IEEE COMMUNICATIONS LETTERS, VOL. 5, NO. 10, OCTOBER 2001
399
A New Generic Multistep Power Control Algorithm for the LEO Satellite Channel With High Dynamics Wenzhen Li, Vimal K. Dubey, and Choi Look Law
Abstract—LEO satellite CDMA systems, characterized by round-trip delay and high variation in slow fading, call for different considerations on power control algorithms. Based on the criteria of fast response, small over-compensation, oscillation-avoiding and minimum power control error, the transient behaviors of the fixed step, adaptive step, and multistep power control algorithms are investigated and compared. A new generic multistep power control algorithm with excellent dynamic performance is proposed for LEO satellite systems. Index Terms—CDMA, LEO satellite, power control.
I. INTRODUCTION
P
OWER control is an indispensable multiuser access interference (MAI) combating and fading compensation technique in CDMA communication systems. The extensively adopted distributed power control is actually an iterative algorithm, which includes transient and stable response stages. It is evident that the response time is a significant indicator of the efficiency of power control algorithms. A faster response results in a smaller control lag and better control performance. However, seeking a fast response may induce the power oscillation and over-compensation. This wastes power resource and increases interference to other users, and hence decreases the system capacity. Therefore, a good power control algorithm should possess fast response, small overcompensation, and oscillation—avoiding capability as well. Power control algorithms in terrestrial CDMA systems include the fixed step schemes as adopted in IS-95, adaptive step [2], and multistep schemes [3]. In terrestrial CDMA systems with short round-trip delay, fast power control algorithms can be employed, whose transient response stage is only a small part of the overall control process and has small influence on the overall performance. Whereas in LEO satellite CDMA systems with much longer round-trip delay, the power update interval should be much longer, and power control can only be used to combat the slow fading caused by shadowing and other geographic factors. Therefore, the transient stage cannot be ignored because it may cause long burst errors. Moreover, the slow fades have higher variations in LEO satellite systems, so the settling time that the power control process comes to the equilibrium is longer. This is especially so when the mobile is moving
Manuscript received May 21, 2001. The associate editor coordinating the review of this letter and approving it for publication was Dr. N. Mandayam. The authors are with the Communications Research Laboratory, School of Electrical and Electronics Engineering, Nanyung Technological University, Singapore 639798 (e-mail:
[email protected]). Publisher Item Identifier S 1089-7798(01)09049-4.
in a nonuniform environment where a multistate channel model is applicable [4]. Therefore, in the LEO satellite channel the performance of the power control significantly depends on its transient state behavior, i.e., dynamic performance. The multiple step power control with better dynamic performance are commonly adopted. Conventional multistep schemes [3] lack mathematical model to formulate the input-output relation, and its parameters are mainly set based on the simulation or trials. This is not convenient for system analysis and design when the system conditions are changing. In this letter, a new generic multistep power control scheme is proposed for the LEO satellite CDMA system over a generic multistate channel model. This scheme utilizing a multilevel quantizer with logarithmic characteristics, has much faster response than the other algorithms especially during channel state transitions. Moreover, it avoids the problem of overcompensation and successfully limits the noise or error driven power correction in the control loop. II. POWER CONTROL ALGORITHM The distributed power control iteratively adjusts the power levels of each transmitted signal, only using the local measurements. Thus, in reasonable time, all users will achieve and maintain the desired signal-to-interference ratio (SIR). In the considered system, power update interval is assumed to be 10 ms equal to the round-trip delay (This assumption is justified if the altitude of satellite is about 1000 km and the minimum elevation angle is 40 as in Teledesic system). A generic iterative method for power control can be written as
where is the transmit power of user at th is the standard interference power update interval and function at interval when the power vector of all users are . Without considering power constraint, a popular iterative power control algorithm, given in [1], is (1) is the SIR of user at th where is the desired SIR and power control iteration. In practical systems, it is difficult to estimate the local SIR with high accuracy. Fortunately, only long-term SIR is needed in the adopted closed-loop power control, and it is quite stable when the users number remains unchanged. Thus the receiver only need to estimate the average square of the corresponding
1089–7798/01$10.00 © 2001 IEEE
400
IEEE COMMUNICATIONS LETTERS, VOL. 5, NO. 10, OCTOBER 2001
matched filter output. Evidently, SIR threshold can be , here represents the target power rewritten as denotes the interference to maintain the required SIR and , power of mobile at time . Similarly, denotes the power estimation of mobile . Subwhere and into (1) and rewriting (1) in nepers, the stituting following expression is obtained:
where is the magnitude of the input; is the magnitude of the output; and is a parameter that is selected to give the desired compression characteristic. Following this technique used in voice coding, let and assume that ( )-byte PCC is where is the sign bit. adopted is represented as Then (2)
Define , which represents the required as the actual power correcpower correction value. Using tion value is actually an ideal continuous power control scheme, which is impossible to implement as it requires a wide bandto the mobile. width to transmit the channel information In a practical closed-loop power control algorithm, the forming has two stages. In the first stage, the satellite receiver of to form power control comquantizes the difference . In the second stage, is sent back to the mand mobile and is decoded to the value of power correction according to specific power correction scheme. Based on the , various iterative methods have been develgeneration of oped, while trying to accomplish a fst convergence rate. In a fixed step power control, one bit PCC is formed in the satellite receiver:
where and denote increasing and deis sent back creasing the transmit power, respectively. to the mobile to adjust its transmit power in a fixed step, namely . Generally, ranges from 0.5 to 1 dB. The PCC format of the adaptive step power control is different. The of the adaptive scheme depends on the pattern of the received PCC, i.e., both the current PCC bit and the previous PCC bits [2]. III. MULTISTEP POWER CONTROL In multistep power control, a multi-byte PCC is used to carry channel information. As we know the generation of PCC is ac. Since tually the quantization of the analog signal small amplitude fades occur more frequently than the large ones in the considered channel, a nonuniform quantizer is generally adopted. Conventional multistep schemes based on segment functions [3] lack an uniform mathematical base to formulate the input–output relation. In the following, a generic multistep scheme is proposed. A nonuniform quantizer characteristic is usually obtained by passing the signal through a nonlinear device that compresses the signal amplitude, followed by a uniform quantizer. Here an optimized quantizer with logarithm characteristics is suggested. This quantizer is widely used in voice coding [5, Ch. 3.5]. Using it, a normalized logarithmic compressor has an input–output magnitude characteristic:
; denotes the dynamic range of power where means the largest integer no greater than . adjustment; and is obtained by decoding the The power correction step is actually the quantization level , which corPCC, thus . can be obresponds to the specific PCC, tained by using the inversion of the PCC generation function (2), thus (3) We define the step size of the quantizer as , which is the difference between two successive quantization levels . Using (3), the above equation can be rewritten as (4) are constant for the specific . Evidently, the where and power control error caused by quantization is in the range of ), which can be considered to be uniformly distributed if ( the number of quantization level is large enough [5]. Therefore, . the quantization error for each quantization level is The proposed power control scheme has several advantages over other schemes.. First, (4) clearly shows that the small fades can be quantified quite accurately, and large fade variation induces large quantization error which occurs with much smaller probability. Secondly, since the decoded step takes the lowest value of each amplitude level as indicated in (2) instead of the median value, which avoids the problem of overcompensation and oscillation. Thirdly, when the estimated fade is close to the target, PCC is noisy or estimation error driven. It is desirable to limit the amount of noise or estimated error driven power correction in the control loop. The proposed algorithm solves this problem in the following manner. If the dynamic range of is 20 dB and , then the first the power adjustment, dB. When the differstep of the encoder will be ence of the estimated strength and threshold is within 0.65 dB, the corresponding power command obtained is . In the decoder, this command is decoded as . Thus the proposed scheme allows no update of the power when the estimated power differs from the target by less than . IV. NUMERICAL RESULTS AND CONCLUSIONS Lutz’s two-state land mobile satellite model [4] is employed. Namely, the channel is fluctuating between shadowing and non-shadowing states. The state transition is a Markov chain in time series. The power control error (PCE) is defined in term of the mean square error at iteration : . Assuming that channel gain
LI et al.: A NEW GENERIC MULTISTEP POWER CONTROL ALGORITHM FOR THE LEO SATELLITE CHANNEL WITH HIGH DYNAMICS
(a)
(b)
(c)
(d)
401
Fig. 1. Performance comparisons of various power control algorithms. (a) Transient behavior comparison. (b) PCE versus power control cycles, (c) mean PCE versus f and (d) BER performance.
is fixed being dB, dB and , the transient behaviors of various power control schemes are shown in Fig. 1(a). Compared to the other power control schemes, the proposed scheme has shorter capture time and smaller compensation error. The fixed and adaptive step schemes [4] may introduce power oscillation or large overcompensation, while the proposed scheme with flexible design can avoid these problems. This feature can be further demonstrated by the results shown in Fig. 1(b), which clearly shows the transient and stable behaviors of various schemes when channel state transition . In the stable response stage, occurs around iteration the proposed scheme does not outperform the other schemes. However, once channel state transition occurs, the process of power control is disturbed and enters the transient response stage, which is quite long due to long round-trip delay and slow response speed when the conventional schemes are adopted. Whereas the proposed scheme introduces much smaller overall power control error with excellent dynamics performance as it can stabilize swiftly. We can anticipate that when the transition of channel states becomes more frequent, this merit becomes more pronounced. In Fig. 1(c), denotes the reciprocal of the correlation time is the power control period, thus of the shadowing and is the normalized dynamics of the slow fading. We can see that the average PCE of the conventional schemes increases quickly
with the increase of , whereas the average PCE of the proposed scheme increases much slower. A coherent BPSK system with various power control algorithms is simulated, the obtained BER curves are shown in Fig. 1(d). Evidently the proposed scheme achieves much better BER performance than the other schemes. Moreover, Fig. 1(a) and (d) also show the performance comparison of ideal continuous measurement scheme and the , the proposed scheme, which indicates that only with proposed scheme can achieve almost the same performance as the ideal scheme.
REFERENCES [1] A. El-Osery and C. Abdallah, “Distributed power control in CDMA cellular systems,” IEEE Antennas Proprogat. Mag., vol. 42, pp. 152–159, Aug. 2000. [2] J. H. Kim, S. J. Lee, and Y. W. Kim, “Performance of single-bit adaptive step-size closed-loop power control scheme in DS-CDMA system,” IEICE Trans. Commun., vol. E81-B, no. 7, pp. 1548–1552, July 1998. [3] R. D. Gaudenzi and F. Giannetti, “DS-CDMA satellite diversity reception for personal satellite communication: Satellite to mobile link performance analysis,” IEEE Trans. Veh. Technol., vol. 47, pp. 658–672, May 1998. [4] Y. Xie and Y. Fang, “A general statistical channel model for mobile satellite systems,” IEEE Trans. Veh. Technol., vol. 49, pp. 744–752, May 2000. [5] J. G. Proakis, Digital Communications, 3rd ed. New York: McGrawHill, 1995.
