More Realistic Performance Analysis for SDMA Systems

Transcription

1 More Realistic Performance Analysis for SDMA Systems Xuming Fang College of Computer and Communications Engineering Southwest Jiaotong University Chengdu, Sichuan , P. R. China Abstract-The proliferating demands for mobile services propel us to develop more sophisticated techniques to overcome the limitation of wireless radio resource. With the introduction of cell splitting and sectorization in cellular communications systems, system capacity can be significantly increased. Space Division and Multiple Access (SDMA) technology along this line has therefore gained a great deal of attention recently, intensive research on resource allocation for SDMA systems has been undertaken in the last few years. In this paper, we carry out more realistic performance analysis for a few resource allocation schemes in SDMA systems and obtain more accurate analytical results for blocking probability. I. INTRODUCTION How to deal with the finite and scarce radio resource problem is, and will always be, an important research topic. Flexible utilization of such resource in space, time and code has shown great improvement for system capacity. For example, cell splitting and sectorization, space reuse schemes of spectral resource, could result in a significant increase in system capacity over the omni-directional antenna cellular systems [ 1,2]. TDMA and CDMA have greatly increased the system capacity over the conventional FDMA. Recently, Space Division Multiple Access (SDMA) has attracted much attention when it is shown that smart antenna array and space-time signal process can greatly increase the spectrum efficiency, SDMA seems becomes one of the important techniques to in increase the spectrum efficiency in the next generation communications systems [ In SDMA systems, the systems capacity is closely related to the resource allocation schemes. A dynamic channel allocation (DCA) algorithm for SDMA systems was presented and simulated in [12], where, instead of searching channels from the idle ones in the cell [13,14], this algorithm searches for the first channel available with desired SIR. However, the exhaustive SIR search may be too time consuming. In [IO], the authors presented two channel allocation schemes -- FD (First Duplicate) and DL (Duplicate at Last) for spectrum reuses in space and derived the theoretical formulae for call blocking probability in an SDMA system. We observe that all their results were obtained under the assumption that the probability P,y (the probability of acquiring a channel current in use for supporting a user in another beam) is a fixed parameter in the whole state process. However, in many situations, this probability depends on the usage of the channel pool and may be state-dependent. Thus, the results in [lo] only provide some approximations to the call blocking probability. Another interesting analysis was given in [ll], where the system performance was analyzed under some specific scenarios and various traffic load conditions using simulations. In this paper, we attempt to carry out a more general theoretical but realistic analysis for the call blocking probability for the SDMA systems using two channel allocation schemes proposed in [lo]. We present theoretical results for the call blocking probability for the cases when the permission probability P,, is not fixed and may be statedependent, hence represent improvements over the results given in [lo]. The remaining parts of this paper are organized as follows: Section I1 outlines the basic idea of two channel allocation schemes, FD and DL, proposed in [lo], for the convenience of presentation. In Section 111, we present our theoretical results and numerical analysis. Finally, in Section IV, we draw some conclusions. 11. TWO CHANNEL ALLOCATION SCHEMES FOR SDMA SYSTEMS FD (First Duplicate) and DL (Duplicate ut Lust) ([lo]) are two channel allocation schemes for SDMA systems in which channels can be dynamically reused in a cell more efficiently than the traditional sectorization does. The goal of these channel allocation schemes is to allocate the assigned channels to a cell (called primary channels in [lo]) and reuse them as many times as possible in the cell. For example, as long as the desired Signal-to-Interference Ratio (SIR) requirements for the current ongoing calls are met upon allocating a channel current in use to another user in a different beam (sector), this channel allocation will be acceptable. If N is the number of channels assigned to a cell, the FD and DL schemes with reuse factor RF = 2 are characterized as follows: In the FD scheme, we first reuse a primary channel currently in use, which has not been reused (duplicated). If the duplicated channel is unavailable (i.e., the reuse of this channel may violate the desired quality of the ongoing calls), we will allocate the next primary channel. If all N channels are used up and no duplicate channels are available upon a call arrival, the call will be blocked. In the DL scheme, we allocate primary channels first. Once all N primary channels have been used up for ongoing calls, we will attempt to reuse each of the primary channels one by one as long as the reuse of a primary channel does not violate the desired quality of service (QoS) for the ongoing calls. If there are no channels (either primary or duplicate) available upon a call arrival, the call will be blocked. The basic idea for FD is to reuse the primary channels as early as possible so that the system capacity can be increased (i.e., more users can be supported by this early arrangement for channel reuse). This is because a primary channel can be used anywhere in the cell, hence it has more flexibility than a /01/$ IEEE 1533

2 duplicate channel (a duplicate channel cannot be used in the same area with its primary counterpart. However, we have to check the SIR each time we attempt to reuse a primary channel, which makes the allocation scheme much more complicated. While the DL trades the simplicity for slight degradation of capacity by using the primary channels first, then duplicating channels whenever necessary after then. We can observe that FD always works better than DL in terms of call blocking probability in [lo]. The performance analysis for thest: two schemes with reuse factor is 2 (i.e., each channel Ican at most be reused once) has been carried out in [lo] using the two-dimensional Markov chain. The state transition diagrams are shown in Fig. 2 and Fig. 5 of [IO], in which the state is characterized by (x, y), where x is the number of the primary channels currently in use in the cell and y is the number of currently reused channels in the cell. Let Px.y denote the state probability, let P, (Pf= 1- P, ) be the probability of successfully acquiring a channel that was already in use by another user (i.e., the probability that a channel can be reused). The call blocking probability is then given by y=o By solving the set of balance equations for the twodimensional Markov chain, we can calculate the blocking probability ([lo]). It was concluded that when P, approaches 1, i.e., the duplicate channel of any primary channel can be used in almost any situation, the blocking probability is close to what is obtained from the Erlang-B formula for double channel resources. For relatively low traffic load, different schemes reveal significant differences in the blocking probability, whereas with the increase of traffic load, the difference tends to be minor. One important observation is that the FD and DL can be easily generalized to the cases where the reuse factor greater than 2 (i.e., a primary channel can be used multiple times in a cell dynamically) MORE REALISTIC ANALYSIS METHOD One important observation from studies for SDMA systems ([1,2,15]) is that the probability of successfully acquiring a duplicated channel P, depends on the state of the operational cellular systems, such as the traffic and SIR. When the state or the number of active users changes, P, will also change, thus P, is a state-dependent parameter, which depends not only on the spatial occupation of an allocated channel (beam width), but also on the angular separation (cochannel interference). If each channel is reused one time as described in FD and DL schemes, the expressions for traffic flow rate will be more complicated than those in [IO]. Since two cochannel beams cannot overlap in the same area, even though the channel pool still contains free possible duplicated channels, the user may fail acquiring a channel. Thus, the theoretical results presented in [lo] are at most approximations to the actual call blocking probability. In order to obtain more realistic analytical results, we extend the definition of P,, i.e., the probability of acquiring a channel from a state to its successor. Let Ps(;,y+l) (x U) and P$:/,y, denote the probabilities of successfully acquiring a channel from state (x, y) to (x, y + 1) and from Fig. 1. State transition diagram with N = 4 for FD scheme Subsequently, we obtain the general balance equations for x < N as follows (x + y + k, + k6)px,y = k,px-,,y + k2px,y-l + k,px+i,y + k Px,y+I where I lo k3 ={o x-y+l I =O ;x-y20 ;x-y<o (2) ;x-y=l (3) ;x-y<l (4) 1534

3 k, = I Y- -l x- w+l ;x-y=o ;x-y<o Besides, the normalization eqution provides another constraint in order to obtain the unique solution for the steady-state probability distribution. The blocking probability is then given by the equation: I =o which is obtained from the following observation: a call will be blocked if all N primary channels are used up and, for any i, when i duplicated channels are used, the rest (N - i) un-reused channels cannot be used. Let us present an example to illustrate how P,y is obtained and affect the system performance. Consider an SDMAKDMA system, which is limited and operated in an AWGN channel environment with perfect power control and with no interference from adjacent cells. The adaptive antenna provides a spot beam for each user. A beam pattern, G(@, is formed such that the pattern has maximum gain in the direction of the intended user ([15]). It is also assumed that users in the single cell system are uniformly distributed throughout the cell. Without the CO-channel interference, when a user arrives, at the base station the total interference power, I, seen by the user when the total channels in use is K is given by where P, is the power incident at the base station antenna from each user. D is the directivity of the antenna, which ranges from 3 db to 10 db ([15]). Thus the carrier to interference ratio (CIR) is given by CIR = - K-1 where Mis the spreading factor ([15]). In our example, we assume the special case, i.e., each beam only contains one channel (code). If the possible duplicate channel of the reference primary channel is used, then at state (x, Y)> I=- P,(X+Y) D and CIR is given by 7) (9) CIR = - X+Y If the reference primary channel is going to be duplicated, which means there will be a co-channel of the reference primary channel in the cell, when a user arrives, at the base station the total interference power, I, seen by the user when at state (x, y) is approximately deduced as (14) from equation (1.3) - (1.7) in [15]: I= P,(x + y D) D and CIR is given by CIR = x+y-l+d (15) If we define CIR threshold as T, then (13) and (15) could be written as x+yl-=t T and However, if a user uses a duplicated channel, the user has the probability of 4I2n being blocked because the user cannot locate at the same area as the user using the primary channel. Therefore, we can approximately obtain ;x + y > t For instance, if 4 = d6, D = 5.1 db, M = 51 1, and T = 18 db, then t dB = 14.1 db = 25 t = t+l- D = = 22.8 w 23 In order to demonstrate how P,, depends on the state (x, y), here we raise the threshold T to 22 db and obtain two sets of parameters. 4 = ni6, D = 5.1 db, M = 51 1, T = 22 db, t = 10 and t = 7.8 U 8 4 =d3, D = 4.3dB, M = 51 1, T = 22dB,t = 8mdt = 6.3 s 7 In these cases, equation (9) is given as follows: N,=O x+y=r xfn Two sets of plots are shown in Fig.2. For comparison, we also show the blocking probabilities corresponding to Erlang- 1535

4 B formula for N and 2N channels and the one for stateindependent (S-I) case obtained from [ E M 22-0" m 1, I But with the incease of T, the perfermance difference between FD and DL becomes larger. On the other hand, if CIR threshold is relatively large enough, such as T = 18 db in our exmaple, our results are coincident with those presented in [lo]. But if T is increased, which means some idle channels (including both primary and possible duplicate) can not be used due to the interferece constrains, then at some states, P, will become 0. Therefore, the blocking probability would be increased crespondently Traffic (Erlangs) Fig. 2. Blocking probability for FD scheme with N = 5 ( S-I: state-independent) From Fig. 2, we find that the trend what we obtained are coincident with those in [lo]. But the difference is that the blocking probability is quite large than those in [lo]. It is obvious that when the the number of allocated channels increases, the probability of successfully aquiring a channel would be reduced with the decrease of CIR. But the fact is still true, that is, if P, is quite higher, the plot would be much Coincident with the plot of Erlang-B with 2N channels. As for DL scheme, similar to the modified formulas in FD scheme, the state diagram in [lo] could be modified as Fig. 3. But equations (3), (4), (7) and (8) are replaced by (23) - (26). Fig. 3. State transition diagram with N = 4 for DL scheme { ^I A,V(x*Y-') k, = s(x~y) J)){%;c:) ; = N (24) 1 r=o 0 ;x<n ;x=n (25).o ;x<n Here we also give the same examples under the same conditions as those in FD scheme. The plots are shown in Fig. 4. As we expected that the blocking probability of DL is t-dl N=5 phi=pi/3 DL N=5 phi=pi/3 (SI) --Jt Erlang-B N=5 between the plots Erlang-B with Nand 2N channels. In order Q5,5 $?5 $ 55 8,5 to compare the FD with DL, we re-draw the plots with the parameters q5 = 7d3, D = 4.3 db, M = 51 1, T = 22 db, and t = Traffic (Erlangs) 8 shown in Fig.5. And also we present another pair of plots Fig. 4. Blocking probability for DL scheme with = with the parameters 4 = d3, D = 4.3 db, M= 51 1, T= 21 db, ( S-I: state-independent) and t = 11. The results demonstrate that FD is better than DL. 1536

5 ooooo I Traffic (Erlanp) Fig. 5. Blocking probability comparison between FD and DL schemes IV. CONCLUSIONS So far at this point, we could conclude that P, significantly affects the performance of the whole system. Because P, is a state-dependent parameter, it obviously influences the system performance with the state changing. Based on the results what we obtained, the effect could not be ignored. But only when the state reaches a threshold, the effect of interference would be obvious. In addition, only under the ideal conditions, the system capacity approaches to double the original one without channel duplication if two beams share a same channel resource in a cell. ACKNOWLEDGMENT Many thanks are due to Dr. Imrich Chlamtac (University of Texas at Dallas) and Dr. Yuguang Fang (University of Florida), who viewed this paper, and presented many valuable comments and suggestions. [SI Christof FARSAKH, and Josef A. NOSSEK, A Real 1 Time Downlink Channel Allocation Scheme for an SDMA Mobile Radio System, IEEE PIMRC 96, 1996, pp [6] Benjamin NG, and Elvino S. SOUSA, Performance enhancement of DS-CDMA system for Wireless Local LOOP, SBTiIEEE ITS 98, 1998, vol. 1, pp [7] Christof FARSAKH, and Josef A. NOSSEK, On the Radio Capacity Increase Through SDMA, IEEE International Zurich Seminar on Broadband Communications, 1998, pp [SI Budi PURBA, and Richard HARRIS, etc., A Performance Analysis of A Cellular SDMA System with an Adaptive Array, IEEE TENCON 97, 1997, pp [9] Pregrag B. RAPAJIC, Information Capacity of the Soace Division Multiole Access Mobile Communication Sistem, IEEE SATA 98, 1998, pp [lo] G. M. GALYAN-TAJADA, and J. G. GARDINER, Theoretical blocking probability for SDMA, IEE Proc.-Commun., 1999, 146(5), pp [l 11 Flavio PIOLINI, and Anna ROLANDO, Smart Channel-Assignment Algorithm for SDMA Systems, IEEE Trans. m, 1999,47(6), pp [12] Lan CHEN, and Hidekazu MURATA, etc., Dynamic Channel Assignment Algorithms with Adaptive Array Antennas in Cellular Systems, IEICE Trans. Fundamentals, 1999, E82-A(7), pp [13] Zhenghe FENG, and Zhijun ZHANG, Smart Antenna and Spatial Division Multiple Access, IEEE ICMMT 98, 1998, pp [14] Tskeo OHGANE, and Yasutaka OGAWA, etc., A Study on Channel Allocation Scheme with an Adaptive Array in SDMA, IEEE VTC 97, vol. 2, 1997, pp [15] J. C. Jr. LIBERTI, and T. S. RAPPAPORT, Analytical Results for Capacity Improvements in CDMA, IEEE Trans. Veh. Tech., 43(3), 1994, pp REFERENCES L. C. GODARA, Applications of Antenna Arrays to Mobile Communications, Part I: Performance Improvement, Feasibility, and System Considerations, Proc. of the IEEE, 1997,85(7), pp L. C. GODARA, Applications of Antenna Arrays to Mobile Communications, Part 11: Beam-Forming and Direction-of-Arrival Considerations, Proc. of the IEEE, 1997,85(8), pp Richard H. ROY, Spatial Division Multiple Access Technology and Its Application to Wireless Communication Systems, IEEE VTC 97, 1997, pp Rupam SINHA, and Terece D. TODD, etc., Forward Link Capacity in Smart Antenna Basestation with Dynamic Slot Allocation, IEEE PRMRC 98, 1998, vol. 2, pp