etwork Protocols and Algorthms Adaptve Technque for CI/MC-CDMA System usng Combned Strategy of Genetc Algorthms and eural etwork Sant P. Maty Department of Informaton Technology, Bengal Engneerng and Scence Unversty, Shbpur Howrah, 711 103, West Bengal (Inda) Tel: +91-9830023316 E-mal: santpmaty@t.becs.ac.n Sumanta Hat Dept. of Informaton Technology, Bengal Engneerng and Scence Unversty Shbpur, Howrah, 711 103, West Bengal (Inda) Tel: +91-9883112079 E-mal: sumanta.hat@redffmal.com Receved: January 31, 2012 Accepted: May 16, 2010 Publshed: May 30, 2010 DOI: 10.5296/npa.v41.1330 URL: http://dx.do.org/10.5296/npa.v41.1330 Abstract Multcarrer Code Dvson Multple Access (MC-CDMA) s one of the most promsng technques for hgh bt rate and hgh user capacty transmsson n future broadband moble servces. The use of carrer nterferometry (CI) codes further mproves ths user capacty relatve to the conventonal spreadng codes. Genetc Algorthms (GA) may be used to fnd the optmum transmtted powers that maxmze the channel transmsson capacty as well as to reduce bt error rate (BER) values. On the other hand, neural networks () are traned to optmze the weght factors n mnmum mean square error combnng recever (MMSEC) va back propagaton type algorthm. Optmum values of weght factors gve stable decson varables that lead to mproved recever performance wthout havng the knowledge of channel state nformaton (CSI) and transmt sgnal powers. Decson varables are then used for realzaton of an effcent block parallel nterference cancellaton (BPIC) as multuser detecton (MUD). Smulaton results show that BER performance usng GA- s better than any other exstng works. 34 www.macrothnk.org/npa
etwork Protocols and Algorthms eywords: MC-CDMA, Carrer Interferometry Code, Power Allocaton, PIC, eural etwork, Genetc Algorthms. 1. Introducton On growng demand of data ntensve applcatons such as nteractve and multmeda servces, the need of relable and hgh rate data transmsson over a wreless moble channel becomes essental. However, hgh data rate transmsson ncreases the ntersymbol nterference (ISI) caused by the tme dspersve nature of the rado moble channel. In code dvson multple access (CDMA), multple number of users share the same channel bandwdth at the same tme through the use of (near) orthogonal spreadng codes. So t has potental to provde hgher user capacty compared to ts other close compettors such as tme dvson multple access (TDMA) and frequency dvson multple access (FDMA). Multcarrer code dvson multple access (MC-CDMA), whch s a combnaton of orthogonal frequency dvson multplexng (OFDM) and CDMA, provdes a flexble multpath propagaton. OFDM, (hence MC-CDMA also) reduces ISI by ntroducng a guard nterval whch s a cyclc extenson of any multcarrer sgnal. Development of spreadng codes had drawn a great nterest snce ncepton of CDMA wth an obectve to ncrease n user capacty wth low multple access nterference (MAI). A thorough analyss and comparson of exstng MC-CDMA codes that nclude Hadamard-Walsh, Gold, orthogonal Gold, Zadoff Chu sequences s presented n [1]. Wavelet and subband theores are also used to develop a multvalued set of orthogonal codes [2]. The wdely used Hadamard-Walsh codes support ether users orthogonally or more than users pseudo-orthogonally at the cost of degraded performance. Recently, the concept of nterferometry s exploted to develop set of code patterns wth carefully chosen phase offsets that ensures a perodc man lobe n tme doman and sde lobe actvty at ntermedate tmes. The usage of carrer nterferometry (CI) codes n MC-CDMA system supports users orthogonally and addtonal -1 users pseudo-orthogonally. Moreover, there s no restrcton on the length of the CI codes (.e., I), unlke Hadamard Walsh codes where s lmted to 2 n or 2 n ± 1 (n I) [3]. Accordng to Shannon channel capacty theorem, ncrease n sgnal power ncreases sgnal-to-nose rato (SR) for a gven nose power. Ths n turn mproves the system s channel capacty (c).e. data transmsson rate for sngle user communcaton. However, n the presence of multple users, f all users try to ncrease ther data rates by ncreasng ther transmt power, the users nterfere. As a matter of fact both the sgnal and nterference power ncrease. Consequently, the sgnal-to-nterference plus nose power- rato (SIR) and therefore the users rates saturate at a constant value [4]. In other words, hgh SR values of other users act as strong nterferng effect to the nearby users n multuser envronment transmttng n the same set of subcarrers. Ths suggests that optmum power allocaton s essental n order to ncrease channel capacty and to reduce BER values. Ths s often done by explotng the channel state nformaton (CSI) that s fed back from transmtter to recever [5]. 35 www.macrothnk.org/npa
etwork Protocols and Algorthms In rado moble communcaton, mnmum mean square error combnng (MMSEC) recever has shown to provde the best performance n frequency selectve fadng channel usng the CSI. However, CSI estmaton may not be accurate always and may also be outdated due to feedback delay. To allevate ths problem, calculaton of proper weght factors n MMSEC correlator becomes mportant so that recever performance can be mproved wthout havng knowledge of transmsson power and CSI. Weght factors calculaton may be done through learnng/tranng. Hence, neural network (), due to ts nherent learnng and adaptve capablty, may be used. Furthermore, multuser detecton (MUD) n CDMA can be used effcently to mprove recever performance explotng the cancelaton of MAI. Among varous MAI cancelaton strateges, successve nterference cancelaton (SIC), parallel nterference cancelaton (PIC) and ts varous varants lke partal PIC (PPIC), block PIC (BPIC) have been proposed and related lterature s qute rch. In ths paper, we have developed an effcent power allocaton scheme n CI/MC-CDMA system usng combned Genetc algorthms (GA) and. GA s used here to optmze the transmtted power for each user n respectve subcarrer n order to reduce nterferng effect wth a hope to ncrease channel capacty. On the other hand, s used here to calculate the subcarrer weght factors n MMSEC of dfferent users under frequency selectve Raylegh fadng channel. s traned to optmze the weght factors va back propagaton type algorthm. Experment s carred out through smulaton on frequency selectve Raylegh fadng channel. Results show that channel capacty and bt error rate (BER) performance obtaned for the adaptve system s sgnfcantly better than the non-power adaptve system. The rest of the paper s organzed as follows: Secton 2 presents revew of the pror works, lmtatons and scope of the present work. Secton 3 descrbes system model for synchronous CI/MC-CDMA uplnk system. Secton 4 represents proposed GA based power allocaton algorthm, whle Secton 5 presents asssted MMSEC recever wth BPIC model. Secton 6 presents performance evaluaton and wth dscusson. Fnally conclusons are drawn n Secton 7 along wth the scope of future work. 2. Revew of Pror Works, lmtatons and scope of the present work Channel capacty mprovement by adaptve power allocaton n multcarrer system s an mportant research topc and several solutons are reported n lterature. In [6], Shen et al propose an optmal power allocaton algorthm n ther OFDM system that maxmzes the sum capacty and at the same tme each user mantans a requred data rate. Luo et al [7] studed the power allocaton problem n decode and forward cooperatve relayng system. The algorthm proposed an equal power allocaton wth a channel selecton algorthm based on mnmzng the outage probablty. An algorthm for optmal transmtted power control s proposed by Zhang et al n [8]. They consder controlled transmt power for a two-band system as a lnear functon of the power attenuaton dfference (between the two bands) for a large range of these attenuaton dfferences. 36 www.macrothnk.org/npa
etwork Protocols and Algorthms Multuser detecton n CDMA has ganed wde popularty over the last decade and lterature s qute rch. The optmum multuser detector proposed n [9] acheves sgnfcant performance mprovement relatve to sngle user recevers but the computatonal complexty ncreases exponentally wth the number of users. Ths has motvated the use of low complexty lnear and decson drven suboptmal multuser detecton technques [4]. In [10], Aazhang and Pars mprove the performance of MUD n CDMA system usng. Here s traned for the demodulaton of sgnals va back-propagaton type algorthm. echrots and Manolakos have mplemented an optmal CDMA multuser detector usng Hopfeld n [11]. Also the performance of Hopfeld recever s better compared to any other suboptmal recever. A fast tranng algorthm for A usng feed forward multlayer perceptron archtecture s proposed by Valadon and Tafazoll n [12]. The applcaton of ths algorthm to the problem of multuser detecton n the synchronous drect-sequence code-dvson multple access (DS-CDMA) channel s nvestgated. J. W. Hsun ao et al [13] propose a blnd multuser detector usng a machne learnng technque called support vector machne (SVM) on a chaos-based CDMA system. Smulaton results show that the performance acheved usng SVM s comparable to exstng MMSEC detector under both addtve whte gaussan nose (AWG) and Raylegh fadng condtons. S. Chen et al [14] propose an addtve tranng of usng some stochastc gradent algorthm that ams to mnmze the mean square error (MSE). Ths method developes a nonlnear adaptve near mnmum error rate algorthm called the nonlnear least bt error rate (LBER) for the tranng of. Multlayer perceptron based recever archtecture for the recovery of the nformaton bts of a DS-CDMA users s proposed by Matyas et al n [15]. Here a fast convergng adaptve tranng algorthm s developed that mnmzes BER. A recurrent for solvng the nonlnear optmzaton problem nvolved n multuser detecton n CDMA s proposed by S. Lu and J. Wang n [16]. Compared wth other exstng works, the proposed globally converges to the exact optmal soluton of the nonlnear optmzaton problem wth nonlnear constrants and has relatvely low structural complexty. Revew works reveal the fact that the ont capacty maxmzaton and BER mnmzaton n multuser communcaton system s a non-convex nteger problem and a closed form soluton s dffcult to fnd. Suboptmal solutons are proposed n many cases. Moreover, maorty of the above algorthms suffer from exponental computaton cost wth the ncrease of number of subcarrers and users. Attempt s also made for some of these works to reduce the computaton complexty from exponental to lnear wth the number of subcarrers (users) n OFDM (CDMA) system. However, when these concepts are used for mplementaton n MC-CDMA system, power allocatons are not effcent due to the presence of n-band MAI. Hence, development of an effcent power allocaton algorthm wth low computaton cost for multuser multcarrer system s hghly demandng. It s also seen from the revew works that the use of dfferent soft-computng tools lke GAs, A, fuzzy logc (FL) etc. offer low cost, tractable, ease of mplementaton and optmal solutons n desgnng optmzed communcaton system. To ths am, GA- 37 www.macrothnk.org/npa
etwork Protocols and Algorthms hybrdzaton may be used to desgn optmzed and adaptve system through learnng/tranng. In bref, the contrbutons of the work are as follows: an effcent power allocaton scheme n CI/MC-CDMA system s proposed usng GA- hybrdzaton under power constrant scenaro. GA s used for optmal power allocaton, whle s used to calculate weght factors n MMSEC recever. Stable decson varables so obtaned enable better user groupng that leads to effcent block PIC. The obectve functon of GA s developed from the weghted average of channel capacty and mnmum transmsson power. On the other hand, tan-sgmod transfer functon s used n. Performance of the proposed work hghlghts the relatve merts and demerts wth respectng to the exstng related works. 3. System Model MC-CDMA was frst proposed n [17] and s a combnaton of CDMA and OFDM wth the spreadng codes appled n frequency doman. CI/MC-CDMA s an MC-CDMA scheme employng complex carrer nterferometry (CI) spreadng codes. The CI code, for the k th user, corresponds to [1, e Δθ, k e2δθ k, e (-1)Δθ k ] [9], Δθk = (2π/) *k. The CI codes [3] of length have a unque feature that allows CI/MC-CDMA systems to support users orthogonally. Then as system demand ncreases, codes can be selected to accommodate up to an addtonal (-1) users pseudo-orthogonally. Addtonally, there s no restrcton on the length of the CI code (.e., I) makng t more sutable for dverse wreless envronments. 3.1 Transmtter Model In CI/MC-CDMA transmtter [18], the ncomng data a k for the k th user, s transmtted over narrowband subcarrers each multpled wth an element of the k th user s spreadng code. Bnary phase shft keyng (BPS) modulaton s assumed,.e., a k = ± 1. The mathematcal form of total transmtted sgnal for number of user s gven n Eq. (1) below S(t) = k 1 1 0 a k [n] β k, Cos(2πf t + θ k )*P(t) (1) where f = f c + f and P(t) s a rectangular pulse of duraton T b. The parameter β k, s the ampltude of k th user at th subcarrer whch controls the transmtted power. Subcarrer spacng f s selected such that the carrer frequences f, = 0,1, -1 are orthogonal to each other,.e. f = 1/ T b. 3.2 Channel Model An uplnk model has been consdered where all the user s transmssons are synchronzed. It s assumed that every user experences an ndependent propagaton envronment that s modeled as a slowly varyng multpath channel. Multpath propagaton n 38 www.macrothnk.org/npa
etwork Protocols and Algorthms tme translates nto frequency selectvty n the frequency doman [4]. Frequency selectvty refers to the selectvty over the entre bandwdth of transmsson and not over each subcarrer transmsson. Ths s because 1/ T b << ( Δf C ) < BW where, Δf C s the coherence bandwdth and BW s the total bandwdth. 3.3 Recever Model The receved sgnal wthout dspreadng operaton s wrtten n Eq.(2) gven below r(t) = k 1 1 0 a k [n] β k, α k, Cos(2πf t + θ k + Φ k, )*P(t) +η(t) (2) where α k, s the Raylegh fadng gan and Φ k, s unformly dstrbuted phase offset of the k th user n the th carrer and η(t) represents addtve whte gaussan nose (AWG). The receved sgnal s proected onto orthogonal carrers and s dspread usng th users CI code resultng n r = (r 0, r 1, r 2,.. r -1). The term r s shown n Eq. (3) below r = a [n] β, α, + k 1,k a k [n] β k, α k, Cos(( θ k - θ ) + Φ k, Φ, ) + η (3) where n s a gaussan random varable wth mean 0 and varance 0 /2. ow, a sutable combnng strategy s used to create a decson varable D, whch then enters a decson devce that outputs â. MMSEC s employed as t s shown to provde the best performance n a frequency selectve fadng channel [19]. The decson varable D corresponds to [18] D n = 1 r W, (4) where W, = and, Var( a ) A,, 2 0 (5) A = k 1,k β 2 k, α 2 k, Cos((( θ k - θ ) + Φ k, - Φ, ) 2 (6) wth Var(a ) = 1. Thus, the outputs of all the sngle user detecton of all users generate a decson vector D = [D 1, D 2,. D ] whch s used to obtan the ntal estmates of the data a^ = [a^1, a^2,...a^]. These ntal estmates are then used to evaluate the MAI experenced by each user n the nterference cancellaton technques [20]. Eq. (4) and (5) are effectve when CSI s avalable. However n many cases CSI estmaton n real tme operaton s 39 www.macrothnk.org/npa
etwork Protocols and Algorthms computatonally expensve and may be outdated due to feedback delay. One possble soluton may be to calculate weght factor n eq. (4) through learnng and may be used for blnd detecton. 3.4 Antenna Dversty Dversty usng two antennas, for smplcty, s used here although t can be extended for multple antenna systems to acheve mproved performance at the cost of greater computaton. Receved sgnal from two antennas are then weghted averaged accordng to ther ndvdual SIR. Ths dversty technque has the advantage of producng an acceptable weghted SIR even when none of the ndvdual SIRs are themselves acceptable. The receved sgnal from antenna system 1, derved from equaton (2) s rewrtten here as follows for further analyss. Subscrpt 1 stands for antenna system 1. r(t) 1 = k 1 1 0 a k [n] β k, α k, Cos(2πf t + θ k + ϕ k, )*P(t) +η(t) So the receved sgnal for the th user may be wrtten as (7a) r = a [n] β, α, + k 1,k 1 0 a k [n] β k, α k, Cos(( θ k - θ ) + ϕ k, - ϕ, ) + η, =a [n]β, α, + I MAI + (7b) The frst term of Eq. (6b) s desred sgnal term, whle the second and the thrd terms are MAI and AWG term, respectvely. Multple access nterference IMAI I MAI = k 1,k 1 0 a k [n] β k, α k, Cos(( θ k - θ ) + ϕ k, - ϕ, ) = [I 1 MAI, I2 MAI. Ik MAI ] and the nose term = [n 1, n 2. n k ] (8) For the Raylegh fadng channel and the large value of ''.e. the number of users, the dstrbuton of MAI s approxmately Gaussan (accordng to central lmt theorem). ose s also a Gaussan random varable wth mean 0 and varance 0 /2. Therefore the nterference and nose power s equal to varance of the nterference and nose terms of all the users. ow the nterference power and nose power, shown n Eq. (9) and (10), respectvely can be expressed as follows: σ 2 MAI = Var (I MAI ) (9) and σ 2 = Var () (10) The SIR for the th user of antenna system 1s shown n Eq.(11) below SIR 1 = a 2 [n] * α 2, * β, / (σ 2 MAI + σ 2 ) (11) 40 www.macrothnk.org/npa
etwork Protocols and Algorthms So the total SIR for the antenna system 1 can be wrtten SIR 1 = 1 SIR 1 (11a) Smlarly total SIR for the antenna system 2 can be wrtten SIR 2 = 1 SIR 2 (11b) Total weghted SIR of two-antenna recever system s shown n Eq. (12) below SIR TW = W 1 * SIR 1 + W 2 * SIR 2 (12) where W 1 = 10* SIR 1 /(SIR 1 + SIR 2 ), and W 2 = 10* SIR 2 /(SIR 1 + SIR 2 ) Fg.1 Block dagram for GA based power control and based weght calculaton. 4. Proposed GA Based Power Allocaton Algorthm Ths secton brefly descrbes proposed GA based adaptve power allocaton for the antenna dversty asssted CI/MC-CDMA system descrbed n prevous secton. The proposed system s also shown n Fg. 1 as block dagram representaton. The man obectve of ths work s to maxmze the overall channel capacty as well as mantanng BER performance 41 www.macrothnk.org/npa
etwork Protocols and Algorthms wthn a lmt under the constrant of transmt power. We frst defne obectve functon followed by GA mplementaton for power allocaton. 4.1 Formulaton of Obectve Functon Wreless channel s hghly nonlnear and random n nature. In the present system, t s assumed that durng tranng process CSI s avalable n transmtter (feedback from recever) and s used to modfy sgnal ampltude so that the channel capacty s maxmzed and the probablty of bt error s mantaned wthn the lmt, subect to transmt power constrants. Mathematcally t s a nonlnear nteger problem of conflctng nature and s dffcult to fnd the close from soluton. Hence, one sub-optmal soluton may be used to fnd adaptve power for each user on each subcarrer. The ftness (obectve) functon s shown n Eq. (13) as follows F = λ 1 * k 1 1 0 log 2 [1 + 2 k, 2 MA1 p k, 2 ] + λ 2 * ( k 1 1 0 p, - P total ) (13) k subect to b e B where b e s the probablty of bt error.e BER (bt error rate), B s threshold or upper lmt an acceptable BER value, p k,, P total denote the transmtted power of k th user on th subcarrer, and the maxmum allowable transmt power, respectvely. The symbols λ 1 and λ 2 are the weght factors such that λ 1 + λ 2 =1. We assume equal value for both the weght factor.e. λ 1 = λ 2 =0.5. The expresson of σ MAI may be stated as follows: σ MAI = f (ρ,k, α k,, β k, ) where ρ,k s the cross-correlaton between th and k th users. Incorporatng the correlaton coeffcent ρ, we may wrte the nterference power σ 2 MAI = ρ 2 *α 2 k,*β 2 k, and nose power σ 2 = 0. Puttng these values n eq. (13), we get ftness functon F = λ 1 * k 1 1 0 log 2 [1 + 2 k, 2 k, 2 2 2 * k, k, 0 ] + λ 2 * ( k 1 1 0 β 2 k, - P total ) (14) Our goal s to maxmze eq. (14) subect to b e B. 4.2 GA Based Adaptve Power Allocaton Genetc algorthm (GA) s one of the robust global optmzaton tools wdely explored n solvng complex optmzaton problems n numerous felds. The operatons of GA depend on ntal populaton, crossover and mutaton. In the present study, adaptve power of each user on each subcarrer s calculated based on maxmzaton of ftness functon F defned n eq. (14). The expermental condtons of GA for the present problem are depcted as follows: sze of populaton s 20, number of generatons 100, probablty of crossover per generaton s 0. 8, and probablty of mutaton per bt s 0.09, upper lmt set on MMSEC recever s BER value.e. B=10-2. Dfferent steps for mplementng GA based adaptve transmtter power allocaton are descrbed as follows: 42 www.macrothnk.org/npa
etwork Protocols and Algorthms Step 1: Intalzaton of twenty sets of random values of transmtted power wthn the maxmum lmt allowed by the power constrant channel. Step 2: Calculate the ftness value F for the twenty sets of random transmt power obtaned n step 1. A predefned threshold (F u ) value of F s assgned to dentfy the ft parameter sets. Step 3: The partcular set of transmt powers whch produce the ftness value F above (F u ) are duplcated and the remanng sets are gnored from the populaton. Step 4: A set of bnary strng s generated through decmal-to-bnary converson of all selected transmtted powers. ow crossover and mutaton operaton are done accordng to ther respectve probabltes stated above. Step 5: A new set of transmtted power wthn the range are generated through bnary-to-decmal converson of the strngs obtaned n step 4. Step 6: Repeat step 1 to step 5 for the desred number of teratons or tll a predefned acceptable values for channel capacty and BER (b e ) are acheved. Fg. 2 shows the flow dagram of the proposed GA based adaptve power allocaton. 43 www.macrothnk.org/npa
etwork Protocols and Algorthms Fg.2 Flow dagram for GA based Adaptve Power Allocaton. 5. eural etwork Asssted PIC Model Parallel nterference cancellaton (PIC) s a method to decrease the multple access nterference (MAI) by cancellng the effect of the other users. In ths paper, we compare the BER values between conventonal PIC and PIC wth neural network. The receved sgnal s proected onto orthogonal carrers and s dspread usng th users CI code resultng n r ( r analyss 1, r, r,... r 0 2 1 ), where r corresponds to Eq. (3) s rewrtten here for convenence of r = a [n] β, α, + k 1,k a k [n] β k, α k, Cos(( θ k - θ ) + Φ k, Φ, ) + η (15) The frst term of eq. (15) s the data of th user at th subcarrer, the second term s MAI 44 www.macrothnk.org/npa
etwork Protocols and Algorthms due to the users other than th user and the thrd term s nose term for addtve whte Gaussan nose spread by th user code pattern. Fg. 3 eural network based ampltude estmaton for th user. Here r s the nput to and W s the weght factor of th user at th subcarrer as shown n Fg. 3. So the output of summaton unt I (smlar to eq. (4)) s shown n Eq. (16) below I 1 0 W * r s = 1 W * a,, akk, k, Cos( ( k ) k,, ) 0 k 1, k 1 W * a,, IOS 0 1 0 1 I (16) 0 S where I OS W * a k, k, Cos( ( k ) k,, ) s the MAI due to the users k k 1, k other than th user and I * s the nterference due to nose. ote that Eq. (16) S W contans three terms: desred sgnal term, MAI and nose term, respectvely as n Eq. (7b). The output of for the th user s O. ow we have to apply back propagaton algorthm (BP) to adust the weght factors 0 1 W, W, 1 W on dfferent subcarrers. The target output nformaton for the th user, T. But the computed output for the th user by the neuron s O ^ ^ Mathematcal expresson of error sgnal s gven n Eq. (17) below 45 www.macrothnk.org/npa
etwork Protocols and Algorthms E 1 1 (17) 2 2 ^ ^ 2 2, [ TO] [ ] In a partcular tranng sesson, the error E can be wrtten as a functon of the correlaton values r between the receved sgnal and the sgnature/spreadng waveform and weght factor W lke the followng E f( r, W) Fg. 4 A hypothetcal error functon. Fg.4 shows the plot of a hypothetcal error functon E. Let us assume that the pont X 1 denotes an error n predcton correspondng to a set of ntal weghts. The am of the tranng sesson s to reach pont X 2, at whch the error n predcton E reaches ts mnmum value. In back propagaton algorthm, the error E s mnmzed usng steepest gradent descend method, where the changes n weght factor values can be obtaned as follows [21] E W where represents the learnng rate lyng between 0 to 1. It s known as the W Delta Rule. It s mportant to menton that the smaller the value of, the slower wll be the rate of convergence resultng nto a smoother network. On the other hand, a hgher value of wll make the convergence faster but the resultng network may become unstable. as To update the connectng weght for th subcarrer, the followng relaton may be wrtten W, Updated W,Prevous ΔW where the change n weght factor can be determned as (18) E W (19) W Eq. (18) and (19) ndcate updated weght and change n weght. ow, E can be computed usng the chan rule of dfferentaton as gven n Eq. (20) W 46 www.macrothnk.org/npa
etwork Protocols and Algorthms below. E W E O O I I W (20) Fg. 5 Tan-sgmod transfer functon Actually O s the fnal output of the neuron obtaned after passng through a non lnear flter, known as actvaton functon. As BPS modulaton s used, tan-sgmod functon s used here as transfer functon as t produces values between -1 to 1. Fg. 5 shows tan-sgmod transfer functon. So we have assumed that the neurons lyng on the output layer to have tan-sgmod transfer functon. The output of the th user neuron can be estmated as O I I e e tan sg( I) (21) I I e e where λ s the coeffcent of the transfer functon. ow from eq. (17), (21) and (16) we obtan E O T O (22a) O I, 1 O 1 O (22b) I W r (22c) E Substtutng the values of, O, O I and I W n eq. (20), we get E W T O 1 O 1 O r (22d) 47 www.macrothnk.org/npa
Agan, substtutng the value of E W etwork Protocols and Algorthms from Eq. (22d) n eq. (19), the change of weght factor W can be determned as follows T O 1 O O r W 1 (23) Substtutng the value of target output T n eq. (24), we get the followng equaton O 1 O O r 1O 1 O r O 1O 1 O r W 1 follows We obtan the rate of change of (24) W wth respect to learnng rate ( ) n Eq. (25) as W O 1 O 1 O r 1 (25) T From the above equaton, t may be stated that the rate of change of weght factor W wth learnng rate s largely affected by term. So stronger user s weght updaton must be hgher. Also when the output of neuron O s equal to the target output T, then rate of change of any thng more. W wth respect to learnng rate ( ) wll be zero ths means no need to learn Also the updated value of weght factor can be easly obtaned usng from Eq. (23). T O 1 O O r W, Updated W,Pr evous 1 (26) Based on ths updated weght factor W, n Eq. (26), we have calculated the BER performance usng MMSEC strategy. W 5.1 Block PIC To acheve mproved recever performance through nterference cancellaton, block PIC (BPIC) s employed. Ths operaton takes care the degradng effect of MAI. The decson varables (D ) are mapped to the nterval [0, 1] through normalzaton.e. dvdng each D by the maxmum D value. The four BPIC method s descrbed as follows. 1. The greater the magntude of normalzed decson varable D normal, the stronger the 48 www.macrothnk.org/npa
etwork Protocols and Algorthms nterference effect of the respectve users data. Thus, the users for whch decson varables Dnormal correspondng to the magntude of decsons varables satsfy the condton 0.75 D 1are classfed as very strong user group. Smlar rule s followed for the other normal users, the bts for whch the decson varables satsfy the condton0.50 D 0. 75, 0.25 D 0.50 and 0 D 0. 25 are classfed as strong, weak and very weak user normal groups, respectvely. normal 2. BPIC s performed wthn the group of very strong user by smultaneously cancelng the nterference of all other user bts except the desred one and the very strong data bts are thus estmated. 3. Usng the updated data of very strong users, the nterferences due to these bts are removed and BPIC s employed wthn the block of strong user bts. The strong user s data are thus estmated. 4. Usng the updated data of strong user s bts and very strong bts, the nterferences due to these user s bts are removed. Then BPIC s employed wthn the group of weak users. The same processes are contnued for all other remanng groups. normal 5. The updated decson statstcs of the all user s bts are used to compute the Dnormal values. The BPIC process.e. steps 1, 2, 3, 4 are repeated teratvely untl a desred BER value for the decoded data s acheved or preset numbers of teratons are completed. 6. Performance Evaluaton Ths secton presents performance evaluaton of the proposed GA- hybrdzaton for gan n channel capacty and BER performance. As the desgn goal was to show mproved transmtter performance (channel capacty) usng GA and recever performance usng, smulaton results need to vald the clams. To ths am, performance evaluaton for the adaptve synchronous CI/MC-CDMA system has been nvestgated va MATLAB smulaton n terms of data transmsson rate.e. channel capacty vs number of users, comparson wth [3] and [4], BER performance n MMSEC recever and based BPIC system. Performance results are also reported for dfferent combnatons of the (non) adaptve systems, namely () non adaptve power and normal BPIC (wthout use of both GA and ), () adaptve power and normal BPIC (uses GA but wthout ), () non adaptve power wth based BPIC (wthout GA but usng ), (v) adaptve power control wth based BPIC (usng both GA and ). Smulatons are done at SR = 7dB, number of users varyng from 10 to 80, the number of subcarrer s 24 and maxmum allowable transmt power s 5 unt (mw). 49 www.macrothnk.org/npa
etwork Protocols and Algorthms Fg.6 Performance comparson results for capacty vs. number of the users. Fg.6 shows that the overall system channel capacty (data transmsson rate) vs number of users. As expected, wth the ncrease of number of users, sum capacty ncreases, however, ths ncrease s hgher n the proposed work than the exstng methods [3] and [4]. It s also seen from the graphcal results that channel capacty mprovement n power adaptve system n [4] s sgnfcantly hgher than the non power adaptve system [3]. Ths s due to the fact that power adaptve system takes nto consderaton the effect of MAI whch n turn ncrease n SIR value. An mprovement n channel capacty of the order of ~ 300 s acheved (vertcal axs of the graph s plotted n sem log) n power adaptve system n [4] over non power adaptve system [3]. Furthermore, ths channel capacty mprovement s ~200 order at user 80 for the proposed power adaptve system compared to [4] at 5mW total transmsson power. Channel capacty varaton of the proposed system s also reported for total transmsson power at 6mW and 7mW. Smulaton results also hghlght that an ncrease ~100 order n capacty s acheved for an ncrease n 1 mw total transmsson power. 50 www.macrothnk.org/npa
etwork Protocols and Algorthms Fg.7 Performance comparson results for the lowest capacty vs. number of users. Fg.7 shows that the lowest channel capacty of the worst user (data transmssons rate of the worst user.e the user havng worst fadng gan) vs. number of users. As expected, wth the ncrease of number of users, lowest channel capacty decreases due to MAI effect. Snce the prmary goal of ths power allocaton scheme s to ncrease SIR value, the overall lowest channel capacty s hgher n the proposed work than the exstng methods [3] and [4]. It s also seen from the graphcal results that the lowest channel capacty mprovement n power adaptve system n [4] s sgnfcantly hgher than the non power adaptve system [3]. Ths s due to the fact that power adaptve system takes nto consderaton the effect of MAI whch n turn ncrease n SIR value. An mprovement n the lowest channel capacty of the order of ~ 4 order s acheved (vertcal axs of the graph s plotted n sem log) n power adaptve system n [4] over non power adaptve system [3]. Furthermore, ths channel capacty mprovement s ~5 order at user 80 for the proposed power adaptve system compared to [4] at 5mW total transmsson power. 51 www.macrothnk.org/npa
etwork Protocols and Algorthms Fg.8 BER performance analyss for MMSEC recever wth number of users Fg.8 represents BER performance for MMSEC recever for power adaptve (usng GA) and non adaptve system. MMSEC recever s desgned wth and wthout usng. Smulaton results show that use of GA for power control and use of for weght calculaton offer the best performance. On the other hand, wthout use of GA and, as expected, shows the worst BER performance. Snce s used for effcent recever desgn, non power adaptve but based MMSEC recever offers relatvely better BER performance compared to power adaptve (GA based) but non based MMSEC recever. Smulaton results also show that BER values for 80 users are 0.020 (for both GA-), 0.0235 ( only), 0.0265 (GA only) and 0.0425 (wthout GA and ). Smulaton results hghlght the mportance of not only the adaptve power allocaton but also mproved/weghted correlator recever. BER performance shows are obtaned wthout usng any error-control code (ECC), needless to mantan that BER values would be lowered sgnfcantly usng ECC It s seen that upper lmt for BER value durng smulaton s set to 10-2 whch s not always acceptable n many multmeda communcaton. To mprove further BER performance several forms of multuser detecton n CDMA s reported lke [4]. We fnally ntegrate block PIC scheme n [20] wth the proposed adaptve power allocaton scheme to mprove BER performance at hgh user capacty. In bref, users are classfed nto dfferent groups, namely, very strong, strong, weak and very weak based on the magntudes of decson statstcs. The nterferences wthn the ndvdual groups of large decson magntudes lke very strong, strong, weak and very weak n order of sequence are removed to mprove BER performance for the weakest group. 52 www.macrothnk.org/npa
etwork Protocols and Algorthms Fg.9 BER performance analyss for non-power adaptve normal BPIC Fg.9 shows BER performance for the non power adaptve system (wthout use of GA and ) but usng BPIC. At greater number of users, BER at the ntal stage beng hgh, nterference cancelaton wll not mprove much n BER performance. Although BPIC scheme s employed but BER performance s not satsfactory due to MAI effect at subcarrer level. Multstage nterference cancellaton s used to reduce ths MAI effect. An mprovement n BER performance for users 80 s acheved from 0.1235 to 0.0300 at thrd stage nterference cancellaton of 4BPIC (4 group BPIC) over snge stage PIC scheme. Fg.10 BER performance analyss for power adaptve normal BPIC 53 www.macrothnk.org/npa
etwork Protocols and Algorthms Fg.10 shows BER performance for the power adaptve (usng GA and wthout ) but usng BPIC. An mprovement n BER performance for users 80 s acheved from 0.0885 to 0.0190 at thrd stage nterference cancellaton of 4BPIC over snge stage PIC scheme. As expected, wth the ncrease of number of blocks, BER performance mprovement s acheved at the cost of greater computaton. Fg.11 BER performance analyss for non-adaptve asssted BPIC. Fg.11 shows BER performance for the non power adaptve (wthout GA but usng ) but usng BPIC. An mprovement n BER performance for users 80 s acheved from 0.0805 to 0.0170 at thrd stage nterference cancellaton of 4BPIC over snge stage PIC scheme. Relatve performance mprovement s acheved for 3BPIC, 2BPIC, 1BPIC etc. Fg.12 BER performance analyss for adaptve asssted BPIC. 54 www.macrothnk.org/npa
etwork Protocols and Algorthms Fnally Fg. 12 shows BER performance for the power adaptve (usng both GA and ) and usng BPIC.BER performance results are agan shown for 4BPIC, 3BPIC, 2BPIC wth sngle, two and three tmes/stages nterference cancelaton. An mprovement n BER performance for users 80 s acheved from 0.0735 to 0.0155 at thrd stage nterference cancellaton of 4BPIC over snge stage PIC scheme. umercal values reflect that four block PIC after three stage teratons for power adaptve (usng both GA and ) system can support number of users upto twce the number of subcarrers wth BER of the order of 0.0029. It can support users upto three tmes the number of subcarrers wth BER of the order of 0.0115, whle the smlar values for non-power adaptve (wthout both GA and ) system are ~0.015 and 0.026, respectvely. 7. Conclusons and Scope of Future Work The paper nvestgates the scope of usage of GA for adaptve power allocaton n CI/MC-CDMA system n order to ncrease channel capacty, whle based MMSEC s desgned for mantanng BER value under transmt power constrant. Smulaton results show that channel capacty and BER performance for the proposed power adaptve system have been mproved sgnfcantly compared to non-power adaptve system. Smulaton results show that based four BPIC usng proposed power allocaton can support number of users upto three tmes the number of subcarrers at the end of thrd stage whle BER value s of the order of 0.0115. Future work would extend ths concept for MC-CDMA based cogntve rado system desgn for capacty mprovement n secondary user under the nterference constrant to prmary user. Future work would also consder GA based phase optmzaton of CI codes for reducton n peak to average power rato (PAPR). References [1] Popovc, B. M.: Spreadng Sequences for Multcarrer CDMA Systems IEEE Trans. Commun. Vol.47, pp. 918-926(1992); http://dx.do.org/10.1109/26.771348. [2] Akansu, A.. et al: Wavelet and Subband Transforms: Fundamentals and Communcaton Applcatons, IEEE Commun. Mag. pp. 104-115 (1997); http://dx.do.org/10.1109/35.642839. [3] ataraan, B., assar, C.R., Shattl, S., Mcheln, M., Wu, Z.: Hgh performance mc-cdma va carrer Interferometry codes, IEEE Trans. on Vehcular Tech. 50, pp.1344 1353, (2001); http://dx.do.org/10.1109/25.966567. [4] Maty, S. P., Mukheree, M.: On Optmzaton of CI/MC-CDMA System. Proc. 20th IEEE Personal, Indoor and Moble Rado Comm. Symp., Japan, pp. 3203 3207(2009); http://dx.do.org/10.1109/pimrc.2009.5450194. [5] Care, G., Tarcco, G., Bgler, E.: Optmum Power Control Over Fadng Channels. IEEE Trans. Inform. Theory 45, pp. 1468 1489 (1999); http://dx.do.org/10.1109/18.771147. [6] Shen, Z., Andrews, J.G., Evans, B.L.: Adaptve Resource Allocaton n Mult-user 55 www.macrothnk.org/npa
etwork Protocols and Algorthms OFDM Systems wth Proportonal Rate Constrants. IEEE Trans. on Wreless Commun. 42, pp. 2726 273( 2005); http://dx.do.org/10.1109/twc.2005.858010. [7] Luo, J., Blum, R.S., Cmn, L., Cmn, L., Hamovch, A.: Power Allocaton n a Transmt Dversty System wth Mean Channel Gan Informaton. IEEE Commun. Lett. 9, pp. 2726 2737 (2005); http://dx.do.org/10.1109/lcomm.2005.1461682. [8] Zhang, J., Matolak, D.W.: Transmtted Power Allocaton/control for Multband MC-CDMA, Journal of Physcal Commun. Vol. 3, pp.139 146 (2009); http://dx.do.org/10.1016/.phycom.2009.08.001. [9] Verdu, S.: Mnmum probablty of error for asynchronous Gaussan multple access channels, IEEE Transactons on Inform. Theory, vol. 32, pp. 85-96(1986); http://dx.do.org/10.1109/tit.1986.1057121. [10] Aazhang, B., Pars, B. P. and Orsak, G. C. : eural etworks for Mult-user Detecton n Code-Dvson Multple-Access Communcatons, IEEE Transactons on Communcatons, Vol.40, o.7, pp.1212-1222(1992); http://dx.do.org/10.1109/26.153366. [11] [11] echrots, G. I. and Manolakos, E. S.: Hopfeld eural etwork Implementaton Of the Optmal CDMA Mult-user Detector, IEEE Transactons on eural etworks, Vol.7, o.1, pp.131-41(1996); http://dx.do.org/1045-9227(96)00159-2. [12] Valadon, C. and Tafazoll, R.: A Fast Adaptve Multuser Detector For DS-CDMA Communcatons Based On An Artfcal eural etwork Archtecture, Proc. Of 5th IEEE Internatonal Symposum on Spread Spectrum Technques and Applcatons, Vol. 3, pp. 873 877(1998); http://dx.do.org/10.1109/isssta.1998.722503. [13] ao, J. W.-H., Berber, S. M. and ecman, V.: Blnd Multuser Detector for Chaos-Based CDMA Usng Support Vector Machne, IEEE Transacton on eural etworks, Vol. 21(2010); http://dx.do.org/10.1109/t.2010.2048758. [14] Chen, S., Samngan, A.. and Hanzo, L. Adaptve ear Mnmum Error Rate Tranng for eural etworks wth Applcaton to Multuser Detecton n CDMA Communcaton Systems, Sgnal Processng, 85(7). pp. 1435-1448 (2005); http://dx.do.org/10.1016/.sgpro.2005.02.005. [15] Matyas, J. D, Psaromlgkos, I., Batalama, S. and Medley, M. J.: Fast Convergng Mnmum Probablty of Error eural etwork Recevers for DS-CDMA Communcatons, IEEE Transactons on eural etworks, Vol. 15, pp. 445-454 (2004); http://dx.do.org/10.1117/12.487977. [16] Lu, S. and Wang, J.: Blnd Adaptve Multuser Detectve Usng a Recurrent eural etwork, Proc. In Int. Conf. on Communcatons, crcuts and systems, vol. 2,pp. 1071-1705(2004) [17] Yee,., Lnnartz, J. P. and Fettwes, G.: BER of multcarrer CDMA n ndoor wreless networks, IEEE Personal Indoor and Moble Rado Communcatons (PIMRC) Int. Conference, Sept. 1993, Yokohama, Japan, pp. 109-113. [18] Thppavaula, V. and ataraan, B.: Parallel Interference Cancellaton Technques for Synchronous Carrer Interferometry/MC-CDMA Uplnk, IEEE conf. on Vehcular Technology, pp. 69-78 (2004); http://dx.do.org/10.1109/vetecf.2004.1400032. [19] Ca, X. and Akansu, A..: Multcarrer CDMA Systems wth Transmt Dversty, IEEE Trans. On52nd Conf. on Vehcular Technology, vol. 6, pp. 2817-2821(2000). 56 www.macrothnk.org/npa
etwork Protocols and Algorthms [20] Maty, S.P., Hat, S., Maty, S.: Dversty-Asssted Block PIC for synchronous CI/MC-CDMA uplnk system usng Genetc Algorthm. In: Proc. of Thrd IEEE Int. Conf. on Industral and Informaton Systems (ICIIS 2008), pp. 1 6. Indan Insttute of Technology, haragpur (2008), Inda; http://dx.do.org/10.1109/iciifs.2008.4798486. [21] Prathar, D..: Soft Computng, 1st Edton, arosa Publshng House Pvt. Ltd, 2009. Copyrght Dsclamer Copyrght reserved by the author(s). Ths artcle s an open-access artcle dstrbuted under the terms and condtons of the Creatve Commons Attrbuton lcense (http://creatvecommons.org/lcenses/by/3.0/). 57 www.macrothnk.org/npa