems with Ideal Bit-Iterleavig ad Hard-Decisio Decodig, i Proc. IEEE It. Coferece o Commuicatios (ICC), 3, vol. 5, pp [9] W. Rhee ad J. Cioffi, Icrease i capacity of multiuser OFDM system usig dyamic subchael allocatio, i Proc. Vehicular Techology Coferece (VTC),, pp [1] J. Cavers, Mobile Chael Characteristics, chapter 1.3, Kluwer Academic,. [11] A. Schrijver, Combiatorial Optimizatio, Spriger, 3. [1] D. Kivac, G. Li, ad H. Liu, Computatioally efficiet badwidth allocatio ad power cotrol for OFDMA, IEEE Trasactios o Wireless Commuicatios, vol., o. 6, pp , 3. [13] M. Bohge, Bit loadig versus dyamic sub-carrier assigmet i multiuser OFDM-FDMA systems, September 4, Diploma Thesis at Techical Uiversity of Berli, Germay. [14] J. Medbo ad P. Schramm, Chael Models for HIPERLAN/, ETSI EP BRAN documet 3ERI85B, March IEEE Globecom /5/$. 5 IEEE

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