Combined Rate and Power Adaptation in DS/CDMA Communications over Nakagami Fading Channels

162 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 48, NO. 1, JANUARY 2000 Combined Rate Power Adaptation in DS/CDMA Communications over Nakagami Fading Channels Sang Wu Kim, Senior Member, IEEE, Ye Hoon Lee, Student Member, IEEE Abstract We consider combined rate power adaptations in direct-sequence code-division multiple-access communications, the transmission power the data rate are adapted relative to channel variations. We discuss the power gain that the combined adaptations provide over power adaptation. Then, we consider an integrated voice data transmission system that offers a constant bit rate voice service, using power adaptation a variable bit rate data service with rate adaptation. We present an expression for the required average transmission power of each traffic type having different quality-of-service specifications discuss the capacity gain over power adaptation for voice data. Index Terms Combined rate power adaptation, DS/CDMA, Nakagami fading. I. INTRODUCTION THE RADIO link for either a portable or a vehicular unit can be characterized by a time-varying multipath fading, which causes the link quality to vary with time. When the transmitter is provided with channel fading information, the transmission schemes can be adapted to it, allowing the channel to be used more efficiently. In general, the transmitter may adapt its data rate transmission power. Adaptive variation of transmission power was considered in [1], following adaptive variation of data rate [2], constellation size [3], adaptive coding scheme [4], all for narrow-b systems. For code-division multiple-access (CDMA) cellular systems (IS-95), power adaptation is employed to maintain the received power of each mobile at a desired level [5]. Adaptive code rate processing gain control in cellular direct-sequence/cdma (DS/CDMA) systems is considered in [6]. The optimization of powers, both powers rates in achieving a given quality-of-service (QoS) requirement for multimedia CDMA systems, is considered in [7] [8], respectively. In [8], the optimization is performed with a maximum transmission power a minimum rate requirement. In [9], a combined power/rate control scheme is considered that limits the increase in power by some fixed value gets the extra gain required by reducing the rate. In this paper, we consider the average data rate that meets adequate QoS requirements, subject to an average transmission power constraint a maximum transmission power limit. We propose two combined rate power adaptation schemes that Paper approved by A. Goldsmith, the Editor for Wireless Communication of the IEEE Communications Society. Manuscript received June 1, 1998; revised February 15, 1999. This work was supported by the Korea Science Engineering Foundation (KOSEF), Korea. The authors are with the Department of Electrical Engineering, Korea Advanced Institute of Science Technology, Taejon 305-701, Korea (e-mail: swkim@san.kaist.ac.kr). Publisher Item Identifier S 0090-6778(00)00515-8. limit the transmission power when the channel gain is low. We derive the average data rate as a function of average transmission power then derive the power gain that proposed adaptation schemes provide over power adaptation. We find that the power gain is more significant for channels with faster decaying multipath intensity profiles or weaker line-of-sight components for transmitters with lower peak-to-average power ratios. The power gain implies a power reduction at the transmitter, which translates into a reduction of interference to other users, leading to a capacity increase. Then, we consider an integrated voice data transmission system which offers a constant bit rate (CBR) voice service using power adaptation a variable bit rate (VBR) data service, such as e-mail file transfer, using rate adaptation. The motivation for applying rate adaptation to the data traffic is that the rate adaptation provides a power gain over the power adaptation, while still maintaining both the same average data rate (or throughput) bit-error rate (BER). We present a closed-form expression for the required average transmission power for each traffic type having different QoS specifications then discuss the capacity gain over the power adaptation for voice data. The remainder of this paper is organized as follows. In Section II, we describe the system model analyze the average data rate in general. In Section III, we propose two combined rate power adaptation schemes investigate the power gain that they provide over power adaptation. In Section IV, we analyze the performance of an integrated voice data transmission system that employs power adaptation for voice rate adaptation for data. In Section V, conclusions are made. II. SYSTEM MODEL AND ANALYSIS We assume that the channel is frequency-selective with respect to the spreading bwidth. Also, the channel variation, due to multipath fading, is slow relative to the bit duration. We further assume that the multipath fading is characterized by the Nakagami- probability density function (pdf). We look only at a single cell system. The implications of a multiple cell system can be accounted for by the out-of-cell interference coefficient [5]. We assume that there are users in the system, each nonreference-user signal is misaligned relative to the reference signal by an amount, which is uniformly distributed over a bit interval. The Nakagami- distribution spans a range of fading environments from one-sided Gaussian fading (, which corresponds to worst case fading) to nonfading ( ). It is well known that corresponds to Rayleigh fading, the Rician lognormal distributions can be closely approximated 0090 6778/00$10.00 2000 IEEE

KIM AND LEE: COMBINED RATE AND POWER ADAPTATION IN DS/CDMA COMMUNICATIONS 163 by the Nakagami distribution with. The Nakagamifading model fits experimental data from a variety of fading environments, including urban indoor multipath propagation [10]. The bit energy-to-equivalent noise spectral density ratio at the -finger RAKE receiver output for user is given by can be expressed by (10) (1) (2) (11) is the pdf of is the characteristic function of. However, since is a convex function, a lower bound on the average data rate can be obtained by using Jensen s inequality [12] is the channel power gain due to multipath fading for user on the th path, is the transmission power for user, is the bit duration for user, is the chip time, is the one-sided power spectral density of the background noise. We assume that are independently, identically distributed rom variables with (3) reflects the rate at which decay occurs. The pdf of is given by [11] It follows from (1) that in order to maintain an adequate transmission quality, the data rate [bits/s] the transmission power of user should be given by is the value required for adequate performance of the modem decoder is the chip rate. Typically, depends on its implementation, use of error correcting coding, channel impairments, such as fading, error rate requirements. Then, the average data rate is given by (4) (5) (6) (7) (8) (9) (12) (13) We will see later that the lower bound is very close to the exact value. It should be noted that the instantaneous data rate should not exceed the chip rate, in order to keep the bwidth constant. Therefore, when, i.e., should be limited by. However, since the probability of is negligibly small for parameter values of practical interests, (9) yields the actual average data rate. III. COMBINED RATE AND POWER ADAPTATION The major disadvantage of power adaptation is that much of the transmission power is used in compensation for deep fades in order to maintain a CBR. This translates into large interference to other users, leading to a capacity reduction. This problem can be solved by limiting the transmission power when the channel gain is low, if the users can tolerate some delay in their transmission. In this section, we consider two combined rate power adaptation schemes that reduce the average transmission power, while still maintaining the same average data rate BER. We assume that transmitters are subject to a maximum transmission power limit of. A full compensation of fading can be attained by power adaptation if or (14) (15) is the target received signal power that meets requirement. In the first scheme, the data rate is fixed when the transmission power is adjusted such that is equal to a desired value. When, the transmission power is fixed at, the data rate is adapted such that can be attained. This will be called power rate adaptation. The truncated power adaptation in [13] the power adaptation are special cases of (or ), respectively. In the second scheme, the data transmission is suspended when

164 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 48, NO. 1, JANUARY 2000. Otherwise, the data rate is adapted with a fixed transmission power. This will be called truncated rate adaptation. The rate adaptation is a special case of (or ). Note that both schemes save power by limiting the transmission power when. 1) Power Rate Adaptation: When the power rate adaptation is employed, is given by (16) the average transmission power given by at the mobile unit is Let (17) (18) (19) (20) (21) (22) (23) Fig. 1. The average data rate R versus S =N with power rate adaptation; R = 5M; L = 3; m = 1; (E =N ) = 7 (db), =0:5; =1; =0:3; S= S. The average data rate can be obtained by combining (9), (11), (16), (27). A lower bound on can be obtained by combining (12), (16), (17) as shown in (28), at the bottom of the page. Fig. 1 indicates that the lower bound is virtually identical to the exact value. Since the power adaptation makes, for all, it follows from (9) the fact that that the (average) data rate is given by Then, the pdf of is given by (24) (29) with power adaptation. Comparison of (28) (29) indicates that the power rate adaptation provides a power gain (25) (26) are the unit step function the Dirac delta function, respectively, the characteristic function of is given by (27) (30) over the power adaptation. 2) Truncated Rate Adaptation: When the truncated rate adaptation is employed, (28)

KIM AND LEE: COMBINED RATE AND POWER ADAPTATION IN DS/CDMA COMMUNICATIONS 165 represents the fraction of time during which no data transmission occurs. For example, when 99% of the time data transmissions are required, then. Another definition of an outage event is discussed in [14], the outage event is defined as the signal-to-noise ratio going below a threshold staying longer than a minimum duration. The notion of minimum duration outage will lead to a different performance measure. Comparison of (29) (34) indicates that the truncated rate adaptation provides a power gain (36) (37) Fig. 2. The average data rate R versus S =N with truncated rate adaptation; R = 5M; L =3;m=1; (E =N ) =7(dB), =0:5; =1; = 0:3.. The pdf the characteristic function of are given by (31) (32) (33) respectively. The average data rate can be obtained by combining (9), (11), (33). A lower bound on can be obtained from (12) (34) Fig. 2 shows that the lower bound is also virtually identical to the exact value. Since no data is transmitted (i.e., no service) if, the outage probability is given by (35) over the power adaptation. The power adaptation the rate adaptation are special cases ( ) of the power rate adaptation the truncated rate adaptation, respectively. So the difference between, when, is the power gain that the rate adaptation provides over the power adaptation. An intuitive explanation for this power gain is that the power adaptation uses a lot of the transmission power in compensating for deep fades in order to maintain a CBR. However, the rate adaptation uses a constant power compensates for deep fades by reducing the rate rather than using a large power. Thus, rate adaptation saves power during bad channels may use power more effectively for better channels. However, rate adaptation experiences a time delay when the channel gain is low. The relative benefits of rate power adaptations can be utilized in multimedia communications, users can tolerate some delay in their transmission. Fig. 3 is a plot of power gains versus.we find that the power gain is more significant for channels with a faster decaying multipath intensity profile (larger ) or weaker line-of-sight component (smaller ). We also find that is higher than. The higher gain is attained at a cost of a wider range of rate variations. Also, the power gains increase as increases. This indicates that traffic which tolerates a longer delay requires less transmission power. IV. INTEGRATED VOICE AND DATA TRANSMISSION We have seen previously that rate adaptation requires less transmission power than power adaptation in maintaining a given average data rate a given BER requirement. Since data traffic can tolerate a larger delay, a VBR service can be provided to data users with a significant advantage in saving transmission power also producing less interference to other users. In this section, we consider an integrated voice data DS/CDMA system that offers a CBR voice service using power adaptation a VBR data service, such as e-mail file transfer using rate adaptation. We assume that there are users transmitting voice traffic at a fixed rate of bits/s with an average transmission power users transmitting data traffic at an average rate of bits/s with fixed transmission power. Let be the transmission powers of voice user data user, respectively, with, are the channel gains of voice user

166 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 48, NO. 1, JANUARY 2000 TABLE I REQUIRED AVERAGE TRANSMISSION POWER FOR VOICE AND DATA USERS: m =1;L=3;=0:5; R =8 (kb/s), R = 32(kb/s), R = 5M; = 6(dB), = 10(dB), =3=8; =1 Fig. 3. Power gains G G versus ; =1;L=3;S= S. data user, respectively. Note that there are two indices, one corresponding to the information types (superscripts), the other corresponding to the user numbers (subscripts). Then, the bit energy-to-equivalent noise spectral density ratio for voice user 1 data user 1 are, respectively, given by (42). The validity of the approximation is justified later by a Monte Carlo simulation. For, are the desired average data rate for data traffic, respectively, it follows from (42) that (43) (38) Similarly, for, are the desired data rate for voice traffic, respectively, it follows from (41) that (44) (39) is the bit duration for voice is the bit duration for data, namely, is the voice activity factor of user. Since power adaptation is applied to voice traffic such that for some desired received power, we obtain (40) we assumed that voice activity factors are the same for all users, namely. If we approximate the interference by the data traffic by its mean value, then we get (41) Therefore, it follows from (43) (44) the relationships that the required average transmission powers for voice data users are approximately given by (45) (46) we assumed that. Table I presents the required average transmission powers for each type of traffic. It should be noted that the number of data users has a significant influence on. This is because the average data rate the requirements for the data traffic are much higher than for voice traffic.

KIM AND LEE: COMBINED RATE AND POWER ADAPTATION IN DS/CDMA COMMUNICATIONS 167 V. CONCLUSIONS Fig. 4. The maximum number of voice data users in an integrated voice data system; m = 1; = 0:5; L = 3; S =N = 65 (db), S =N = 60 (db), R = 8 (kb/s), R = 32 (kb/s), = 6 (db), =10(dB), =3=8; R =5M. The maximum number of voice data users,, can be obtained from (43) (44) as We have considered combined rate power adaptations in CDMA communication systems, the transmission power the data rate are jointly adapted relative to channel variations. First, we considered the power rate adaptation scheme which performs the rate adaptation when the transmission power required to meet a target QoS exceeds the maximum transmission power limit of adapts otherwise the transmission power to ensure a fixed-rate transmission. Then, we considered a truncated rate adaptation scheme that suspends transmitting data when the channel gain is below a threshold then otherwise adapts the rate with a constant power. We derived the average data rate as a function of the average transmission power the power gain that the combined adaptation schemes provide over the power adaptation scheme. The power gains are found to be more significant for channels with a faster decaying multipath intensity profile weaker line-of-sight components. The power gain translates into a reduction interference to other users, therefore leading to a capacity increase, prolongs battery life at the transmitter. Next, we considered an integrated voice data transmission system which offers a CBR voice service using power adaptation a VBR data service using rate adaptation. We presented an expression for the required average transmission power for each type of traffic having different quality of service specifications then discussed the capacity gain over the power adaptation for voice data. REFERENCES (47) When voice data are both power adapted, then in (41) (42) is equal to a desired received power,. Following the same procedure in obtaining (47), the maximum number of voice data users,, with power adaptation are given by (48) Fig. 4 is a plot of the maximum number of voice data users in an integrated voice data transmission system. Fig. 4 shows that the estimate on the maximum number of users by (47) (48) is very close to the Monte Carlo simulation result. For comparison purposes, we also plotted the maximum number of users when voice data users are both power adapted. As expected, the proposed scheme provides a higher capacity than the power adaptation for voice data, while still maintaining the same average data rates BER requirements. [1] J. F. Hayes, Adaptive feedback communications, IEEE Trans. Commun., vol. COM-16, pp. 29 34, Feb. 1968. [2] J. K. Cavers, Variable-rate transmission for Rayleigh fading channels, IEEE Trans. Commun., vol. COM-20, pp. 15 22, Feb. 1972. [3] W. T. Webb R. Steele, Variable rate QAM for mobile radio, IEEE Trans. Commun., vol. 43, pp. 2223 2230, July 1995. [4] S. M. Alamouti S. Kallel, Adaptive trellis-coded multiple-phaseshift keying for Rayleigh fading channels, IEEE Trans. Commun., vol. 42, pp. 2305 2314, June 1994. [5] K. S. Gilhousen et al., On the capacity of a cellular CDMA system, IEEE Trans. Veh. Technol., vol. 40, pp. 303 312, May 1991. [6] S. Abeta, S. Sampei, N. Morinaga, Channel activation with adaptive coding rate processing gain control for cellular DS/CDMA systems, in Proc. IEEE VTC, May 1996, pp. 1115 1119. [7] L. C. Yun D. G. Messerschmitt, Variable quality of service in CDMA systems by statistical power control, in Proc. IEEE ICC, June 1995, pp. 713 719. [8] A. Sampath, P. S. Kumar, J. M. Holtzman, Power control resource management for a multimedia CDMA wireless system, in Proc. IEEE PIMRC, Sept. 1995, pp. 21 25. [9] B. Hashem E. Sousa, A combined power/rate control scheme for data transmission over a DS/CDMA system, in Proc. IEEE VTC, May 1998, pp. 1096 1100. [10] H. Suzuki, A statistical model for urban multipath propagation, IEEE Trans. Commun., vol. COM-25, pp. 673 680, July 1977. [11] M. Nakagami, The m-distribution A general formula of intensity distribution of rapid fading, in Statistical Methods in Radio Wave Propagation. New York: Pergamon Press, 1960, pp. 3 36. [12] W. Feller, An Introduction to Probability Theory Its Applications, 2nd ed. New York: Wiley, 1971, vol. II. [13] S. W. Kim A. Goldsmith, Truncated power control in code division multiple access communications, in Proc. IEEE GLOBECOM, Nov. 1997, pp. 1488 1493. [14] N. B. Mayam, P. Chen, J. M. Holtzman, Minimum duration outage for cellular systems: A level crossing analysis, in Proc. IEEE VTC, Apr. 1996, pp. 879 883.

168 IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 48, NO. 1, JANUARY 2000 San Wu Kim (SM 98) received the Ph.D. degree in electrical engineering from the University of Michigan, Ann Arbor, in 1987. Since 1987, he has been with the Korea Advanced Institute of Science Technology (KAIST), Taejon, Korea, he is currently a Professor of Electrical Engineering. His research interests include spread-spectrum communications, wireless communications, error correction coding. From 1996 to 1997, he was a Visiting Associate Professor at the California Institute of Technology, Pasadena. Ye Hoon Lee (S 99) was born in Taegu, Korea, in 1968. He received the B.S. M.S. degrees in electrical engineering from the Korea Advanced Institute of Science Technology (KAIST), Taejon, Korea, in 1990 1992, respectively. Currently, he is working toward the Ph.D. degree in electrical engineering at KAIST. His research interests include spread-spectrum techniques in wireless mobile communications error control coding.