Performance Analysis of DS/SSMA Unslotted ALOHA System With Variable Length Data Traffic

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1 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 19, NO. 11, NOVEMBER Performance Analysis of DS/SSMA Unslotted ALOHA System With Variable Length Data Traffic Jae-Woo So, Student Member, IEEE, Il Han, Student Member, IEEE, Byung-Cheol Shin, and Dong-Ho Cho, Senior Member, IEEE Abstract In this paper, we analyze the throughput of a directsequence spread spectrum multiple access (DS/SSMA) unslotted ALOHA system with variable length data traffic. The system is analyzed for two cases: 1) systems without channel load sensing protocol (CLSP) and 2) systems with CLSP. The bit-error probability and the throughput are obtained as a function of the signal-to-noise ratio (SNR) during message transmission, considering the number of overlapped messages and the amount of time overlap. We assume that the generation of data messages is Poisson distributed and that the messages are divided into packets before transmission. The system is modeled as a Markov chain under the assumption that the number of packets in a message is geometrically distributed with a constant packet length. The throughput variance of the DS/SSMA unslotted ALOHA system with variable length data traffic is obtained as the Reed Solomon code rate varies. Results show that a signicant throughput improvement can be obtained by using an error-correcting code. Index Terms CDMA, CLSP, spread spectrum, throughput, unslotted ALOHA. I. INTRODUCTION SPREAD spectrum techniques have recently become popular in third-generation mobile communication systems because they offer a random access capability, a potential for high throughput performance, and low peak power demands during transmission. This is shown in that most proposals for radio transmission technology (RTT) in IMT-2000 are based on code division multiple access (CDMA) [1]. Packet radio systems based on CDMA can be classied into two categories according to the access scheme. These are: 1) a CDMA slotted ALOHA system and 2) a CDMA unslotted ALOHA system. Packet transmission in the CDMA slotted ALOHA system is initiated only at the beginning of a slot and the success of packet transmission depends on the amount of user interference within the slot. However, packets in the CDMA unslotted ALOHA system can be transmitted at any time. Hence, the CDMA unslotted ALOHA system requires no synchronization and the level of user interference fluctuates during packet transmission. Because of this fluctuation, analysis of a CDMA unslotted ALOHA system is more dficult than analysis of a CDMA Manuscript received April 9, 1999; revised November 3, 2000 and April 12, J.-W. So, I. Han, and D.-H. Cho are with the Department of Electrical Engineering and Computer Science, Korea Advanced Institute of Science and Technology (KAIST), Taejon, Korea ( israin@comis.kaist.ac.kr; ilhan@comis.kaist.ac.kr; dhcho@ee.kaist.ac.kr). B.-C. Shin is with the School of Electrical and Electronics Engineering, Chungbuk National University, Cheongju, Korea ( bcshin@cbucc. chungbuk.ac.kr). Publisher Item Identier S (01) slotted ALOHA system. Most previous analyses have been based on complete enumeration or were done using restricted traffic models. There have been many studies regarding analysis and improvement of CDMA ALOHA systems. Dferent studies have assumed either constant or variable arrival packet lengths. Yin and Li [2] introduced a new technique to analyze the throughput of a -channel CDMA network. Their analysis of the unslotted CDMA system with a fixed packet length was based on the ballot theory considering the signal-to-noise ratio (SNR) during packet transmission. Toshimitsh et al. [3] presented a novel spread slotted ALOHA system using channel load sensing protocol (CLSP). The slot size of this system was assumed to be less than the packet size. Therefore, CLSP could be applied and the throughput of the system was improved. Sato et al. [4] analyzed a DS/SSMA unslotted ALOHA system with a fixed packet length. The packet success probability was calculated as the level of multiuser interference fluctuated during packet transmission. They also analyzed the channel load sensing protocol and found that the channel load sensing protocol improves the performance of the system. Joseph et al. [5] studied unslotted DS/SSMA channels with block forward error correction (FEC) coding. The error probability of a bit packet was calculated with a variable message length and FEC-coding in a DS/SSMA environment and throughput versus channel traffic was compared. The major data traffic types in third-generation mobile communications will be electronic mail, file transfers, and web traffic, which can all be modeled as variable length traffic [6], [7]. Also, in wireless communication with a high bit-error rate, generated messages are divided into packets before transmission [8]. However, previous research on DS/SSMA unslotted ALOHA systems with variable length data traffic was based on environments where generated messages were transmitted on the basis of a message. That is, generated messages were not divided into packets to be transmitted. In this paper, under the assumption that generated messages are divided into packets before transmission, the throughput of a DS/SSMA unslotted ALOHA system with variable length data traffic is analyzed and simulated. Moreover, the effect of the Reed Solomon (RS) code for the system throughput was investigated. This paper is organized as follows: In Section II, the system model is presented. The packet success probability and the throughput are analyzed in Section III. The system is analyzed with consideration given to CLSP in Section IV, and a computer simulation is presented in Section V. Concluding remarks are presented in Section VI /01$ IEEE

2 2216 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 19, NO. 11, NOVEMBER 2001 II. SYSTEM DESCRIPTION AND MODELING To evaluate the throughput performance of a DS/SSMA unslotted ALOHA system with variable length data traffic, we consider a single-hop spread spectrum packet radio network with the following assumptions. 1) The packet radio network consists of an infinite number of independent mobile terminals (MTs) and a hub station. The MTs are assumed to transmit messages at any bit time using a common spreading sequence. Although a common spreading sequence is used, the hub station can distinguish between the received messages there are sufficient time offsets between received messages [9]. 2) Messages that enter into the system are generated by a Poisson distribution with an arrival rate of and the generated messages are divided into packets. The message length is ( ) bits and each message consists of up to packets where the number of packets in a message is geometrically distributed with a mean of and a packet length is fixed at bits. In practical applications, data traffic with these characteristics may be electronic mail, file transfers [6], and web traffic [7]. 3) Using Reed Solomon coding where is the block length and is the number of data bits per block, bits are correctable in a packet [10]. 4) Every transmitted packet is received with equal power. 5) Bit errors in a packet are caused by the effect of multiple access interference and additive white Gaussian noise (AWGN) [4]. The bit-error probability of an asynchronous DS/SSMA system [11] is expressed as III. THROUGHPUT ANALYSIS OF DS/SSMA UNSLOTTED ALOHA SYSTEM A. System Offered Load The offered load, defined as the average number of generated packets within a packet duration, can be expressed as where packet duration (i.e., ); [bits] length of a packet; [bits/s] data rate. The value is the average number of several continuous packets transmitted immediately by an MT. We define the normalized offered load as (4) [bits/hz/s] (5) where is a spreading factor. Since we assume that, the number of continuous packets transmitted immediately by an MT is geometrically distributed with a mean of, the probability that is is given by B. Transition of the Number of Interfering Messages As shown in Fig. 1, the interference level varies during message transmission because MTs attempt to transmit messages at any bit time. When the system state is defined as the number of interfering messages, we consider the state transition during the bit duration. When the generation of messages is assumed to be Poisson distributed with an arrival rate of, the probability that messages are transmitted during is given by (6) messages are transmitted during with (1) (2) Here, is the number of chips per bit, is the number of interfering packets, is the energy per bit, is the two-sided spectral density of Gaussian noise, and is given by (3) In a DS/SSMA unslotted ALOHA system, the probability that an error occurs in a received bit is calculated as (1). In a DS/SSMA unslotted ALOHA system, an MT transmits a message at any time. Here, the phrase at any time means at any chip time. In general, the chip time is so small that the probability that two or more users simultaneously transmit messages at the same chip time can be neglected. For example, when the data rate is 9.6 kbits/s and the spreading factor is 30, the probability that two or more messages are transmitted during the chip duration is almost zero under the assumption that the messages are generated by a Poisson distribution. However, we assume that an MT transmits a message not at any chip time, but at any bit time. The probability that two or more messages are transmitted during the bit duration is given by where is the bit duration and. Under the circumstance that kbits/s and the normalized offered load is less than 9600 bits/hz/s, the probability that two or more messages are transmitted during the bit duration is less than (7) (8)

3 SO et al.: PERFORMANCE ANALYSIS OF DS/SSMA UNSLOTTED ALOHA SYSTEM 2217 Fig. 1. An example of fluctuation of the interference level during message transmission. Fig. 2. State transition of the number of interfering messages. 0.01%. Therefore, for simplicity, we assume that the number of messages increases by only one during the bit duration. We also assume that the length of a message is geometrically distributed with a mean of packets and a constant packet length of bits. Therefore, although the arrival times of messages are dferent, the probability that messages depart at the same time is not zero. To calculate, we consider a reference message with a length of packets and a packet length of bits. If a message of length ( ) packets arrives at ( ) bits of the reference message, the message and the reference message would depart at the same time, where is a natural number between. Also, the arrival of messages can be assumed to be unormly distributed since a Poisson process has a completely random arrival. Therefore, under the assumption that the probability that two or more messages are transmitted during the bit duration is zero, is calculated as follows: Messages which arrived at dferent time depart at the same time (9) where is the maximum number of several continuous packets that an MT transmits immediately. For example, when kbits/s and bits/hz/s, is less than 0.05%. Therefore, we assume that the arrival times of messages are dferent, we can assume that the departure times of the messages are also dferent. Consequently, under the assumption that the probability that two or more messages are transmitted during the bit duration is zero, the state is changed only by one during the bit duration and therefore is modeled as a birth death process. That is, the bit duration is very small (let the bit duration be ), then the system can be approximately modeled as a Markov chain, as shown in Fig. 2. To evaluate the packet success probability, we suppose a tagged packet (Fig. 2) and investigate the variation in the number of interfering messages during transmission of the tagged packet. Under the assumption that the bit duration is very small, when the number of interfering messages at the th bit of the tagged packet is, the number of interfering messages: 1) increases to ; 2) decreases to ; or 3) remains the same during the bit duration. Let be the number of messages at the first bit of the tagged packet. If messages among messages depart during the packet duration, as shown in Fig. 3, the average service time of the messages is. Therefore, the death rate of messages is derived as [4] (10)

4 2218 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 19, NO. 11, NOVEMBER 2001 Fig. 3. A fluctuation of the interference level during tagged packet transmission. Also, the birth rate is obtained from (4) as follows: where is the offered load. Thus, the conditional state transition probability from th bits to th bits is given by otherwise. (11) (12) We now evaluate the probability messages that messages are observed, as shown in Fig. 3 where the time is the first bit time of the tagged packet. In Fig. 3, we define index sets as follows. Let index set denote the bit time axis where the interval between and is the packet duration which is equivalent to bits. Also, let the interval be period. Consider an index set. When observed, the labeled arrival is the number of messages that enter the hub station in the period ( ) and depart after time. The symbol denotes the length of message, that is, the number of packets in a message. Then At time in period the number of messages that enter and depart after time messages arrive during period messages arrive during period (13) where, which is the probability that an MT transmits or more packets in a message immediately, is calculated as follows: for (14) For (13), the following items can be applied. 1) The messages arrive during the period and depart after the beginning of period (after time ). 2) Only messages among messages are observed at time. We define a probability as the probability that the number of messages that enter into period, period,, period,, and depart from the channel after time is equal to. As packet arrivals are independently generated, the probability is obtained by multiplication of each as follows: (15) Thus, the probability messages that messages are observed is given by messages At time the number of messages (16) where is the set. The probability messages is equal to the probability that we see messages in a steady state since the time can be regarded as the time observed. C. Derivation of Packet Success Probability To calculate the packet success probability, we define a function as follows [4], [5]. 1) The function is the probability that the tagged packet is transmitted from the first bit to the th bit and bit errors in the tagged packet occur. Here, is the number of interfering messages at the th bit of the tagged packet. 2) The value is the number of messages that depart during the packet duration among messages when the level of interference at the first bit is. For example, means as follows. The number of interfering messages is four at the first bit of the tagged packet. The number of messages that depart during the packet duration among four messages is two. The number of interfering messages is five at the th bit of the tagged packet. The tagged packet is transmitted from the first bit to the bit and one bit error occurs. We evaluate the function recursively based on the Markovian property of. We see that for, is zero since there are no previous bits. Therefore, is equal to, which is the probability that messages depart during the packet duration among messages when the level of interference at the first bit of the tagged packet is. Hence, we have for (17)

5 SO et al.: PERFORMANCE ANALYSIS OF DS/SSMA UNSLOTTED ALOHA SYSTEM 2219 We assume that a certain message arrives within period. Let be the probability that the message departs during period and let be the probability that the message departs after the period (including the period ), where the period is greater than the period. Then, the ratio of to is a constant value of regardless of the arrival time of the message Accordingly, the message arriving during period departs during period the message arriving during period departs after period is calculated as follows: (18) (19) where is obtained by (16). When is not the first bit of the tagged packet, the probability that the packet transmitted from the first bit to the th bit has bit errors is calculated recursively as follows: (20) The case that errors occur from the first bit to the th bit can be described as follows: 1) errors occur from the first bit to the th bit and no errors exist in the next bit. 2) errors occur from the first bit to the th bit and an error exists in the next bit. Using, we recursively calculate the packet success probability. Since the packet length is a constant value of bits, the packet success probability is calculated by setting as follows: (21) duration. The system throughput is thus obtained with consideration of the RS coding rate as follows: Normalized throughput is then defined as follows: (22) [bits/hz/s] (23) IV. THROUGHPUT ANALYSIS OF DS/SSMA UNSLOTTED ALOHA SYSTEM WITH CLSP A. System Description and Modeling If the channel load (defined as the number of simultaneous transmissions) is controlled to reduce severe multiuser interference, considerable throughput improvement can be obtained, especially for a network where the multiuser interference is the dominant factor in performance degradation [3], [12]. In a system with CLSP, a hub station continuously senses the channel load and broadcasts the status information of the channel load. Fig. 4 depicts the transmission procedure when an MT in the idle state attempts to transmit a message. When a new message arrives and the MT is in the idle state, the MT sets the parameters,, and the backoff parameters, where is the number of access attempts and is the maximum number of access attempts. After an increment of, is less than or equal to, the MT proceeds to monitor the channel load status information, which is the number of active transmissions. Otherwise, the MT discards the message. If the monitored channel load is below a certain threshold, the message will be transmitted. Otherwise, the message is either rejected or is backed off. Therefore, the number of ongoing messages on the channel is always less than or equal to. In a system with CLSP, the system offered load is given by (24) where is the number of messages and is the probability that there are messages at a certain time, as obtained from (16). B. Throughput Analysis Because the number of ongoing messages on a channel is always less than or equal to, the number of interfering messages is always less than or equal to. The state transition of interfering messages is shown in Fig. 5. The conditional state transition probability is the same as (12) the number of interfering messages is less than. Otherwise, the value can be calculated as follows: where is the maximum number of correctable bits per packet. On the other hand, the system throughput is defined as the average number of successful transmissions during the packet

6 2220 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 19, NO. 11, NOVEMBER 2001 TABLE I SIMULATION PARAMETERS Thus, in the system with CLSP, we can obtain the packet success probability and the throughput as follows: (28) (29) Fig. 4. Transmission flow of a mobile terminal with CLSP. Then, the normalized throughput of is given by [bits/hz/s] (30) Fig. 5. State transition of the number of interfering messages considering CLSP. (25) The previously defined value of is given by for (26) where the probability is obtained from (19), and for (27) V. ANALYTICAL AND SIMULATION RESULTS We now compare analytical results with simulation results of the DS/SSMA unslotted ALOHA system with variable length data traffic. We assume that the probability that two or more messages are transmitted during the bit duration is very small and can be neglected. Therefore, a packet collision does not occur due to the same spreading sequence since the hub station can dferentiate the received packets [9]. That is, bit errors in a packet are caused only by multiuser interference and AWGN. Input traffic is assumed to be variable length data traffic with an average message length of 320 bytes, based on web traffic [7]. The data rate is assumed to be 9.6 kb/s [13]. The simulation parameters are summarized in Table I. Fig. 6 shows the system throughput versus the various values of. The infinity value of means that the effect of AWGN is neglected. Therefore, bit errors can only occur due to multiuser interference. Results show that the throughput of the DS/SSM unslotted ALOHA system with variable length data traffic also exhibits an ALOHA-like throughput versus the offered channel load. increases with but eventually decreases as becomes larger. In Figs. 7 and 8, the throughput versus the offered load of the DS/SSMA unslotted ALOHA system with CLSP is shown for various values of. Here, only multiuser interference is considered. For, the throughput is less than the system without CLSP because of overrejection of CLSP. When,

7 SO et al.: PERFORMANCE ANALYSIS OF DS/SSMA UNSLOTTED ALOHA SYSTEM 2221 Fig. 6. Normalized throughput versus normalized offered load for various values of E =N. Fig. 7. Normalized throughput versus normalized offered load for various values of ( 8; t =0). the maximum throughput is obtained. In the case of, the throughput decreases under heavy traffic conditions and the same throughput as the system without CLSP is obtained for. These results indicate that determining the optimum threshold value of CLSP is important. When bits per packet are correctable using the RS code, the throughput versus the offered load for various values of is shown in Fig. 9. A signicant throughput improvement is achieved by using bit error-correcting codes of only a few bits. The maximum 60% throughput improvement is obtained with one-bit error-correcting code. A throughput improvement of 145% is obtained using five-bit error-correcting code. At a low offered load value, the throughput of the system with coding is degraded slightly compared with the system without coding. This degradation, however, can be neglected. In the system with five-bit error-correcting code, the

8 2222 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 19, NO. 11, NOVEMBER 2001 Fig. 8. Normalized throughput versus normalized offered load for various values of ( 8; t=0). Fig. 9. Normalized throughput versus normalized offered load for various numbers of correctable bits t. throughput versus the offered load of a DS/SSMA unslotted ALOHA system with CLSP is shown for various values of in Figs. 10 and 11. While the throughput of the system with coding exhibits a variation similar to the variation of a system without coding, the optimum threshold to maximize the number of simultaneous transmissions ( ) is approximately two times the threshold value of a system without coding ( ). These results show that a signicant throughput improvement can be achieved by using error-correcting codes in a wireless channel with a high bit-error rate. VI. CONCLUSION Packet radio systems based on CDMA have received signicant attention as a third-generation mobile communication system. Major data traffic types on the system will be ,

9 SO et al.: PERFORMANCE ANALYSIS OF DS/SSMA UNSLOTTED ALOHA SYSTEM 2223 Fig. 10. Normalized throughput versus normalized offered load for various values of ( 15; t=5). Fig. 11. Normalized throughput versus normalized offered load for various values of ( 15; t =5). ftp, and web traffic with the characteristics of variable length data traffic. We analyzed the throughput of the DS/SSMA unslotted ALOHA system with variable length data traffic under the assumption that generated messages are divided into packets. The system has been analyzed for two cases: 1) systems without CLSP and 2) with CLSP. The throughput performance for various coding rates was investigated. When bit errors only occur due to multiuser interference, results show that the maximum throughput improvement is 60% in the system with one-bit error-correcting code and that a throughput improvement of 145% is obtained in the system with five-bit error-correcting code. Also, an increase in the number of users who can simultaneously transmit messages is obtained for the system with coding. The optimum threshold to maximize the number of simultaneously transmitted messages is derived for the system with CLSP.

10 2224 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 19, NO. 11, NOVEMBER 2001 REFERENCES [1] TIA TR45.5, The cdma2000 RTT candidate submission to ITU-R, Draft Document, June [2] M. Yin and V. O. K. Li, Unslotted CDMA with fixed packet length, IEEE J. Select. Areas Commun., vol. 8, pp , May [3] K. Toshimitsu, T. Yamazato, M. Katayama, and A. Ogawa, A novel spread slotted aloha system with channel load sensing protocol, IEEE J. Select. Areas Commun., vol. 12, pp , May [4] T. Sato, H. Okada, T. Yamazato, M. Katayama, and A. Ogawa, Throughput analysis of DS/SSMA unslotted ALOHA system with fixed packet length, IEEE J. Select. Areas Commun., vol. 14, pp , May [5] K. Joseph and D. Raychaudhuri, Throughput of unslotted direct-sequence spread-spectrum multiple-access channels with block FEC coding, IEEE Trans. Commun., vol. 41, pp , Sept [6] T. Liu and J. A. Silvester, Joint admissin/congestion control for wireless CDMA systems supporting integrated services, IEEE J. Select. Areas Commun., vol. 16, pp , Aug [7] B. A. Mah, An empirical model of HTTP network traffic, in Proc. INFOCOM 97, pp [8] W. A. Massey and R. Srinivasan, A packet delay analysis for cellular digital packet data, IEEE J. Select. Areas Commun., vol. 15, pp , Sept [9] N. Abramson, Multiple access in wireless digital networks, Proc. IEEE, vol. 82, pp , Sept [10] E. R. Berlekamp, The technology of error-correcting codes, Proc. IEEE, vol. 68, pp , May [11] J. M. Holtzman, A simple, accurate method to calculate spread-spectrum multiple-access error probabilities, IEEE Trans. Commun., vol. 40, pp , Mar [12] A. H. Abdelmonem and T. N. Saadawi, Performance analysis of spread spectrum packet radio of spread spectrum packet radio networks with channel load sensing, IEEE J. Select. Areas Commun., vol. 7, pp , Jan [13] TIA/EIA/IS-95-A, Mobile station-base station compatibility standard for dual-mode wideband spread spectrum cellular system, Telecommun. Indust. Assn., May Il Han (S 99) received the B.S. degree in electronic engineering from Kyungpook National University, Taegu, Korea, in 1995, and the M.S. degree in electrical engineering from the Korea Advanced Institute of Science and Technology (KAIST), Taejon, Korea, in He is currently pursuing the Ph.D. degree in electrical engineering at the KAIST. His research interests include resource management and mobility management in PCS and IMT-2000 systems. Byung-Cheol Shin received the B.S. degree in electrical engineering from the Seoul National University, in 1975, and the M.S. and Ph.D. degrees, both in electrical and electronics engineering, from the Korea Advanced Institute of Science and Technology (KAIST), in 1977 and 1984, respectively. He worked as a Research Staff Member for the Electronics and Telecommunications Research Institute, Korea, from 1977 to He visited SRI International, Menlo Park, CA, as an International Fellow in He also visited Rutgers University in Piscataway, NJ, as a Visiting Scholar in From 1984 to 1998, he was with KAIST. Since August 1998, he has been with Chungbuk National University as a Faculty Member in the School of Electrical and Electronics Engineering. His research interests include real-time/multimedia communication and performance analysis of ATM, high speed networks, and wireless networks. Jae-Woo So (S 98) received the B.S. degree in electronic engineering from Yonsei University, Seoul, Korea, in 1997 and the M.S. degree in electrical engineering from the Korea Advanced Institute of Science and Technology (KAIST), Taejon, Korea, in He is currently working toward the Ph.D. degree in electrical engineering at the KAIST. His research interests include CDMA mobile communications, multiple access protocols in wireless communications network, and multimedia communications. Dong-Ho Cho (S 80 M 85 SM 00) received the B.S. degree in electrical engineering from the Seoul National University, in 1979, and the M.S. and Ph.D. degrees, both in electrical and electronics engineering, from the Korea Advanced Institute of Science and Technology (KAIST), in 1981 and 1985, respectively. From 1987 to 1997, he was a Professor of Computer Engineering at the Kyunghee University. Since 1998, he has been a Professor of Electrical Engineering at KAIST. His research interests include wire/wireless communication network, protocol, and services.

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