W-CDMA Uplink Capacity and Interference Statistics of a LongGroove-Shaped Road Microcells Using A Hybrid Propagation Model

20 B. TAHA-AHMED, M. CALVO-RAMÓN, L. DE HARO-ARIET, W-CDMA UPLINK CAPACITY AND INTERFERENCE STATISTICS … W-CDMA Uplink Capacity and Interference Statistics of a Long Groove-Shaped Road Microcells Using A Hybrid Propagation Model Bazil TAHA-AHMED, Miguel CALVO-RAMÓN, Leandro de HARO-ARIET Departamento Sistemas, Señales y Radiocomunicaciones, ETSI Telecomunicación, Universidad Politécnica de Madrid, Ciudad Universitaria, Madrid, 28040, Spain [email protected].es Abstract. The uplink capacity and the interference statistics of the sectors of a long groove-shaped road W-CDMA microcell are studied. A model of 9 microcells in a grooveshaped road is used to analyze the uplink. A hybrid model for the propagation is used in the analysis. The capacity and the interference statistics of the cell are studied for different sector ranges, different specific attenuation factors, different antenna side lobe levels and different bend losses. Keywords W-CDMA, cells capacity, shadowing. 1. Introduction CDMA is characterized as being interference-limited, so reducing the interference results in increasing the capacity. Three factors are mainly used to reduce the interference: power control (PC), voice activity monitoring and sectorization. It is well known that urban microcell shapes may approximately follow the street pattern and that it is possible to have cigarshaped cells [1]. This type of cells appears also in tunnels and groove-shaped roads. The conditions that describe the long groove road cigar-shaped microcells under this study are • The number of directive sectors of the cigar-shaped cell is two and a directive antenna is used in each sector. • The sector has typically a range of about one kilometer. • The groove length is of the order 3 to 5 km. • The user speed in the tunnel can reach 120 km/h. Fig. 1 shows the coverage of the sector and the cigarshaped cell. Min et al studied the performance of the CDMA highway microcells [2]. Hashem et al studied the capacity and the interference statistics for hexagonal cells using a propagation exponent of 4.0 [3]. Ahmed et al studied the capacity and interference statistics of highway cigar-shaped microcells [4]. In [5], Ahmed et al studied the capacity and interference statistics of a tunnel cigar-shaped microcells using a two exponent propagation model. In this work, we introduce a model for cigar-shaped cells in groove road, with general propagation exponent using a two-slope attenuation model and then investigate the sector capacity and interference statistics of the uplink. A Base station Sector 1 coverage Sector 2 coverage B Fig. 1. The sector and cell coverage. A – the sector coverage. B – the cell coverage. The paper has been organized as follows. In section 2, the propagation model is given. Section 3 explains the method to obtain the capacity and the interference statistics of the uplink. Numerical results are presented in section 4. Finally, conclusions are drawn in section 5. 2. The Propagation Model From the measurements presented in [6], the propagation model in the groove road can be approximated by a two or more slopes model applicable in the microwave frequency range. A hybrid propagation model with lognormal shadowing is used in our calculations. The propagation exponent until the break point Rb is assumed to be s. For a distance r greater than Rb, the signal is assumed to be attenuated by a specific attenuation factor of n dB/m. In this way, the path loss is given by: 11 5 log10)( ξ +++= LrKdBLp, (1) 22 5)(log10)( ξ ++−++= LRrnRKdBL bbp . (2) Eqn. (1) is valid for r ≤ Rb, and eqn. (2) is used for r > Rb. RADIOENGINEERING, VOL. 12, NO. 3, SEPTEMBER 2003 21 for rid > Rb and rim > Rb. In (1) and (2), s is the propagation exponent until Rb, K is the attenuation at a distance of 1 m, n is the specific attenuation after Rb, Li is the tunnel bend loss between the source and the observation point d if applicable, ξ 1 and ξ 2 are Gaussian random variables of zero-mean and a standard deviation of σ 1 and σ 2 respectively. In the above-given equations, Lbij is the bend loss between the user i and the base station j. Now the normalized interference signal I( rid, rim) due to the distance, the bends and shadowing is given by For the tunnel environment, r is the distance between the base station of the cell C and the mobile and the breakpoint distance Rb is given by: ),(10),( 10/)( imidimid rrLrrI imid ξξ − = (8) where ξ id and ξ im are given as λ 2 aRb≈ (3) • ξ id = ξ 1 and ξ im = ξ 1 for rid ≤ Rb and rim ≤ Rb; • ξ id = ξ 2 and ξ im = ξ 1 for rid > Rb and rim ≤ Rb; where a is the groove road width, normally 6 to 8 meters, and λ is the wavelength. Typical value of s is around 2 and n = 0.02 – 0.06 dB/m [6] and [7]. • ξ id = ξ 1 and ξ im = ξ 2 for rid ≤ Rb and rim > Rb; • ξ id = ξ 2 and ξ im = ξ 2 for rid > Rb and rim > Rb. [dBr] Signal Power s ~ 2 n [dB/m] RbRange [m] We will divide the total intercellular interference (Iinter, t) in the interference from users in the S0 region (IS0) and the interference from users in the S1 region (IS1), where the regions are shown in Fig. 3. We will find the interference at the right sector (drawn in black) of the central cell C1 assuming it to be the reference cell d. We assume that users in the region S0, communicate with the reference cell d (cell under consideration) and the other closest base station. In the S1 region we will consider the user server base station as the closest one [3]. We have to mention that we assume that users in this region cannot communicate with the reference cell. Fig. 2. The field intensity profile. Fig. 2 depicts the general shape of the propagation loss profile for the groove road microcell. Left S1 Region S0 Region Right S1 Region Left S0 Right S0 C5 C3 C1 = d C2 C4 3. Uplink Analysis The configuration of the multi-microcells model is shown in Fig. 3. In this case, each cell controls the transmitted power of its users. The sector range is assumed to be R. If the interfering user i is at a distance rim from its base station and at a distance rid from the base station of the reference cell d as shown in Fig. 4, then the normalized interference signal L( rid, rim) due only to the distance and bends is given as: Fig. 3. The microcells model (5 out of 9 microcells are shown). [] [] 10/log10 10/log10 10 10 ),( bid s id bim s im Lr Lr imid rrL + + = (4) Let be S the desired signal level. Then, the interference from an active user communicating with the home cell will be also S. A user i in the S0 region will not communicate with the reference cell d but rather with base station m, if φ ( ξ id – ξ im , rid / rim) = 1 for for rid ≤ Rb and rim ≤ Rb; [] [] 10/)(log10 10/log10 10 10 ),( bidbid s b bim s im LRrnR Lr imid rrL +−+ + = (5) 110),( 10/)( ≤ −imid imid rrL ξξ (9) and φ ( ξ id – ξ im , rid / rim) = 0 otherwise. for rid > Rb and rim ≤ Rb; [] [] 10/log10 10/)(log10 10 10 ),( bid s id bimbim s b Lr LRrnR imid rrL + +−+ = (6) for rid ≤ Rb and rim > Rb; [] [] 10/)( 10/)( 10 10 ),( bidbid bimbim LRrn LRrn imid rrL +− +− = (7) rid im Cell d Cell m Sector 1 User i Interference Uplink r Fig. 4. Schematic diagram of base stations and mobiles for the groove road microcells. 22 B. TAHA-AHMED, M. CALVO-RAMÓN, L. DE HARO-ARIET, W-CDMA UPLINK CAPACITY AND INTERFERENCE STATISTICS … It is assumed that the number of users in each sector is Nu and that the activity factor is α . For a uniform distribution of users, density of users in each sector is ρ = Nu/R users per unit length. [] [ drErrLSllIE imid im S id l S 10/)( 1 110),( ξξ ρα − ∫ ≈ ] . (20) The expected value of the intercellular interference from the left side of the regions S0 and S1 is Then, for the right part of S0 the expected value of IS0 is given as: [] dr r r frrLIE im id im S id r S)(),( 0 0∫ = αρ (10) [ ] [ ] [ ] l S l S lIEIEIE 10 + = . (21) Thus the expected value of the total interference from the left and right sides is given as [ ] [ ] [ ] lrter IEIEIE + = ,int . (22) where [ )/,(10)( 10/)( imidimid im id rrE r r fimid ξξφ ξξ −= − ] (11, 12) The expected value of the total intercellular interference power is given as {}      −= ),(/1log 10 10/10ln 10 2 22/)( 2 imid rrLQe σ σ βσ [ ] [ ] ter er IESIpE ,int int = . (23) The intracellular interference power is proportional to source activity factor, number of users and the side lobe level. It is given by being β = ln10/10. The general value of σ 2 is given as: • If (rid and rim ≤ Rb) then σ id = σ 1 , also σ im = σ 1 then 2 1 2)1(2 σσ dm C−= (13) )1( int SllSNI ura + ≈ α . (24) Finally, the total interference-to-signal ratio is given by [ ] S IpE S I S Ier rat int int += . (25) where Cdm is the correlation coefficient between the random variables ξ id and ξ im. • If rid ≤ Rb and rim > Rb or rid > Rb and rim ≤ Rb then the value of σ 2 is given by So the uplink carrier-to-interference ratio (C/I)up is given as 21 2 21 2)1(2)( σσσσσ dm C−+−= . (14) tup ISIC = )/( (26) and (Eb / N0)up is given as • If rid > Rb and rim > Rb then σ id = σ 2, and also σ im = σ 2 then pupupb GICNE )/()/( 0 = (27) 2 2 2)1(2 σσ dm C−= . (15) where Gp is the processing gain. Q(x) is given by ∫ ∞ − = x vdvexQ π 2/)( 2/ 2. (16) For a voice user that has a velocity of 120 km/h, the relation (Eb/N0)up has to be 7 dB or more [8] and for a data user with a bit rate of 144 kbits/sec., the ratio (Eb/N0)up has to be 3 dB or more [8]. The expected number of users E(Nu) can be calculated from (27). The procedure to obtain the variance of the number of users is as follows. The expected value of IS1 due to right part of the S1 region is approximated as The variance of IS0 due to right part of S0 is given as [] [ drErrLIE imid im S id r S 10/)( 1 110),( ξξ αρ − ∫ ≈ ] . (17) var [] [ ] dr r r f r r grrLI m d m d S imid r S     −= ∫)()(),( 22 0 2 0 ααρ (28) where The expected value of the intercellular interference from the right side of the regions S0 and S1 is then [] [ ] [ ] r S r S rIEIEIE 10 += . (18) [ ] 2 10/)( )/,(10)( imidimid m drrE r r gimid ξξφ ξξ −= − (29) {}      −= ),(/1log 10 5/10ln 10 2 2)(2 2 imid rrLQe σ σ βσ (30) For the left part of S0 the expected value of IS0 is given as [] dr r r frrLSllIE im id im S id l S)(),( 0 0∫ = ρα (19) The variance of IS1 due to right part of S1 is given as [ ] [] [][ {} drEErrL I imidimid S imid r S )( 222 )( 1 2 1 10)10(),( var ξξξξ ααρ −− − ] ≈ ∫ (31) where Sll is the side lobe (back lobe) level of the directive antenna used in each sector. And the expected value of IS1 due to the left part of S1 is given as RADIOENGINEERING, VOL. 12, NO. 3, SEPTEMBER 2003 23 The variance of IS0 due to left part of S0 is given as [] [] dr r r f r r grrLSll I m d m d S imid l S      − = ∫)()(),( var 22 0 2 0 ααρ (32) We present first the case of voice users (Gp = 256) assuming that the activity factor α is 0.5. The variance of IS1 due to left part of S1 is given as [] [] [][ { drEErrLSll I imidimid S imid l S )( 222 )( 1 2 1 10)10(),( var ξξξξ ααρ −− − ≈ ∫ ] } (33) Fig. 5 shows the outage probability of the sector. We can notice that the sector capacity is 91 voice users while the average capacity (50% outage) is 94 users. Thus the practical capacity is 96% of the average one which is an advantage in this case. This is because of the very steep curve, which has been also noticed in cigar shaped microcells in highways [4]. In macro-cellular environment, practical capacity is of the order 60 to 70 % of the average one. Thus the total variance due to the total region S0 and S1 is given by [] [ ] [ ] { } [] [ ] { } l S l S r S r S tIIIII 1010 varvarvarvarvar + + += . (34) The variance of the number of user var(Nu) is calculated as [] )(var)var( u t uNEIN =. (35) -2 Finally, the outage probability is calculated as        − =)var( )( u uu rN NNE QP (36) 10 -3 85 95 100 10 10 -1 Groove-shaped Road Microcell Performance Number of users/sector 90 Outage Probability and the F factor is calculated as Fig. 5. The outage probability of the sector (voice users only). [] ra er I IpE ceInterferenlarIntracellu ceInterferenlarIntercellu F int int == . (37) Fig. 6 shows the effect of the sector range. We can notice that the capacity of the sector increases with the increment of the sector range R. Fig. 7 shows the effect of the side lobe (back lobe) level on the sector capacity. Reducing the side lobe (back lobe) level will increase the capacity of the sector. An antenna with side lobe (back lobe) level of -15 dB or better is a good choice. 4. Numerical Results A nine microcells model is used in the analysis. We have assumed that the W-CDMA chip rate is 3.84 Mchip per sec. For our calculations, some reasonable figures are applied. The azimuth side lobe level (back lobe) is assumed to be –15 dB, the correlation coefficients are Cdm = 0.0, we consider s = 2, n = 0.04 dB/m, σ 1 = 2 dB, σ 2 = 2 dB, Rb = 300 m and R = 1000 m unless other values are mentioned. We assume that the accepted outage probability is 1% and that the capacity of the sectors is calculated at this probability. 300 500 700 900 1100 1300 75 80 85 90 95 b R = 300 m Sector Range [m] Sector Capacity (users) Tab. 1 gives the calculated values of E[I]t, var[I]t and the F factor for different conditions assuming α =0.5. Conditions E[I]inter,t var[I]t F s = 2, n = 0.02 dB/m 0.0557 0.0202 0.108 s = 2, n = 0.04 dB/m 0.0277 0.0100 0.054 s = 2 , n = 0.06 dB/m 0.0183 0.0066 0.035 s = 2, n = 0.04 dB/m, σ1=2 dB, σ2= 4 dB 0.0278 0.0114 0.054 Fig. 6. Sector performance for different values of the sector range R. To study the effect of the bend loss, we assume that there is a bend between cells C1-C2. From Fig. 8, we notice that the higher is the bend loss, the higher is the sector capacity. Next, we consider data users case where Gp = 26.66 and α = 1. Fig. 9 shows the performance of the sector. It can be noticed that, the sector capacity is 12 data users. Tab. 1. The value of E[I]t, var[I]t and the F factor for different conditions. 24 B. TAHA-AHMED, M. CALVO-RAMÓN, L. DE HARO-ARIET, W-CDMA UPLINK CAPACITY AND INTERFERENCE STATISTICS … It has been noticed that: -20 -19 -18 -17 -16 -15 -14 -13 -12 -11 -10 80 82 84 86 88 90 92 94 96 Side lobe level [dBr] Sector Capacity (users) • Increasing the sector range R, increases the sector capacity. • With antenna side lobe (back lobe) level of –15 dB, the capacity is quasi the maximum possible. • The lower is the bend loss; the lower is the sector capacity. • Increasing s1 and s2 will reduce the sector capacity. • The microcells that most strongly contribute to the interference are the three cells those exist in the center of the nine microcells model. Fig. 7. Effect of the antenna side lobe level on the sector capacity. 5. Conclusion References We have presented a model that gives the capacity and interference statistics of a W-CDMA groove road cigar-shaped microcells. The effect of the sector range and the side lobe level of the directive antenna is studied. The capacity of the sector is studied using a two-slope propagation model with lognormal shadowing and bends loss. [1] CHO, H. S., CHUNG, M. Y., KANG, S. H., SUNG, D. K. Performance analysis of crossand cigar shaped urban microcells considering user mobility characteristics. IEEE Transactions on Vehicular Technology. 2000, vol. 49, no. 1, p 105 – 115. [2] MIN, S., BERTONI, H. L. Effect of path loss model on CDMA system design for highway microcells. In Proceedings of the 48th Vehicular Technology Congress. Ottawa (Canada), 1998, p 1009 – 1013. L = 0 dB 85 90 95 100 10-3 10-2 10-1 Groove-Shaped Road Microcell Performance Number of users/sector b L = 3 dB b Outage Probability [3] HASHEM, B., SOUSA, E. S. Reverse link capacity and interference statistics of a fixed-step power-controlled DS/CDMA system under slow multipath fading. IEEE Transactions on Communication. 1999, vol. 47, no. 12, p. 1905 – 1912. [4] AHMED, B. T., RAMÓN, M. C., ARIET, L. H. Shaped W-CDMA cells performance in highways. IJECE. 2002, vol. 1, no. 2, p. 80 to 84. [5] AHMED, B. T., RAMÓN, M. C., ARIET, L. H. W-CDMA uplink capacity and interference statistics of a long tunnel cigar-shaped microcells. JCN, submitted. [6] OHTAKI, Y., SENGOKU, M., SAKURI, K., YAMAGUCHI, Y., ABE, T. Propagation characteristics in open-groove waveguides surrounded by rough sidewalls. IEEE Transactions on Electromagnetic Compatibility. 1990, vol. 32, no. 3, p 177 – 184. Fig. 8. Effect of the groove road bends loss. [7] ZHANG, Y. P., HWANG, Y., PARSONS, J. D. UHF radio propagation characteristics in straight open-groove structure. IEEE Transactions on Vehicular Technology. 1999, vol. 48, no. 1, p. 249 – 254. 810 141618 20 10 -3 10 -2 10 -1 Groove-Shaped Road Microcell Performance Number of users/sector Outage Probability 12 [8] MELIS, B., ROMANO, G. UMTS W-CDMA: Evaluation of radio performance by means of link level simulations. IEEE Transactions on Personal Communications. 2000, vol. 7, no. 3, p. 42 – 49. About Authors... For authors’ biographies, see Radioengineering, 2003, vol. 12, no. 3, p. 19. Fig. 9. The outage probability of the sector (data users only).