Optimum Rate Allocation for Two-Class Services in CDMA Smart Antenna Systems

810 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 51, NO. 5, MAY 2003 Optimum Rate Allocation for Two-Class Services in CDMA Smart Antenna Systems Il-Min Kim, Member, IEEE, Hyung-Myung Kim, Senior Member, IEEE, and Dong Seung Kwon Abstract Transmission bit rates are optimized for two-class traffic in variable spreading gain code-division multiple-access systems with antenna arrays. In an array antenna system, the interference levels experienced by the users belonging to different beams are not the same. Thus, it is not efficient to allocate the same rates to all the data users even though they belong to a cell. Considering this, an optimum rate allocation scheme is proposed for delay-tolerant data users. Additionally, we also propose the optimum rate allocation scheme for voice and data users when a packet scheduling scheme is considered. Numerical results show that, in array antenna systems, the proposed schemes considerably outperform the conventional scheme designed for omniantenna systems. Index Terms Array antenna systems, code-division multiple access (CDMA), rate allocation, variable spreading gain. I. INTRODUCTION THIRD-GENERATION communications systems must provide multimedia services. In omniantenna code-division multiple-access (CDMA) systems, various rate allocation schemes have been proposed for two-class traffic [1] [4]. These schemes allow delay-tolerant data users to dynamically utilize the unused capacity left by the real-time voice users. In these schemes, the transmission rates for the data users are generally controlled by considering the interference levels induced by the voice users. In omniantenna systems, the data users signals received at a base station (BS) experience the same intracell and intercell interferences. Thus, the previous schemes [1] [3] allocate the same transmission rates to the data users of a cell for a given interference level induced by the voice users. The optimum scheme in [4] also allocates the same transmission rates for the data users whose channel gains are the same. Recently, array antenna systems have received increasing interest for improving the performance of wireless radio systems. In array antenna systems, however, the data users signals received at a BS may experience different intracell and intercell interferences according to their beams or their direction of arrivals (DOAs). This interference difference may come from the nonuniform distribution of the voice and/or data users. However, even if all the users are distributed uniformly, the difference may Paper approved by R. Kohno, the Editor for Spread Spectrum Theory and Applications of the IEEE Communications Society. Manuscript received February 1, 2002; revised March 30, 2002; August 8, 2002; and January 27, 2003. I.-M. Kim is with the Division of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138 USA (e-mail: ilmin@deas.harvard.edu). H.-M. Kim is with the Department of Electrical Engineering and Computer Science, Korea Advanced Institute of Science and Technology (KAIST), Taejon 305-701, Korea (e-mail: hmkim@csplah.kaist.ac.kr). D. S. Kwon is with the Electronics and Telecommunications Research Institute (ETRI), Daejeon 305-350, Korea (e-mail: dskwon@etri.re.kr). Digital Object Identifier 10.1109/TCOMM.2003.811413 exist due to the voice activity. Thus, applying the conventional scheme may not be efficient, and it is necessary to study new proper rate allocation schemes for array antenna systems. Although a few heuristic rate allocation schemes [5] were proposed for antenna array systems, optimum rate allocation has seldom been studied. In this paper, we focus on the optimum rate allocation for two-class traffic in CDMA systems with antenna arrays. We consider short-term traffic control: the number of connected voice and data users is fixed. The transmission time scale is organized in slots and a voice or data packet is transmitted during a slot. We assume quasi-static flat fading: the path gain is constant during a slot. We also assume perfect instantaneous power control in the uplink of an array antenna system: at each BS, the received power of every user is always maintained at the desired level. For real-time voice users, a constant bit rate is provided. The received signal power for every voice user in the th cell is assumed to be proportional to the number of existing voice and data users in the cell. Then the transmission power for voice user in cell at slot is given by, where represents the channel gain at slot between the th voice user of cell and BS. Thus, the maximum required transmission power is given by, where and. We assume that there exists a constraint on the maximum transmission power, i.e.,, where is the peak allowed transmission power for voice users. For delay-tolerant data users, the transmission bit rates can be controlled at the slot layer. Let be the transmission bit rate of the th data user in cell at slot. We assume as in [2]. Note that, unlike the conventional scheme, the transmission rates of the data users may be different even though they belong to the same cell. To accommodate multiple transmission rates and multiple quality of service (QoS) requirements, we adopt two principles of the variable spreading gain CDMA technique [6], [7]. First, for the users with different rates and the same QoS, the amount of the received power should be proportional to the rates. Second, for the users with different QoSs and the same rate, the amount of the received power should be proportional to the QoSs. That is, the received power for the th data user in cell at slot will be proportional to the transmission bit rates and the QoS requirements where and are the required energy-per-bit-to-interference-plus-noise density ratio (EINR) for the data and voice (1) 0090-6778/03$17.00 2003 IEEE

KIM et al.: OPTIMUM RATE ALLOCATION FOR TWO-CLASS SERVICES IN CDMA SMART ANTENNA SYSTEMS 811 users, respectively. The transmission power of data user in cell at slot is given by, where represents the channel gain at slot between the th data user of cell and BS. As in the case of voice users, we also assume that there exists a constraint on the maximum transmission power, i.e.,, where is the peak allowed transmission power for data users, and. The outline of the paper is as follows. The EINR of the array antenna system is presented in Section II. In Section III, an optimum transmission rate allocation scheme is proposed for the data users in variable spreading gain CDMA systems with antenna arrays. Additionally, with packet scheduling, another optimum rate allocation scheme is proposed for voice and data users. In Section IV, numerical results are presented in order to evaluate the performance of the proposed schemes. In Section V, conclusions are given. II. EINR IN THE ANTENNA ARRAY SYSTEM Let and be the array response vectors from BS to the th voice user and the th data user, respectively, in cell at slot. The array response vectors may be calculated by various DOA estimation schemes such as the multiple signal classification (MUSIC) method and the estimation of signal parameters via rotational invariance technique (ESPRIT) method [8]. In this paper, we assume that the BSs have perfect DOA information of the users as in [9]. Let and be the beamforming weighting vectors at slot, by which the received signals of the th voice user and the th data user are weighted at BS, respectively. For calculating the beamforming vectors, numerous schemes may be used such as the conventional beamformer, the null-steering beamformer, and the optimal beamformer [8]. Because our proposed schemes are not specific to beamforming methods, any beamformer can be used. Let voice users and data users exist in the th cell. The state of each voice user, active or inactive, can vary at each slot. Let represent the voice activity of the th voice user in cell at the th slot. It is a Bernoulli variable with success probability. If the th voice user in cell is active at the th slot, is equal to one; otherwise, is equal to zero. Let be the number of antenna elements, the thermal noise power, the spreading bandwidth, and the number of cells. At the th slot, the EINRs of the th voice user and the th data user in cell can be expressed as [7], [9] where (2) (3) (4) III. OPTIMUM RATE ALLOCATION A. Optimum Rate Allocation for Data Users Without Packet Scheduling To maximize the data throughput, we formulate an optimization problem. Let and. The optimum data rate vector which maximizes the total data throughput at the th slot is obtained by solving the following problem: subject to (9) (10) (11) (12) where is the column vector whose elements are equal to one, the set of active voice users in BS at slot, and. In the above optimization problem, (9) and (10) mean that the EINR requirements of all the voice and data users must be satisfied. Additionally, the constraint on the maximum allowed peak transmission power for the data users is represented by (11). Finally, (12) denotes that the minimum transmission rate for the data users must be equal to or greater than the minimum rate requirement. When the optimum rates are obtained, the received powers are calculated by (1). Since all the constraints of (9) (12) can be expressed as linear inequalities in terms of, the optimum solution can be obtained by several methods such as the Simplex method (5) (6) (7) (8)

812 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 51, NO. 5, MAY 2003 (a) (b) Fig. 1. Packet scheduling scheme. (a) Without packet scheduling (b) With packet scheduling. [10]. Given, the average throughput per data user during slots is calculated as th slot of the th group. We define,,,,, and as follows: (13) B. Optimum Rate Allocation for Voice and Data Users With Packet Scheduling Because of nonzero finite beam widths in array antenna systems, the signals belonging to the adjacent beams may function as interferences to one another. Thus, if we reduce the number of simultaneously existing beams and locate these beams as sparsely as possible, the interbeam interference is decreased. This results in the reduction of intracell and intercell interferences to every user. Based on this fact, a packet scheduling scheme has been proposed for one-class traffic in array antenna systems [7]. In this scheme [7], a slot is divided into multiple subslots and these subslots are scheduled. In this section, we extend the previous scheme to two-class traffic environments. However, we consider the grouping of slots rather than the splitting of slots, because the splitting slots may not be allowed and may increase the signaling overheads. Fig. 1 shows the packet scheduling scheme with grouping when 16 users exist in a cell. denotes the slot duration and denotes the received power, which is assumed to be the same for all the users in this figure. We observe that the interbeam interference can be decreased by this packet scheduling. We assume that slots are grouped and they are optimized at the same time. Let and be the rates of the th voice and the th data users, respectively, in cell at the Because we assume variable spreading gain technique, the received powers for the th voice user and the th data user in cell at the th slot of the th group are given by (14) (15) Let and be the sets of the voice and data users who transmit the voice and data packets, respectively, in cell during the th slot at the th group. The packet scheduling can be realized by determining and in an appropriate way. For efficient packet scheduling, and must be chosen so that the number of simultaneously existing beams can be reduced and these beams can be located as sparsely as possible. We assume that the number of active voice users does not change during slots. For small such

KIM et al.: OPTIMUM RATE ALLOCATION FOR TWO-CLASS SERVICES IN CDMA SMART ANTENNA SYSTEMS 813 as or, this assumption is reasonable because the talk spurt, whose average duration is about 1.2 s [11], is much longer than the duration of a slot. Then, under the assumption that all the users are uniformly distributed, and can be determined as in Appendix A. For nonuniform distribution, other choices can be more efficient. Using,,,,, and, we can define,,, and in a similar way to the previous sections. To maximize the total data throughput with the packet scheduling at the th group, we formulate an optimization problem subject to where,, and (16) (17) (18) (19) (20) (21) (22) (23) (24). In this optimization problem, (17) and (18) mean that the EINR requirements of all the voice and data users must be satisfied. Additionally, the constraints on the maximum allowed peak transmission powers for the voice and data users are represented by (19) and (20). For the voice users, (21) denotes that the average transmission rate during slots must be equal to. For the data users, (22) denotes that the average minimum transmission rate during slots must be equal to or greater than the minimum rate requirement. Finally, (23) and (24) are the nonnegativity constraints on the transmission rates of the voice and data users, respectively. When the optimum rates are obtained, the received powers are calculated by (14) and (15). Since all the constraints can be expressed in linear forms with respect to, the optimum solution can be obtained with various methods. Then the average data throughput per data user during slots can be calculated as (25) C. Computational Complexity and the Peak Transmission Power As previously stated, the proposed optimization problems can be solved by linear programming such as the Simplex method. In view of computational complexity, the Simplex method or any of its variants is a good algorithm, on average [10]. Let be the number of variables of a linear problem. Let denote the number of equality or inequality constraints of the linear program, excluding the nonnegativity constraints. The time complexity of the ellipsoid algorithm is, on average, where is referred to as the digital size and it generally depends on and [10]. That is, the Simplex method is a polynomial algorithm rather than an exponential algorithm, on average. Additionally, more efficient schemes such as the projective algorithm could reduce the computational complexity further. In practice, it was reported that the problems with and could be solved in very short computing times [10]. Considering the low computational complexity of the Simplex method or its variants, we can see that the proposed problems can be easily solved. Assume that active voice users and data users exist in each cell. First, in the optimization without packet scheduling, the number of variables per cell is. Because (12) can be considered as the nonnegativity constraints, the number of constraints per cell, excluding the nonnegativity constraints, is. This problem can definitely be solved very easily. Next, in the optimization with packet scheduling, the number of variables per cell is. Under the assumption that and are determined as in Appendix A, the number of constraints per cell, excluding the nonnegativity constraints, is independent of and is given by (see Appendix B). Although this problem is a little more complex, this can also be solved very easily for small such as 2, 3, 4. The optimum scheme with packet scheduling may improve the data throughput, and this improvement tends to be more significant for larger. However, the hardware complexity may be also increased because, at some slots, the packet scheduling scheme may request voice and/or data users to increase the instantaneous transmission rates maximally up to times, compared with the scheme without packet scheduling. Thus, the peak transmission power must also be increased sufficiently, especially for the users near cell boundaries, although the average power consumption may be the same. However, these high peak-to-average power ratios of the transmitted signals may give rise to the inefficient operation of the radio frequency power amplifier. Without the sufficient increase of the peak transmission power, the performance of the packet scheduling may deteriorate because the users, whose channel gains are very small, may not increase their transmission rates to the levels requested by the packet scheduling. IV. PERFORMANCE COMPARISON A. Conventional Data Rate Allocation Scheme In the conventional schemes [1] [3] for omniantenna systems, the transmission rates are the same for the data users of a cell. Let be the transmission rates of the data users in cell at slot. Then, in the conventional schemes, the maximum transmission rates are obtained as follows: is chosen so that can be maximized while the minimum EINR, the minimum data rate, and the maximum transmission power constraints are satisfied as in

814 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 51, NO. 5, MAY 2003 TABLE I SYSTEM PARAMETERS Fig. 2. Data throughput gains (G1 and G2) versus the number of data users (N ) when N =30. (9) (12). Since this is a linear optimization problem, the optimum solution can be obtained. Given the optimum solution, the average data throughput per data user during slots is calculated as (26) B. Numerical Results In the simulation, a circular array antenna with radius is assumed at each BS, where is the wave length at the carrier frequency of the signals. As a weighting vector calculation method, we use the conventional beamformer [8]. We assume that,,,. We choose and as in Appendix A. For the proposed schemes, signaling is required in order to control the transmission rates of the delay-tolerant data users. We use 10 bits per slot for the signaling. For the voice users, the signaling is not necessary because the transmission rate is when and are determined as in Appendix A. Other system parameters are summarized in Table I. As performance measures, we define the throughput gain by the optimum scheme without packet scheduling over the conventional scheme, and the gain by the optimum scheme with the presented packet scheduling scheme. Note that, for performance comparison of the proposed and the conventional schemes, we assume the same system environment, i.e., we use the same array antenna system, the same beamforming algorithm, and the same system parameters. Fig. 3. Data throughput gains (G1 and G2) versus the number of voice users (N ) when N =20. Fig. 2 shows and versus when. We can see that the proposed schemes considerably outperform the conventional scheme. The gain is improved when the packet scheduling is applied. In particular, the larger is, the higher the gain is. In addition, as the number of the data users decreases, the gains become larger because the data users can control their transmission bit rates more dynamically. Fig. 3 shows and versus when. Fig. 4 shows the additional signaling overhead normalized by the throughput of the conventional scheme. The range of the normalized signaling overhead is between 1% and 5%. In practice, the maximum normalized overhead is, at most, 7% because 10 bits per slot are used for additional signaling and the minimum transmission rate of data users is 14.4 kbits/s. Note that the additional signaling overhead is negligible compared to the throughput improvement (from 40% to 380% depending on the number of voice and data users).

KIM et al.: OPTIMUM RATE ALLOCATION FOR TWO-CLASS SERVICES IN CDMA SMART ANTENNA SYSTEMS 815 beams as sparsely as possible, we choose and as shown in the equation at the bottom of the page, where and denote the th voice and the th data users, respectively, in the th cell. As an example, when,, and, the beam locations are presented in Fig. 1. APPENDIX B NUMBER OF CONSTRAINTS IN (17) (22) Let active voice users and data users exist per cell. When and are chosen as in Appendix A, the number of constraints per cell from (17) is calculated as follows: Fig. 4. Signaling overhead normalized by T versus the number of data users (N ). V. CONCLUSION Because array antenna systems increase the capacity considerably, they will be used in third-generation communications systems. In this paper, we have considered optimum rate allocation for two-class traffic in variable spreading gain CDMA systems with antenna arrays. In array antenna systems, the residual capacity which can be allocated to data users varies according to the beams or the DOAs, even in a cell. Considering this, we have optimized the transmission rates of the data users. We have also proposed an optimum voice and data rate allocation method when a packet scheduling scheme is applied. Numerical results show that the proposed schemes outperform the conventional scheme considerably. APPENDIX A AND UNDER THE ASSUMPTION OF UNIFORM TRAFFIC DISTRIBUTION Let be the number of voice users who are in the active state at the th group. Without loss of generality, we assume that and,,, where and denote the angles of the DOA of the th voice and the th data users, respectively, in the th cell at group. Assume that all the users are uniformly distributed in each cell. In order to locate (B.1) In the same way, the number of constraints from (18), from (19), from(20), from (21), and from (22), are given as follows:,,,, and. Thus, the total number of constraints per cell from (17) (22) is given by Note that (23) and (24) are nonnegativity constraints. (B.2) REFERENCES [1] S. Ramakrishna and J. M. Holtzman, A scheme for throughput maximization in a dual-class CDMA system, IEEE J. Select. Areas Commun., vol. 16, pp. 830 844, Aug. 1998. [2] J. M. Jacobsmeyer, Congestion relief on power-controlled CDMA networks, IEEE J. Select. Areas Commun., vol. 14, pp. 1758 1761, Dec. 1996. [3] S.-J. Oh and K. M. Wasserman, Dynamic spreading gain control in multiservice CDMA networks, IEEE J. Select. Areas Commun., vol. 17, pp. 918 927, May 1999. [4] S.-J. Oh, T. L. Olsen, and K. M. Wasserman, Distributed power control and spreading gain allocation in CDMA data networks, in Proc. INFOCOM, 2000, pp. 379 385. [5] Y.-C. Liang, F. P. S. Chin, and K. J. R. Liu, Joint downlink beamforming, power control, and data rate allocation for DS-CDMA mobile ratio with multimedia services, in Proc. ICME, 2000, pp. 1455 1458. [6] C. L. I. Sabnani and K. K. Sabnani, Variable spreading gain CDMA with adaptive control for true packet switching wireless networks, in Proc. ICC, 1995, pp. 725 730. [7] I.-M. Kim and H.-M. Kim, Scheme for enhancing performance of smart antenna in variable processing gain packet CDMA systems, Electron. Lett., vol. 35, pp. 518 520, Apr. 1999. for otherwise for otherwise

816 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 51, NO. 5, MAY 2003 [8] L. C. Godara, Application of antenna arrays to mobile communications Part II: beam-forming and direction of arrival considerations, Proc. IEEE, vol. 85, pp. 1195 1245, Aug. 1997. [9] A. F. Naguib, A. Paulraj, and T. Kailath, Capacity improvement with base-station arrays in cellular CDMA, IEEE Trans. Veh. Technol., vol. 43, pp. 691 698, Aug. 1994. [10] M. Padberg, Linear Optimization and Extensions. New York: Springer-Verlag, 1995. [11] P. T. Trady, A statistical analysis of on off patterns in 16 conversations, Bell Syst. Tech. J., vol. 47, pp. 73 91, Sept. 1967. Il-Min Kim (M 03) received the B.S. degree in electronics engineering from Yonsei University, Seoul, Korea, in 1996, and the M.S. and Ph.D. degrees in electrical engineering from the Korea Advanced Institute of Science and Technology (KAIST), Taejon, Korea, in 1998 and 2001, respectively. From July 1997 to August 2001, he worked as a Member of Technical Staff at the Electronics and Telecommunications Research Institute (ETRI). From October 2001 to August 2002, he was with the Department of Electrical Engineering and Computer Sciences at the Massachusetts Institute of Technology, Cambridge, as a Postdoctoral Research Fellow. Since September 2002, he has been continuing his research as a Postdoctoral Research Fellow with the Department of Electrical Engineering at Harvard University, Cambridge, MA. His research interests include space time codes, resource management for wireless communications, wireless video, power control for CDMA systems, and smart antennas. Dr. Kim was awarded the Gold Prize in the 2001 Samsung Humantech International Paper Contest. Hyung-Myung Kim (S 86 M 86 SM 99) received the B.S. degree in electronics engineering from Seoul National University, Seoul, Korea, in 1974, and the M.S. and Ph.D. degrees in electrical engineering from the University of Pittsburgh, Pittsburgh, PA, in 1982 and 1985, respectively. Since 1986, he has been with the Department of Electrical Engineering and Computer Science, the Korea Advanced Institute of Science and Technology (KAIST), Taejon, Korea, and is currently a Professor there. During the summer of 1997, he was on sabbatical leave as a Visiting Researcher at the Department of Electrical Engineering, Pennsylvania State University, University Park. His research interests include digital signal/image processing, digital transmission of voice and communications data, and image and multidimensional system theory. Dr. Kim was the Treasurer of the IEEE Taejon Section in 1992. He has been an editorial board member of Multidimensional Systems and Signal Processing since 1990. Dong Seung Kwon received the B.S. and M.S. degrees in electrical engineering in 1985 and 1987, respectively, from Yonsei University, Seoul, Korea, where he is currently working toward the Ph.D. degree. In 1988, he joined the Electronics and Telecommunications Research Institute (ETRI), Taejon, Korea, where he is currently a Principal Member of Research Staff and the Project Manager. His current research interests are mainly concentrated on digital mobile modem and radio transmission technology of high-speed mobile internet.