Collision Resolution Based on Independent Component Analysis

Transcription

1 Collson Resoluton Based on Indeendent Comonent Analyss X Chen, Qnyu Zhang Communcaton Engneerng Research Center Harbn Insttute of echnology Guangdong, P.R.Chna zqy@ht.edu.cn Ye Wang Communcaton Engneerng Research Center Harbn Insttute of echnology Guangdong, P.R.Chna Abstract hs aer roosed a retransmsson scheme based on the blnd searaton method, named ndeendent comonent analyss(),to resolve the collson roblem n random access wreless network and a new method to devse the Identfcaton(ID)sequences whch can resolve the roblems of and hel to reduce the length of ID sequences. he roosed method can work effectvely under the fast-varyng and slow-varyng channels from the smulaton results. Keywords- blnd searaton, retransmsson scheme, random access I. INRODUCION In ths eoch of the eruton of nformaton, the demand of the communcaton servces s ncreasng dramatcally, so the tradtonal fxed bandwdth allocaton schemes whch have been successfully used to multlex a lot of users n the same cell whle rovdng rotecton from mult-user nterference are extremely neffcent. here are many methods to resolve the collson roblem from sgnal searaton technques and varous medum access rotocols. In [], satsans frst roosed a scheme called network-asssted dversty multle accesses (NDMA) whch exlots network dversty to searate the collded ackets. Subsequently some of mroved schemes were roosed. However, all these methods just only get the better throughut through the dfferent retransmsson schemes. For examle, Ru Ln roosed a new wreless network medum access rotocol based on the cooeraton n [].Dr. WeJ resented a novel medum access scheme to deal the unfarness selecton of the relay[3]. he drawbacks of these schemes are not only that they need to detect the channel nformaton erfectly, but also the length of the ID sequences s so long whch reduces the effcency of transmsson. If the channel vares fast, the recever must detect the channel frequently. he result of the channel detecton also decdes the erformance ofmaxmum lkelhood (ML) and zero forcng(). So f the detecton of the channel s not erfect, the erformance of the decoder must be worse. In addton, these schemes detect the actve users based on tranng sequences embedded n each user s acket head. In order to make the detecton roblem tractable, those tranng (or ID) sequences are orthogonal to each other [8].he orthogonalty of the ID sequences makes the system senstve to synchronzatonand multath effects. On the other hand, the length of the ID sequences s the same as the number of the users, so f there are a number of users n the system, the longer overhead may be substantal whch has a negatve mact on the bandwdth that carres the acket ayload []. o overcome these drawbacks, there have been many consderable researches on blnd and sem-blnd searaton n recent years. he concet of s a relatvely effectve method. Indeendent Comonent Analyss () was frst used n the unverse of neural network model n the 8th of century. Untl 9th, some research grous brng n some successful methods, such as demo of the cocktal arty roblem. can fnd every eole s voce wave from the mxture sgnals. A.J.Bel and.j.sejnowsk resented ther methods based on Infomax [4], [5]. It s further detaled by the method called natural gradent method whch s devsed by S.I.Amar and hs colleagues, and establshed the relaton wth the MLand Cchock- Unbehauen method. Some years later, JuhaKarhunen roosed the fx ont method [6],[7].hs method makes much contrbuton on theroblem of the large-scale alcatons. hs aer rooses a method whch combnesthe retransmsson scheme wth to resolve the collson roblem and a new method to desgn the ID sequences to resolve the roblems of. Because every user s sgnal s ndeendent wth each other and non-gaussan dstrbuton, all these rovde the condtons for the alcaton of. hs algorthm converges very fast, and can solve the collson roblem when there are many ndeendent sources. Because the algorthm doesn t need to set the learnng rate and any other arameters, so t s much robust and smle. hrough searchng the drecton of the maxmum nongausssnty of the receved mxture sgnal matrx, can searate the mxture sgnals wthout the knowledge of the channel coeffcents; In addton, log the length of ID sequences s only ( J ) + (J s the number of the users n the system). he rest of the aer s organzed as follows. In Secton II, we descrbe the system model. he algorthm descrton and a new method that devse the ID sequences are ntroduced n Secton III. he smulatons and analyss are carred out n Secton IV and we ut conclusons n Secton V. II. SYSEM MODEL Fg. shows the model of the retransmsson model based on. In ths aer we consder a wreless cellular network, 493

2 where there are J users. Every nodess equed wth only one antenna.he system s slotted and every user transmts a acket consstng of N symbols n one slot. Once the collson s detected, the system enters a retransmsson eoch.assume that K( K J )users are collded n the nth slot. At ths tme all the nodes and the destnaton wll know the number of the collson users, and then the BS wll send a control bt to all users n the system ndcatng the begnnng of the retransmsson eoch. In the followng K -slots, the collson users retransmt the ackets whch they transmtted durng slot n(collson slot)and the other users whch don t send the data durng slot n kee slence durng ths eoch. Fg. shows the two users model. We can see that the collson haens when user anduser send the data smultaneous n slot N. In the next slot, two collson users wll retransmt ther ackets whch send durng slot n. wd (n) x (n ) x ' ( n ) wd (n+k ) x k (n ) x 'k ( n ) Fgure. Multle Packet Retransmsson Scheme Based On C ollson U SER N + slo t N sl ot BASE SAION Fgure. wo users retransmsson In ths aer, we consder a fast-fadng channel. he mxture sgnals n the recever can be exressed by the followng model: YK N = H K K XK N + WK N () Y = [ y N ( n ),, y N ( n + K )] denotes the matrx of y (n ) the observe sgnals durng K slots at the base staton, N conssts of a mxture of collson data durng slot n, whch has N bts; users n X= xn,( n),, xn,k ( n) slot n, W= wn ( n),,wn ( n+ K ) E {Y'Y' } andd denotes the data of K collson xn, (n) s the th user s data; denotes the nose matrx; Durng the K slots, the matrx of the channel coeffcents between the collson users and BS s exressed as: ad ( n ) akd ( n ) H= ad ( n + K ) akd ( n + K ) () akd ( n ) s the channel gan between the Kth user and the BS durng slot n. s the D = dag ( d,, d n ) dagonal matrx of ts egenvalues,.he utlty of whtenng s resdes n the fact that the new mxng matrx H orthogonal. hen we use the searated matrxp to make a lnear change on Y. So we can get a K-dmensons outut vectorz. Our goal s to make Z aroach to the source sgnals, beng the estmaton of the ndeendent comonents X, =X Z = P Y = P HX (5) P = [,,, k ] s the nverse matrx of H. III. US ER Because the users sgnals dstrbute non-gaussan and are ndeendent wth each other, and the channel coeffcents matrx s full rank, the can be used to searate the sgnals. Before the alcaton of the algorthm, we rerocess the data through centerng and whtenng to make t a zero-mean and unt-varance varable. Centerng Y' = Y E [ Y ] (3) Whtenng Y = ED- EY ' = HX (4) E s the orthogonal matrx of egenvectors of ALGORIHM DESCRIPION A. Algorthm ntroducton From the nformaton theory: A Gaussan varable has the largest entroy among all random varables of equal varance. o obtan a measure of non-gaussan that s zero for a Gaussan varable and always nonnegatve, we should use the negentroy whch can measure the ndeendence among the sgnals. he maxmum of the outut negentroy means that the outut sgnals are ndeendent wth each other, so we can searate the mxture sgnals. herefore, the negentroy s often used as the target functon of the blnd searaton. he exresson of the negentroy s K { } J ( Z ) a E G ( Z ) E G (V ) (6) a are some ostve constants, and V s a Gaussan varable wth zero mean and unt varance. he varable Z s assumed to be of zero mean and unt varance, and the functon Gs anonquadratc functon. In the case where only one nonquadratc functon Gs used, the aroxmaton becomes = J ( Z ) E {G ( Z )} E {G (V )} (7) G (u ) = u 4 Here we choose. hen the aroxmaton functon of negentroy s exressed as: { } J ( P Y ) E G ( Y ) E {G (V )} J ( P Y ) (8) s maxmal, t means that the When negentroy th source sgnal s searated. It notes that the maxma of the 494

3 aroxmaton of the negentroy of Y are obtaned at E Y E Y certan otma of. he otma of under E {( Y ) } = = are obtaned at onts: the constrant E ' G ( Y ) = E Y g ( Y ) = (9) Here g(x) s the dfferental of G(x). We can solve ths by Newton s method E Y g ( Y ) ' = E Y Y g ' ( Y ) E Y g ( Y ) = E g ' ( Y ) () Equaton () can be further smlfed by multlyng E g ' ( Y ) both sdes by, then ' E g' ( Y ) = E g' ( Y ) E Yg ( Y ) = ' E g ' ( Y ) (3) If the algorthm s not convergence, the above rocess wll be reeated. Because the algorthm needs to estmate K vectors (from to k ), to revent dfferent vectors from convergng to the same maxma, t decorrelates the Y,, k Y after every teraton. In ths aer oututs we use a symmetrc decorrelaton P = ( PP ) - P (4) he rocess of the algorthm s dected as follow: Select m, the number of the ndeendent comonents. Intate all, =,,..., m. Every has a ordnary norm. he matrx P should be decorrelated at the 4th method. For =,,m, refresh : E Y g ( Y ) E g ' ( Y ). P = (,, m ) : hen decorrelate P ( PP ) -/ P, If the teraton s not convergence, then return 3. From the above, t can be seen that the method doesn t need to obtan the mxture matrx coeffcents. B. orthogonal to the others. It overcomes the drawbacks of the log ( J ) ) bnary tradtonal ID sequences. We use m(m= numbers to exress J users. hen we use the dea of the dfferental encodng to encode the k bnary numbers. For examle, there are 3 users n the system, and the 5th user s ID sequence s (,,,,) and we encode t by dfferental log ( J ) +. BPSK encodng (,,,-,-,-), wth the length hough the changes the lus-mnus of the searated sgnals, the relatonsh between the codes s not changed. IV. () nto () and we can Substtutng obtan: = E Y g ' ( Y ) E g ' ( Y ) () hen renormalze : + = to whch user. he reason s that both H and X beng unknown, t can freely change the order of the terms n (). So n the stage of user detecton, ID sequences are needed to dentfy the users; Secondly, the sgn of the searated sgnals may be changed, such as the nformaton of user changng from [, -,, -] nto [-,, -, ] after the rocessng. In ths aer, we desgn the new ID sequences for the roblems of. he length of the new ID sequences s only log ( J ) + and every user s ID sequences are not to be User detecton has two roblems hard to solve: Frst, t s dffcult to dentfy the order of the ndeendent comonents whch means that we can t make sure the searated sgnals belong SIMULAION Frst, we use two users model to see whether the can searate the mxed sgnals. he channel matrx durng two slots s H = And the users ackets are encoded by BPSK. he SNR were db. From the Fgure 3, t s obvous that can comletely searate the mxture sgnals.so the collson n the random access network s seem to be resolved by. We smulate the throughut of the roosed scheme n ML. Here the throughut of the system s defned as: successful receved ackets throughut = retransmsson tmes (5) he total number of users n the system s J=3, and the users ID sequences are encoded by dfferental encodng as above ntroducton. We defne traffc load λ, as the number of ackets that are fed nto the network durng a secfc tme slot. Every user s data s encoded bybpsk. he channel between eachuser and the BS s Raylegh fadng and every acket contans 44bts. he smulaton s under SNR=dB scenaros. We comlete trals. In one tral, each user sends out the acket wth robablty λ / J.we set bt error rate s at most. and ackets receved at the AP wth bt error rate hgher than. are consdered lost or corruted. If the number of teraton of s over tmes, we thnk the algorthm s false and the acket s lost. We can see that the throughut of method s better than the method wthout the coeffcents of the channel. hrough the throughut of s worse than ML, t s known that the comlexty of ML s very hgh and the comlexty of s lower than ML. Fg. 5 shows the relaton between the throughut and SNR, t exresses that 495

4 the throughut s become lower as the SNR decreases. Here SNR s from db to db. Fg. 6 shows that the throughut of and at the data rate R=56kb/s and R=Mb/s, we can see that when the data rate s Mbs, the channel s slow varyng channel, thus the channel coeffcents are correlated. Both throughut decrease a lttle, but the result of s stll better than. From the above smulatons, algorthm can searate the mxture sgnals very well. Because the retransmsson scheme tself do have some drawbacks, so the result of the s a lttle bad. But we can see that the result of s stll better than based on the same scheme. source sgnal searated sgnal hroughut ML raffc Load ML Fgure 5. he throughut of the,, ML.R=56kbs, user source sgnal searated sgnal hroughut.. R=Mb/s R=56Kb/s R=Mb/s R=56Kb/s raffc load Fgure 6. hroughut versus traffc load of, : R=Mb/s and R=56kb/s user Fgure 3. wo users model:source sgnals and searated sgnals hroughut.8. decrease raffc Load 4 SNR Fgure 4. hroughut vs SNR 6 8 V. CONCLUSION In ths aer, we resent a new multle ackets retransmsson scheme based on and devse the new ID sequences. can searate the mxture sgnals wthout the knowledge of the channel, so t can reduce the BS staton comlexty. Accordng to the smulaton results, the method can get a better erformance comared wth. he new ID sequences can mrove the transmt effcency and solve the roblems of the. So the roosed scheme s a fully blnd random access technque wth hgh erformance. REFERENCES [] M.K.satsans, R.Zhang, and S.Banerjee, Network-Asssted Dversty for Random Access Wreless Networks, IEEE rans. Sgnal Process, vol. 48,. 7-7,Mar. [] Ru Ln and Athna P.Petroulu, A New Wreless Nerwork Medum Access Protocol Basedon Cooeraton, IEEE ransactonson Sgnal Processng, vol, 53, No.. December 5. [3] J We, Communcaton and Informaton Systems. School of electroncs, nformaton and electrcal engneerng Shangha Jao ong Unversty, December 8. [4] A.J.Bell and.j.sejnowsk. A non-lnear nformaton maxmzaton algorthm that erforms blnd searaton. In Advances n Neural Informaton Processng Systems 7 ages he MI Press, Cambrdge, MA 995. [5] A.J.Bell and.j.sejnowsk. An nformaton maxmzaton aroach to blnd searaton and blnd deconvoluton. Neural Comutaton, 7: 9-59,

5 [6] A.Hyvarnen and E.Oja.A fast fxed-ont algorthm for ndeendent comonent analyss.neural Coutaton, 9(7): , 997. [7] A.Hyvarnen. A famly of fxed-ont algorthms for ndeendent comonent analyss.in roc.ieee Int.Conf.on Acoustcs, Seech and Sgnal Processng, ages , Munch, Germany, 997. [8] R. Zhang, N. D. Sdrooulos, and M. satsans, Collson Resoluton n Packet Rado Networks Usng Rotatonal Invarance echnques, IEEE rans. Com. submtted. [9] M. satsans, R. Bang and S. Banerjee, CollsonResoluton echnques for Wreless Random Access Networks wthout hroughut Penalty, Proc. of IEEE 998 Internatonal Conference on Unversal Personal Communcatons llclipc98). Florence. Italy, Oct. 5-9, 998, [] Ozgul, B.; Delc, H.;, "Blnd collson resoluton for moble networks n fast-fadng channels," Communcatons, 3. ICC '3. IEEE Internatonal Conference on, vol., no.,. 8-3 vol., -5 May 3 497