Increase in Multicast OFDM Data Rate in PLC Network using Adaptive LP-OFDM

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1 Athor manscript, plished in "IEEE ICAST, Accra : Ghana (2009)" Increase in Mlticast OFDM Data Rate in PLC Network sing Adaptive LP-OFDM Ali Maiga, Jean-Yves Badais and Jean-François Hélard Institte of Electronics and Telecommnications of Rennes Rennes Cedex, France {ali.maiga, jean-yves.adais, jean-francois.helard}@insa-rennes.fr Astract Linear precoding (LP) techniqe applied to OFDM systems has already proved its aility to significantly increase the system throghpt in a powerline commnication (PLC) context. In this paper, we propose resorce allocation algorithms ased on the LP techniqe to increase the mlticast OFDM systems it rate. The conventional mlticast capacity is limited y the ser which experiences the worst channel conditions. To increase the mlticast it rate, these proposed algorithms assign scarriers and its to different mlticast sers. Simlations are rn over PLC channels and it is shown that the proposed soltions offer a it rate gain p to 37% compared to the conventional mlticast it rate. I. INTRODUCTION Initially developed in the 90 s for low it rate applications, sch as telemetry, infrastrctre control and consmption measrement, powerline commnication (PLC) technologies have recently drawn an increasing interest within the scientific commnity for high it rate commnications over the power grid. De to significant advances achieved in terms of modlation and signal processing schemes on one hand, and owing to the iqity of the otlet on the other hand, PLC is today considered as a soltion of high potential for indoor applications and constittes a convenient and cheap alternative to already existing technologies. We are witnessing the increase of data applications with high andwidth rirements and the demand for mltimedia services sch as video and adio conferencing, online training is increasing. So far, the mltimedia services are nicasted (roght separately) to each ser of the PLC network, leading to data dplication and lost of time and andwidth. For these applications, mlticasting offers a significant improvement compared to nicasting, since it allows the transmission of packets to mltiple destinations sing less resorces []. The powerline channel exhiits mltipaths cased y reflections on the discontinities of the network and offers implse responses that can e assmed as qasi-static and encorages the exploitation of the channel state information (CSI) at the transmitter side. Yet, the difference in link conditions of sers makes it difficlt to apply resorce allocation process ecase the rirements of each mlticast ser shold e satisfied. The conventional resorce allocation method in mlticast orthogonal frency division mltiplexing (OFDM) is to serve the worst ser. Consently, this method may not provide efficient performances when the nmer of mlticast sers increases. To increase the mlticast it rate, it has een sggested to exploit hierarchy in mlticast data, when employing mltiresoltion coding [-3]. The data is compressed into a nmer of layers, arranged in a hierarchy, which provides progressive refinement. If only the first layer is received y the ser with the lowest data rate, the decoder prodces the worst qality version. As more layers are received y more capale sers, the decoder comines the layers to prodce improved qality []. Few stdies have een carried ot on mlticast OFDM systems for PLC, and even lesser stdies seeking to increase the mlticast it rate withot sing hierarchical data. In this paper, resorce allocation algorithms for mlticast OFDM systems are proposed in order to increase the data rate in non-hierarchical data context. These algorithms allocate dynamically scarriers and its and are ased on the linear precoding techniqe. De to power spectral density (PSD) constraint in PLC systems, all sers have the same peak power constraint on each scarrier and there is no power allocation. Linear precoded OFDM (LP-OFDM) is a comination of mlticarrier and spread spectrm techniqes also known as MC-SS techniqes. This techniqe has shown very good performances in difficlt environments and rings a significant increase in it rate compared to classical OFDM systems [4], [5], []. In the following, it is discssed how to take advantage of linear precoding techniqe for mlticast services in mlticarrier systems. New resorce allocation algorithms are proposed for LP-OFDM to increase the mlticast it rate. This paper is organized as follows. Section II descries the LP-OFDM systems. Section III presents the optimization prolem in mlticast OFDM systems. Section IV gives the proposed soltions to the optimization prolem. The performances of these soltions are given in section V over PLC channels. Finally, section VI concldes the paper. In the following, pper (resp. lower) oldface symols are sed for matrices (resp. colmn vector), lower symols represent scalar vales. Besides, (.) T and (.) H denote transpose and Hermitian operators respectively, and I N stands for the N N identity matrix. II. LP-OFDM SYSTEM DESCRIPTION A. Adaptive linear precoded OFDM system model The stdied LP-OFDM system is ased on the comination of OFDM with linear precoding. In a general approach, the

2 N-dimensional generated symol vector s can e written as s = F H W x. () Vector x = [x,..., x K ] T is the reslt of the serial to parallel conversion of the inpt data stream containing the K QAM-mapped symols to transmit. W stands for the N K precoding matrix applied to x which precodes K symols over N scarriers. The precoded symol vector is finally mltiplied y the N N nitary Forier matrix F that realizes the mlticarrier modlation. N represents the nmer of scarriers sed in the system. Note that for W = I N, the system amonts to the classical non-precoded OFDM system. Depending on the strctre of the precoding matrix, it is in fact possile to precode the symol stream following different strategies. In this paper, we focs on a particlar instance of this road category of LP-OFDM signals where the precoding fnction is applied to different locks of scarriers independently. The lock model of the proposed LP-OFDM system is depicted in Fig. and the reslting signal is then C 0 s = F H Z... } 0 {{ C B } W=ZC x. x B, (2) with B the nmer of locks to consider. Matrices C = {c l,k } l L, k K are the individal precoding matrices containing the K precoding sences of length L to apply to each lock S, = [; B]. Note that L is also ivalent to the size of the th lock S, i.e. to the nmer of gathered scarriers in that lock. From (), we can write L = N, and K = K. x = [x,,..., x,k ] T are K -dimensional vectors of QAM symols to e transmitted within the different locks. We se M-QAM constellations of orders m,k [; 0] like in PLC systems. Within each lock, note that each QAM symol x,k is associated to a certain precoding sence. Finally, Z is a permtation matrix that asically realizes an interleaving of the precoded QAM symols in the frency domain. Consently, one has to keep in mind that locks are not necessarily made of adjacent scarriers. After classical cyclic prefix extension, the generated data stream is sent across the PLC channel. Assming perfect synchronization and cyclic prefix removal at the receiver, the channel can e modeled y one single complex coefficient per scarrier [5]. After mlticarrier demodlation the received signal is then y = HWx + n 0, (3) where H = diag([h,..., h N ]) is the N N diagonal complex matrix earing on its diagonal the frency domain channel gains associated to each scarrier n [; N]. Vector n 0 represents the additive white Gassian noise sch that E[n 0 n H 0 ] = N 0 I N. The channel effects are finally compensated for sing a simple zero-forcing (ZF) alizer efore desinterleaving and inverse precoding operations. Denoting G = H QAM QAM QAM QAM Fig.. x K K2 K3 KB C C2 C3 CB Cx L L2 L3 LB INTERLEAVING Precoding Wx N O F D M Proposed LP-OFDM transmitter the diagonal alization matrix, the received vector of data symol d then writes d = W Gy. (4) The following expressions are derived from [5], [], where there are more details. The optimm achieved it rate of the LP-OFDM system sing ZF detection is given y R = L log 2 ( + Γ L h n 2 s ) E, (5) where E is the PSD constraint, Γ is the signal-to-noise ratio (SNR) gap and K = L. The classical OFDM system is otained for L =. Choice of the L scarriers To maximize the it rate R given y (5), it sffices to minimize the sm 2. This corresponds to choose h n the scarriers with est channel gains h n 2. A simpler soltion is to sort scarriers in descending order and to choose the first L scarriers. B. Performance of LP-OFDM in PLC context In or stdy, the LP component is sed to mltiplex different data symols of a given ser. The mltiplexed data symols are sent in ssets of scarriers which are merged with precoding sences. If the merging process is jdiciosly done, each reslting sset holds an ivalent SNR sch that the total spported throghpt is greater than the sm of the individal throghpts spported y each scarrier taken separately. Fig. 2 shows the performance of LP-OFDM system over a Rayleigh fading channel in single ser context. The precoding sence length is al to 4 or 32. Fig. 2a shows the loaded it per scarrier for OFDM and LP-OFDM itloading algorithms when the average channel gain varies. The LP-OFDM system increases the classical OFDM system it N 0

3 Loaded it per scarrier (it) Used energy per scarrier (dbm/hz) 0 4 (a) OFDM 2 LP OFDM, L=4 LP OFDM, L= Average channel gain (db) () OFDM 54 LP OFDM, L=4 LP OFDM, L= Sorted scarrier indexes Fig. 2. Performance of LP-OFDM system over a Rayleigh fading channel in single ser context. (a) loaded it per scarrier; () sed energy per scarrier for average channel gain of -30 db. rate and the gain roght y the linear precoding component is more important for a longer precoding sence. The reason for the etter performance of the LP-OFDM system is explained in Fig. 2, where the sed energy of different algorithms are compared. To highlight the energy distrition, scarriers are sorted in descending order. The sed energy is the minimal rired energy allowing the transmission of the maximm data rate. Jmp positions in crves correspond to the change in modlation orders. It is clear that the OFDM algorithm is not flly exploiting the availale energy on each scarrier de to discrete modlation orders. The precoding component accmlates the residal lost energies of a given lock of scarriers to transmit additional its. The adaptive LP-OFDM system tilizes more efficiently the PSD limit. The longer the precoding sence, the etter the sed energy. However, a compromise on precoding sence length has to e made ecase the self interference (interference etween precoding sences) increases with the precoding sence length, de to channel selectivity. The additional complexities of LP-OFDM are the precoding matrix which is composed of Hadamard orthogonal matrices, and the interleaver at the transmitter side. At the receiver side, their inverse fnctions are sed. III. BIT RATE OPTIMIZATION PROBLEM IN MULTICAST OFDM SYSTEMS In mlticast OFDM systems, the modlation shold e adjsted to serve the ser with the worst channel conditions, in non-hierarchical data context. The classical method in mlticast OFDM, LCG (low channel gain, []) consists in allocating resorces while satisfying rirements of all sers. This method sets the achieved it rate per scarrier with the lowest it rate of sers over this scarrier. Hence, the achieved it rate with LCG method over scarrier n in PLC context writes R LCG n = min log 2 ( + E ΓN 0 h,n 2 ), () where h,n 2 is the channel gain of ser on scarrier n. When considering the LP-OFDM system, the achieved mlticast it rate over the lock S of scarriers will e the lowest it rate of sers over this lock. This it rate writes ( ) R LP = min R, = min L log 2 + Γ L h,n 2 (7) De to PSD constraint in PLC systems, all sers have the same peak power constraint E on each scarrier. Hence, there is no power allocation. For simplicity, it is assmed that all sers tilize the same precoding sence length L for all locks. The lock index can then e removed in the following for the precoding sence length. To maximize the mlticast it rate, we need to choose the lock S that maximizes the worst ser it rate. As, min R, max h,n 2 and max R, min h,n 2, the optimization prolem writes min max S h,n 2. () This is a cominatorial and min-max-sm resorce allocation prolem which is an NP-hard prolem [7]. IV. PROPOSED SOLUTIONS TO THE OPTIMIZATION PROBLEM In (), we need to find the optimal S which maximizes the worst ser it rate. Proposed soltions to distrite scarriers in locks are given in the following. A asic resoltion which consists in testing all possiilities of defining locks is first analyzed. Then, a two-step heristic procedre is proposed. This procedre aims at finding the optimal lock for each mlticast ser efore selecting the est case. Finally, an ivalent channel which is the comination of sers channel conditions is generated. This ivalent channel is sed to define the locks of scarriers. E N 0.

4 A. Cominatorial soltion The asic resoltion of finding the optimal lock of scarriers is to test all possiilities of gathering scarriers in locks and then to choose the est case. As oth the order of scarrier indexes within a lock and the order of locks do not change the reslt, the nmer of possiilities can e considered as C L N CL N L CL N 2L... CL 2L ( N L )! = N!, (9) (L!) ( N L ) ( N L )! where the nmer N of scarriers is mltiple of the nmer L of scarriers per lock. This nmer of possiilities depicts the nmer of cominations of L ot of N, and the nmer of cominations of L ot of N L, ntil all cominations are taken into accont. Then, the total nmer of cominations is divided y the nmer of arrangements of locks. For N = and L = 4, the nmer of possiilities, needed to find the optimm mlticast it rate, is more than 0 million. This nmer is very high and will lead to high simlation time. B. Heristic soltion In this soltion, each ser is considered as the worst ser and we try to choose the optimal lock of scarriers. The est it rate of sers defines the mlticast it rate. Considering the optimization prolem (), the following can e derived = arg max h,n 2 h,n 2 h,n 2. Assming that is known, the prolem () can e converted into classical minimization prolem nder constraints where, min S h,n 2 sject to d,v,n 0, d,v,n = (0) h,n 2 h v,n 2, () where v is the index of other sers. Hence, a soltion to prolem (0) will consist in a two-step approach. Considering that the system has B locks of scarriers, this method optimizes the mlticast system it rate for each lock. ) For each mlticast ser, find the lock S of availale scarriers, where the ser achieves its est minimm it rate. 2) Choose the ser who achieves the est minimm it rate and its corresponding lock S. Considering a system with U sers, N scarriers that can e gathered in B locks of L scarriers, the algorithm gives a soltion of prolem (0). Algorithm : Heristic soltion algorithm Data: N, U, B, L, h,n 2, n Reslt: R it rate per ser egin 2 R 0; 3 As {,, N}; //set of availale scarriers 4 for all lock, [; B] do 5 for all ser, [; U] do sort availale h,n 2 in descending order; let I e the set of sorted indexes; 7 S I( : L) if n S d,v,n 0 then 9 elses is defined 0 i ; // while 2 n S d,v,n < 0 & i < As L do 3 find n = arg min n v V d,v,n, n S and V = {v/d,v,n < 0} 4 S S n ; 5 S S + I(L + i); Compte d,v,n ; 7 find arg min n S set S S ; 9 compte R, from (5); end set R R + R,; set As As S ; C. Exploitation of classical LCG method h,n 2 ; In the LCG method, the mlticast it rate can e considered as the it rate compted over an ivalent channel in single ser context. This ivalent mlticast channel is the comination of channel conditions of different sers. Actally, for each index of scarrier, the ivalent gain of the channel is given y the gain of the worst ser scarrier. Let h n 2 e the ivalent mlticast channel gain on scarrier n. Hence, h n 2 = min h,n 2. (2) Compting this ivalent mlticast channel, the mlticast resorce allocation is the same as the single link resorce allocation. Bit-loading algorithms in single ser context can then e applied to this channel. LCG method gives reslts for classical OFDM it-loading algorithm. To increase the it rate of this LCG method, the LP-OFDM it-loading in single ser context [4], is applied on the ivalent channel and this method will e considered as linear precoding ased LCG (LP- LCG) method. Then, scarriers of the ivalent channel are sorted in descending order and est availale scarriers are gathered in a lock.

5 D. Proposed Improved-LP-LCG method Considering locks of scarriers, we show, for all n S and for all, h,n 2 h n 2 max h,n 2 h 2 n min max S h,n 2 min S h n 2. (3) From (3), we derive that the worst ser over lock S offers a etter it rate than the LP-LCG method. We aim at finding the soltion of the left hand side of inality (3) according to (). Minimize the right hand side of the inality redces the left hand side and sing the est availale L scarriers of the ivalent channel to form S minimizes the right hand side. This soltion, called Improved-LP-LCG, consists in sorting the scarriers of the ivalent channel in descending order and the indexes of sorted scarriers define the different locks. The algorithm 2 descries how to compte the mlticast it rate with the improved-lp-lcg method. Reslts for the classical LCG method is otained for L =. Algorithm 2: Improved LP-LCG algorithm Data: N, U, B, L, h,n 2, n Reslt: R it rate per ser egin 2 R 0 ; 3 for all scarrier n, n [; N] do compte h n 2 4 from (2) ; sort h 5 2 n in descending order; let I e the set of sorted indexes; for all lock, [; B] do 7 S I(( )L : L) ; for all ser, [; U] do 9 compte R, from (5) ; 0 2 end R LP min R, ; R R + R LP ; E. Comparison of different soltions For a fix precoding sence length, the cominatorial soltion gives the optimm mlticast it rate, t the nmer of possiilities to e tested significantly increases when the nmer of scarriers increases. Fig. 3 gives the comparison of proposed cominatorial soltion and others, over an i.i.d. Rayleigh fading channel. The total nmer of scarriers is N = 2 and the precoding sence length is L = 4. As expected, the cominatorial soltion otperforms the other ones and the LP component improves the classical mlticast OFDM system (LCG). The improved-lp-lcg method gives performance near the cominatorial one when the nmer Loaded it per scarrier (it) LCG (Conventional) LP LCG Heristic Improved LP LCG Cominatorial Nmer of mlticast sers Fig. 3. Comparison of cominatorial soltion with others for N = 2 and L = 4 over Rayleigh fading channels of sers increases. Yet, this tendency cannot e generalized to a given nmer N ecase of difficlties in performing the cominatorial soltion when N is high. In the following, simlations are not performed for the cominatorial soltion. Compared to the classical LCG method, the LP-LCG method rings the same additional complexity as the LP- OFDM system to classical OFDM system. The improvement of this LP-LCG method (Improved-LP-LCG) needs the comptation of different R,. Tale I shows the different comptational times over Rayleigh fading channel with 2 scarriers and 00 sers. Algorithm LCG LP-LCG Improved-LP-LCG Heristic Time (ms) (0.490) (0.75) (3.73) (53.44) TABLE I MEAN (WORST CASE) COMPUTATION TIMES IN MILLISECONDS FOR N=2, U=00 AND L=4 USING MATLAB WITH INTEL CORE2@2.GHZ. V. SIMULATION RESULTS In this section, simlation reslts for the proposed LP- OFDM schemes applied to mlticast systems are presented and the performances of the different algorithms are compared with the conventional mlticast approach LCG. The generated signal is composed of N = 024 scarriers transmitted in the and [0.3; 20] MHz. Perfect synchronization and channel estimation are assmed. A high ackgrond noise level of 0 dbm/hz is assmed and the signal is transmitted with respect to a flat PSD of 50 dbm/hz for all sers. Reslts are given for a fixed target symol error rate (SER) of 0. A constant coding gain γ c of db for all modlation orders is sed and a system margin γ m is set to 3 db. In order to take into accont the coding gain and the system margin, the SNR gap Γ is given y []: Γ(dB) = 9. γ c + γ m. (4)

6 The maximm nmer of its per symol is limited to 0. The mltipath channel model for PLC as proposed in [9] is sed. This channel model is randomized to generate enogh channels for simlations in mltiser context. The reference model of this channel model is 0 m link 5-path model which frency response is given y 5 H(f) = g i e (a0+af k ) d i e 2jπf(τi). (5) i= The parameters of the 5-path model are detailed in [9] and Fig. 4 shows 3 examples of sed channel transfer fnctions. H(f) in db reference model channel channel 2 channel frency in MHz Fig path reference channel model and generated channels for PLC Fig. 5 depicts the comparison of proposed LP-OFDM ased soltions with conventional LCG method. It shows that the conventional mlticast (LCG) it rate significantly decreases when the nmer of sers increases. The figre also shows that the mlticast it rate is increased y sing the linear precoding component. When there is a ser with very ad channel conditions, the mlticast it rate significantly decreases. For example, for a 9-ser system, aot 2 it per scarrier are lost compared to a -ser system. As previosly stated, the calclation of the ivalent mlticast channel makes the mlticast resorce allocation ivalent to single ser one. Therefore, the difference performance etween LCG and LP- LCG methods confirms the fact that LP-OFDM offers more it rate in single ser context. The heristic soltion offers etter it rate when the nmer of sers is less than 25. Ths, the optimization of locks for each ser, efore selecting the est case (i.e. heristic soltion), rings etter reslts for lower nmer of sers, t ecomes less efficient for higher nmer of sers. This figre confirms also the fact that the improved-lp-lcg method garantees a etter mlticast it rate compared to others for higher nmer of sers and gives performance near the heristic soltion for lower nmer of sers. Compared to the conventional mlticast LCG method, the improved-lp-lcg method offers a it rate gain near 37% for a 00-ser system. This method is qite simpler and can e Loaded it per scarrier (it) LCG (Conventional) LP LCG Heristic Improved LP LCG Nmer of mlticast sers Fig. 5. Comparison of different proposed algorithms considered for resorce allocation soltion in mlticast OFDM systems for PLC. VI. CONCLUSION In this paper, linear precoding techniqe has een adapted to mlticast OFDM systems in PLC context. To increase the mlticast it rate, different new resorce allocation algorithms have een proposed ased on linear precoding techniqe. It has een shown throgh simlations that proposed algorithms ring a it rate gain p to 37% compared to conventional mlticast resorce allocation method. ACKNOWLEDGMENT The research leading to these reslts has received fnding from the Eropean Commnity s Seventh Framework Programme FP7/ nder grant agreement n o 233 also referred to as OMEGA. REFERENCES [] C. Sh, J. Mo, Resorce allocation for mlticast services in mlticarrier wireless commnications, in Proc. of IEEE Infocom 200, Apr. 200, Barcelona, Spain. [2] C. Sh, C. S. Hwang, Dynamic schannel and it allocation for mlticast OFDM systems, in Proc. of IEEE PIRMC 04, Sept 2004, Barcelona, Spain. [3] C.-S. Hwang and Y. Kim, An adaptive modlation method for mlticast commnications of hierarchical data in wireless networks, Proc. of IEEE ICC., pp , [4] A. Maiga, J-Y. Badais, and J-F. Hélard, Very High Bit Rate Power Line Commnications For Home Networks, IEEE ISPLC09, April 2009, Dresden, Germany. [5] M. Crssière, J-Y. Badais, and J-F. Hélard, Adaptive linear precoded DMT as an efficient resorce allocation scheme for power-line commnications, Proc. of IEEE GLOBECOM 0, San Francisco, USA, Novemer 200. [] M. Crssière, J-Y. Badais, and J-F. Hélard, Adaptive Spread-Sprectrm Mlticarrier Mltiple-Access Over Wirelines, IEEE JSAC, Vol. 24, No. 7, Jly 200. [7] S. Karaati, P. Kovelis, and G. Y, A min-max-sm resorce allocation prolem and its applications, Operations Research, 200, Nov-Dec, Vol. 49, Isse., [] J. M. Cioffi, A mlticarrier primer, Novemer 99, ANSI Contrition TE.4/9-57, Clearfield, Fla, USA. [9] M. Zimmermann and K. Dostert, A mltipath model for the powerline channel, IEEE Trans. Commn., vol. 50, no. 4, pp. 553, Apr