Blind Interference Suppression for DS/CDMA LEO Satellite Communication Systems

Transcription

1 Blid Iterferece Suppressio for DS/CDMA LEO Satellite Commuicatio Systems Stepha Fischer, Berd-Ludwig Weig, Volker Küh, Karl-Dirk Kammeyer Uiversity of Breme - Departmet of Commuicatios Egieerig - P.O. Box D Breme - Germay Phoe: (49)421 / / Fax: (49)421 / , fischer@comm.ui-breme.de ABSRAC his paper focuses o iterferece suppressio aspects for DS/CDMA (Direct Sequece / Code Divisio Multiple Access) LEO (Low Earth Orbit) satellite commuicatio systems. he iterferece of other users represets a serious problem for LEO satellite CDMA systems. he applicatio of iterferece suppressio systems is a promisig approach to mitigate the multiuser problem. With the cocetratio o the forward lik the user has o iformatio about the other users ad so a blid algorithm is eeded. Furthermore, due to the movemet of the satellite the user s costellatio i a beam varies ad therefore a adaptive algorithm must be implemeted. I this paper three blid adaptive iterferece algorithms are applied to a LEO satellite commuicatio system ad their performace is compared. he LMS (Least Mea Squares) detector has a good performace compared to the covetioal receiver, aside from havig a slower covergece. he AS-LMS (Adaptive Step Size Least Mea Squares) algorithm is based o the LMS detector with a adaptive step-size. Its adaptatio rate is improved ad also i the steady state it performs better tha the LMS. he best performace was that of the RLS (Recursive Least Squares) algorithm, however, this method requires a icreased processig power. 1. INRODUCION I the last years, mobile wireless commuicatio became more ad more importat. I order to provide for future worldwide wireless commuicatio, satellite commuicatio systems such as LEO (Low Earth Orbit) offer a possible solutio. Especially i areas with low populatio desity or low ifrastructure, satellite commuicatio is superior to terrestrial mobile commuicatio. Satellite systems ca also complemet existig commuicatio etworks i order to icrease the availability of services. he realizatio of the hadover betwee differet satellites ad the multiple access is very importat for a LEO satellite commuicatio system. Both issuses ca be maaged by usig CDMA (Code Divisio Multiple Access) techology [1]. Ufortuately the performace of a CDMA system degrades with the umber of active users. he multiple access iterferece (MAI) limits the capacity of a CDMA system. For our aalysis the Globalstar satellite system is take as a basic model. Globalstar is a LEO satellite commuicatio system with CDMA techology, which is already olie. Recetly multi user iterferece suppressio has become very pertiet, due to the fact that it improves the system performace sigificatly compared to a covetioal correlatio receiver. I the forward lik, i which the trasmissio from the gateway statio via the satellite to the mobile user, the user has o iformatio about the iterferig sigals. his is why a blid algorithm is implemeted. Also, i LEO satellite commuicatio systems the satellites are i the view of each user for oly a short time. Due to this fact the iterferece for each user varies ad the iterferece suppressio detector must adapt. Cocerig obstacles i the lie of sight betwee the satellite ad the mobile user, oe satellite ca be shadowed or eve blocked. Sice there are always two or more satellites i view, shadowig leads to heavy chages i the iterferece sceario. Compared to the terrestrial multi user iterferece the satellite iterferece situatio is subject to stroger chages, thus, the adaptatio speed becomes eve more importat. Besides the adaptatio speed ad the performace i the steady state the computig time has to be researched as well. he multi user detectio has to be performed i the mobile phoe of the user ad due to this fact the complexity of the algorithms must be low. he paper is orgaized as follows. I chapter 2 the system outlie is described ad the iterferece problem is illustrated. he blid iterferece suppressio algorithms are the discussed i sectio 3. Lastly, the simulatio results are preseted i sectio 4. Fially the paper is summarized. 2. SYSEM OULINE I this chapter the basebad trasmissio model based o the Globalstar satellite system [2, 3] is described. We focus our iterest o the forward lik; the trasmissio from the gateway statio via satellite to the mobile user. he footprit of a Globalstar satellite is divided ito 16 spot beams by phased array ateas. Each spot beam has a badwidth of B beam = 16. 5MHz. his badwidth is divided ito 13 FDM (Frequecy Divisio Multiplex) sub chaels, each 1.23MHz wide. he basic structure of the trasmitter is show i Figure 1.

2 d w PNiI PNiQ PNout PNout Fig. 1. rasmitter of the Globalstar system he data bits d of rate 4.8kB/s are covolutioally ecoded (rate R = 1/ 2, costrait legth cl = 9 ) ad iterleaved. herefore, a 20ms block iterleaver is used. he iterleaver delay of 20ms is equivalet to a iterleaver size of is = 192bits. he iterleaved bit stream b is the spread by Walsh sequeces of legth 128 (spreadig factor N p = 128 ). his leads to a chip rate of 1.23MHz. he processig gai ca be calculated as follows s output of the Rake figers ca be combied or the stroger sigal ca be selected. Furthero, for simplificatio purposes just oe Rake figer is assumed. Oe commo problem for CDMA systems is the multiuser iterferece. Whe applyig just oe sub beam, there is o iterferece because of the orthogoal Walsh codes, which provide perfect user separatio. However, the differet spot beams of a satellite overlap ad other satellites i view ca iterfere as well. his leads to iterferece due to the imperfect seperatio properties of the PN codes. Orthogoal codes ca be applied i the sub beam due to the fact that all sigals are sychroized. his is ot the case cosiderig the trasmissio from two satellites. If the sigals are asychroous PN codes have a better performace tha the Walsh codes. Also, the orthogoal codes have a limited code book size. he spot beam geometry of a satellite is show i Figure 2 [6]. G = N = 128 = 256 R ld( M ) p 1/ 2 ld(2), (1) where M is the order of the modulatio scheme. Orthogoal Walsh codes are used to separate differet users i a beam. I the ext step the bits are split betwee the I ad Q braches ad are multiplied with two differet ier PN (Pseudo Noise) sequeces. wo idepedet PN sequeces are used for the iphase ad the quadrature phase i order to maage imperfect carrier sychroizatio ad oliear distortios. After that a outer PN sequece is overlaid o the I ad Q compoet. Both multiplicatios do ot lead to further spreadig. he PN codes are used to distiguish differet beams ad differet satellites. Accordig to this descriptio the sigature sequece c of the user of iterest cosistig of the user specific Walsh code w ad the beam ad satellite specific ier PN codes PNiI ad PNiQ (the outer PN sequeces are omitted) ca be deoted as follows ci = wi ( PNiI + j * PNiQ) i=0, N p. (2) I order to apply blid iterferece suppressio detectors we assume short spreadig sequeces, which meas that the sigature sequece is the same for all symbols. his is ot the case i the Globalstar system, where log PN sequeces are utilized with a legth of 2 10 chips. Additioally o outer PN sequece is assumed. At the receiver a covetioal Rake receiver [4] is proposed. Due to the small delay time of the reflectio paths of the satellite chael o distiguishable echo paths exist. he Rake figers (two figers are advised) poit to distict satellites to gai diversity [3,5]. he Fig. 2. Spot beam geometry O the circle aroud each spot beam the sigal eergy is 1dB lower tha i the ceter of the spot beam. A worstcase positio is give, if the user of the referece spot beam (#1) is at poit P1, where the power of the iterferig two eighbor spot beams (#2 ad #3) is as high as his/her ow. he other spot beams are more atteuated depedig o their distace from poit P1. he atteuatios are give i table 1 [7]. I Figure 3 it is show how the bit error rate (BER) icreases if the user is i the worst-case positio ad differet umbers of users are trasmittig o the spot beams of oe satellite. Normalized distace from ceter of spot beam Normalized atea gai (db) r r r

3 able 1. Atea characteristics {( r ( c x)) 2 } E + (7) ca be developed. he eergy at the output cosists of the eergy of the desired sigal ad the eergy of the iterferig sigals plus AWGN (Additive White Gaussia Noise). It ca be show that miimizig the mea output eergy leads to a MMSE solutio [8]. he sigal x ca be adaptively determied with the help of the stochastic gradiet method ( r h )[ r ( r c) c] x + 1 = x γ (8) Fig. 3. Multiuser iterferece for oe satellite with spot beams 3. INERFERENCE SUPPRESSION ALGORIHMS he Globalstar system applies a covetioal correlatio receiver. As depicted i Figure 3 the BER icreases dramatically with the umber of active users. I this sectio three blid iterferece suppressio algorithms are preseted. A appliace of the least mea squares (LMS) algorithm was derived i [8]. Usig this detector a scheme with a adaptive step size (AS-LMS) was developed i [9]. he third algorithm is a recursive least squares adaptive algorithm (RLS) [10]. LMS A miimum mea-square-error (MMSE) liear multiuser detector computes the sigal h that miimizes the mea square error (MSE) E {( Ab r h) 2 } (3) where A deotes the received amplitude, b stads for the ecoded bits ad r is the received sigal ( deotes traspositio). User 1 is the user of iterest ad so the idices are omitted ( h 1 = h, d1 = d,... ). he sigal h ca be writte i caoical form h = c + x (4) where c is the sigature waveform of user 1 ad x is orthogoal to c. c x = 0. (5) Furthermore, the followig ormalizatio is adopted 2 = h c = c 1. (6) Utilizig this caoical form a detector that tries to miimize the mea output eergy (MOE) of the detector give by whereas the step size γ has to be a compromise betwee the acquisitio speed ad the steady state jitter. AS-LMS Whe applyig the LMS detector by startig the receptio of a sigal a large step size for acquisitio is helpful. However, if the steady state is reached a larger step size leads to larger jitter problems. hus, a adaptive step size would be desirable. he AS-LMS algorithm computes the sigal x like the LMS detector ad i additio to that it utilizes a secod LMS algorithm miimizig 2 E ( h ) r with respect to γ to adjust the step size. his leads to the followig estimate of the step size [9] γ γ [ γ α ] + r hr Y γ + = 1 (9) where α deotes the learig rate of the secod LMS algorithm ad Y is the derivative h / γ. he values γ- ad γ+ deote a lower limit for the step size ad a upper limit. I [9] it is show that the derivative Y ca be calculated as follows Y [ I γ r r ] Y + r Y ( r c) c r h ( r ( r c) c) + 1 = γ where I is the idetity matrix. RLS (10) he afore metioed MMSE detector ca be give as where ( h r) bˆ = sig (11) 1 1 h = R c (12) 1 c R c ad R is the autocorrelatio matrix of the received sigal r. I order to fid a adaptatio rule for the RLS algorithm a vector h is searched that miimizes the expoetially weighted output eergy

4 [ h ] r 1 2 mi λ (13) where h = 1 ad λ is the forgettig factor, which esures that the data of the past caot ifluece the adaptatio for too log. his miimizatio problem ca be solved by c period ca be compared with the situatio i this simulatio. he adaptatio process has bee computed several times ad the umber of frame errors was averaged. he MMSE solutio (11) was computed with the help of the autocorrelatio matrix of the received sigal (12). It is give i the followig figures for compariso purposes. h R 1 1 = R c (14) 1 c R c i = λ r i = ir 1 i. (15) Basig o this solutio a adaptive algorithm ca be derived: 1 R 1r 1 + r R 1r 1 1 = R c = l 1 kr l 1 k l h R = λ (16) l [ ] λ (17) 1 = c l (18) 1 1 [ R k r R ] 1 1 = 1 1 λ. (19) he complexity of the AS-LMS is justifiably higher tha the complexity of the LMS due to the fact that a secod LMS algorithm is eeded for adjustig the step size. Both computatioal complexities are fuctios of N p. he complexity of the RLS is proportioal to O( N ) ad due to this fact the RLS algorithm requires the most computig time. 2 p Figure 4. Performace of the covetioal correlatio receiver he performace of the covetioal correlatio receiver is show i Figure 4. As the umber of users icreases, so does the umber of frame errors. his umber also stays costat at a high level. he LMS 4 detector with a step size of γ = 1 10 also has a icreased umber of frame errors at frame 50, however, approximately 100 frames later the umber of frame errors decreases to a lower level as depicted i Figure NUMERICAL RESULS I order to implemet the described iterferece suppressio algorithms i a LEO satellite system some poits have to be kept i mid. Due to the differet PN sequeces for the real ad the quadrature part of the sigal, two differet detectors are ecessary. For simplificatio purposes we assume the trasmissio via oe satellite with a spot beam geometry as depicted i Figure 2. he user of iterest is i the described worstcase positio. I order to focus o the iterferece suppressio aspects a AWGN chael is cosidered ad o ecodig is performed. First the adaptatio speed of the three detectors is compared. herefore the algorithms are i the steady state with 10 users o each spot beam ad a E B / N o (Bit Eergy per Noise) of 10dB. he bits are trasmitted block by block whereby each frame cotais 192 bits. At the 50 th frame the umber of users per beam icreases to 40. his is of course a urealistic situatio, however, if we cosider a two-satellite case with oe shadowed or blocked satellite, the ed of the shadowig Figure 5. Adaptatio of the LMS algorithm It is apparet that the adaptatio of the sigature sequece works. he Adaptatio could be sped up by icreasig the step size, however, this would lead to a higher umber of errors i the steady state.

5 covetioal correlatio receiver. However, the bit error rate of the adaptive detectors is worse tha i the case of o MAI. As a importat poit, oe must keep i mid that the sigature sequece c is composed by the Walsh sequece w ad the PN sequeces PNiI ad PNiQ. he Walsh sequece guaraties o iterferece i a spot beam due to the orthogoaltiy of the Walsh codes. Adaptig the sigature sequece the iterferece of the other beams is reduced, however, also the orthogoality i user beam is destroyed ad this results i additioal iterferece. Figure 6. Adaptatio of the AS-LMS algorithm I order to solve this problem the AS-LMS algorithm was iveted. It ca be see i Figure 6 that this algorithm reaches the steady state aroud 50 frames after the umber of users icreased. Furthermore, the umber of frame errors is lower compared to the LMS detector. Figure 8. Bit error rates of the detectio algorithms with 20 users per beam he case of 40 users per spot beam is depicted i Figure 9. he frame error rate of the detectors icreases, however, the adaptive detectors provide a large gai compared to the covetioal correlatio detector. Figure 7. Adaptatio of the RLS algorithm As show i Figure 7 the performace of the RLS algorithm is the most efficiet. It adapts the ew iterferece sceario very fast ad also i the steady state the umber of errors is low. he bit error rates of the iterferece suppressio detectors are compared to the error rates of the covetioal receiver ad the case with o MAI i Figure 8. he umber of users is set to 20 users per beam. he three adaptive algorithms have almost the same performace. For the LMS algorithm a step size of 4 γ = 1 10 is set. Utilizig this low step size the adaptatio speed is low but the steady state error rate is good. Compared to the MMSE solutio the blid adaptive detectors perform well. Oly a small degradatio is viewable. Also oe ca recogize the ifluece of the step size of the LMS algorithm i the steady state. Its frame error rate is slightly higher tha the error rate of the other adaptive detectors. he three adaptive detectors perform sigificatly better tha the Figure 9. Bit error rates of the detectio algorithms with 40 users per beam 5. SUMMARY AND CONCLUSIONS I this paper three blid adaptive iterferece suppressio algorithms are applied to a LEO satellite commuicatio system. heir performace is compared to the performace of the covetioal correlatio receiver. he LMS, the AS-LMS, ad the RLS algorithm have a sigificatly better bit error rate tha

6 the correlatio receiver. he RLS algorithm ad the AS- LMS detector react more quickly to a chaged iterferece situatio tha the LMS algorithm. I cosiderig the computatioal costs, oe must ackowledge that the RLS is very expesive whereas as the LMS algorithm eeds the least computig time. he AS-LMS is a good compromise betwee adaptatio speed ad bit error rate ad o the oe had ad computig costs o the other. REFERENCES [1] B. R. Vojcic, L. B. Milstei, R. L. Pickholtz, Dowlik DS CDMA Performace Over a Mobile Satellite Chael, IEE ras. Veh. echol., vol.45, No. 3, pp , August [2] F. J. Dietrich, P. Metze, P. Mote, he Globalstar Cellular Satellite System, IEEE ras. Ateas ad Propagatio, vol.46, No. 6, pp , Jue, [3] P. Mote, S. Carter, he Globalstar air iterface modulatio ad access, Proc. 15 th AIAA Itl. Comm. Satellite Cof., pp , February [4] K. D. Kammeyer, Nachrichteuebertragug, ISBN: , 1996 (i Germa) [5] S. Fischer, S. Kudras, V. Küh, K.D. Kammeyer, Aalysis of Diversity Effects for Satellite Commuicatio Systems, accepted for i Proceedigs Globecom, Sa Atoio, USA, [6] E. Lutz, M. Werer, A. Jah, Satellite Systems for Persoal ad Broadbad Commuicatios, ISBN: , [7] R. De Gaudezi, F. Giaetti, DS-CDMA Satellite Diversity Receptio for Persoal Satellite Commuicatio: Satellite-to-Mobile Lik Performace Aalysis, IEE ras. Veh. echol., vol.47, No. 2, pp , May [8] M. Hoig, U. Madhow, S. Verdu, Blid Adaptive Multiuser Detectio, i IEEE rasactios o Iformatio heory, Vol. 41, No. 4, July 1995, pp [9] V. Krishamurthy, G. Yi, S. Sigh, Adaptive Step- Size Algorithms for Blid Iterferece Suppressio i DS/CDMA Systems, i IEEE rasactios o Sigal Processig, Vol. 49, No. 1, Jauary 2001, pp [10] H.V. Poor, X. Wag, Code-Aided Iterferece Suppressio for DS/CDMA Commuicatios-Part 2: Parallel Blid Adaptive Implemetatios, i IEEE rasactios o Commuicatios, Vol. 45, No. 9, September 1997, pp