Robust modeling and throughput optimization in CDMA networks

Transcription

1 Robust modeling and throughput optimization in CDMA networks Moses Ekpenyong University of Uyo Joseph Isabona University of Uyo Aniekan Akpaeti University of Uyo ABSTRACT In this paper we study two resource management issues: transmit power control and the number of terminals that should be admitted into a CDMA system in order to maximize the base station throughput. We develop a simulator that effectively handles these issues for N number of terminals: N = 2,3,...,. Using empirical data, we discover that when noise and interference are negligible, received power balancing maximizes the base station throughput, provided the population of active terminals does not exceed an optimum size. INDEX TERMS Power balancing, Processing gain, Transmit power, Throughput I. INTRODUCTION Code Division Multiple Access (CDMA) has been the fastest growing digital wireless network technology, since its first commercialization in CDMA is a third- generation (3G) technology that provides users (mobile stations) both within a cell (base station) and across different cells to transmit and receive on the entire frequency spectrum (bandwidth), a phenomenon referred to as frequency reuse. According to the 2009 subscribers statistics of the CDMA Development Group (CDG); in March 2009, the CDMA subscribers base closed in on half a billion [1]. The major markets for CDMA are North America, Latin America, and Asia (particularly Japan and Korea). CDMA technology can offer about seven to ten times the capacity of analog technologies and up to six times the capacity of digital technologies such as Time Division Multiple Access (TDMA) and Frequency Division Multiple Access (FDMA) [2],[3]. The advantages of CDMA technology over TDMA and FDMA technologies are voice quality, system reliability, and handset battery life, which have created a multitude of research on CDMA systems. Following the success of cellular telephone services in the 1990s, the technical community has turned its attention to data transmission [4]. CDMA has become the focus of current research to provide higher data rates for end users over wireless channels [5]. Throughput is a key measure of the quality of a wireless data link. It is the average rate of successful message delivery over a communication channel. It could also be defined as the number of information bits received without error per second. Throughput is, therefore, a good measure of the channel capacity of a communication link. The message or information delivery may be over a physical or logical link, or over a wireless channel, passing through a certain network node such as data passed between two specific computers. Throughput is usually measured in bits per second (bps) and sometimes data packets per second or data packets per time slot. The throughput of a wireless data communication system depends on a number of variables which include: packet size, transmission rate, the number of overhead bits in each packet, received signal power, received noise power spectral density, modulation technique, and channel conditions. The key to maximizing throughput is maintaining the signal-to-interference-and-noise ratio (SINR) at an optimum level [4]. Users of telecommunication devices, system designers, and researchers involved in communication theory are often interested in knowing the expected performance of a system. The performance long-term achievable data transmission rate a network can support, could be measured in terms of efficiency, timeliness, and cost. System Robust modeling 5 and throughput optimization in CDMA networks 5

2 designers are often interested in selecting the most effective architecture or design constraints for a system, which drives its final performance. In most cases, the benchmark of what a system is capable of doing or its maximum performance is what the user or designer is interested in. II. BACKGROUND A simplified approach to the throughput optimization problem is to assume continuous rate and power assignments, instead of practical discrete system parameters, at the expense of an approximate solution [6]. This method is valid because throughput is continuously distributed over time and improves with continuous power assignments. CDMA has been considered and recognized as a viable alternative to both FDMA and TDMA. CDMA schemes have many advantages, but these advantages are hindered by the increasing interference caused by other active terminals, since all signals in the CDMA system share the same transmission bandwidth. Blocking occurs when the tolerance limit to interference is exceeded. Hence, in CDMA, the level of interference is a limiting factor. Let us consider a receiver and two terminals (transmitters) with one closer to the receiver and the other farther away. If they transmit simultaneously at equal powers, then the receiver will receive more power from the near transmitter. Since one s transmission signal is the other s noise, the signal-tonoise ratio (SNR) for the farther transmitter is much lower. If the nearer transmitter transmits a signal of magnitude higher than the farther transmitter, then the SNR for the latter may be below detectability and may as well not transmit. This effectively jams the communication channel. This problem is commonly solved by dynamic output power adjustment of the transmitters [6] [11]. That is, the nearer transmitter uses less power so that the SNR for all transmitters at the receiver is roughly the same. This sometimes can have a noticeable impact on handset battery life, which varies depending on distance from the base station. In high-noise situations, closer transmitters may boost their output power, which forces distant transmitters to boost their output to maintain a good SNR, and other transmitters react to the rising noise floor by increasing their output. This process continues, and eventually, distant transmitters lose their ability to maintain a usable SNR and drop from the network. If there are optimum numbers of active terminals, when noise and out-of-cell interference are negligible, then the transmitter power levels should be controlled to achieve power balancing. With power balancing, all signals arrive at the base station with equal power. On the other hand, when noise and interference from other cells are not negligible, the power optimization problem is more complicated. The optimum set of transmitter powers depends on the maximum achievable SNR of the terminals, say N, and the optimum received power levels are unequal. Goodman et al. [12] observe that in order to maximize base station throughput with any power control algorithm, the number of active transmitters, N, should be limited to N N*, where N* is a property of the frame success function. It maximizes the systems throughput, when the signals of the transmitting terminals arrive at the receiver with equal power. The specific form of the frame success function depends on the details of the CDMA transmission system including the bandwidth, packet size, modem configuration, channel coding, antennas, and radio propagation details. To enhance the quality of the system, there is a need to optimize the throughput of a CDMA network by finding the transmitter power levels, given a number of terminals transmitting simultaneously. This can be achieved through study of resource management issues such as: total transmit power, total bandwidth, individual quality of service requirement, and transmitter power control, which is the goal of the study. The objectives of the paper include: a. To maximize network utilization and the ser- vice requirement of each user (fairness) or delay. b. To minimize the total transmit power subject to constraints such as: total bandwidth, individual transmit power assignment, and quality of reception in terms of signal-to-interference-and-noise ratio (SINR) target. III. methodology A. Throughput Optimization Model Parameters In [12], a data source generates packets of length L bits at each terminal of a CDMA system. A forward error correction (FEC) encoder, if present, and a cyclic redundancy check (CRC) encoder together expand the packet size to M bits. The data rate of the coded packets is R s b/s. The digital modulator 6 journal of applied science & engineering technology 2009

3 spreads the signal to produce R c chips/s. The CDMA processing gain is G = W/R S (1) where W (Hz) is the system bandwidth and is proportional to R c. Terminal i also contains a radio modulator and a transmitter radiating power P i watts. The path gain from transmitter i to the base station is h i and the signal from terminal i arrives at the base station at a received power level of Q i = P i h i (W) (2) The base station also receives noise and out-of-cell interference with a total power of s 2 W. The base station has N receivers, each containing a demodulator, a correlator for de-spreading the received signal, and a cyclic redundancy check decoder. Each receiver also has a channel decoder if the transmitter includes forward error correction. In this analysis, the details of the transmission system are embodied in a mathematical function f(x), which is the probability that a packet arrives at the CRC decoder without errors. The dependent variable g is the received SINR. For terminal i, (3) In the case of practical interest, f(g) is a continuously increasing S-shaped function of g, with f (0)=2 -M 0 and f ( ) =1 [13]. If the probability of undetected errors at the CRC decoder is negligible, the throughput of signal i, defined as the number of information bits per second received without error, is: where T i is the throughput of terminal i (b/s) L is the packet length (bit) M is the packet size expanded by both FEC encoder and the CRC encoder (bit) R s is the packet data rate (b/s) f (g) is the probability function that a packet arrives at the CRC decoder without errors. The aggregate throughput, T total, is the sum of the N individual throughput measures in (7). Assuming that L, M, and R s are system constants, the normalized throughput, U, is analyzed and defined as: (8) (7) substituting (2) into (3), we obtain Messages acknowledged from the receiver inform the transmitter of errors detected at the CRC decoder that have not been corrected by the channel decoder. The transmitter employs selectiverepeat retransmission of packets received in error. It is assumed in parts of this analysis that intra-cell interference dominates the total distortion and study of system performance when s 2 = 0. When s 2 > 0, the signal-to-noise ratio of the receiver is defined as (5) (4) Substituting this into (4), we obtain (6) where U is dimensionless and bounded by 0 U N. To find the optimum transmitter power levels, it is convenient mathematically to maximize equation (8) with respect to the received powers Q 1, Q 2,, Q N. This is done by differentiating (8) with respect to each of the received power levels Q i. N derivatives are then examined under the power balancing condition Q i = Q for i = 1, 2,, N. Under this condition, all of the derivatives are equal. They have the following properties: These formulas indicate that when performance is limited by intra-cell interference (s 2 = 0) it is possible that maximum throughput will occur when all signals reach the base station at the same power level. The optimization problem is more complex when s 2 > 0. This case will be treated in future research and will (9) (10) Robust modeling and throughput optimization in CDMA networks 7

4 not be discussed further. Maximum Throughput with no Additive Noise Before a performance analysis for arbitrary values of N is carried out, let us examine the two-terminal case (N=2) to have an idea of the effects of power levels on base station throughput. (i) Two Terminals In [14], the simplest, nontrivial maximization of equation (8) occurs when N=2 and s 2 = 0 In this case the normalized throughput U is a function of just one variable, z = Q 2 /Q 1. Moreover, g 2 = Gz and g 1 = G/z. By adopting the notation U 2 (z) = f(gz)+ f(g/z) as the normalized throughput when N=2 and s 2 = 0 it is found that This suggests that U 2 (1) = 2f(G) could be a local maximum, depending on the sign of the second derivative at z=1. Examining the second derivative for arbitrary S-shaped f(g) we find that U 2 (1) is a local minimum at low values of G and a local maximum at high values. Specifically, (11) The sign of the second derivative of U 2 is the same as that of the derivative of xf ( x). For the class of functions f(x), xf ( x ) has a bell shape reaching a single maximum at some point x = G*. Therefore, the derivative of xf ( x ) is positive for any x to the left of G* and is negative otherwise. This means that U 2 (1) is a local maximum when G is large enough to exceed G* and is a local minimum otherwise. It is determined whether there is a global maximum at the boundaries of the feasible region when z=1 yields a local minimum, i.e., at z = 0 and z =. Even when z = 1 is a local maximum, the probability that the global maximum lies at the boundary of the feasible region must be considered. This suggests that we compare the equal-received-power condition (z=1) with the condition that terminal two does not transmit at all (z=0). The comparison reveals that z=1 produces higher throughput when 2f(G)>1, while z=0 produces higher throughput when 2f(G)<1. Accordingly, the critical processing gain G c is defined as the value of G for which f(g) = 0.5. G c has the property that single terminal transmission (z = 0 or z = ) is better than equal-received-power transmission when G<G c and, conversely, when G>G c. Because G is proportional to the bandwidth, we can state that the system requires a bandwidth corresponding to at least G = G c to support two data terminals. (ii) Arbitrary Number of Terminals Equation (9) encourages us to explore power balancing to determine whether it provides maximum or minimum throughput. Rather than examine second derivatives, we extend the approach adopted in the case when N=2. To achieve this, we assume that f signals from k transmitters arrive at the base station with equal power and that the other (N-k) terminals turn off their transmitters. When Q i = Q for i =1, 2,, k and s 2 =0, (4) and (7) imply (12) where U(k) is the power balancing throughput as a function of k k are the transmitters f are the signals transmitted by k transmitters G is the processing gain For values of G>G c, this function has a maximum value for an integer k=n* 2. Throughput is maximum when N* signals are received with equal power and the other (N-N*) signals are not transmitted at all. This analysis leads to the observation that maximizing (12) with respect to k is equivalent to maximizing f(g) / g For the class of functions f being considered, f(x)/x has a unique maximum at the point where a line from the origin is tangent to f(x). The notation g* is used for the signal-to-interference ratio that maximizes f(x)/x. g* is the unique solution to the equation: (13) For maximum throughput, the system should operate with a value of k that produces g = G / (k-1) g *. Since k has to be an integer, we infer that N* is the integer just above or just below 1+G/g *. Maximum Throughput with Noise Present We now expand the study to take into account the effects of additive noise and interference from 8 journal of applied science & engineering technology 2009

5 other cells. The total power in these impairments is s 2 watts (and we refer to these effects as noise, to be concise). The noise appears at the receiver as an additional signal that does not contribute to the overall throughput of the system. The system has to use some of its power and bandwidth resources to overcome the effects of noise. The effects of noise depend on the power limits of practical terminals. With unlimited power, we would increase all the received powers Q i indefinitely until the effect of noise is negligible. (i) Two Terminals With s 2 = 0 and N = 2, we derive two principal conditions that: a. There is a critical processing gain G c that permits two terminals to share the channel with higher total throughput than one terminal alone can achieve, and b. When G>G c, the throughput is maximum when both signals arrive at the base station with equal power. This section explores the same issues in the presence of additive noise, s 2 > 0. Thus, we conclude that with s 2 > 0, power balancing is sub-optimal, and the throughput with Q 1 = Q 2 is a lower bound on the maximum possible throughput. When Q 1 = Q 2 = Q 2, max, the lower bound is S 2,max U = U = 2 2 f G (14) S 2,max + 1 When Q 2 = 0, U = U 1 = f(gs 1 ) 1, it follows that a sufficient condition for admitting two terminals is U 2 1. Equation (14) implies that the minimum G cc that achieves U 2 1 satisfies: recalling that with s 2 = 0, the critical processing gain G c satisfies f(g c )=0.5 and we conclude that noise increases the bandwidth sufficient for admitting two terminals by the factor: S + 2,max 1 S 2,max (16) (15) Another way to assess the effects of noise is to consider the processing gain fixed at G >G c, and examine equation (14) to find the value of S 2,max, sufficient for U 2 1. This analysis leads to the conclusion that a sufficient condition for admitting two terminals is: This critical SNR corresponds to a critical distance (d c meters) between transmitter 2 (second transmitter) and the base station. When the actual distance is greater than the critical distance (d>d c ), the system s throughput is higher when Q 2 = 0. To determine d c, recall that: where h 2 is the distance-dependent path gain of the second terminal. Referring to a simple propagation model in which h 2 =Const/d 2 ) a, where a is the propagation exponent, we adopt the policy Q 2 =Q 2,max when (ii) Arbitrary Number of Terminals Extending the analysis for N=2 terminals, we assumed that terminal N, with minimum Q i,max, transmits at maximum power, P N =P N,max and achieves a signal-to-noise ratio, S N,max. If all other terminals adjust their transmit powers to achieve Q i =Q N,max, the normalized throughput, according to (6) and (8) is: Therefore, (19) and (20) give the simulation models for the study. IV. RESULTS AND ANALYSIS (20) (17) (18) (19) In the previous section, two mathematical models were derived. We then simulated these models taking into consideration the cases of two terminals and an arbitrary number of terminals. The simulator has a graphical user interface (GUI) that captures data corresponding to the parameters in the models. Empirical inputs were made and results were obtained from the simulation. The following is a discussion of the simulation results. Robust modeling and throughput optimization in CDMA networks 9

6 Distance vs. Propagation Exponent The effect of the desired terminal propagation exponent on operating range is shown in Figure 1. We observe that a small value of propagation exponent for a terminal yields a wider operating range (longer distance) and thus a significant increase in the system performance than a larger value of the propagation exponent. The reason for such performance is that increased values of the propagation exponent for terminals leads to more frequent attenuation of signals, thus yielding reduced operating range and a higher SNR for the terminals. We fit an exponential trend equation to enable the prediction of new empirical results. achieve equal receive power. We fit a power trend equation to predict new empirical results. Distance vs. Processing Gain Figure 2 illustrates a trade-off between processing gain and operating range for the system under study. In this study, we set G c = 8; the graph pertains to a = and This scaling factor implies that a terminal transmitting with maximum power at a distance of 120m from the receiver achieves SNR S 2,max = 1,000. Here, the operating range increases rapidly as a function of processing gain as the propagation exponent increases. Then a further increase in processing gain brings a more gradual increase in the operating range. Trend equations are fitted to help predict new empirical results. Figure 3 illustrates the normalized throughput as a function of the number of terminals. With the processing gain ranging from 8 to 64, the analysis predicts that the optimum number of terminals, N 4, as confirmed by the graph. This means that throughput is maximum with number of terminals N = N* = 4. Therefore, with maximum throughput, the system should operate with a k value that produces g = G/(k-1) g*. Since k has to be an integer, we infer that N* is the integer just above or below 1+ G/g. Figure 4 depicts a graph of throughput versus processing gain. It is observed in this graph that throughput increases with an increase in processing gain. This suggests that with a processing gain of G 8, it would be better to turn off the transmitter in one of the terminals and allow the other terminal to use the entire base station. But with G 9, it would be better to have both terminals transmitting, to Figure 1. A Graph of Distance vs. Propagation Exponent Figure 2. A Graph of Distance vs. Processing Gain V. CONCLUSION We have been able to optimize the throughput in CDMA networks through power control by simulating models with relevant parameters. Some practical issues regarding the application of this paper 10 journal of applied science & engineering technology 2009

7 network technologies such as GSM is highly uncertain due to rapid development and widespread of the third generation (3G) technologies, especially CDMA. Figure 3. A Graph of Throughput vs. Number of Terminals Figure 4. A Graph of Throughput vs. Processing Gain have been identified and a series of investigations identifying the key features and parameters, as well as how they influence CDMA systems network have been presented. Numerical results and discussion have shown that the interference generated by users of the network in the form of noise has been minimized with the help of the models derived, which can aid in transmitting signals to the base station of CDMA systems with equal strongest possible power. Finally, the future of the second generation (2G) VI. REFERENCES [1] CDMA Development Group, CDG 1Q 2009 Subscribers Statistics, March 2009, [2] V. K. Garg, IS-95 CDMA and CDMA2000: Cellular/PCS Systems Implementation, Prentice Hall Communication Engineering and Emerging Technologies Series, T. Rappaport, Ed. New Jersey: Prentice Hall, [3] K. V. Ravi, Comparison of multi-accessing schemes for mobile communication systems, IEEE Int. Conf. on Personal Wireless Commun., 1994, pp [4] R. J. Lavery, Throughput optimization for wireless data transmission, M.S. thesis, Polytechnic University, Brooklyn, NY, [5] A. R Abdul Rajak, The performance of CDMA system with novel concatenated FEC schemes in AWGN channel, Asian J. of Inf. Technol., vol. 5, no. 10, pp , [6] M. K. Karakayali, R. Yates, and L. V. Razoumov, Downlink throughput maximization in CDMA wireless networks, in Proc. of IEEE Wireless Commun. and Netw. Conf., [7] D. Goodman, and N. Mandayam, Network assisted power control for wireless data, Mobile Netw. and Appl., vol. 6, no. 5, pp , Sept [8] F. Gunnarsson, Power control in wireless networks: characteristics and fundamentals, in Wireless Commuications Systems and Networks, M. Guizani, Ed. New York: Plenum Press, 2004, pp [9] P. Chevellat, J. Jelitto, and H. L. Truong, Dynamic data rate and transmit power adjustment in IEEE wireless LANs, Int. J. of Wireless Inf. Netw., vol. 12, no. 3, pp , July [10] T. Alpcan, X., Fan, M. Arcak, and J. T. Wen, Power control for multicell CDMA wireless networks: by team optimization approach, in Proc. of the WiOpt 05 Workshop on Modeling and Optimization in Mobile, Ad Hoc and Wireless Netw., 2005, pp [11] I. Broustis, J. Eriksson, S. V. Krishnamurthy, Robust modeling and throughput optimization in CDMA networks 11

8 and M. Faloutsos, Implications of power control in wireless networks: a qualitative study, in Passive and Active Network Measurement, vol. 4427/2007, S. Uhlig, K. Papagiannaki, O. Bonaventure, Eds. Lecture Notes in Computer Science. Berlin-Heidelberg, New York: Springer, 2007, pp [12] D. Goodman, Z. Marantz, P. Orenstein, and V. Rodriquez, Maximizing the throughput of CDMA data communications, in IEEE 58th Veh. Technol. Conf., vol. 5, 2003, pp [13] V. Rodriquez, Robust modeling and analysis for wireless data resource management, IEEE Wireless Commun. and Netw. Conf., vol. 2, 2003, pp [14] V. Rodriquez and D. J. Goodman, Prioritized throughput maximization via rate and power control for 3G CDMA: the 2 terminal scenario, in Proc. of 40th Allerton Conf. on Commun., Control and Comput., Oct Aniekan Akpaeti is a B.Sc. Graduate of the Department of Mathematics Statistics and Computer Science, University of Uyo, Nigeria. He has developed keen interest in the field of wireless communications by researching into it during his B.Sc. research. Moses Ekpenyong, B.Sc., M.Sc., Computer Science, PhD, Speech Technology (in view) is a staff of the Department of Mathematics, Statistics and Computer Science, University of Uyo, Nigeria and is the corresponding author of this paper. He is a member of the following professional bodies: Nigerian Association of Mathematical Physics (NAMP), Nigeria Computer Society (NCS), International Speech and Communications Association (ISCA), Nigeria Mathematical Society (NMS), Nigerian Statistical Association (NSA) and West-African Linguistics Society (WALS). He is an international scholar and has published widely in the area of wireless communications. His area of specialization is speech modeling and communications technology. Joseph Isabona, Joseph Isabona, B.Sc., Theoretical Physics, M.Sc., Physics (Electronics/Communications), PhD, Physics Electronics (in view) is in the Department of Physics, University of Uyo, Nigeria. He is a member of the Nigerian Association of Mathematical Physics (NAMP). He has published both nationally and internationally in the area of wireless communications. His area of specialization is signal processing and radio resource management in wireless networks. 12 journal of applied science & engineering technology 2009