Reverse Link Erlang Capacity of Multiclass CDMA Cellular System Considering Nonideal Antenna Sectorization

Transcription

1 1476 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 52, NO. 6, NOVEMBER 2003 Reverse Link Erlang Capacity of Multiclass CDMA Cellular System Considering Nonideal Antenna Sectorization Josefina Castañeda-Camacho, Student Member, IEEE, Carlos Eduardo Uc-Rios, Student Member, IEEE, and Domingo Lara-Rodríguez, Member, IEEE Abstract In this paper, the effect of antenna sectorization in the reverse link Erlang capacity of a multiclass code-division multiple-access (CDMA) cellular system is studied. Traditionally, it has been considered that the capacity is multiplied by a factor equal to the number of sectors introduced. This is true only in the ideal antenna sectored system. However, due to the nonideal antenna radiation pattern, the sectorization gain is smaller than the number of sectors. Our contribution is the analytical study of the effect of nonideal antenna patterns on the capacity of a multiclass CDMA system. We also present an approximated analysis of the Erlang capacity, considering that blocking in CDMA occurs when the interference reaches a predetermined level above the background noise level of mainly thermal origin. The analysis also includes the effects of imperfect power control and service activity detection. We found that the capacity losses due to the consideration of antenna sectorization are about 20.20% for the nonideal antenna radiation pattern and 30.32% for the evaluated commercial radiation pattern. This percentage loss implies that the sectorization gain is approximately 2.39 for a nonideal antenna pattern and 2.09 for a commercial antenna pattern in typical conditions, =4and =8dB. Index Terms Antenna sectorization, capacity, macrocells, other-cell interference. I. INTRODUCTION CURRENTLY, third-generation mobile communication systems are being implemented in all major regions of the world. These systems, which go under the International Telecommunications Union (ITU) name of International Mobile Telecommunications in the year 2000 (IMT-2000) and within the European Telecommunications Standards Institute (ETSI) as the Universal Mobile Telecommunications System (UMTS), extend the services provided by current second-generation systems [Global System for Mobile Communications (GSM), Public Digital Cellular (PDC), Interim Standard (IS) 136, and IS-95] with high-rate data capacities [1]. In 1999, the ITU approved five different radio interface standards: 1) IMT Direct Spread (DS); 2) IMT Multicarrier (MC); 3) IMT Time Carrier (TC); 4) IMT Single Carrier (SC); 5) IMT Frequency Time (FT). Manuscript received November 6, 2001; revised December 20, 2002 and April 24, This work was supported in part by CONACYT under Project A. The authors are with the Communication Section, Center for Research and Advanced Studies IPN (CINVESTAV-IPN), Mexico City CP 07360, Mexico ( jcastane@mail.cinvestav.mx). Digital Object Identifier /TVT IMT-DS is the name for the Euro-Japanese wide-band code-division multiple-access (WCDMA) UMTS terrestrial radio access (UTRA) frequency-division duplexing wide-band CDMA air interface. IMT-MC is the American CDMA2000 multicarrier CDMA proposal. The two TDMA proposals are IMT-FT, which is the European Digital Enhanced Cordless Telecommunications system, and IMT-SC, which is the UWC-136 Enhanced Data Rates for GSM Evolution (EDGE) proposal. IMT-TC combines the TD-SCDMA and UTRA TDD proposals. Looking at different standards, time-division and code-division multiple access seem to be the main contenders. It is clear that CDMA systems have been proposed to offer the potential of high spectrum efficiency, together with other features, such as soft capacity, multipath resistance, inherent frequency diversity, and interference rejection, and the potential use of advanced antenna and receiver structures [2] [6]. The requirements of a third-generation system include support for multiclass services (voice, data, video, etc.), global roaming, operation in multiple environments, both fixed and mobile, and high-speed data services with different quality requirements [7], [8]. However, the ability to achieve high bit rates at low error rates over wireless channels is severely limited by the propagation characteristics of wireless environments, where signals typically arrive at the receiver via multiple propagation paths with different time delays, attenuations, and phases. There are mainly two strategies to support multiple data rates, henceforth multirate services in CDMA communications: the single-code transmission scheme using a variable processing gain, which is defined as the ratio of spread bandwidth to user information bit rate, and the multicode scheme [3], [9], [10]. In the single-code transmission scheme, each data rate is spread by a unique code with different chip rate in order to match the variable data rate. In the multicode scheme, a high data rate stream is first split into several fixed low-rate streams. The multiple data streams are spread by different short codes with the same chip rate and then added together. In order to obtain a reasonable performance in designing a multiclass CDMA cellular system, additional considerations are required. Power control, sectorization, and service activity detection have been proposed to decrease the interference power detected at the receiving antenna. In practice, power control errors occur and, due to antenna imperfections, the sectorization is not perfect. Ideally, system capacity is proportional to the number of sectors, with a proportional factor equal to the number of sectors introduced. However, the situation is different /03$ IEEE

2 CASTAÑEDA-CAMACHO et al.: REVERSE LINK ERLANG CAPACITY OF MULTICLASS CDMA CELLULAR SYSTEM 1477 if we consider nonideal antenna patterns. Some studies have been carried out to show how the sectorization of the base stations influences the performance of a cellular system [11] [17]. Wang et al. [11] compare the performance of the forward link of three-sectored and six-sectored CDMA systems by simulation. Wang and Wang [12], [13] present computer simulations results of the frequency reuse efficiency and sectorization gain for the reverse link CDMA system, considering a nonideal sector antenna pattern. Wacker et al. [14] show with simulations how the sectorization of the base stations influences the performance of a WCDMA radio network. Mahmoudi and Sousa [15] and Wang et al. [16] analyze the effects of sectorization considering a nonideal antenna pattern with a simulation. Jansen and Prasad [17] develop an analytical model to evaluate the performance of a cellular slotted DS CDMA system in terms of user capacity, throughput, and delay for the reverse link. They assume a simplified radiation pattern, where the antenna imperfections are modeled by an overlap angle. Then, they derive the antenna gain as a simple relationship between the total interference power received in a sectored system and the total interference power received in a nonsectored system. In this paper, we present an analytical model to evaluate the reverse link Erlang capacity of a multiclass CDMA cellular system considering the effects of nonideal sectorization on the other-cell interference evaluation [18], [19]. We present an approximated analysis of the Erlang capacity, considering that blocking in CDMA occurs when the interference reaches a predetermined level above the background noise level of mainly thermal origin [18]. This paper is organized and presented as follows. Section II is devoted to a discussion of the system model for the reverse link. Section III deals with the impact of the antenna sectorization on the other-cell interference factor. In Section IV, extending the Erlang analysis proposed in [18], we derive the capacities of a single-code and multicode CDMA system accommodating multiclass services in a multiple-cell environment. Section V presents numerical results. Finally, Section VI presents conclusions and remarks. II. SYSTEM MODEL Third-generation CDMA cellular systems are primarily concerned with the greatly varying information bit rates and communication quality requirements of various traffic types as well as the different characteristics of the wireless environments. Different traffic types with different rates and different transmission activity factors (or duty cycles) are spread with the same chip rate over the entire available bandwidth (1.25, 5, 10, 15, and 20 MHz for CDMA2000 and 5, 10, 15, and 20 MHz for WCDMA) [8], [20] [22]. In this paper, we focus on the stream class of traffic, which consists of various sources with different rates, quality requirements, and activity factors, assuming a single-code and multicode scheme. We consider a CDMA cellular system consisting of equal size hexagonal cells with the base stations located in their centers and a uniform distribution of users across the hexagonal cells. Each base station transmits a pilot tone to mobiles for handoff, power control, and synchronization. All base stations are connected to a central switching office. Power control is employed to compensate the propagation path loss and channel attenuation due to shadowing and fading. Multipath fading can be greatly eliminated by employing multipath combining techniques or fast power control, or it could be included in the outage requirement [23], [24]. Ideal soft handoff, in which the user is connected to the base station that offers the best path, is assumed [25]. A mobile in the handoff zone is served by all involved adjacent cells. However, in order to simplify the analysis, we investigate the performance of a system in which the three closest base stations are involved in the soft handoff operation. The interference generated by the users power controlled by the reference base station is defined as intracell interference. The interference from users that are controlled by other base stations is defined as intercell interference. An energy-to-interference ratio requirement, db, has been suggested in [26] for voice service in IS-95 CDMA system, but we know that the mean value, which results in a certain bit error rate (BER), is dependent on a number of factors. However, due to the improvement on diversity, coding and combining schemes and the use of the coherent detection in the reverse link, the requirements have been reduced for third-generation systems. For instance, db for voice service [8]. In this paper, the required is considered as a parameter that depends on the service type. In our model we assume that base stations are present and classes of services are supported. The transmission rate, the required, and the maximum number of users define the th class of service, where. Some other important considerations are listed bellow. A. Imperfect Power Control In CDMA systems, for capacity evaluation, variations in the received power levels due to imperfections in the control loop are well modeled as a log-normal distributed random variable with a standard deviation of less than 2.5 db [26], [27]. In this way, the random variable models the energy to interference ratio for each user of class in each base station under given propagation conditions. This random variable is completely characterized by its mean value and standard deviation. In third-generation multiclass systems, the standard deviation has been observed to be 1.5 db from simulations [28], [29]. In this paper, the numerical evaluations have been carried out for three main circuit-switched services: 8-Kbps voice and long delay constrained data services (LCD) at 64 and 144 Kbps [28], [30], [31]. The voice service is characterized by a low delay constraint with a BER of 10, while the data services require high performance (BER of 10 ). It was also assumed that each user of a particular service requires the same bit rate for communication and the same signal-to-interference ratio, thus the requirement for these services is taken from the different UTRA evaluation works, as can be observed in Table I. However, all the equations were derived in general and can be used for other services and requirements.

3 1478 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 52, NO. 6, NOVEMBER 2003 TABLE I UTRA SIMULATION RESULTS [28], [30], [31] B. Traffic Model We have considered that the number of active calls for each class of service is a Poisson random variable with mean, where is the offered load of the th service, defined as the product of the arrival rate and the mean service time. C. Service Activity Detection The activity factor for each class are modeled as a binary distributed random variable, with and. D. Other-Cell Interference Factor We have considered that the intercell interference can be modeled by a fraction of the intracell interference, in terms of the other-cell interference factor, defined as [25] average total interference due to other-cell users (1) average total interference due to intracell users As we can see in [25], includes the effect of soft handoff. In Section III, we will consider the effect of nonideal antenna sectorization in the derivation of the other-cell interference factor [19]. III. EFFECT OF NONIDEAL ANTENNA PATTERN IN THE OTHER-CELL INTERFERENCE FACTOR There are two kinds of handoffs in a sectored CDMA system: handoff between two sectors in different cells and handoff between two neighboring sectors in the same cell. The first one is named soft handoff and the second one is named softer handoff [32]. In this paper, we study the effect of nonideal antenna patterns on the reverse link capacity, considering the soft and softer handoffs of a multiclass CDMA cellular system. Sectorization is used in CDMA to increase system capacity, where cells are divided into sectors and the same frequency spectrum is reused in every sector. Traditionally, it has been considered that the capacity is multiplied by a factor that has the same value as the number of sectors introduced [16], [33]. This is true only in the ideal antenna system. However, due to the nonideal antenna radiation pattern, the sectorization gain is smaller than the number of sectors. One way to calculate the sectorization effect in a directional antenna system implies a separate evaluation of the capacity; this approach was followed in [14] and [17]. However, the capacity is dependent on the other-cell interference factor and sectorization gain. Therefore, in this work we have considered that capacity and sectorization gain are not independent; thus we have evaluated the other-cell interference factor including the sectorization effect. To evaluate the other-cell interference factor including the nonideal sector antenna pattern, in our investigation we limit the sectorization to three sectors per cell, although the results Fig. 1. Attenuation path. could be easily extended to other arrangements, e.g., four or six sectors per cell. We have also considered power control, which means that the signal received at the base station BS from any mobile controlled by this base station will be approximately equal. We assume that the received signal is affected only by shadowing and path loss. Thanks to the use of the RAKE receiver together with bit interleaving, channel coding, and space diversity reception, the Rayleigh distribution effect of the fast fading can be reduced to a minimum or it could be accounted for in the energy-to-interference ratio requirement. Then, the general signal power attenuation is given by As we can see in Fig. 1, is the distance between the th sector of the th base station, BS, and the mobile,, represents the sector antenna gain along the direction from the mobile to the th sector of BS, is the angle between and the maximum antenna gain direction, is a random variable with zero mean and standard deviation that models the log-normal shadowing for the th sector of BS, and is the path loss propagation factor. Since any analysis of other-cell interference involves a comparison of propagation losses among two or more base stations, the model must take into consideration the dependence of the propagation losses to two different base stations from a mobile user [25]. Since the propagation losses in db are Gaussian, we assume a joint Gaussian probability density for the losses to two base stations [25], [34]. The random component of the db loss can be viewed as the sum of a component in the near field of the user, which is common to all base stations, and a component that belongs only to the receiving base station and is independent from one base station to another. Thus the random component of the db loss for the th sector of BS can be expressed as (3) where, with (2) for all for all for all and (4)

4 CASTAÑEDA-CAMACHO et al.: REVERSE LINK ERLANG CAPACITY OF MULTICLASS CDMA CELLULAR SYSTEM 1479 Fig. 2. Nonideal antenna radiation pattern. Fig. 3. Commercial antenna radiation pattern. and its normalized covariance (correlation coefficient) of the losses to two sectors and of the base stations and is for all and (5) Notice that this model includes the limiting cases of independent attenuations and highly correlated attenuations. Also, as the paths from any sectors that belong to the same base station to the mobile are the same, we assume for all (6) In the evaluation was approximated by a parabolic function in the main beam and by a constant average for the sidelobe, and it can be expressed as [12] if if (7) where represents the antenna gain level (normalized to the maximum gain) at 60 sector crossover from the maximum gain direction and represents the average normalized gain level for the sidelobe. Fig. 2 shows the assumed antenna patterns for, and db and db. The nominal values chosen in some of our evaluations for and were 4 and 15 db, respectively. This corresponds to a typical cellular sector antenna with 3-dB horizontal beamwidth around [12]. In our evaluations we also have considered a commercial antenna radiation pattern, as we can see in Fig A. Soft Handoff Reception by the Best of the Three Nearest Cells We normalize to one the radius of each cell, which is defined as the maximum distance from any point in the cell to the base station at its center; and we assume a uniform density of users throughout all sectors. Given, the average number of users per sector, then considering an hexagonal shape of the normalized cell, its density is given by Users (8) Unit area To approach the performance of a soft handoff system, we consider the other-cell interference when the user is permitted 1 Andrew Corporation, Fig. 4. Region S, S, and S. to be in soft handoff to only the three nearest sectors. In a system with three sectors, the other-cell interference can be evaluated in three different regions, and, as we can see in Fig. 4. Taking the zeroth sector as the one under consideration, the region for which this sector can be in soft handoff, denoted by, is shown in Fig. 4 as the hatched area. is the region for which the remaining sectors of the zeroth cell can be in soft handoff (dotted area). Finally, is the region for which all the sectors outside the zeroth cell can be in soft handoff (gray area). The region models the users who could be controlled by three neighboring sectors inside the main beam of the zeroth sector antenna of BS. Within, any user that is communicating with one of the two nearest zeroth sector neighbors will introduce interference into the zeroth sector only if the propagation loss to that neighbor is less than to zeroth sector, in which case it is power controlled by the former. Thus the mean total interference to the zeroth sector of BS from the region is show in (9) at the bottom of the next page, where the distance from the user to the zeroth antenna sector of BS is denoted as and the distance from the user to the second and first antenna sector of BS and BS, respectively, as and.,, and refer to the corresponding random propagation components that model the log-normal shadowing for paths between the user and the corresponding sectors of BS,BS, and BS.

5 1480 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 52, NO. 6, NOVEMBER 2003,, and are the antenna radiation patterns relative to the previous paths. In order to simplify the equations, let us define and the logarithmic (db) attenuation to each user as (10) (11) Using (10) and (11) in (9), and solving as in [25], we have (12), as shown at the bottom of the page, where and (13) The region includes the users who could be controlled by the remaining sectors of the zeroth cell. In this area, the three nearest sectors involved in a potential soft handoff operation are denoted by the paths,, (note that in this case, the notation of BS and BS has changed and corresponds to Fig. 4). Hence, we have that the total interference to the zeroth sector of BS from the region is as shown in (14) at the bottom of the page, where if we consider (6) we have that. Thus, solving (14) as in the previous case, we have (15) at the bottom of the next page. Finally, is the region where the users are not controlled by the sectors of the base station of the zeroth cell. Thus we have that the total mean interference to the zeroth sector of BS from region is given by (16) at the bottom of the next page. In this case the notation of BS,BS, and BS has been given according to the top left-hand corner of Fig. 4. Solving (16) as in the previous cases, we have (17) as shown at the bottom of the next page. From (1), (12), (15), and (17), we obtain the other-cell interference factor for nonideal antenna sectorization (18) where is the average number of users per sector. The relative interference factor is evaluated numerically considering only three rings of adjacent cells for and, several values of, and. The results for nonideal sectorization considering the nonideal antenna radiation pattern for db and db and the commercial antenna radiation pattern of Fig. 3 are shown in Table II, where we can see that the value of is greater than the value of, obtained before with the ideal sectorization [25]. Table III shows the results for nonideal sectorization considering a nonideal radiation pattern but for and db and db. (9) (12) (14)

6 CASTAÑEDA-CAMACHO et al.: REVERSE LINK ERLANG CAPACITY OF MULTICLASS CDMA CELLULAR SYSTEM 1481 TABLE II OTHER-CELL INTERFERENCE FACTOR COMPARISON TABLE III OTHER-CELL INTERFERENCE FACTOR CONSIDERING A NONIDEAL ANTENNA SECTORIZATION B. Soft Handoff Reception by the Best of Multiple Nearest Cells (NNC) We generalize the results obtained in the previous section by increasing the candidate set for handoff to base stations, including the zeroth sector of the base station in the zeroth cell and the 1 base stations nearest to the zeroth cell [25], [34]. Generalizing the analysis of the last section, we find that the mean total interference to the zeroth sector of BS from the region is shown in (19) at the bottom of the next page where the value depends on the base station involved in the soft handoff operation, as we can see in Fig. 4. According to Fig. 4, where,if, then ; and if, then (15) (16) (17)

7 1482 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 52, NO. 6, NOVEMBER For the region, we have (20) as shown at the bottom of the page, where from Fig. 4, if, then ;if, then ; and if, then. In a similar way, the mean total interference to the zeroth sector from users located in the region are given by (21) at the bottom of the page, where, according to Fig. 4, if, then ;if, then ; and if, then. Again, the factor is obtained substituting (19) (21) into (18). It should be noted that when we have, Fig. 4 will change according to the values and of the previous equations. The same trend occurs on the value if we increment the number of sectors per cell. IV. EVALUATION OF THE ERLANG CAPACITY For CDMA, blocking is defined to occur when the total collection of the users both within the given cell and in the other cells introduce an amount of interference density so large that it exceeds the background noise level by an amount, taken to be less than 10 db [26]. For simplicity, we continue to assume that all cells are equally loaded (with the same number of users per cell, uniformly distributed over each cell). The interference power on the reference base station for the th user of class is given by Intracell interference other-cell interference (22) where is the thermal noise density, is the maximum total acceptable interference density, and is the available bandwidth. Then, the general condition for no blocking on the CDMA system is [26] Intracell interference other-cell interference (23) (19) for all (20) for all (21)

8 CASTAÑEDA-CAMACHO et al.: REVERSE LINK ERLANG CAPACITY OF MULTICLASS CDMA CELLULAR SYSTEM 1483 With the assumptions of Section II, considering a single-code system and (23), the condition for no blocking for the user of class becomes where, as we mentioned before,, and multicode (24) where is the maximum total interference power, and and are the number of users of class and, respectively, who are modeled as Poisson random variables. is the total number of services and is the total number of base stations. and are the activity factors for the th user of class in the zeroth cell or class in the th cell, respectively, which are modeled in both cases as binary random variables. and are the bit energies of the th user of class or in the reference cell or in the th cell. and are the bit rates of the users of class and, respectively, and is the power of thermal noise. We can see in (24) that the first term is the intracell interference from its own class of users (type ), the second term is the intracell interference from other class of users, and the third term is the intercell interference from all class of users. For a multicode system, we assume that the transmission rate requirements and are an integer multiple of the source rate. That is, and, where and are the number of codes to transmit the th and th class of services. Then, we have that the condition for no blocking for the user of class in a multicode system is (25) where the second term of the sum (25) is the interference generated by the -1 codes utilized to transmit the th class of service [23], [24], [35]. Dividing (24) and (25) by and defining and (26) as the energy-to-interference ratio for the th user of class or, modeled as a log-normal random variable, the condition for no blocking becomes (28) Hence, the blocking probability for multiclass CDMA system becomes single-code (29) and multicode multicode (30) We note that this is a soft blocking phenomenon, which can be occasionally relaxed by allowing, and consequently 1-, to increase. Naturally, when (29) or (30) are exceeded, call quality will suffer. Thus, if this probability is kept sufficiently low, we can ensure high availability of good quality service [26]. To evaluate this blocking probability, we have considered a simple approach assuming a central limit theorem approximation for and, and computing its mean and variance. Then the blocking probability of the reference user of class is described as and (31) (32) In Appendix A, we derive the mean and variance of a system with a single sector where no interference from other cells is considered. We note that each user controlled by an other-cell base station will also have an that is log-normal distributed. Hence, this other-cell interference can also be modeled by the same log-normal (26) distribution as assumed for the users of the desired cell. We can now modify the values in the Appendix to accommodate other-cell users as well [26]. Thus, we find for the single-code system that the mean and variance are given by single-code (33) and for the multicode system, we have that the mean and variance are (27) (34)

9 1484 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 52, NO. 6, NOVEMBER 2003 Then, substituting the values of Appendix A, we have for the single-code system The final system capacity that includes the and blocking probability requirements for each class of service is defined as the vector, given by the solution of (31) for a single-code system and (32) for a multicode system. The ideal antenna sectorization can be considered if we change the value of previous equations to. Inverting (31) and (32) yields the quadratic equation as shown in (39) at the bottom of the page, where for a single-code system we have and (35) (36) where and are the offered traffics of the th or th class of service, and are the activity factors of the th or th class of service, and. We assume that the standard deviation of the energy-to-interference ratio is equal for all classes of services, that is, db, and the mean value of the energy-to-interference ratio is and for each service, which are given in Table I. For the multicode system, we have and for a multicode system we change in (40) only (40) (41) We can obtain the Erlang capacity for a single-code and multicode systems by solving the second-order simultaneous equations system given by (39) (41). and (37) (38) V. NUMERICAL RESULTS In our evaluations, we consider a multiclass CDMA2000 system with a total available bandwidth of 10 MHz and a blocking probability for all classes of services. We evaluate a system supporting three classes of services, whose requirements are given in Table I for a standard deviation db. Additionally, we assume that the user activities factors are,, and. To see the effect of the path-loss propagation factor and the standard deviation of the shadowing, in the Erlang capacity, we have evaluated the performance for a single-code system assuming different values of the other cell interference factor. These values were taken from Tables II and III for the different (39)

10 CASTAÑEDA-CAMACHO et al.: REVERSE LINK ERLANG CAPACITY OF MULTICLASS CDMA CELLULAR SYSTEM 1485 Fig. 5. Single-code Erlang capacity for = 4(0)LCD64K = 0 (00)LCD64K =10. Fig. 7. Multicode Erlang capacity (0)f = 0:58, (00)f = 0:98, (0:)f =1:27. Fig. 6. Single-code Erlang capacity (0)f =0:58, (00)f =0:98, (0:)f =1:27. channel conditions. The results are shown in Fig. 5 for two services, where we can see that the capacity decreases as is decreased, that is, as the propagation conditions get worst. The same effect occurs if we increment. Fig. 5 shows the load of voice users for 0 and 10 LCD64k users; observe that the capacity achieves its highest values for the ideal antenna radiation pattern and that value decreases as is incremented for the nonideal sectorization. This is so because for the ideal pattern, a zero gain is considered for the sidelobe, and for the nonideal sectorization as is increased, the other-cell interference is also increased due to the fact that the angle from the antenna gain direction is higher as is increased. The most realistic values of the capacity were obtained using the commercial antenna radiation pattern. Figs. 6 and 7 show the numerical results of the Erlang capacity for a single-code and a multicode system assuming typical channel conditions, that is, pathloss exponent and standard deviation of shadowing db. In that case, from Table II, is equal to 0.98 if we consider a nonideal antenna radiation pattern and db, and is equal to 1.27 if we consider the commercial radiation pattern. For the ideal antenna radiation pattern. As we can see, high transmission rates will reduce low-rate users capacity. Comparing Figs. 6 and 7, that is, single-code and multicode systems, we have a capacity improvement due to the multicode scheme, especially for high transmission rates where the degradation introduced by the codes is not perceptible; for low transmission rates the additional interference introduced by the codes is more no- Fig. 8. Single-code Erlang capacity for different activity factors, f =0:98, (-) LCD64K, ( ) LCD144K. TABLE IV LOAD OF VOICE USERS FOR f = 0:58 IN A SINGLE-CODE SYSTEM, IDEAL ANTENNA RADIATION PATTERN table. However, for these channel conditions the performance of both systems is almost equal. In single-code and multicode systems, the losses due to the consideration of antenna sectorization, which remain approximately constant for all capacity values, are about 20.20% for the nonideal antenna radiation pattern and 30.32% for a commercial radiation pattern. This percentage of loss implies that the sectorization gain is found to be approximately 2.39 for a nonideal antenna pattern and 2.09 for a commercial antenna pattern in typical conditions, and db. Fig. 8 shows the effects of user activity on the available voice capacity. As the activity of data users decreases, more voice and data load can be accommodated. High data transmission rates can also significantly affect the available voice capacity. Tables IV VI show the voice and data Erlang capacities when we consider a single-code system with three services. We can

11 1486 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 52, NO. 6, NOVEMBER 2003 TABLE V LOAD OF VOICE USERS FOR f = 0:98 IN A SINGLE-CODE SYSTEM, NONIDEAL ANTENNA RADIATION PATTERN where is the interference due to the own class of service and is the interference due to the other class of services in the same cell, both given by (A.2) Since and are the sum of and independent random variables, we have from [36] that TABLE VI LOAD OF VOICE USERS FOR f =1:27 IN A SINGLE-CODE SYSTEM, COMMERCIAL ANTENNA RADIATION PATTERN (A.3) where and are themselves random variables. From [37], if we have that (A.4) see the same effects observed before, but there is an additional reduction in the voice and data capacities due to the increment in the number of the services. VI. CONCLUSION In this paper, we have evaluated the other-cell interference factor for nonideal sectorization and the Erlang capacity for a multiclass CDMA system. Using an available bandwidth of 10 MHz and considering the effects of imperfect power control and service activity detection, we have seen the capacity improvement of the third-generation systems due to coherent detection on the reverse link. Additionally, we can conclude that the impact of the choice of transmission rate is dominated by its effect on the low-rate users, because high transmission rates will reduce low-rate users capacity. The comparison of a single-code and a multicode system shows a capacity improvement in the multicode scheme, especially for highest transmission rates; although under the given channel conditions the performance of both schemes is almost equal. Finally we have shown that the capacity losses in a single-code and in a multicode system due to the antenna sectorization are about 20.20% for the nonideal antenna radiation pattern and 30.32% for the commercial radiation pattern. This percentage of loss implies that the sectorization gain is found to be approximately 2.39 for a nonideal antenna pattern and 2.09 for the commercial antenna pattern in typical conditions, and db. APPENDIX A where is a nonnegative integer-valued random variable and is a sequence of independent identically distributed, nonnegative random variables, the mean and variance of the random variable are given by (A.5) Considering that, and, in (A.2), we can obtain the mean values of and from (A.4) and (A.5) as and the variance of and as (A.6) Starting from (31) for the single-code system, but without considering other-cell interference, we can set (A.1) (A.7)

12 CASTAÑEDA-CAMACHO et al.: REVERSE LINK ERLANG CAPACITY OF MULTICLASS CDMA CELLULAR SYSTEM 1487 Following with (32) for the multicode system, but without considering other-cell interference, we can set (A.8) where is the interference due to the own class of service and is the interference due to the other class of services in the same cell, both given by (A.9) Since and are the sum of and independent random variables, we have that (A.10) Considering, and, (A.4), and (A.5) in (A.9), we can obtain the mean values for and as and the variance of and as (A.11) (A.12) ACKNOWLEDGMENT The authors would like to thank the anonymous reviewers for their valuable comments and suggestions, which enhanced the quality of this paper. REFERENCES [1] L. B. Milstein, Wideband code division multiple access, IEEE J. Select. Areas Commun., vol. 18, pp , Aug [2] E. Dahlman, P. Beming, J. Knutsson, F. Ovesjö, M. Persson, and C. Roobol, WCDMA-the radio interface for future mobile multimedia communications, IEEE Trans. Veh. Technol., vol. 47, pp , Nov [3] M. F. Madkour and S. C. Gupta, Performance analysis of a wireless multirate direct-sequence CDMA using fast walsh transform and decorrelating detection, IEEE Trans. Commun., vol. 48, pp , Aug [4] E. H. Dinan and B. Jabbari, Spreading codes for direct sequence CDMA and wideband CDMA cellular networks, IEEE Commun. Mag., pp , Sept [5] D. N. Knisely, S. Kumar, S. Laha, and S. Nanda, Evolution of wireless data services: IS-95 to cdma2000, IEEE Commun. Mag., pp , Oct [6] A. Baier, U. Fiebig, W. Granzow, W. Koch, P. Tender, and J. Thielecke, Design study for a CDMA-based third-generation mobile radio system, IEEE J. Select. Areas Commun., vol. 12, pp , May [7] D. N. Knisely, Q. Li, and N. S. Ramesh, Cdma2000: a third-generation radio transmission technology, Bell Labs Tech. J., pp , July-Sept [8] T. Ojanaperä and R. Prasad, An overview of air interface multiple access for IMT-2000/UMTS, IEEE Commun. Mag., pp , Sept [9] D. I. Kim and V. K. Bharghava, Performance of multidimensional multicode DS-CDMA using code diversity and error detection, IEEE Trans. Commun., vol. 49, pp , May [10] S. J. Lee, T. S. Kim, and D. K. Sung, Bit-error probabilities of multicode direct-sequence spread-spectrum multiple-access systems, IEEE Trans. Commun., vol. 49, pp , Jan [11] W.-J.Wearn-Juhn Wang, I.-T.I.-Tai Lu, and S.-C.Shang-Chieh Liu, Soft handoff performance of 3-sector and 6-sector multicell CDMA system, in IEEE Vehicular Technology Conf. (VTC 2001), vol. 1, Spring 2001, p. 35. [12] S.-W.Szu-Wei Wang and I. Wang, Effect of soft handoff, frequency reuse and nonideal antenna sectorization on CDMA system capacity, in IEEE Vehicular Technology Conf. (VTC 1993), vol. 1, Spring 1993, pp [13], Simulation results on CDMA forward link system capacity, in Wireless and Mobile Communications, J. M. Holtzman and D. J. Goodman, Eds. Norwell, MA: Kluwer Academic, [14] A. Wacker, J. Laiho-Steffens, K. Sipilä, and K. Heiska, The impact of the base station sectorization on WCDMA radio network performance, in IEEE Vehicular Technology Conf. (VTC 1999), Fall 1999, pp [15] M. Mahmoudi and E. S. Sousa, Sectored antenna system for cellular networks, in IEEE Vehicular Technology Conf. (VTC 1997), vol. 1, Spring 1997, pp [16] L.-C.Li-Chun Wang, K. Chawla, and L. J. Greenstein, Performance studies of narrow-beam trisector cellular systems, in IEEE Vehicular Technology Conf. (VTC 1998), Spring 1998, pp [17] M. G. Jansen and R. Prasad, Capacity, throughput, and delay analysis of a cellular DS CDMA system with imperfect power control and imperfect sectorization, IEEE Trans. Veh. Technol., vol. 44, pp , Feb [18] J. Castañeda-Camacho and D. Lara-Rodriguez, Erlang capacity of multiclass CDMA cellular system, in IEEE Vehicular Technology Conf. (VTC 2001), vol. 1, Spring 2001, p [19] C. E. UC-Rios and D. Lara-Rodríguez, On the effect of directional antennas on the reverse link capacity of CDMA cellular systems, in IEEE Vehicular Technology Conf. (VTC 2001), Fall [20] L. B. Milstein, Waveforms and receiver design considerations on wideband CDMA, IEEE Personal Commun. Mag., pp , Oct [21] T. Ojanaperá and R. Prasad, An overview of third generation wireless personal communications: a european perspective, IEEE Personal Commun. Mag., pp , Dec

13 1488 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 52, NO. 6, NOVEMBER 2003 [22], A survey on CDMA: evolution toward wideband CDMA, in IEEE ISSSTA Conf., 1998, pp [23] D. Ayyagari and A. Ephramides, Cellular multicode capacity for integrated (voice and data) services, IEEE J. Select. Areas Commun., vol. 17, pp , May [24] J. Zou and V. K. Bhargava, Design issues in a CDMA cellular system with heterogeneous traffic types, IEEE Trans. Veh. Technol, vol. 47, pp , Aug [25] A. J. Viterbi, A. M. Viterbi, K. S. Gilhousen, and E. Zehavi, Soft handoff extends CDMA cell coverage and increases reverse link capacity, IEEE J. Select. Areas Commun., vol. 12, pp , Oct [26] A. M. Viterbi and A. J. Viterbi, Erlang capacity of power controlled CDMA system, IEEE J. Select. Areas Commun., vol. 11, pp , Aug [27] A. J. Viterbi, The orthogonal-random waveform dichtonomy for digital mobile personal communication, IEEE Personal Commun. Mag., pp , [28] Q. Zhang and O.-C.On-Chin Yue, UMTS air interface voice/data capacity part 1: reverse link analysis, in IEEE Vehicular Technology Conf. (VTC 2001), vol. 1, Spring 2001, p [29] S. Sarkar, Reverse link capacity for CDMA2000, in IEEE Vehicular Technology Conf. (VTC 2001), vol. 1, Spring 2001, p [30] A.-G.Anne-Gaële Acx and P. Mendribil, Capacity evaluation of the UTRA FDD and TDD modes, in IEEE Vehicular Technology Conf. (VTC 1999), Spring 1999, pp [31] S. Akhtar and D. Zeghlache, Capacity evaluation of the UTRA WCDMA interface, in IEEE Vehicular Technology Conf. (VTC 1999), Fall 1999, pp [32] C.-C.Chin-Chun Lee and R.Raymond Steele, Effect of soft and softer handoff on CDMA system capacity, IEEE Trans. Veh. Technol., vol. 47, pp , Aug [33] P. Newson and M. Heath, The capacity of spread spectrum CDMA system for cellular mobile radio with consideration of system imperfections, IEEE J.. Select. Areas Commun., vol. 12, pp , May [34] A. J. Viterbi, A. M. Viterbi, and E. Zehavi, Other-cell interference in cellular power controlled CDMA, IEEE Trans. Commun., vol. 42, pp , Feb./Mar./Apr [35] S. J. Lee, H. W. Lee, and D. K. Sung, Capacities of single-code and multicode DS-CDMA systems accommodating multiclass services, IEEE Trans. Veh. Technol., vol. 48, pp , Mar [36] A. Papoulis, Probability, Random iables, and Stochastic Process, 3rd ed. New York: McGraw-Hill, [37] R. B. Cooper, Introduction to Queuing Theory, 3rd ed. Washington, DC: CEEP Press, 1990, pp provisioning. Josefina Castañeda-Camacho (S 99) was born in Puebla, Mexico, in She received the B.Sc. degree from the Autonomous University of Puebla (UAP), Mexico, in 1996 and the M.Sc. degree from CINVESTAV-IPN, Mexico, in 2000, both in electrical engineering. Currently, she is pursuing the Ph.D. degree at CINVESTAV-IPN. Her main research interests include teletraffic analysis, cellular system dimensioning, and performance evaluation of overlaid systems. Carlos Eduardo Uc-Rios (S 99) was born in Campeche, Mexico, in He received the B.Sc. degree in electronic and communications engineering from the University of Campeche, Mexico, in 1998 and the M.Sc. degree in electrical engineering from CINVESTAV-IPN, Mexico, in In 2000, he was with the University of Carmen, Mexico. In 2001, he joined the University of Campeche as a Lecturer. His areas of interest include cellular systems dimensioning and quality-of-service Domingo Lara-Rodríguez (S 97 M 00) received the B.Sc. degree in electronics and communications engineering from the National Polytechnic Institute of Mexico (IPN) and the M.Sc. and Ph.D. degrees in electrical engineering from CINVESTAV-IPN, Mexico. Currently, he is with the Mobile Telecommunications Research Group, Center for Research Advanced Studies, IPN. His main research interests include radio resource management, performance modeling, and architectural design in mobile cellular, indoor, and wireless local loop systems.