Spread ALOHA Based Random Access Scheme for Macro Cell CDMA Systems

Spread ALOHA Based Random Access Scheme for Macro Cell CDMA Systems Zhenyu Xiao, Wentao Chen, Depeng Jin, Lieguang Zeng State Key Laboratory on Microwave and Digital Communications Tsinghua National Laboratory for Information Science and Technology Department of Electronic Engineering, Tsinghua University, Beijing, China Email: xiaozy@mails.tsinghua.edu.cn Abstract The based random access faces the low throughput and long access delay problems when used in macro cell CDMA systems. This paper proposes the Spread ALOHA based random access scheme as a solution. In our physical layer model, we studied the impact of multi-path on conflict interval and the Multiple Access Interference (MAI from both the traffic channels and the request channel. Based on this model, the close-form theoretical results of throughput and average access delay are derived. Numerical results show that the proposed scheme has much better access performance, which is much higher throughput and much shorter access delay than the based scheme. The improvement is enhanced as the load gets heavier. Index Terms CDMA, Spread ALOHA, SAMA, multi-path. I. INTRODUCTION In micro cell CDMA systems, such as WCDMA and CDMA, the access frequency (the total access times within unit time is always low with a small number of users in each cell. Therefore, the simple and efficient based random access scheme is generally adopted [] []. However, it would result in the low throughput and long access delay when used in the macro cell CDMA systems. Because as the users get large in each cell, the access frequency increases, and thus the request load gets heavy. In this paper, the Spread ALOHA based random access scheme is proposed to increase the access throughput, and meanwhile shorten the average access delay of the macro cell CDMA systems. Spread ALOHA Multiple Access (SAMA was first proposed by Norman Abramson [] []. In SAMA systems, all the users use the same PN code in their spread spectrum modulation, and the receiver gets message via the correlation with that PN code. The SAMA signal is nearly the same as the CDMA signal, except that the later uses different PN codes in spread spectrum modulation. The access performance of SAMA system, such as throughput, retransmitting probability and average access delay, have been derived [], and some strategies have been studied to increase the throughput of the SAMA system []. However, all the researches above are This work is supported by the National Basic Research Program of China (9 program under grant No. CB. based on a pure random access system, which means there are only SAMA channels in the system, and all the traffic are transmitted on the SAMA channels. While the CDMA system has both random access channels and traffic channels. Users send request frames on the random channel to apply for a traffic channel before sending traffic frames on that traffic channel. Our scheme is to use Spread ALOHA to the CDMA random access channel, which has not been proposed before. As we know, the multi-path increases the BER of wireless channels, but to SAMA channel, the multi-path would increase the conflict interval, which would result in a significant impact on the access performance. There are almost no SAMA related researches which have studied it before. A more accurate physical layer model is built in this paper, taking the impact of multi-path into account. Moreover, There are two kinds of MAI when building the SAMA channel model under a CDMA system, which are MAI from other request frames on the same random access channel and MAI from traffic frames on the traffic channel. There are differences between these two kinds of MAI []. The differences are also considered in this paper. The rest of the paper is organized as follows. In section II, we describe the system model and the scheme. In section III, we derive the access performance of the scheme via theoretical analysis. In section IV, we present the numrical results. In section V, we conclude the paper. II. SPREAD ALOHA BASED RANDOM ACCESS SCHEME The architecture of the CDMA system with a single Spread ALOHA based random access channel is shown in Fig.. In the system, each user may apply for an exclusive traffic channel, which is identified by an exclusive scrambling code, to transmit traffic frames. All the users use the same random access channel, which is also identified by an exclusive scrambling code, to transmit request frames. The traffic frames are first correlated with a channelizing code, then transmitted to the channel after scrambling. While the request frames are first correlated with the same PN code, then transmitted to the channel after scrambling. The channelizing codes are orthogonal with the PN code. ---//$. IEEE ICCS

Traffic of user Traffic of user M Request data Channelizing code Channelizing code Scrambling code for user Scrambling code for user M PN code Scrambling code for random access channel Fig.. Architecture of CDMA system with a Spread ALOHA based random access channel In the system, the request frames have the same length of L bits, and the transmitting delay for a frame is T,asshown in Fig.. The length of the PN code is N, so the chip interval T c = T b /N = T /(LN, wheret b is the bit interval. T c is the least time unit in the system. If the request frame of another user dislocates m chips modulo N ( m <N with the frame being received, then the signal to interference noise (SIN is ne b /N via correlation reception, where E b is the bit energy received and n is usually small when m.ifn is large, then n N, thesinis so small that no conflict would happen. Only when m =, which means the two frames are bit aligned, then n = N, the SIN is E b, which is usually significant, so there would be a conflict between the two frames, hence we say the conflict interval for that user is T c within T b. However, when multi-path exists, we suppose there are δ influential rays, if a user transmits a request frame to the random access channel, there would be δ frames arriving at the base station at different time. Each of the δ frames may result in a conflict with the frame being received if they are bit aligned. So it is equivalent to that the conflict interval for that user is δt c within T b. As shown in Fig., frame a is the frame being received. Frame a has replicas, and frame a has replicas. The conflict interval is T c within in T b for a, and T c within in T b for a. one replica of frame a is bit aligned with a, so it would conflict with a, while replicas of a would not. It would result in a mess that multiple replicas of a single frame are all correctly received, so strategies should be studied to prevent it. While it is not the focus of this paper. Without loss of generality, we assume the process of the request frames arrival on the random access channel is a Poisson Process. The propagating delay of a frame could be ignored compared to the transmitting delay T. III. PERFORMANCE ANALYSIS A. BER of the random access Channel The BER of BPSK modulation for the optimum receiving is given in [] by P b = Q( SNR, wheresnr is the signal to a Fig.. N chip a b( t b ( t Fig.. b ( M t a Conflict intervals when there is multi-path Delay Aa ( tcos( w t c Aa ( tcos( w t c M Aa (cos( t w t M c M T nt ( rt ( Receiver Signals received by the receiver on the random access channel noise ratio, and Q(x =/ π x exp( u /du. Onthe other hand, the noise consists of white Gaussian noise and the MAI in CDMA systems. Since the white Gaussian noise is always much less than the MAI in realistic systems, and the MAI could be treated as a Gaussian distribution variable, then we could ignore the white Gaussian noise, and then the BER is evolved as P b (K =Q( SINR ( where K is the total active access users who are transmitting request frames. Because the MAI is related to K, sotheber is also related to K. Although we assume the modulation is BPSK here, the proposed scheme and the analysis are also available for other modulation. The signal received on the random access channel is shown in Fig., where τ k is the relative delay, θ k is the phases of the carriers, b k (t is data, a k (t is the PN code and P k is the power, all these parameters are for frame k. So the signal for frame k is S k (t τ k = P k b k (t τ k a k (t τ k cos(w c t + θ k ( There are request frames and traffic frames here. Since all the request frames have the same SINR, we only need to consider the frame of the first user, whose frame is assumed to be b (t. The following process is similar to the process in [], so we directly present the result here. We demodulate the signal by correlating with the PN code of the first user a (t after down convertor and filter, and normalize the power by

assuming P =and P k =α k. The normalization here does not effect the SINR, and the influence of the multi-path is reacted via α k. α k would be larger if there are more rays. The output is Z = N + K M K α k W k cos Θ k + β r W r cos Θ r ( k= r= where N is the length of the PN code, the second item is the MAI caused by request frames of other users on the random access channel, while the third item is the MAI caused by traffic frames on the traffic channels. β r = α r+k. Θ k and Θ r are carrier phases, both of which are uniform on [, π, and W k = X k +( τ k /T c Y k +( τ k /T c U k + (τ k /T c V k ( W r = X r +( τ r /T c Y r +( τ r /T c U r + ( (τ r /T c V r +( τ r /T c where τ k and τ r are uniform on [,T c, X k, U k, V k and X r, U r, V r are composed of disjoint set of symmetric Bernoulli trials as described in []. From [] we could get Var(W k cos Θ k = (N +/, andvar(w r cos Θ r =N/. so Var(Z =μ (N +/+μn/ ( where μ = K k= α k =(K γ, μ = M K r= βr.hereγ is the average power of the request frames relative to P,and μ is the total power of the traffic frames relative to P.Both of them are not related to K, and both of them are larger if there are more rays. Since the average power of the signal is N,thenweget SINR = N/ γ(k (N +/+μn/ ( Since N, then N + N. We substitute for SINR from ( to ( and get P b (K +=Q( N/(γK + μ ( B. Throughput We assume the system is in a stable state. A request frame may conflict with frames transmitted before it or after it, so the total interval to be considered is T, and the conflict interval is Lδ i T c within the T for a δ i -ray user. We denote G as the frames arriving on the random access channel within T,then G = λt,andgis the offered load. Since the arrival process of request frames is a Poisson Process with a parameter λ, the probability for K request frames arriving on the random access channel within T is f(k, T = ((G K /K! exp( G (9 It is given in [9] that, for a Poisson Process, under the condition that n events have occurred in a certain interval (,t, the times s,s,..., s n at which events occur, considered as unordered random variables, are distributed independently and uniformly in the interval (,t. So the probability that the frame under receiving does not conflict with the K frames is K K p = ((T Lδ i T c /T = ( δ i /N ( i= δ i is always much smaller than N. We denote δ = /K K i= δ i, thenp ( δ/n K.So within T, the probability that there are K request frames on arrival and none of them conflicts with the frame being received is P (K =f(k, T p =(G K /K!exp( G( δ/n K ( We denote P ch (K as the probability that the frames are correctly transmitted when there are K frames on the random access channel, P G as the average probability that a request frame are correctly transmitted. Then P G = P (KP ch (K += K= i= P (K( P b (K + L K= ( We substitute P (K and P b (K + from ( and (, and then we get P G =exp( G (G K /K!( δ/n K K= ( Q( ( N/(γK + μ L We denote S as the request frames correctly transmitted within T,thenS = GP G,andS is the throughput of the system. So we get S = G exp( G (G K /K!( δ/n K K= ( Q( ( N/(γK + μ L C. Average Access Delay To analyze the average access delay of the system, usually a back-off and retransmitting strategy on the MAC layer would be adopted. However, the average access delay would vary with different strategies, and theoretical formula could be hardly derived, because the arrival process of the frames is not strictly a Poisson Process any more when there is a control strategy on the MAC layer. Our main purpose focuses on the difference between the average access delay of Spread ALOHA and. No matter what kind of strategy is adopted, the relative difference could be derived. So we could choose one to simplify our analysis. The strategy we adopted here is simple. The arrival process of the frames is assumed to be a Poisson Process. No matter the transmitting of a frame succeeds or fails, it has nothing to

do with the transmitting of the next frame. If the transmitting fails, then the next frame is assumed to be the retransmitted frame. This strategy makes sure the arrival process of the frames is a Poisson Process, and just like there is no control on the MAC layer. Base on the strategy above, a frame is averagely transmitted G/S times before it is successfully transmitted. We denote D as the average access delay of Spread ALOHA scheme, then where G/S could be easily get from (. D = T G/S ( IV. NUMERICAL RESULTS As we know, the throughput of is S s = Ge G, while the throughput of Spread ALOHA is shown as (, which is a infinite series. We could hardly get the performance difference between Spread ALOHA and Slotted ALOHA intuitionally. So we would calculate the value of throughput versus different offered load G. First we need to evaluate the three parameters in (, which are δ, γ and μ separately. δ is the average rays for the access users, γ is the average power of the request frames relative to P,andμ is the total power of the traffic frames relative to P. γ and μ are both related to δ. We could hardly build an accurate model for the parameters here, because the numbers of rays for each access user are different, the power of different rays is different, and the power of different traffic frames is different. We could only build a coarse model. That is, from the sense of average, except the direct-arrival ray which has power of P, the other influential rays has average power of /P.Thenwehaveγ =+/(δ, andμ = η( + /(δ, whereη is a constant. Although this parameter model is coarse, it is sensible in realistic CDMA systems. Because of the power control, the direct-arrival ray for each user does have power of P.The rays with very low power is ignored, so the average power of the rest influential rays is about /P.Theremaybea little difference for the everage power, but it is so limited that it would almost not impact the performance of the system. The number of the other influential rays is usually no more than, the typical value is about. What is more, the average number of traffic frames and the average power relative to P of each traffic frame could be treated as fixed values, and η is the product of them. So the traffic is heavier, η is larger. The throughput comparison between Spread ALOHA and is as shown in Fig.. The values of the parameters is as follows, δ =, L =, N = and η =. These values are all typical, however, the parameters are not limited to them, other values are also available. From the figure we can see that, the throughput of Spread ALOHA could be larger than, while the largest throughput of Slotted ALOHA is only e when G =, and the throughput of would get even less if taking the MAI from traffic frames into account. That is to say, The Spread ALOHA Fig.. ALOHA Thoughput (frames per T Average Access Delay (T Spread ALOHA Throughput comparison between Spread ALOHA and Slotted Spread ALOHA.. Fig.. Average access delay comparison between Spread ALOHA and has much larger throughput, and is more suitable for high offered load CDMA systems than. The average access delay comparison between Spread ALOHA and is as shown in Fig.. From the figure we can see that when the offered load is light, the average access delay of Spread ALOHA is very close to T, which means there is almost no retransmitting frames. While the average access delay of increases as a exponential law versus the offered load, which means the average access delay is large and the is not available for heavy load CDMA systems. Obviously the parameters δ and η have impact on the performance of Spread ALOHA. That is to say, the number of rays and the traffic load are related to the performance of Spread ALOHA. We set L =, N = and η =,and get the curves of throughput versus δ for Spread ALOHA as Fig.. We set L =, N = and δ =, and get the curves of throughput versus η for Spread ALOHA as Fig.. We set L =, N = and η =,and get the curves of average access delay versus δ for Spread ALOHA as Fig.. We set L =, N = and δ =,

9 δ = δ = δ = δ = δ = δ = Throughput (frames per T Average Access Delay (T Fig.. Throughput versus δ for Spread ALOHA Fig.. Average access Delay versus δ for Spread ALOHA Throughput (frames per T η = η = η = η = Average Access Delay (T η = η = η = η = Fig.. Throughput versus η for Spread ALOHA Fig. 9. Average access Delay versus η for Spread ALOHA and get the curves of average access delay versus η for Spread ALOHA as Fig. 9. From these figures we can see that, as the number of the rays increases, the throughput of Spread ALOHA decreases significantly, and the average access delay is lengthened significantly, as the traffic get heavier, the throughput of Spread ALOHA decreases significantly, and the average access delay is lengthened significantly. These figures shown that both the number of the rays and the traffic load of the system have a significant impact on the performance of Spread ALOHA. V. CONCLUSIONS The Spread ALOHA based random access scheme is proposed to solve the problems of low throughput and long access delay in macro cell CDMA systems. An accurate physical model is built for the system, taking multi-path and the two kinds of MAI into account. The theoretical analysis and numerical results show the Spread ALOHA based random access could greatly increase the throughput and shorten the average access delay, especially when the traffic load are heavy. The results also show that both the number of the rays and the traffic load of the system have a significant impact on the performance of the Spread ALOHA based scheme. REFERENCES [] J. He, Z. Tang, D. Kaleshi, A. Munro, Simple analytical model for the random access channel in WCDMA, Electronics Letters, vol., pp. -, September [] Yumei Zhang, Dacheng Yang, Xin Zhang, QoS-Aware Multichannel Random Access in CDMA Nx EV-DO Systems, Vehicular Technology Conference, vol., pp. -, April [] N.Abramson, Multiple access in wireless digital networks, Proceeding IEEE, vol., pp. -, September 99 [] N.Abramson, VSAT data networks, Proceeding IEEE, vol., pp. -, July 99 [] H.Achi, W.Jibrail, R.Liyana-pathirana, Performance Analysis For Spread ALOHA Wireless Systems, Proc. ICCT, vol., pp. 9-9, April [] A.Ribeiro, Y.Yu, G.B.Giannakis, N.D.Sidiropoulos, Increasing the Throuhput of Spread-Aloha Protocols via Long PN Spreading Codes, ICC, vol., pp. -, May [] Andrea Goldsmith, Wireless Communications, st ed., Cambridge University Press,, pp. - [] Robert K.Morrow, JR., James S.Lehenrt, Bit-to-Bit Error Dependence in Slotted DS/SSMA Packet Systems with Random Signature Sequences, IEEE Transactions on Communications, vol., pp.-, October 99 [9] Sheldon M. Ross, Stochastic Processes, nd ed., New York: John Wiley and Sons, 99, pp. -