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Wireless Sensor Network, 2010, 2, 93-99 doi:10.4236/wsn.2010.22013 y 2010 (http://www.SciRP.org/journal/wsn/). Copyright © 2010 SciRes. WSN Published Online Februar Evaluation of Multiusers’ Interference on Radiolocation in CDMA Cellular Networks A. J. Bamisaye, M. O. Kolawole, V. S. A. Adeloye Department of Electrical and Electronics Engineering, The Federal University of Technology, Akure, Nigeria E-mail: {ayobamisaye, kolawolm, vadeloye}@yahoo.com Received October 17, 2009; revised November 15, 2009; accepted December 16, 2009 Abstract Radiolocation has been previously studied for CDMA networks, the effect of Multiple Access Interference has been ignored. In this paper we investigate the problem of Radiolocation in the presence of Multiple Ac- cess Interference. An extensive simulation technique was developed, which measures the error in location estimation for different network and user configurations. We include the effects of lognormal shadow and Rayleigh fading. Results that illustrate the effects of varying shadowing losses, number of base stations in- volved in position location, early-late discriminator offset and cell sizes in conjunction with the varying number of users per cell on the accuracy of radiolocation estimation was presented. Keywords: Code Division Multiple Access, Radiolocation, Multiple Access Interference , Base Station, Mobile Station. 1. Introduction Radiolocation involves: a) identifying the base station (BS) that would participate in the process of subscriber location by selecting a set of BSs within the coverage area that receives intelligible levels of signal from the mobile station (MS) under consideration. b) estimating one-dimensional position which involves each BS, par- ticipating in the process, independently producing an estimate of the subscriber location based on its meas- urements; c) location estimation, that is, estimates from all the participating BSs are used by position location algorithms to produce an accurate estimate of the sub- scriber location within the coverage area. But, the esti- mates produced are not always very accurate. The major sources of error in subscriber location systems are: mul- tipath propagation, non-line-of-sight (NLOS), and mul- tiple access interference (MAI). In the case of multipath propagation, a ccuracy is greatly affected when the re- flected rays arrive within a very small period of the first arriving ray. Case is even more worsened when the power of reflected rays is more than the first arriving ray [1]. Several methods have been developed to mitigate the effects of multipath on radiolocation. Typically propaga- tion in wireless communications accrues up to an aver- age of 400-700m [2,3] and biases the estimations. By using the a prior information about range error statistics, range estimations made over a period of time and cor- rupted by NLOS errors can be adjusted to near their cor- rect values. An alternative approach is to reduce the weights of the BSs prone to NLOS reception while esti- mating location using position location algorithms [4,5]. Co-channel interference is a problem faced by all the cel lular systems. In Code Division Multiple Access (CDMA) networks, users share the same frequency band, but use unique pseudo-noise (PN) codes. Near far effects in CDMA networks are the biggest source of errors in position estimation. Multiple cellular users who are using the same frequency allocation at the same time cause MAI: it greatly affects the performance of Time of Arri- val (ToA) estimation of CDMA systems. In CDMA cel- lular systems, the MSs are power controlled to combat the near-far effect. Thus, for a CDMA network, time based approach is the most promising technique. This paper investigates the effect of MAI and the accuracy of Radiolocation in CDMA cellular network. This paper models the intracellular and intercellular multiple access interference (MAI) in Section 2, simula- tion results are presented in Section 3, and finally in Sec- tion 4, the conclusion drawn from the study is summa- rised. 2. System Model In a CDMA system all the users share the same frequency band. As a result, at a CDMA receiver signals from users, A. J. BAMISAYE ET AL. Copyright © 2010 SciRes. WSN 94 other than the intended user, act as interfering signals, thereby giving rise to multiple access interference. Figure 1 represents such a situation. With reference to Figure 1, the coverage area comprises of cells, , and . These cells have , i C, j C p C i n j n users respectively. The BS’s i, j ,k ,.... and p exercise power control over the users they serve. Let Ai, Aj , Ak....and Ap denote their areas. Only few cells have been considered for simplicity of explanation. ,and k np C 2.1. Modeling Intracellular Multiple Access Interference In a CDMA system using binary signaling, the radio sig- nal from the kth user, arriving at the BS is given by: ()2()()cos( kkkkkkk ck StPctbtt ) (1) where, is the power received from the k th user at the BS. Assuming, perfect power control is exercised, we can replace by P, where P represents the nominal power received at the BS from a user under its power con- trol. k P k P ck (t) is the spreading (or chip) sequence for a user k. bk (t) is the data sequence for a user k. k is the delay for user k relative to a user 0. k is the phase change for user k relative to a user 0. k is the carrier frequency. In the above equation we assume that there is no multi- path interference in the channel. A PN sequence ck (t) is of the form: [10] 1 , 0 () ()( ) M c kki ji c tijMT ct aT (2) ,{1.1} ki a where c T represents the chip duration. c M T represents the chip repetition period. Cell i C i BS Cell n C n BS k B S Cell k C Cell j C j BS Cell p C p BS Cell l C l BS Cell m C m BS Figure 1. Coverage area. Π represents thven by e unit pulse function gi 10 1t ()t0otherwise (3) i is an index to denote a particular chip within a PN Tb = GTc where G represents the factor or gain of the cycle. For data sequence bk(t), Tb is the bit period such that spreading CDMA system. It is not necessary that the gain G of a CDMA system be equal to M. In case they are same, a PN sequence would be repeated for every bit period Tb. The user data sequence bk(t) is given by , ()( ) b kki jb tjT btb T (4) ,1,1 ki b the signal received at the BS is given by (5) where n(t) esents a zero-mean white Gaussian noise 0 ()() () kk k rtStnt p n repr with two sided power spectral density 2 o N , and n represents the number of users power contro BS To derive a decision statistic, the received signal r(t) is p lled by p. m g that the receiver is phase and delay syn- ch ixed with the base band, multiplied with the PN se- quence of the desired user, and integrated over the bit period T b . Assumin ronized with the k th user, the output of the correlator can be written as [6,7] (j1)() ()cos() b kc b T Z krtct jT tdt (6) Assume 0, kk 0 Substi , and that the desired user is user 0. Hentuting Equations (1) and (5) in Equation (6) we obtain T ce k=0. 00 [() ()cos() 0 b c Z rtc ttdt t 1 0 [(2()() cos() 0 p n b kkkkc k k Tpctkb tt t 0 ()] ()cos() c nt c ttdt (7) Z0 is a decision statistic for the desired user. Equation (7) can be expressed as Z0 = I0 + + η where he contribution from the desired user, i.e., 1) I0 is t 22 00 2()()cos() 0 b kk c TPbtctt dt t (8) I A. J.BAMISAYE ET AL.95 As Hence 2 {1,1},1 kk cc 0 I reduces to 0 00 () 2b P I btT (9) 2) mati represents the contribution of MAI and is the sumon of ms, Ik, wher1 p n tere 2( )() kkkkkk Ipctbt 0 ()()cos ck tctcos( ) c tdt (10) 1 0 p n k k I (11) 3) η represents the contribution of noise and is given by (12) To determine the variance and mean of η t (13) Variance 0 0t() ()cos()] b c Tntctt dt 0 0c t [][() ()cos()]0 b T EEntcttd 2 222 0 [() ][] [()()cos() ()cos()] 00 bb cc EE T Entncttdtd t T Now, 0 )()() N tn t[( 2 En 20 00 ()cos() ()cos()() 00 2 bb cc TT Ncctttdtd t 0 222 0()cos() 02 b c TNct tdt t 0 2() 1ct Hence 20(1 cos(2)) 00 4 bb c TT Ntdt t 20 4 b NT (14) Assuming a large number of interferes, by virtue of the central limit theorem (CLT), the distribution of can be approximated by a zero-mean Gaussian distribution [4,7,8] with variance2 given by [7] 1 2 21 6 p n ck k GT P (15) Let, Assuming that the MAI and noise are independent proc- , the variance of (16) esses can be written as 222 (17) 1 2 10 n ck GTP NT 6 p kb (18) 2.2. Modeling Intercellular Mult ed by the at epresented by 4 iple Access Interference Expression for the intercellular interference caus users of cell CiBS j,rij I can be derived. Le h lponent e t the p patoss ex y be m. Let th fading on path from this user to cell i C be Rayleigh distributed, and reresented b i x . Similarly, let the fading on the path from this user to cell j C be Rayleigh distributed, and represented by j x . The average of 2 i x is the log-normal fading on the path from this user to cell i , i.e , /10 2 [10 i ii Ex , where i is the decibel at- tenuation due to shadowing, and is a Gaussian random variable with zero-mean and standard deviation s [9,10]. verage of 2 Similarly the a j x is the log-normal fading on the path from this user to cell.j Let k Pbe the nominal power received at BS i from user i n.It is as- sumed that the power control mhanism overcomes both the large scale path loss and shadow fadin How- ever, it does not overcome fast fluctuationof signal power due to Rayleigh fading [8,11]. As BS i exercises a power control over the MS, the actual transmission power i ac Pof the MS would be /10 [(,)10 ] i i m aci i PPrxy (19) where (x, y) is the distance ec g. s i r quent of the MS from BS i. Consey, assuming uniform user the relative average interference ldensity in the cell, ij I at cell C caused by j sall the uers in cell Ci is given by [9] /10 2 1(,)10 [(,)] (, ) i m ii ij m i ii nrxy j I EdAxy c Arxy x (20) by using iterated expectations, 22 10 10 [10 .][ [10 .,]] ii jjij ExEEx 2 10 [[10. ]] i ij jij EE x Given i and j 2 [,]] j ij Ex is log normal and is equal to Copyright © 2010 SciRes. WSN A. J. BAMISAYE ET AL. Copyright © 2010 SciRes. WSN 96 10 10 i Thus, () 2 10 [10 .] i j Ex 10 [10 ] ij E Let ij X Thus, X is o 2 a Gaussian variable of zero-mean and variance equal t2 S 2 10 [10 .][] i x j ExEe 2 2 4 iS x x 2 10 2 [10 .] 4 j ee Ex dx S 2 () 2 10 [10 .] i s j Exe (21) where = In(10)/10 =.2303. Substituting the result back in0) we obtain (2 2 () 1(, )(,) (, ) m i ij s m ii ij nrxy I edA xy (22) c Arx y If denotes the voic equation becomes e activity factor, then the above 2 () 1(,)(,) (,) s m ii ij m i ij nrxy I edAxy c Arx y Let ij (23) K denote inter-cell interference factor due to a user in cell i at BS j. Hence, ij ij i Kn (24) I 2 () s 1(,)(,) (,) m i m i ij rxy edAxy c Arxy (25) In our model ii K 0 ij is zer ). It o at cel wise (i.e, portant to point out the im- portance l ii, but not zero other- ij K of is im K . ij K gives the interference at BS j caused by a sin user in cell i. Thus, if the total number of users in celwere to change, the new interference levels can ned by simply taking a product of ij gle l i obtaibe K and the numbf rs. This simplifies our calculations as the interference need not be recalculated for the new number of users. Thus, using Equation (23) we can compute relative average intercellular interference uniform user distribution. Thus, for an uniform user dis- tribution, we can write the total intercellular interference at BS j due to users in cell i a ij i ij er ouse for I nK (26) It should be noted that the above interference calcula- tions are assuming nominal power as unity. If P is the nominal power from a power controlled user received at home BS, then Equation (26) would be modified as ijiij I pn K (27) Equation (27) gives the total intercellular interference at cell j C due to users in cell i C. 3. Simulation and Results latwith the following set of d parameters: selected. Hence, Rc = system is 128. Hence Simuion was carried out fixe A chip rate of 1.2288MHz was 1.2288 Mcps; gain of the CDMA G=128; Path loss exponent for mobile communications is 4 [11]. Hence, m=4;As we are restricting the interference from the first tier of interferer’s, number of cells in the coverage area is 7. Hence, NBS = 7; Nominal power of MS, Pk = 1; Speed of radio signal, C = 3x108 m/s; Ther- mal noise, 8 010 2 N ; User distribution per cell is uni- form and every cell has same number of users N. The variable sets of parameters include: a) N: Numer of users per cell; b) b s : Td deviation of shadowing losses in every cell; c) he standar B S N: Number of BS’s participating in radioloca- tion; d) : DLL(delay-locked loop) resolution. e) R: Radius of the cells. g th ize of cells on d to study the combined 1) We studied the effects of varying shadow losses, varyine number of BS’s participating in radiolocation, varying the DLL resolution and varying the s theccuracy of estimation. a 3.1. Effect of Varying Shadowing Losses on the Accuracy of Radiolocation This experiment was conducte effect of varying shadowing losses and the number of users per cell on the error in radiolocation. Set 18 , number of BSs participating in radio- any computer system that supports the location = 3, radius of the cell = 1500m. and integration period, T int = 128T c . Generate a cell site BS database for 7 cells of radius 1500m each, using graphical user interface, GUI. Set value of s to 6dB. 2) For the given value of s compute the interference matrix ij F . 3) The number of user is vary per cell from 1 to 100, in steps of 10, and estimate the error in position estima- tio il, set n 4) Simarly s =8dB and 10dB, and go to Step 2. For every setting of s , and number of users per cell, 50 A. J.BAMISAYE ET AL.97 re carried out. The final results are an av- er o ou random locations were chosen within the central cell, and estimations we evident that introdu the third estimator hagnificant impact on the estimation accuracy and 2) There no siant iment intimation accuracy when the nuer of Bincrease 3 to 4: The mean radioloerror es byhen we increase the number of BS’s to ow, there is lower accuracy re- qu for esti- ating the TOA of the received signal. The accuracy of ely the Dined by th study the effect of variation of ∆ on e accuracy of estimation, we have performed experiments age of the resultsbtained at the 50 locations. Similar procedure is carried t for the remaining set of experi- ments. The plot in Figure 2 shows the variation of error in radiolocation with number of users per cell and s . The mean value of the radiolocation error, tabulated below is determined by taking an average of all the points plotted in the Figure 2. When the number of users is varied from 1 to 100, and other conditions remaining the same, the mini- mum, maximum and mean values of the observed errors are tabulated in Table 1. The mean error in two-dimen- sional position estimation remains almost constant when s is increased from 8 dB to 10 dB. 3.2. Effect of Varying the Number of Participat- ing BS’s on the Accuracy of Radiolocation e used 2,3 and 4 BS’s to estimate thWe subscriber location . 1)n under the above heading. The results are plotted in Figure 3 It was observed that: Accuracy improves drastically if we use more tha two BS’s for estimation: The accuracy of estimation im- proves to 71.51m from 697.12m when we employ 3 BS’s to estimate the subscriber location instead of 2. Thus, it is very Figure 2. Variation of radiolocation error with N and s . Table 1. Min and max error in radiolocation for different values of s σs Minimun Maximim Error mean (dB) (m) (m) (m) Error Error 6 26.30 364.33 122.40 8 25.83 122.30 71.51 10 25.85 96.92 75.40 cings a si isgnificprovem the es mb cation S’s is improv d from 6m w 4. This shs that no effect obtained when we increase the number of BS’s from 3 to 4. For applications with irements, 3 BS’s would be sufficient for radiolocation. Table 2, derived from Figure 3, outlines the minimum, maximum and mean values of estimation errors for various values of NBS as the number of users per cell is varied from 1 to 100, other conditions remaining same. 3.3. Effect of Varying the Early-Late Discriminator Offset on the Accuracy of Radiolocation For our work we have used a non-coherent DLL m estimating the TOA using a DLL depends on how clos LL can track the incoming signal, and this is def e parameter ∆. To th with ∆= 11 , 24 and 1 8.The results of the experiment are plotted in Figure 4. Table 2. Min and max error in radiolocation for different val- ues of NBS. NBS Minim Erro (m Maximim mean un r ) Error (m) Error (m) 2 543.10 721.64 697.12 3 26.94 24.29 71.51 4 24.70 111.40 65.39 Figure 3. Variation of radiolocation error with N and NBS. Copyright © 2010 SciRes. WSN A. J. BAMISAYE ET AL. Copyright © 2010 SciRes. WSN 98 la would be inefficient for such cases. igure 4, the accuracy of estimation, falls as the number of ceis because of the degradation oR (signoise) wing num- ber of users pll. 3.4. Eect of Varying the Cell Sizee Accuracy of Radiolocation Figure 4. Variation of radiolocation error with N and ∆. Table 3, derived from Figure 4, outlines minimum and maximum values of errors for different values of ∆ as the number of users per cell are increased from 1 to 100, other conditions remaining same. The mean radiolocation error reduces to 524.22m and 70.79m from 733.13m and 524.22m respectively when ∆ is reduced from 1 2 to 1 4 and from 1 4 to 1 8. But, the lowest value of ∆ is limited by a) In practice, the locally generated PN sequence will have to be phase delayed to generate the early and late PN sequences. As per IS-95 standards, one chip period corre- sponds to 813.80 nSec. Thus, if we were to deploy a trackig loo n caility on the hardware will be a til n PN sequence is delayed by T. If ∆ = 1/k, there are k po- o search through before it can lock to the sub- n p with ∆=1/16, the requirement on the timing resolutio pab ∆t = T c × ∆ = 813.08nSec/16=50.8175nSec Implementing such high precision tracking loops is both challenging and expensive. b) If the DLL employ’s a serial search technique, it will have to search through all potential code delys un the correct delay is identified . Suppose, the icoming c tential delay values between 0 and Tc that the DLL will have t scriber signal. Thus, the size of the set of potential de- Table 3. Min and max error in radiolocation for different values of ∆. ∆ Minimun Error (m) Maximim Error (m) mean Error (m) ½ 84.86 911.02 733.13 ¼ 51.72 735.97 524.22 1/8 26.94 124.29 70.79 ys increases as the value of ∆ decreases. The bigger the set of potential delays, the longer it will take for the tracking loop to achieve a lock. The situation becomes more complicated, if we are also estimating the velocity of the subscriber. The set of potential delays, soon trans- forms into a two-dimensional matrix defining the set of potential delays and velocities. A serial search technique Also, accuracy falls as number of users per cell increases. As seen in F users per f SN ll increases. This nal-to-ith increas er ce ff on th All the earlier experiments were carried out with cells, each of radius 1500m. In this case, we simulated coverage areas with cell radii 100m and 500m. Simulations were carried out under the following conditions: 18; σ s = 8dB ; and number of BSs involved in radiolocation = 3. The number of users is varied from 1 to 100 in steps of 10. The results were then compared wi tthhe results of the ex is better with smaller cells. 100m, ca- tion orks e ps ultiple ac ave studied the effect f MAI in conjunction with varying shadowing envi- racking capability of the DLL, vary- participating in radiolocation, and periment carried out under identical situation but using cells of 1500m radius. The results indicate that under per- fect power control, the degradation in SNR (signal-to-noise) with number of users is independent of the cell size; and the accuracy of estimation For the experiment conducted with cells of radii 500m and 1500m, it is found that accuracy of radiolo is best for cells of radius 100. 4. Conclusions Our study has investigated the possibility of accurate subscriber location in CDMA cellular netwin the presence of multiple access interference. Earlier works have ignored the effect of non-orthogonality of th eudo-noise codes on the estimation accuracy. They usually consider the case of a single MS with no inter- ferers, which is not a practical assumption. In our work, we have studied the effect of number of interferers on the accuracy of estimation by varying the number of users in every cell from 1 to 100. To study the effects of m cess interference on the accuracy of estimation, we have assumed the presence of a line-of-sight component between the MS and the BS. We h o ronments, varying t ng number of BSsi varying cell sizes. The results obtained through the simulations carried out under these different conditions are encouraging and show that radiolocation is possible in a CDMA system, even when multiple access interfer- A. J. BAMISAYE ET AL. Copyright © 2010 SciRes. 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