Multi-user Detection Based on Weight approaching particle filter in Impulsive Noise

Transcription

1 Internatonal Symposum on Computers & Informatcs (ISCI 2015) Mult-user Detecton Based on Weght approachng partcle flter n Impulsve Nose XIAN Jn long 1, a, LI Sheng Je 2,b 1 College of Informaton Scence and Engneerng, Henan Unversty of Technology, Zhengzhou, , Henan, P.R. Chna. 2 College of Informaton Scence and Engneerng, Henan Unversty of Technology, Zhengzhou, , Henan, P.R. Chna. a @vp.sna.com, b lshengje0318@163.com Abstract. To solve the problem of partcle degeneracy and sample mpovershment n conventonal partcle flter, we propose the weght approachng partcle flter(wapf) to ncrease the partcle dversty before resamplng step for adaptve mult-user detecton (MUD) n synchronous code dvson multple access (CDMA) system.. In the resamplng step, partcles are classfed nto two groups accordng to ther partcle-weghts, and then the partcles wth the smaller weghts are replaced by the mean of the two group partcles, so that the partcles can approach from the low lelhood regon to the hgh lelhood regon. Smlar to the carrer wavemethod, the chaotc perturbaton resamplng method adopts the chaotc varable wth the property of global ergodcty to amelorate the dversty of samples and reduce the computaton load. Smulaton results demonstrate the feasblty of the mproved partcle flter. Keywords: Partcle flter, Mult-user detecton, weght approachng, Non-Gaussan nose 1. Introducton Mult-user detecton technology s a good soluton to effectvely resst multple access nterference (MAI) and dstance effect n synchronous code dvson multple access (CDMA) system[1]. In 1993, N.J.Gordon recommended to use partcle flter (PF) method to trac the sgnal n the lterature [2]. Ths technque can be appled to any nonlnear and non-gaussan systems that can be The authors - Publshed by Atlants Press 734

2 represented by a state-space model. Ths feature maes the algorthm has strong adaptablty. A lot of nose n actual lfe are non-gaussan nose[3]. Partcle flter algorthm does not requre the nose model s Gaussan nose. So PF algorthm can be appled n the feld of mult-user detecton, can effectvely reduce the bt error rate and has applcable value. Ths paper s organzed as follow: Secton 2 ncludes the model of the CDMA system and the presentaton of two nds of non-gaussan noses; the applcaton of standard partcle flter algorthm for mult-user detecton s presented n Secton 3; the applcaton of mportance of weght approachng partcle flter algorthm for mult-user detecton s presented n Secton 4; Smulaton results and conclusons are descrbed n Secton CDMA system model Consder a synchronous CDMA system wth K users. The -th receve sgnal s [1][4]: r ( t) K 1 A ( t) g ( t) b ( t) n( t) In the formula, (1) A means the ampltude of the -th sgnal; g means spread spectrum waveform of the -th sgnal; K s 1 ; n(t) s bacground nose. Judgment performed by a matched flter, output, expressed as: 1 T b g ( t) g ( t dt, ) Tb 0 Can be obtaned by expandng: T T K y r t) g ( t) dt A 0 ( t) g 0 1 A b MAI z b means the -th user data, the value ( A b means the sgnal of the -th user; y for the K-th matched flter ( t) b ( t) n( t) g z s nose; nterference (MAI) whch s generated by other users. ( t) dt (2) (3) MAI s multple access 735

3 In order to facltate processng and analyss, the receved vector can be expressed as matrx. y RAb z Where A daga1, A2,, A ampltude. b b, b2,, of 1 b (4) s a dagonal matrx of receved sgnal s user data, R s symmetrc correlaton matrx K K order (,, ). z z, z,, T 2. 1 Colcy factorzaton can be used to R. such that R F T T T y F y F FAb F z FAb z z T F. So we obtan: y s called the whtened matched flter output. Expresson of the receved sgnal s as follows: y K l1 F, l a b z l l (6) On the bass of the spatal model, the purpose of mult-user detecton s to b 1: b1, b2,, b from the matched flter output y y, y, 1: 1 2, y. detect sgnals of the users sgnals (5) 3. Non-Gaussan nose smulaton In practce, there are some nds of nose that they are not happen often, but wth a strong mpact. These nds of nose are not Gaussan nose, such as thunder and lghtnng, all nds of machne motors, etc. do not have Gaussan nature. The followng brefly dscusses two models of the non-gaussan nose. A. Laplace nose Laplace probablty densty functon (PDF) has an obvous smearng. Ths s dfference between the Laplace PDF and the Gaussan PDF. Laplace probablty densty functon[3]: 1 2 p( x) exp( x ), x (7) 736

4 2 In the formula, parameter s varance or power of nose. B. Alpha nose If X s subject to the Alpha stable dstrbuton, ts characterstc functon s: u exp jau u 1 j sgn( u) ( u, ) (8) tan( / 2),, 1 ( u, ) (2 / ) logu,, 1 (9) 1, u 0 sgn( u ) 0, u 0 1, u 0 (10) In the formula, (0,2] s characterstc ndex whch determnes the degree of the dstrbuton pulse characterstcs. When 2, t s Gaussan dstrbuton. When 0 2, ths dstrbuton s called fractonal lower order Alpha stable dstrbuton. 1 1 s called symmetry parameter whch can control the gradent of the dstrbuton. When 0, t s a symmetrc -stable dstrbuton, referred to as S S. s called scatterng coeffcents whch can control the dsperson measure about the samples relatve to the mean. The nose power can be expressed approxmately as 2, but 2 s not equal completely to the true nose power. Sgnal to Nose Rato (SNR) can be expresses as ( S s the sgnal power). SNR S / 2 4. Mult-user detecton based on standard partcle flter algorthm The partcle flter s a Monte Carlo method based on Bayesan theory. Its core dea s that usng the samples and ther correspondng weghts to express the posteror probablty densty functon then we can use the posteror probablty densty to obtan the estmated value of the state. 737

5 The man steps of mult-user detecton based on partcle flter are as follows [5]: Step 1: Samplng for the -th user, mang x q( x x, y ). : 1: 1 1: Step 2: calculate the weghts of the partcles. p( y x ) p( x x 1) 1 (, ) q x x 1: 1 y 1: Step 3: Normalzng the weghts. N s / 1 (11) (12) Step 4: Resamplng for the partcles. Step 5: Accordng to the Maxmum A Posteror rule to estmate the sgnals of the -th user. Step 6: Turn to step1, and estmatng the sgnals of the next user. 5. Mult-user detecton based on weght approachng partcle flter Partcle degradaton s a major problem of conventonal partcle flter. Resamplng can solve problems of partcle degradaton to some extent, but t also brngs a partcle depleton problem[3]. The so-called partcle depleton s that those partcles havng a larger weght s selected tmes, lower weght partcles gradually dsappear after resamplng. It maes that partcles loss the dversty and are not suffcent to descrpton posteror probablty. To solve these problems, ths paper presents a new partcle flter mproved method that weght approachng partcle flter algorthm (WAPF). By preprocessng the predcton set of partcles and ncreasng effectve number of partcles well mprove the performance of conventonal partcle flter. The basc dea of weght approachng partcle flter algorthm s that: After each samplng, the weght of the partcles are sorted n ascendng order; A number of hgh-weght partcles that are selected referrng to the effectve sample of fssle breedng start to do fssle breedng. The method of fssle breedng s startng from the smallest partcle weght, fndng the weghted average between t and hgh weght partcle, usng the weghted average regeneraton partcle to cover orgnal low weght partcles n turn, to regenerate partcles as samplng partcles recalculatng the weght of partcle. So the 738

6 partcles can approach from the low lelhood regon to the hgh lelhood regon. If resamplng condtons are met, the next step s chaotc perturbaton resamplng (CPR). Its man dea s to ntroduce varablty thnng n evolutonary algorthms. The maxmum weght of partcles s gong to be chaotc mutaton and the number of varaton of partcles s the number of degraded partcles. Then the weghts of varaton of partcles were calculated, varaton of partcles are used to cover degraded partcles for state estmaton. CPR's process s summarzed as follows: IF < threshold N eff x are sorted by ts weght j 1 : N Neff * x x chaos( Q) * x s the largest weght partcle, chao(q) j 1 N FOR perturbaton, meanwhle requre all new weghts / mean chaotc, Q s chaotc varable. END END In summary, the steps of mult-user detecton based on auxlary partcle flter are as follows: Step 1: Samplng for the -th user, mang x : q( x x1 : 1, y1 : ). Step 2: Accordng to equaton (11) to calculate the weghts of the partcles. Step 3: Normalzng the weghts accordng to equaton (12). Step 4: Fssle breedng accordng to the above. Step 5: Recalculated weghts. If N eff < threshold, CPR for the partcles. Step 6: Accordng to the Maxmum A Posteror rule to estmate the sgnals of the -th user. Step 7: Turn to step1, and estmatng the sgnals of the next user. 6. Smulaton results and conclusons Consder a synchronous CDMA system, and we select 5 users, nformaton bts, 31-bt gold spread-spectrum code and the user power partal value s 10. Channel noses are addtve Gaussan nose, Laplace nose and Alpha stable nose. The range of sgnal to nose rato (SNR) for all users s -4~10 db. The number of partcles s

7 Fgure1: We can fnd that the performance of the WAPF algorthm s better than the PF algorthm n Gaussan nose. WAPF algorthm can mprove the performance of the system. Fgure1. The BER of PF detecton and WAPF detecton. Fgure2. BER of WAPF detecton under three nds of nose Fgure2: Ths fgure analyzes the error code performance of WAPF detecton amng to Gaussan nose, Alpha stable nose and Laplace nose. We can see from the Fgure 2 that the error code performance of the Gaussan noses and the Laplace nose are almost same. The result also proves that the applcablty of the WAPF algorthm s well n the non-gaussan system. Therefore, ths algorthm has practcal reference value. 740

8 Acnowledgment Sncerely than the Scentfc Research Fund of Henan Unversty of Technology. References [1] Dou zhongzhao, Le xang, CDMA Wreless Communcatons Theory, Tsnghua Unversty Press, Chna, [2] N.J.Gordan, D.J.Salmond, A.F.M.Smth, Novel approach to non-lnear and non-gaussan Bayesan state estmaton, IEEE Proc.F, vol.140, no.2, pp , [3] Steven M.Kay Edted, translated by Peng-fe Luo, Statstcs based on sgnal processng: estmaton and detecton theory, Electronc Industry Press, Chna, [4] Xan Jnlong, Lu Zh, Zhang Qnghu, The Applcaton of Accelerated ECM Algorthm to MUD, Internatonal Journal of Dgtal Content Technology and ts Applcatons, vol.6, no.2, pp , [5] Zhmn CHEN, Yumng BO, Panlong WU, Mngfeng YIN. Quas-Monte Carlo Partcle flter Fault Prognoss Algorthm Based on GRNN, JCIT, vol.7, no.7, pp ,