Achievable-SIR-Based Predictive Closed-Loop Power Control in a CDMA Mobile System

720 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 51, NO. 4, JULY 2002 Achievable-SIR-Based Predictive Closed-Loop Power Control in a CDMA Mobile System F. C. M. Lau, Member, IEEE and W. M. Tam Abstract A power control algorithm with two prediction models based on an achievable signal-to-interference power ratio (SIR) has been proposed under a multipath Rayleigh fading environment in a code-division multiple-access (CDMA) mobile system. An achievable SIR is defined as the maximum minimum SIR among all users at a particular time step. The corresponding mobile transmission powers are denoted as the optimum transmission powers. In the individual power predictor (IPP) model, a linear transversal filter is assigned to each user. The output of the IPP, which is a linear combination of the optimum transmission powers of the mobile during the current and previous power measurement periods, predicts the optimum transmission power of the mobile in the next time step. In the global power predictor (GPP) model, a single predictor, constructed by a linear neural network, is used to predict the optimum transmission powers of all mobiles in the next time step. In both predictor models, the weights of the predictors are updated by using the recursive least squares algorithm. To further improve the performance, a reduced power-measurement period has been studied. Simulation results show that the proposed power control algorithm can achieve a lower outage probability and a smaller dynamic range of transmission power compared with a conventional power control scheme. Index Terms Code division multiple access (CDMA), mobile communications, power control. I. INTRODUCTION CODE division multiple access (CDMA), which has attracted considerable attention in recent years, has been adopted as one of the major technologies in third-generation mobile communication systems. In a CDMA mobile system, closed-loop power control has been employed in the reverse link to combat multipath fading. The power adjustment decision made is normally based on the received signal strength or the signal-to-interference power ratio (SIR) [1] [3]. The aim of the signal-strength-based power control schemes is to achieve constant received power at the base station, while the common goal of the SIR-based power control algorithms is to minimize the difference in SIR between all users. Since interference has been taken into account, SIR-based power control schemes can achieve superior performance compared with signal-strength-based power control techniques. In a SIRbased power control scheme, a preset power control threshold is required. The optimum threshold, however, depends very Manuscript received October 16, 2000; revised September 14, 2001. This work was supported under a Grant by The Hong Kong Polytechnic University of the Hong Kong Special Administrative Region. The authors are with Hong Kong Polytechnic University, Kowloon, Hong Kong (e-mail: encmlau@polyu.edu.hk; tamwm@encserver.en.polyu.edu.hk). Publisher Item Identifier S 0018-9545(02)02482-9. much on the parameters of the mobile environment such as the Doppler frequency and the interference level [4]. One approach to adjust the threshold according to the mobile environment conditions is to add an outer loop control [5], [6], in which the base station checks the error rate of the frames and updates the SIR threshold. If the frame error rate is low, the controller decreases the threshold with a down step size; otherwise, the threshold is increased with an up step size. The up and down step sizes need not be the same and the optimum step sizes used in the outer loop control have been studied in [6]. In [7], it was shown that the system performance can also be enhanced when a combined strength- and SIR-based power control scheme is applied. Another important parameter in closed-loop power control is the required dynamic range of the transmission power. If that range is larger than that supported by the mobile, the mobile transmission power cannot be adjusted according to the received commands once the power has reached its extremes (maximum or minimum). Under such circumstances, the transmission power will only be set to the maximum or minimum transmission value. Therefore, a smaller required dynamic range will ensure that the transmission power can be adjusted accordingly. Until recently, all power control decision metrics were made based on the current measured signal strength or SIR. In [8], Sim et al. made use of channel power gain prediction in closed-loop power control. First, the future power gain of the channel is predicted based on the current and previous measurements. The required mobile transmission power is then determined based on the predicted power gain. In [9], Lau and Tam, taking the predicted power gains of all users into account, propose to select the power control command set that minimizes the difference of SIR among all users. In [10], Wen et al. investigated a short-term fading prediction-based power control method. It begins by predicting the variation of Rayleigh fading from the received signal. With knowledge of the future trend of the short-term fading, a weight is found to convert the slope of short-term fading into the slope of the received SIR. The adjustment of the mobile transmission power is then based on both the power control error and the future information about the short-term fading. Results show that predictive power control algorithms can enhance system performance compared with conventional schemes. In this paper, a predictive power control algorithm based on achievable SIR is proposed. In the proposed method, the power gains are first evaluated based on the channel estimations, the autocorrelations, the cross-correlations of the spreading codes, and the time delays of the mobiles. From the square matrix 0018-9545/02$17.00 2002 IEEE

LAU AND TAM: ACHIEVABLE-SIR-BASED POWER CONTROL IN CDMA MOBILE SYSTEMS 721 Fig. 1. Predictive reverse-link closed-loop power control model with IPP. Structure of IPP and transmission power update block. formed by the normalized power gains, the achievable SIR can be found and the corresponding optimum transmission powers of the mobiles that maximize the minimum SIR are derived. The current and past optimum values are then fed to predict the optimum transmission power in the next time step. Two predictor models have been proposed together with two power measurement schemes. This paper is organized as follows. Section II introduces the proposed power control scheme with two transmission power prediction schemes, two power measurement configurations, and power control command decisions for one to three power control bits. The simulation model is described in Section III. In Section IV, simulation results and discussions are presented. II. PROPOSED POWER CONTROL ALGORITHMS In our analysis, we assume that the distance path loss and shadowing are perfectly compensated for by the open-loop power control. Two predictive reverse-link closed-loop power control models are proposed as shown in Figs. 1 and 2. The base station first estimates the variations of the channels. Together with the autocorrelations and the cross-correlations of the spreading codes, and the delays of the mobiles, the power gains from the transmitters to the receivers can be evaluated, where represents the number of users in the system. Based on the power gains, a normalized power gain matrix is formed. The achievable

722 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 51, NO. 4, JULY 2002 Fig. 2. Predictive reverse-link closed-loop power control model with GPP. SIR is then derived from the largest real eigenvalue of. The elements of the corresponding eigenvector represent the current optimum transmission powers of the mobiles. Such elements, together with the values derived from previous time steps, are then fed to a power prediction block to estimate the optimum transmission powers of the mobiles in the next time step. In Fig. 1, one prediction block has been assigned to each individual user and, in Fig. 2, only one single block is needed to perform all the predictions. For each mobile, at the end of each power control period, the predicted value will be compared with the current mobile transmission power. Based on the difference between them, a power control decision is made and the corresponding power control command is sent to the mobile. After receiving the command, the mobile adjusts its transmission power accordingly in the next power control period. On the base station side, the transmission power of the mobile is also updated. Details on the power control models are described in the following sections. A. Determination of Achievable SIR It has been assumed that open-loop power control can perfectly compensate for the path loss and shadowing. Hence, the remaining power gain from the transmitter to the receiver in the reverse link, caused by multipath fading, is given by where Pt is the transmission power of mobile and is the received power of mobile at receiver. If the transmission powers of the mobiles are assumed to remain unchanged over each power measurement period (PMP), i.e., Pt Pt for, the SIR for mobile over a PMP can thus be obtained from SIR (1) (2)

LAU AND TAM: ACHIEVABLE-SIR-BASED POWER CONTROL IN CDMA MOBILE SYSTEMS 723 Fig. 3. where Linear transversal filter used in IPP. is the link gain from mobile to receiver over a PMP and (4) is the link gain from mobile to receiver normalized to the link gain in the desired path of mobile. In our simulations, the link gains are evaluated through delays of the mobiles and channel estimations, autocorrelations, and cross-correlations of the spreading codes. Next, we introduce the power vector and the normalized link gain matrix. Foragiven, the SIR is achievable if there exists a power vector (all elements of are nonnegative) such that SIR for all. Since the elements of the matrix are nonnegative stochastic variables, the following can be shown [11]: 1) there exists exactly one real positive eigenvalue for which the corresponding eigenvector is positive; 2) the maximum achievable that satisfies SIR and is is given by (5) 3) is also the largest real eigenvalue of matrix. Moreover, the simple bounds on the eigenvalues of derived from row sums of given in [12] ensure that and thus. As a consequence, the solution of eigenvector blocks in Figs. 1 and 2 first use the current power gains to form the normalized link gain matrix. The largest real eigenvalue of the matrix is then evaluated, and the corresponding eigenvector will become the optimum power vector for the current PMP to maximize the minimum SIR. [The achievable SIR can be derived using (5).] The power vector is then fed to the power predictor block(s) in the following stage to predict the optimum power vector in the next time step. B. Prediction of Transmission Power Denote the output power vector of the solution of eigenvector block for the th PMP by. Based on the current and previous power vectors, the optimum transmission powers of the mobiles at the ( 1)th PMP given by the elements of (3) are estimated. Two predictors used for the estimation are described below. 1) Individual Power Predictor (IPP): As shown in Fig. 1, one predictor is assigned to each individual user. The optimum transmission power for the next PMP is assumed to be a linear combination of the current and past optimum transmission powers. The predictor is thus constructed by a linear transversal filter with taps, as shown in Fig. 3. For the th user, the input to the predictor at the th PMP, denoted by, is composed of the th elements of the optimum transmission power vectors. That is Pt Pt Pt (6) where denotes transposition. is the total number of current and past values used in the prediction. In this case, equals the number of taps in the predictor, i.e.,. The output of the predictor is the estimated optimum transmission power, which is given by Pt Pt (7) represents the th estimated tap weight of the predictor for mobile during the th PMP. The estimated tap weight vector is defined as (8) whose elements are updated every PMP using the recursive least squares (RLS) algorithm [13] (9) where is a square matrix of size and denotes a preselected scalar. The superscript denotes Hermitian transposition. 2) Global Power Predictor (GPP): For the individual predictors, the transmission power of each user is estimated separately. Any adjustment in the transmission power of a mobile, however, will lead to changes in SIRs of all other users. A single global predictor, as shown in Fig. 2, to estimate all mobile transmission powers for the next PMP should therefore give better power predictions. The linear neural network shown in Fig. 4 is proposed here to predict the transmission powers. The predicted transmission power of mobile is not only based on its present and previous optimum transmission powers, but also depends on the transmission powers of other mobiles. The input vector to the predictor is given by Pt Pt Pt Pt Pt Pt Pt Pt Pt (10)

724 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 51, NO. 4, JULY 2002 Fig. 4. Linear neural network. and the output gives the predicted optimum transmission power vector Pt Pt Pt (11) The th output element of the predictor is obtained by Pt Pt (12) The estimated tap weight vector corresponding to the th output element is defined as (13) The elements of are updated with the RLS algorithm as described by (9) except that is now replaced by. The total number of taps used in the predictor is, which is larger than that in the IPP. Therefore, the global predictor is much more complex than the individual predictor. C. Power Measurement Period Normally, the PMP is the same as the power control period (PCP). However, in order to achieve a better prediction of the transmission power, the measurement period of the power gain may be reduced. Two PMPs are investigated in this paper and are explained below. Fig. 5. Power measurement periods. Full PCPPM (T = T ). Half PCPPM (T =2T ). 1) Full Power Control Period Power Measurement (Full PCPPM): The PMP and the PCP are identical and completely overlapped, as shown in Fig. 5. Then power control decision will be made every time the transmission powers Pt are predicted. 2) Half PCPPM: Another approach that may render the prediction of Pt more accurately is to shorten the PMP. When the measurement period of is reduced to,as shown in Fig. 5, the power control decision will be made at half the frequency that the transmission powers Pt are predicted. In other words, the power control decision block

LAU AND TAM: ACHIEVABLE-SIR-BASED POWER CONTROL IN CDMA MOBILE SYSTEMS 725 TABLE I STATUS OF POWER CONTROL BIT(S) AND ADJUSTMENT IN TRANSMISSION POWER UNDER VARIOUS err (db) CONDITIONS. NUMBER OF POWER CONTROL BITS q =1; q =2; AND (c) q =3 control command is based on the difference between the next predicted value and the current transmission power. Hence, the current transmission power can be taken as the power control threshold and is assumed to be stored at the base station. If the prediction of the next transmission power is good, the system performance should be enhanced. (c) will operate when is divisible by two, i.e., for some positive integer. Similarly, the transmission power records Pt are updated at a rate of 1, i.e., when is even. D. Power Control Command If the transmission power prediction is perfect, the optimum transmission powers in the next PCP can be obtained correctly. Define err (db) as the difference (in decibels) between the predicted transmission power in the next PCP and the current transmission power of user. That is err (db) Pt (db) Pt (db) for full PCPPM (14a) err (db) Pt (db) Pt (db) for half PCPPM (14b) A power control command (cmd), derived from err (db), the number of power control bits, and the step size (db), will then be sent to instruct mobile to adjust its power. It is well understood that using a finer step size and a larger number of power control bits will allow the transmission power to be controlled more accurately. The price to pay, however, is a lower bandwidth efficiency. Table I (c) shows the status of the power control bit(s) and the adjustment in the mobile transmission power under various err (db) conditions for or bits. In the conventional power control scheme, the adjustment of the power is determined by the received power or SIR and the power control threshold. In our proposed scheme, the power III. SIMULATION MODEL 1) The system is modeled as a direct-sequence CDMA binary phase-shift keying modulation system with a bit rate of kb/s and a carrier frequency of GHz. The chip rate is Mc/s and, hence, the processing gain is PG. Gold code is used as the spreading code, and the length of the code sequence is 2 1. 2) There are ten users in the cell. In each simulation, the mobile velocities of the users are uniformly distributed in one of the speed ranges: low velocity (10 40 km/h), medium velocity (40 70 km/h), and high velocity (70 100 km/h). 3) The signal of each mobile is assumed to be transmitted over four paths of equal strengths. The time delay difference between consecutive paths is, which is the chip duration. Moreover, each of the paths undergoes independent Rayleigh fading, which is generated using Jakes model [14]. 4) The period of the closed-loop power control scheme is ms (1600 Hz), which is 40 times the bit duration. 5) The power control command is 1 to 3 bits in length and the step size is fixed at 0.5 db. 6) For conventional power control, the dynamic range of the transmission power is set at 80 db ( 40 db). Assuming that the transmission power of each user is one unit (0 db) at the beginning of the simulation, the transmission power can then range from 10 to 10 units. 7) In the conventional power control scheme, for a given required SIR, the outage probability of the system is simulated for various threshold values. The threshold value corresponding to the lowest outage probability is defined as the optimum threshold. Note that this optimum threshold varies for different SIRs. 8) For all, the RLS algorithm is initialized by setting ( is the identity matrix of size ), with and. IV. RESULTS AND DISCUSSIONS The outage probability for mobile is defined as the probability that the SIR is below the required value. The average outage probability is given by Po Po SIR SIR. Fig.6 plots the outage probability versus the total number of current and past PMPs used in the predictors under low-, medium-, and high-speed ranges. Full PCPPM is used. The number of power control command bits is and the required SIR db. In the figure, it can be seen that GPP gives a better performance than IPP under the speed ranges considered. This is because a better transmission

726 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 51, NO. 4, JULY 2002 Fig. 6. Outage probability versus the number of periods L used for prediction in low-, medium-, and high-speed ranges (full PCPPM, q =1, and (E =I ) =6dB). power estimation is produced in GPP when interactions between users have been taken into consideration. For IPP, the outage probability improves, but slowly as the number of taps increases. For GPP, it can be observed that the outage probability changes little with when varies from 5 to 25. This shows that collecting more information than required does not improve the prediction process, and most of the required information for prediction is already contained in the latest five measurements. Fig.7 (c) compares the outage probabilities when no power control, conventional power control with optimum threshold (CPCOT), and the proposed power control (PPC) schemes are applied to mobiles at the low-, medium-, and high-speed ranges. The number of power measurement periods used in the predictor is ten for full PCPPM and the corresponding value for half PCPPM is 20. The number of power control bits is one for all curves. Fig. 7 indicates that the PPC outperforms the CPCOT regardless of the configuration used. Among the four PPC configurations, GPP with half PCPPM gives the best performance, followed by GPP with full PCPPM and IPP with half PCPPM, while IPP with full PCPPM is comparatively the worst. It is also found that the performance could be further improved were the transmission power prediction perfect. Fig. 7 and (c) shows the results again when the mobiles are in the medium- and high-speed ranges. In the figures, we note that the outage probability of IPP with full PCPPM is close to that of CPCOT and the performances of other configurations are better than that of CPCOT. Fig. 8 (c) compares the outage probabilities of PPC using GPP with half PCPPM and CPCOT when one to three power control command bits are used at low-, medium-, and highspeed ranges. The number of power measurement periods used in the predictor is 20. Results show that the outage probability of PPC is lower than that of CPCOT in all cases. Moreover, the outage probability is reduced in all speed ranges when the number of power control command bits increases. This is because the transmission powers of the mobiles can be adjusted more accurately when more command bits are transmitted. Note that in Fig. 8, when db and three power control bits are used, no outage is found in the simulation. (c) Fig. 7. Outage probability versus (E =I ) for various power control schemes. L = 10 and 20 for full and half PCPPM, respectively, q = 1. Low-; medium-; and (c) high-speed range. Fig. 9 compares the outage probabilities of PPC using GPP with half PCPPM and CPCOT for low-, medium-, and high-speed ranges when one power control command bit is used. It can be seen that the difference between PPC and CPCOT is large for a mobile at low speed, which means that the improvement made by using PPC is more significant. This result can be explained by a more accurate power prediction when the channel varies slowly.

LAU AND TAM: ACHIEVABLE-SIR-BASED POWER CONTROL IN CDMA MOBILE SYSTEMS 727 Fig. 9. Outage probability versus (E =I ) for conventional power control using optimum threshold and the proposed power control (GPP with half PCPPM, L =20;q=1) under low-, medium-, and high-speed ranges. TABLE II SIMULATED DYNAMIC RANGE OF TRANSMISSION POWER IN DECIBELS. LOW-, MEDIUM-, AND (c) HIGH-SPEED RANGE (c) Fig. 8. Outage probability versus (E =I ) for conventional power control using optimum threshold and the proposed power control (GPP with half PCPPM, L =20) with one to three power control command bits. Low-speed range (P =0when (E =I ) =3dB and three power control bits are used). Medium-speed range. (c) High-speed range. (c) In Table II, the simulated dynamic ranges of the transmission power for PPC using GPP with half PCPPM and CPCOT are shown when one to three power control command bits are used. In the conventional power control scheme, if the transmission power is not restricted, the simulated power range diverges to infinity. When the transmission power is limited to a dynamic range of 80 db, i.e., db Pt db, the simulated power range is now finite. In the table, the simulated dynamic range for CPCOT with 80 db dynamic power limitation lies between 42.5 49 db. In PPC, when GPP with half PCPPM is used, the dynamic range lies from 10 to 22 db. Hence, PPC can achieve a dynamic range reduction of 20.5 39 db. With a smaller dynamic range, the transmission power will not be too large and the average power consumption is expected to decrease. When the mobile moves at a low speed, as shown in Table II, the dynamic range of PPC is close to that of PPC with perfect prediction. However, when the speed of the mobile increases, as shown in Table II and (c), the range of the transmission power of PPC increases. This is because the prediction becomes less accurate when the channel varies faster. The last column in each table also shows the dynamic range when the mobiles transmit at the perfectly predicted values, i.e.,

728 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 51, NO. 4, JULY 2002 Pt Pt Pt for all and. When the optimum values are used as the transmission powers, the dynamic ranges of the transmission power are 15.3, 14.4, and 14.5 db for low-, medium-, and high-speed ranges, respectively. V. CONCLUSION In this paper, a predictive reverse-link power control scheme has been proposed in a CDMA mobile system. The base station first evaluates the power gains. From the power gains, the achievable SIR can be found and the corresponding optimum transmission powers of the mobiles are derived. The current and past optimum transmission powers are then used to predict the optimum transmission powers in the next power control period. Two power prediction methods have been proposed together with two different power measurement periods. Results show that GPP with full/half PCPPM and IPP with half PCPPM outperform the conventional power control with optimum threshold at all speed ranges considered. Moreover, GPP with half PCPPM gives the best performance while the performance of IPP with full PCPPM is comparable to conventional power control scheme. The architecture of GPP, however, is much more complex compared with that of IPP. The proposed power control also reduces the dynamic range of the transmission power. Simulation results show that the dynamic ranges are not more than 16.5, 20, and 22 db for low-, medium-, and high-speed ranges, respectively. REFERENCES [1] S. Ariyavisitakul, Signal and interference statistics of a CDMA system with feedback power control Part II, IEEE Trans. Commun., vol. 42, pp. 597 605, Feb./Mar./Apr. 1994. [2] S. Ariyavisitakul and L. F. Chang, Signal and interference statistics of a CDMA system with feedback power control, IEEE Trans. Commun., vol. 41, pp. 1626 1634, Nov. 1993. [3] S. Seo, T. Dohi, and F. Adachi, SIR-based transmit power control of reverse link for coherent DS-CDMA mobile radio, IEICE Trans. Commun., vol. E81-B, no. 7, pp. 1508 1516, July 1998. [4] C. J. Chang, J. H. Lee, and F. C. Ren, Design of power control mechanisms with PCM realization for the uplink of a DS-CDMA cellular mobile radio system, IEEE Trans. Veh. Technol., vol. 45, pp. 522 530, Aug. 1996. [5] A. J. Viterbi, CDMA: Principles of Spread Spectrum Communication. Reading, MA: Addison-Wesley, 1995. [6] S. H. Won, W. W. Kim, D. H. An, and I. M. Jeong, Capacity enhancement by using optimum step sizes of controlling target SIR in a CDMA system, in Proc. Vehicular Technology Conf. 98, 1998, pp. 1859 1863. [7] Y. J. Yang and J. F. Chang, A strength-and-sir-combined adaptive power control for CDMA mobile radio channels, IEEE Trans. Veh. Technol., vol. 48, pp. 1996 2004, Nov. 1999. [8] M. L. Sim, E. Gunawan, B. H. Soong, and C. B. Soh, Performance study of close-loop power control algorithms for a cellular CDMA system, IEEE Trans. Veh. Technol., vol. 48, pp. 911 921, May 1999. [9] F. C. M. Lau and W. M. Tam, Novel predictive power control in a CDMA mobile radio system, in Vehicular Technology Conf., Tokyo, Japan, May 2000, pp. 1950 1954. [10] J. H. Wen, L. C. Yeh, and J. R. Chiou, Performance of short-term fading prediction-based power control method for DS-CDMA cellular mobile radio networks, IEICE Trans. Commun., vol. E81-B, no. 6, pp. 1231 1237, June 1998. [11] J. Zander, Performance of optimum transmitter power control in cellular radio systems, IEEE Trans. Veh. Technol., vol. 41, pp. 57 62, Feb. 1992. [12] F. R. Gantmacher, The Theory of Matrices. New York: Chelsea, 1994, vol. 2, ch. XIII. [13] S. Haykin, Adaptive Filter Theory. Englewood Cliffs, NJ: Prentice- Hall, 1995, ch. 13. [14] J. D. Parsons, The Mobile Radio Propagation Channel. New York: Halsted, 1992. F. C. M. Lau (M 93) received the B.Eng. and the Ph.D. degrees from King s College London, University of London, U.K., in 1989 and 1993, respectively. He is now an Associate Professor in the Department of Electronic and Information Engineering, Hong Kong Polytechnic University, Hong Kong. His main research interests include power control and capacity analysis in mobile communication systems and chaos-based digital communications. W. M. Tam received the B.Sc. degree in electronics and information systems from Jinan University, China, and the M.Phil. degree in electronic and information engineering from The Hong Kong Polytechnic University, Hong Kong. She is currently working toward the Ph.D. degree at the same university. Her research interests include power control in CDMA mobile cellular systems, third-generation mobile systems, and chaos-based digital communications.