Subcarriers and Bits Allocation in Multiuser Orthogonal Frequency Division Multiplexing System

Transcription

1 Sesors & Trasducers, Vol. 168, Issue 4, April 014, pp Sesors & Trasducers 014 by IFSA Publishig, S. L. Subcarriers ad Bits Allocatio i Multiuser Orthogoal Frequecy Divisio Multiplexig System Shibig Zhag, Jimig Hu, ad Huijia Wag Natog Uiversity, 6019, Chia zhagshb@tu.edu.c Received: 10 February 014 /Accepted: 7 April 014 /Published: 30 April 014 Abstract: I order to optimize the spectrum resource allocatio i the orthogoal frequecy divisio multiplexig system ad miimize the trasmitted power, this paper proposed a modified basic particle swarm optimizatio algorithm to allocate the subcarriers ad bits of the orthogoal frequecy divisio multiplexig system. The algorithm uses the average idividual extreme value istead of idividual extreme value to update the particles. Meawhile, whe the particle velocity is bigger tha the maximum velocity or smaller tha the miimum velocity, a average velocity is take as the updatig velocity. It ot oly maitais the advatage of basic particle swarm optimizatio, but also makes the particle acquire more iformatio to adjust its movemet. Simulatio results showed that the spectrum resource allocatig based o modified basic particle swarm optimizatio algorithm has ~9 db margi i the total trasmitted power tha the geetic algorithm, basic particle swarm optimizatio algorithm ad method joitig basic particle swarm optimizatio algorithm ad geetic algorithm. Copyright 014 IFSA Publishig, S. L. Keywords: Orthogoal frequecy divisio multiplexig, Subcarrier allocatio, Bit allocatio, Modified particle swarm optimizatio algorithm. 1. Itroductio With the rapid developmet of wireless commuicatio techologies ad the growig of wireless commuicatio traffics, the demads for spectrum resource have bee icreasig [1]. It has resulted i that the available spectrum resource is becomig more ad more scarce. Due to the high spectral efficiecy, strog badwidth extesibility, robustess to multipath fadig ad spectrum allocatio flexibility Orthogoal frequecy divisio multiplexig (OFDM) has become a promisig multicarrier modulatio techique ad received cosiderable iterest i the past decade. It would be the key techology of the ext geeratio mobile commuicatio system [, 3]. I OFDM systems, the whole trasmitted chael is divided ito a umber of sub-chaels; data is trasmitted i parallel by modulatig a umber of closely-spaced orthogoal sub-carriers, thereby covertig a frequecy-selective chael ito multiple flat fadig sub-chaels [4]. Each subchael shows differet fadig to each user [5]. Therefore, reasoable subcarrier ad bit allocatio ca ot oly reduce the trasmit power ad bit error rate of the system effectively, but also improve the spectrum efficiecy ad icrease the system capacity. For sigle user OFDM system, it is well kow that the water-fillig [6] is a useful algorithm to fid the subcarriers ad bits allocatio which miimize the total trasmit power. I multiuser OFDM systems, the subcarriers ad bits allocatio will be more complexity. A good subcarrier for oe user may be also good for others. But oe subcarrier should ot be used by several users at the same time [7]. O other had, a bad subcarrier for oe user may be good 10 Article umber P_198

2 Sesors & Trasducers, Vol. 168, Issue 4, April 014, pp for others. It would make the subcarriers ad bits allocatio much more complex i multiuser OFDM systems. However, the resources allocatio i multiuser OFDM system is roughly divided ito two categories: static allocatio ad dyamic allocatio [8, 9]. Bakhtiari ad Khalaj allocated the resources accordig to the chael gai of each user [10]. Although the algorithm is simple, it does t take full use of multiuser diversity gai. Cheog Yui Wog used the Lagrage extreme method to allocate subcarriers [11]. This algorithm has better performace, but it is too complex. Geetic algorithm (GA) ad basic particle swarm optimizatio (BPSO) algorithm are proposed to allocate the subcarriers ad bits i multiuser OFDM [1, 13]. However, BPSO algorithm is easy to fall ito local optima, especially i the case of complex ad multi-peaks problems. Ad the covergece rate of GA is too slow ad the solutio is very sesitive to the choice of the iitial populatio. Therefore, a algorithm combied BPSO ad GA (BPSO-GA) had bee proposed to get better performace [14]. I this paper, we proposed a modified basic particle swarm optimizatio (MBPSO) algorithm to allocate the subcarriers ad bits i OFDM system. I this algorithm, the average of idividual extreme value is used to update the particle rather tha the idividual extreme value. Meawhile, whe the particle velocity updated is bigger tha the maximum particle velocity or smaller tha the miimum particle velocity, a average value is take as the updatig particle velocity. This algorithm ca ot oly esure to complete the optimal search, but also reduce the total trasmitted power of multiuser OFDM system. Simulatio results showed that the performace of the algorithm proposed is better tha the GA ad BPSO algorithms. The rest of the paper is arraged as follows. Sectio described the system model. I Sectio 3, we proposed the subcarrier ad bit allocatio. Simulatio results were give ad aalyzed i Sectio 4. Fially, some coclusios were draw i Sectio 5.. System Model Assume that there are N users ad K subcarriers i multiuser OFDM system, K N, as show i Fig. 1. For th user, there are R bits data to be trasmitted. The badwidth of each subcarrier is much smaller tha the coherece badwidth of the chael. The istataeous iformatio of all subchael gai is available to the trasceiver. The received power whe r k, bits of th user are trasmitted o k th subcarrier is formulated as follows [15]. rk, r N 0 1 BER * k * rk, P ( rk, ) Q = [ ] ( 1), r, (1) k, 6 *( 1) where N 0 deotes the additive oise power spectral desity i the system, BER k deotes the bit error rate o the subcarrier k. I order to obtai the Qos give, the trasmitted power o the k th subcarrier of th user is give by r k, k, Gk, P P ( r ) =, () where G k, is the gai of th user over k th subcarrier. The, the total trasmitted power i multiuser OFDM system is the sum of trasmitted powers of all users o all subcarriers as followig P total f ( r ) K N K N k, Pk, k= 1 = 1 k= 1 = 1 Gk, (3) = = Fig. 1. Block diagram of a multiuser OFDM system. 11

3 Sesors & Trasducers, Vol. 168, Issue 4, April 014, pp Therefore, the optimizatio problem is to fid the best allocatig scheme which miimizes the total trasmitted power uder the give bit error rate ad trasmissio bits as followig arg mi P total rk, K k, = k = 1, (4) s.. t r R BER BER k targ et where R is the bit data of th use to trasmit, BER target is the upper limit of the bit error rate (BER). 3. Subcarrier ad Bit Allocatio There are two kids of allocatio i the optimizatio problems above, subcarrier allocatio ad bit allocatio. It would be very difficult if we optimize subcarrier allocatio ad bit allocatio at the same time. I this paper, we allocate the multiuser OFDM system spectrum resources i two steps. Firstly, we use the water-fillig algorithm to fid out the subcarriers which are allocated to every user accordig to miimizig the trasmitted power of every user. The, we optimize the bits allocatio with MBPSO algorithm based o the subcarriers allocated Basic PSO Algorithm I a L-dimesios search space, a swarm cosists of N particles, the i th particle ca be expressed as [16] X = ( x, x,, x ), (5) i i1 i il where i = 1,,, N. Suppose the object fuctio is f(x). We substitute X i ito the f(x) ad get the adaptive value, which is used to evaluate the performace of X i. Defie the preset flyig velocity of i th particle as V = ( v, v, v ), (6) i i1 i il the best preset positio of the i th particle (idividual extremum), which represet the optimal value of the object fuctio f(x) searched by the i th particle, as ( P, P, P ) P =, (7) i i1 i il ad the best preset positio of the swarm (global extremum), which represet the optimal value of the object fuctio f(x) searched by all particles, as ( P 1, P, P ) P =, (8) g g g gl where g = 1,,, N. The, the velocity ad positio of PSO are updated as followig ( + 1) = () () + 1 rad() ( () ()) + c Rad() P () t x () t v t w t v t c P t x t ad il il il il ( gl il ) ( 1) ( ) ( 1) il il il, (9) x t+ = x t + v t+, (10) where l = 1,,, L, c 1 ad c are two positive costats which are called acceleratio coefficiets, rad() ad Rad() are two radom fuctios i the rage [0,1], x il (t) is the positio of the t th iteratio particle, v il (t) is the velocity of particle, ad w(t) is the iertia weight of the t th iteratio, which is give by [17] wstart wed w( t) = wstart * t, (11) t max where t max is the allowable maximum umber of iteratios, w start represet the iitial iertia weight ad w ed represets the iertia weight value whe the umber of iteratio is equal to t max. I (9), the first part represets the preset behavior of particle, the secod part represets the idividual cogitive actio of particle, which is depeded o the every particle s thikig, ad the third part represets the social actio of particle, which is depeded o the iformatio shared ad mutual cooperatio betwee particles. These three parts determie the mai properties of the algorithm. 3.. MBPSO Algorithm I order to use the experiece of every idividual particle i update of particle, we would modify the updatig formula of the velocity ad positio of PSO. That is to say we use average extreme matrix istead of idividual extreme matrix i update as follows where P l = ( ) P = P1, P,, PL, (1) ( P + P + + P ) 1l l Nl N, l = 1, L. (13) The improved update for velocity ca be rewritte as ( + 1) = () () + 1 rad() ( ( ) ()) + c Rad() P () t x () t v t w t v t c P t x t il il l il ( gl il ), (14) where v il (t+1) is the particle velocity of the (t+1) th iteratio. If v il (t+1) > v max, we would set a average betwee the miimum velocity v mi ad maximum velocity v max istead of v max i our MBPSO algorithm. 1

4 Sesors & Trasducers, Vol. 168, Issue 4, April 014, pp I the same way, if v il (t+1) < v mi, we set a average betwee (v mi, v max ) rather tha v mi. The MBPSO algorithm has followig advatages over BPSO algorithm. 1) Each particle i the improved algorithm could lear experieces from other particles. That is to say, particles ca make use of more iformatio to decide their ow behavior. ) Each particle searches the optimal solutio betwee the global best positio ad the ceter of the idividual best positio rather tha betwee the global best positio ad idividual best positio. 3) Settig average velocity betwee v mi ad v max istead of v mi or v max could make particles easier to reach optimal solutio with appropriate speed. The mai steps of MBPSO algorithm above are summed as followig: 1) Iitializig. Geerate a K-dimesioal array, which represets the K subcarriers of OFDM system. The value of each elemet i the array represets the serial umber of user that occupies the correspodig subcarrier. The, radomly geerate W arrays to obtai W iitial swarms. Each array correspods to a subcarrier allocatio solutio i the system. Meawhile, set acceleratio coefficiets c 1 ad c, the maximum speed of particles v max ad the miimum speed v mi, the iitial iertia weight w start as well as the termiatio of iertia weight w ed. ) Calculatig the particle fitess. For each particle i the swarm, use the water-fillig algorithm to allocate the bits for each subcarrier which correspods to users. Ad the, calculate the total trasmit power of all users. Defie the reciprocal of the total trasmit power (optimizatio goal) as the object fuctio of the particles, that is f ( x) = 1 P total, (15) 3) Determiig Pl ad Pg accordig to the values of f(x). 4) Updatig the velocity ad positio accordig to (14) ad (10). 5) Calculatig the particle fitess accordig to the formula (15) agai. 6) Evaluatig whether the iteratig meets the termiatio coditios. The termiatio coditio is that the fitess value of global extreme uchaged withi 0 times iteratig or the iteratig process reaches the iteratio limit t max. If the iteratig meets the termiatio coditios, the preset global extreme is the optimal solutio of the optimizatio problem. Otherwise, go back step ii ad go o iteratig util the iteratig meets the termiatio coditios. 4. Simulatio Results ad Aalysis I this sectio, we preset the simulatio results to show the performace of the proposed algorithm for differet system parameters usig Mote Carlo simulatios, ad compare it with GA algorithm, BPSO algorithm, BPSO-GA algorithm ad the algorithm which joited MBPSO ad GA (MBPSO-GA). We cosider a multiuser OFDM system with 3 subcarriers (maximum) where the umber of users N chages from to 10. The simulatig parameters are give i Table 1. Table 1. Simulatio parameters. Number of subcarriers (K) 10~3 Number of users (N) ~10 Size of particle swarm 36 Acceleratio coefficiets (c1) Acceleratio coefficiets (c) Maximum iertia weight (wmax) 0.9 Miimum iertia weight (wmix) 0.4 Maximum velocity (vmax) Miimum velocity (vmix) - Bit rate Maximum iteratio umber (tmax) 00 0 kbps Fig. presets the total trasmitted powers of five differet algorithms uder users to 10 users whe 3 subcarriers are used. It is see that the total trasmitted power of OFDM system based o MBPSO algorithm has 7 db, 5 db ad 4 db advatages over GA, BPSO ad BPSO-GA respectively. Although the total trasmitted power usig MBPSO-GA algorithm is a little better tha MBPSO (about 0.5 db), but the complexity is much greater tha MBPSO. Therefore, MBPSO-GA algorithm has o meaig effectively. Total trasmitted power/db MBPSO GA BPSO BPSO-GA MBPSO-GA Number of users Fig.. Total trasmitted power of differet users. Fig. 3 shows the total trasmitted powers of five algorithms uder 10 users whe the umber of subcarriers chages from 10 to 3. The total 13

5 Sesors & Trasducers, Vol. 168, Issue 4, April 014, pp trasmitted power of the system based o MBPSO algorithm is lower about 9 db, 5 db, 4 db tha GA, BPSO ad BPSO-GA respectively. Meawhile, the total trasmitted power based o MBPSO-GA algorithm is slightly lower tha MBPSO. 4 recostructig idividual extreme value ad chagig the update rule of the velocity, the algorithm proposed ot oly miimizes the total trasmitted power of the system but also reduces the umber of iteratio. Simulatio results showed that the MBPSO algorithm has about 9 db, 5 db ad 4 db advatages over GA, BPSO ad BPSO-GA respectively. Ttotal trasmitted power/db MBPSO GA BPSO BPSO-GA MBPSO-GA Ackowledgemets This work was supported by the Natioal Sciece Foudatio of Chia uder grat umbers , ad the Natioal Sciece Foudatio of Natog Uiversity Xigli College uder grat 01K115. Refereces Number of subcarriers Fig. 3. Total trasmitted power uder differet subcarriers. Fig. 4 describes the covergeces of the MBPSO, GA, BPSO ad BPSO-GA algorithms uder 10 users whe 3 subcarriers are used. We ca see that MBPSO ad BPSO algorithms coverged before they iterated about 0 times, GA eeds about 30 times to coverge, ad BPSO-GA will cost about 160 times to coverge. It is obvious that MBPSO ad BPSO algorithms coverge faster tha GA ad BPSO-GA algorithms. Total trasmitted power/db MBPSO BPSO GA BPSO-GA Number of iteratios Fig. 4. Covergeces aalysis of algorithms. From Fig. to Fig. 4, we coclude that MBPSO algorithm proposed is the best oe. 5. Coclusios This paper focused o the subcarriers ad bits allocatio of multiuser OFDM system ad proposed a modified BPSO algorithm (MBPSO algorithm). By [1]. J. H. Reed, J. T. Bermhard, J. M. Park, Spectrum access techologies: the past, the preset, ad the future, Proceedigs of the IEEE, Vol. 100, Special Ceteial Issue, 01, pp []. P. Xue, P. Gog, J. H. Park, D. Park, ad D. K. Kim, Radio resource maagemet with proportioal rate costrait i the heterogeeous etworks, IEEE Trasactios o Wireless Commuicatios, Vol. 11, Issue 3, 01, pp [3]. L. L. Dai, Z. C. Wag, Z. X. Yag, Time-frequecy traiig OFDM with high spectral efficiecy ad reliable performace i high speed eviromets, IEEE Joural o Selected Areas i Commuicatios, Vol. 30, Issue 4, 01, pp [4]. Z. Du, X. Sog, J. Cheg, N. C. Beaulieu, Maximum likelihood based chael estimatio for macrocellular OFDM upliks i dispersive time-varyig chaels, IEEE Trasactios o Wireless Commuicatios, Vol. 10, Issue 1, 011, pp [5]. L. P. David, X. L. Chu, J. Zhag, Dyamic dowlik frequecy ad power allocatio i OFDMA cellular etworks, IEEE Trasactios o Commuicatios, Vol. 60, Issue 10, 01, pp [6]. T. M. Cover, Elemets of iformatio theory, Wiley ad Sos, New York, [7]. J. Jag, K. B. Lee, Trasmit power adaptatio for multiuser OFDM systems, IEEE Joural o Selected Areas i Commuicatios, Vol. 1, Issue, 003, pp [8]. H. Rohlig, R. Gruheid, Performace compariso of differet multiple access schemes for the dowlik of a OFDM commuicatio system, i Proceedigs of the 47 th IEEE Coferece o Vehicular Techology, Phoeix, USA, 4-7 May 1997, pp [9]. T. C. Heg Ale, A. S. Madhukumar, Capacity ehacemet of a multi-user OFDM system usig dyamic frequecy allocatio, IEEE Trasactios o Broadcastig, Vol. 49, Issue 4, 003, pp [10]. E. Bakhtiari, B. H. Khalaj, A ew joit power ad subcarrier allocatio scheme for multiuser OFDM systems, i Proceedigs of the 14 th IEEE Coferece o Persoal, Idoor ad Mobile Radio Commuicatios, Beijig, Chia, 7-10 September, 003, pp [11]. C. Y. Wog, R. S. Cheg, K. B. Lataief, R. D. Murch, Multiuser OFDM with adaptive subcarrier, bit ad power allocatio, IEEE Joural o 14

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