WCDMA Multiservice Uplink Capacity of Highways Cigar-Shaped Microcells

The multiservice uplink capacity and the interference (intracellular and intercellular) statistics (mean and variance) of the sectors of cigar-shaped wideband code-division multiple access (WCDMA) microcell are studied using a model of 5 highway microcells in rural zone. The two-slope propagation loss model with lognormal shadowing is used in the analysis. The capacity and the interference statistics of the microcell are studied for di ﬀ erent sector ranges, antenna side lobe levels, standard deviation of the power control error, breakpoint distance, and di ﬀ erent intersites correlation coe ﬃ cient. It is shown that reducing the antenna side lobe level increases the sector capacity. Also, it is shown that the sector range that gives the quasi the maximum sector capacity is in the order of 800 to 1200 m.


INTRODUCTION
It is well known that WCDMA is characterized as being interference limited, so reducing the interference results in increasing the capacity. Three techniques are used to reduce the interference: power control (PC) which is essential in the uplink and that can double the downlink capacity, voice activity monitoring that can increase the capacity by 50% (assuming an activity factor of 0.66, thus the new capacity will be 1/0.66 = 1.5 times the old one without using voice activity monitoring) and sectorization. It is well known that the microcells shape may approximately follow the street pattern and that it is possible to have cigar-shaped microcells [1]. The conditions that describe the rural highway cigar-shaped microcells under this study are: (1) the number of directional sectors of the cigar-shaped microcell is two and a directional antenna is used in each sector; (2) the sector has typically a range of 1 km. Figure 1 shows the azimuth radiation pattern of the directional antenna used in each sector and the cigar-shaped microcell azimuth coverage.
Min and Bertoni studied the performance of the CDMA highway microcell using both the one-slope propagation model and the two-slope propagation model but without taking into account the interference variance [2]. They have concluded that the two-slope propagation model is most adequate to be used in the study of the microcells capacity. In [3], the impact of the cell size and the propagation model parameters on the performance of microcellular networks have been studied. The two-slope model of propagation has been used in the analysis. In [4], the Erlang capacity was calculated for a tessellated hexagonal code-division multipleaccess (CDMA) cellular system, where transmissions are subject to an inverse fourth-power path-loss law and lognormal fading. Hashem and Sousa [5] studied the capacity and the interference statistics for hexagonal macrocells using a propagation exponent of 4.0. In [6], an analytical computation of the interference statistics with application to mobile radio systems has been given assuming hexagonal macrocells. In [7], the effect of the imperfect power control on the uplink of CDMA cellular networks has been given for hexagonal macrocells calculating the interference statistics assuming a Rayleigh fading channel.
In [8], the capacity and the mean and variance statistics of interference of cigar-shaped microcells for highways in rural zones using wideband code-division multiple access (WCDMA) have been studied. A general propagation exponent using a two-slope propagation model and log-normal shadowing was used. It has been assumed that users are uniformly distributed within the microcells, the intracellular 2 EURASIP Journal on Wireless Communications and Networking  interference variance is null, and that the power control is perfect. In [9], the uplink capacity and interference statistics of WCDMA cigar-shaped microcells for highways in rural zones with nonuniform spatial traffic distribution and imperfect power control were given. In [10], the capacity of cross-shaped microcells has been given assuming imperfect power control and constant interference to noise ratio. In [11], WCDMA uplink capacity and interference statistics of a long tunnel cigar-shaped microcells have been studied using the hybrid model of propagation and assuming imperfect power control, an infinite transmitted power and an activity factor of 0.5 for voice users (over head was not taken into account). In [11], it was shown that the sector capacity increases when the sector radius increases where nothing shows that at a given sector range (1.5 km approximately), the sector capacity should begin to reduce. All this is due to the fact that the transmitted power was assumed to be infinite. Also in [11], it was not taken into account that a percentage of the mobile transmitted power is assigned to the pilot signal. In [12], the WCDMA uplink capacity and interference statistics of cigar-shaped microcells in rural zones highways have been studied assuming imperfect power control and finite equal transmitted power for the voice and data services. It has been assumed that the WCDMA can support only one service at a given time. Thus, the mixed capacity was not given. Also, it was assumed that the maximum transmitted power of the voice and data users is equal but this is not the case in the multi-service situation. Multi-service means that the system can support more than one service in a given time.
In this work, for cigar-shaped microcells in rural highways zones, we use a two-slope propagation model with general exponent and then investigate the multi-service sector capacity and interference statistics (mean and variance values) of the uplink assuming imperfect power control and finite unequal transmitted power by the mobile for the voice and data services. Those assumptions and the multi-service analysis have not been shown in the previous authors works in [8,9,11,12].
The paper has been organized as follows. In Section 2, the propagation model is given. Section 3 explains the method to calculate the capacity and the interference statistics of the uplink. Numerical results are presented in Section 4. Finally, in Section 5 conclusions are drawn.

PROPAGATION MODEL
In [2], it has been shown that the two-slope model of propagation is the best propagation model that can be used to study the capacity of the sector of cigar-shaped microcells in highways. Thus, we will use the two-slope propagation model with lognormal shadowing in the calculations of the capacity and the interference statistics. The exponent of the propagation is assumed to be γ 1 until the break point (R b ) and then it converts into a larger value γ 2 . In this way the path loss at a distance r from the base station is given by where (1) L b (the loss at a distance R b ) and R b are given by L b (dB) = 20 log 10 4π λ + 10γ 1 log 10 R b , (2) L g is the car window penetration loss assumed to be 3 dB, (3) h b is the base station antenna height, (4) h m is the mobile antenna height, (5) λ is the wavelength, (6) ξ 1 and ξ 2 are Gaussian random variables of zero mean and a standard deviation of σ 1 and σ 2 , respectively. ξ 1 and ξ 2 represent the effect of shadowing (loss deviation from the mean value).
Practical values of s 1 , s 2 , σ 1 , σ 2 , and R b are (see [8]) (1) γ 1 = 2.0 to 2.25, (2) γ 2 = 4.0 to 6.0, (3) σ 1 = 2 to 3 dB, (4) σ 2 = 4 to 6 dB, and (5) R b = 300 m. In WCDMA systems, each microcell controls the transmitted power of its users. If the interfering user i is at a distance r im from its base station and at a distance r id from the reference microcell base station, as shown in Figure 3, then the ratio of the interference signals L(r id , r im ) due to the distance only is given as follows.

UPLINK ANALYSIS
(2) If r id < R b and r im > R b then L(r id , r im ) is given as (3) If (r id and r im > R b ) then L(r id , r im ) is given by Now, the ratio of the interference signals L shd (r id , r im ) due to the distance and shadowing is given by where ξ id and ξ im are given as follows.
We will divide the total intercellular interference (I inter ) into interference from users in the S0 region (I S0 ) and interference from users in the S1 region (I S1 ), where these regions are shown in Figure 2. We will find the capacity and the interference statistics of the right sector (drawn in black in Figure 2) that provides half of the coverage to microcell d. We assume that users in the region S0 and S1 connect to the best (with lower propagation loss) of the two nearest microcells. In the S1 region, we will use the upper limit approximation (users in S1 never communicate with C1) to calculate the interference statistics. This will compensate the use of only 6 sectors to calculate the intercellular interference statistics instead of using unlimited number of sectors (microcells).
Let the mean value of the desired signal power received by the base station for a given service s be P r,s . The mean value of the interference from an active user communicating with the reference microcell, assuming the same service, will be also P r,s . A user i in the S0 region will not communicate with the reference base station d (C1) but rather with base station m (C2 or C3) whenever the propagation loss between the user i and base station m is lower than the propagation loss between the user i and the base station C1, that is, if Assuming a uniform density ρ s of users for each service, the density of users in each sector is ρ s = N u,s /R users per unit length. For the right part of S0 the expected value of I S0 for a given service s is given as Being where (1) β = ln 10/10, (2) α s is the activity factor of the user for the service s assumed to be 0.66 for voice users and 1.0 for data users.
Now the general value of σ 2 is given as follows.
(1) If r id ≤ R b and r im > R b or r id > R b and r im ≤ R b then the value of σ 2 is given by where C dm is the inter-sites correlation coefficient. (2) When (r id and r im > R b ) then σ id = σ 2 , also σ im = σ 2 and then The function Q(x) is the complementary distribution function of the standard Gaussian distribution defined as The upper limit of the expected value of I S1 due to right part of the S1 region for the service s is given as E I S1 r,s ≈ α s ρ s S1 r L r id , r im E 10 (ξid−ξim)/10 dr.
The expected value of the intercellular interference from the right side of the regions S0 and S1 for the service s is E[I] r,s = E I S0 r,s + E I S1 r,s .
Thus the expected value of the total interference from the left and right sides for the service s is given by where Sll is the side lobe level of the directional antenna used in each sector. The expected value of the total intercellular interference power for the service s is given as The expected value of the intracellular interference power due to the service s is given by Taking into account an imperfect power control with standard deviation error of σ c (dB), the total expected interference power for the service s will be Using soft handoff, a fraction ψ of the sector users will be in connection with more than one base station (practically with two base stations). In this case, the expected value of the interference power for a given service s will be where K SHO is an interference reduction factor that can be derived from [13], where G SHO is the soft handoff gain. Practical value of K SHO in quasi 1D case (our case when the width of the highways is neglected since it is very narrow in comparison with the sector radius) is 0.95 to 0.98. The expected value of the total interference power due to all services will be where M is the number of the services that the system supports. The variance of the interference power P S0 due to right part of S0 for the service s is given as [7] var P S0 r,s where g r id r im = E 10 (ξid−ξim)/10 φ ξ id − ξ im , r id /r im 2 , = e 2(βσ) 2 Q 2β σ 2 + 10 √ σ 2 log 10 1 L r id , r im , The upper limit of the variance of P S1 due to right part of S1 for the service s is given as var P S1 r,s ≈ ρ s P 2 r,s S1 r L r id , r im 2 pα s E 10 (ξid−ξim)/10 2 − qα 2 s E 2 10 (ξid−ξim)/10 dr.
Thus the variance of total intercellular interference power due to the total region S0 and S1 for the service s is given by The variance of the total interference power due to all services s is given by In the uplink only εP r,s of P r,s is used in the demodulation (ε = 15/16 = 0.9375). Thus, for a given outage probability, the uplink carrier-to-interference ratio [C/I] s for a given service s is given as where P N is the receiver noise power and κ is a factor that depends on the outage probability (2.13 for outage probability of 2% and it is 2.33 for an outage probability of 1%). For a given service, the (E b /N o ) s ratio is given as [14] where G p,s is the processing gain of the service s. Assuming a given number of users for each service, the outage probability versus number of users can be obtained using (30).
For mixed services of voice and data, the ratio between the maximum transmitted power by data users and the maximum transmitted power of the voice users given in dB should be P td P tv dB = (1 + δ) 10 log 10 (1) P td is the transmitted power of the data users located at the sector border, (2) P tv is the transmitted power of the voice users located at the sector border, (3) δ is a constant with a value of 0.0 if only the mean value of the interference is considered. When the interference variance is also considered, it has a value of −0.1 to 0.1 depending on the parameters of the services under study, (4) G pv is the voice service processing gain, (5) G pd is the data service processing gain, for voice service given in natural numbers, and for data service given in natural numbers.

NUMERICAL RESULTS
In our estimation we assumed that the WCDMA chip rate We assume that the accepted outage probability is 1% and that the capacity of the sectors is calculated at this probability.
Firstly, we study the case of voice-only users (15 kbits/sec) assuming that the activity factor α is 0.66 and the required (E b /N o ) is 6.7 dB [15]. Figure 4 shows the outage probability of the sector for three different values of σ c , that is, 1.0, 1.5 and 2.0 dB. For an outage probability of 1%, the capacity of the sector is 54.7, 51.8, and 48.1 voice users, respectively.
Next we study the case of data-only users assuming a bit rate of 120 kbps (G p = 32), required (E b /N o ) = 2.5 dB, and α = 1 [14]. Figure 5 shows the outage probability for three values of σ c , that is, 1.0, 1.5, and 2.0 dB. For an outage probability of 1%, the capacity of the sector is 12.9, 11.8, and 10.6 data users, respectively.
Let us now study the case of mixed services. Figure 6 shows the outage probability as a function of the number of voice users/sector for three values of σ c , that is, 1.0, 1.5, and 2.0 dB assuming that 5 data users exist within each sector. For an outage probability of 1%, the capacity of the sector is 33.8, 30.2, and 25.5 voice users respectively. Figure 7 shows the mixed capacity of the sector when σ c = 1.5 dB.     Figure 8 shows the effect of the sector range R on the sector uplink capacity when σ c = 1.5 dB. It can be noticed that for 300 ≤ R ≤ 900 m the capacity increases when R increases and then it remains constant for 900 ≤ R ≤ 1000 m. At higher sector range, sector capacity reduces monotonically. In practice, R could have a value of 1000 to 2000 m. To start with, one base station could be deployed each 4.0 km of the highway. With the time, another base station could be deployed in between, reducing the distance between the base stations to 2.0 km. Figure 9 shows the effect of the side lobe level Sll on the sector uplink capacity. It can be seen that reducing the side  lobe level will increase the capacity of the sector. An antenna with azimuth side lobe level of −15 dB or better is a good choice. Figure 10 points out the effect of the break point distance R b on the sector uplink capacity. It can be noticed that the effect of the break point distance on the uplink capacity of the sector is very small (0.2 users) and that the maximum capacity is obtained at R b of 450 m. Figure 11 depicts the effect of the inter-sites correlation coefficient C dm on the sector uplink capacity. It can be noticed that the effect of the inter-sites correlation coefficient C dm on the uplink capacity of the sector is very small (0.1 users). This is due to the fact that the intercellular interference affected by the inter-sites correlation coefficient is small compared with the intracellular interference not affected by the inter-sites correlation coefficient. Figure 12 shows the effect of the propagation exponent γ 1 on the sector uplink capacity. It can be noticed that increasing the value of γ 1 will reduce the sector uplink capacity. This is due to the fact that increasing γ 1 will increase the propagation loss which reduces the power level of the received signal reducing the capacity (as shown by (29)). Figure 13 represents the effect of the propagation exponent γ 2 on the sector uplink capacity. It can be noticed that increasing the value of γ 2 from 4 to 4.75 will increase the sector uplink capacity. Also, it can be noticed that increasing γ 2 from 4.75 to 6 will reduce the sector uplink capacity. This is due to the fact that increasing γ 2 will increase the isolation B. Taha-Ahmed and M. C. Ramon (lower intercellular interference and thus higher capacity) between the microcells. Nevertheless, increasing γ 2 increases the propagation loss lowering the sector uplink capacity. For γ 2 between 4 and 4.75, the effect of the isolation is dominant. Thus, the capacity increases. For γ 2 higher than 4.75, the effect of the propagation loss is dominant. Finally, we will study the effect of reducing the base station receiver noise figure using new technologies such as high temperature filters and super low noise amplifiers (amplifiers with noise figure lower than 0.5 dB). Figure 14 shows that the effect of reducing the receiver noise figure is quasi null when the sector radius is 1000 m. Nevertheless, at higher sector range, the effect will be notable. Reducing the noise figure of the receiver from 7 to 5 dB will increase the sector uplink capacity by 0.  to 5 dB will increase the sector uplink capacity by 1.4 voice users. Thus, for a sector range of 1500 m or lower, it is unnecessary to use high-cost components in the receiver since its effect is marginal.
It has been noticed that 98.4% of the interference is due to S0 region (4 sectors). Thus, the 5 microcells (10 sectors) model is sufficient for calculating the interference statistics with a high accuracy.

CONCLUSION
We have presented a model to calculate the capacity and interference statistics of a multi-service WCDMA in rural highway cigar-shaped microcells. The capacity of the sector has been studied using a general two-slope propagation model with lognormal shadowing and imperfect power control and finite transmitted power. The effects of the sector range and the sidelobe level of the directional antenna have been studied. It has been concluded that reducing the antenna side lobe level increases the sector capacity. Also it has been concluded that the optimum sector range to get the maximum sector capacity is in the order of 900 to 1000 m when the break point distance is 300 m. It has been noticed that the effect of the breakpoint distance on the uplink sector capacity is quasi null. Also, it has been noticed that the effect of the inter-sites correlation coefficient on the sector uplink capacity is negligible.
To get the quasi-maximum possible sector capacity, the following conditions should be fulfilled.
(1) The sector range should be higher than 800 m and lower than 1200 m. (2) The sidelobe level of the directional antenna should be −15 dB or better.