IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 5, NO. 1, JANUARY 2006 23
A Channel Effect Prediction-Based Power Control Scheme Using
PRNN/ERLS for Uplinks in DS-CDMA Cellular Mobile Systems
Yih-Shen Chen, Member, IEEE, Chung-Ju Chang, Senior Member, IEEE, and Yi-Lin Hsieh
Abstract—This paper proposes a channel effect prediction-based power control scheme using pipeline recurrent neural network (PRNN)/extended recursive least squares (ERLS) for up-links in direct sequence code division multiple access (DS-CDMA) cellular mobile systems. Conventional signal-to-interference (SIR) prediction-based power control schemes may incur prediction mistakes caused by the adjustment of transmission power. The proposed power control scheme purely tracks the vari-ation of channel effect and, thus, can be immune to any power adjustment. Furthermore, it adopts the PRNN with ERLS for predicting the channel effect. Simulation results show that the channel effect prediction-based power control scheme using PRNN/ERLS achieves a 40% higher system ca-pacity and a lower outage probability than the conventional SIR prediction-based power control scheme using grey prediction method (IEEE Trans. Veh. Technol., Vol. 49, No. 6, p. 2081, 2000).
Index Terms—Channel effect prediction, direct sequence code division multiple access (DS-CDMA), extended recursive least squares (ERLS), power control, pipeline recurrent neural network (PRNN).
I. INTRODUCTION
T
HE direct sequence code division multiple access (DS-CDMA) cellular mobile system is an interference-limited system that requires power control to combat the multiple access interference (MAI) and near–far effect. The general concept of closed-loop power control for the reverse link in the DS-CDMA system is that the transmission power of a mobile is controlled within a required signal-to-interference (SIR) value received at the base station. Many uplink power control schemes have been proposed [1], [2]. However, they exhibit a loop delay. Thus, several prediction-based power con-trol schemes have recently been proposed, including the fuzzy method [3] and grey method [4]. With a priori knowledge of the fading channel, these prediction-based power control schemes, employing predictors to compensate for delay, can reduce the power control error and outperform the non-prediction-based schemes.The prediction objective of these prediction-based power control schemes is the SIR value. This received SIR value is af-fected not only by the channel effect, including the link gain and the interference fluctuation, but also by the transmission power, which is adjusted by the power control command. Notably, the transmission power may inhibit the SIR prediction-based
Manuscript received October 2, 2003; revised August 19, 2004; accepted October 22, 2004. The editor coordinating the review of this paper and approv-ing it for publication is H. Yanikomeroglu. This work was supported by the National Science Council, Taiwan, under Contract NSC 92-2219-E-009-025.
The authors are with the National Chiao Tung University, Hsinchu, Taiwan, R.O.C. (e-mail: atlas@bn3.cm.nctu.edu.tw; cjchang@cc.nctu.edu.tw; telson.cm89g@nctu.edu.tw).
Digital Object Identifier 10.1109/TWC.2005.858033
power control scheme, as in [3], from generating a precise power control command. Consider an example in which the link gain declines at a deep fade period. The SIR prediction-based power control scheme first decides to send a positive command to increase the transmission power if the received SIR is lower than the desired threshold. The received SIR is thereby enhanced. Then, if the SIR predictor is misled and forecasts that the SIR value in the following cycle will exceed the desired SIR value, a negative command is sent to decrease the transmission power in the subsequent control cycle. However, the channel remains in a bad situation actually. In such a case, the received SIR value would exhibit zigzagging along a curve of deteriorated SIR value, and then it takes a long time to be restored to the desired SIR value. This is due to the fact that the transmission power interferes with the SIR prediction, and the SIR prediction-based scheme yields an inappropriate power control command for the adjustment of transmission power. The conventional SIR prediction-based power control schemes do not perform well. Wien et al. proposed a short-term fading prediction-based (SFP) power control scheme [5]. However, it was for downlinks, and only short-term fading needed to be considered.
In this paper, a channel effect prediction-based power control scheme for uplinks is proposed. This scheme tracks only the variation of the channel effect, including both the link gain and the MAI. Without the transmission power factor, the channel effect prediction-based power control scheme does not suffer from unsuitable impact by the transmission power. In addition, a pipeline recurrent neural network (PRNN) with extended re-cursive least squares (ERLS) [6] is employed for the predictor. The PRNN/ERLS predictor has been effectively and success-fully applied to predict the MAI variation in the DS-CDMA/ packet reservation multiple access (PRMA) system [7]. Simu-lation results show that the proposed scheme can improve the accuracy of power control and increase the system capacity.
II. CHANNELEFFECTPREDICTION-BASEDPOWER
CONTROLSCHEMEUSINGPRNN/ERLS PREDICTOR A. Channel Effect Prediction-Based Power Control Scheme
Fig. 1 depicts the block diagram of the channel effect prediction-based power control scheme using a PRNN/ERLS predictor. The channel effect Ch(n) at time nTp is designed
as the prediction objective of the predictor, where Tp is the
updating period. It is defined to be the ratio of link gain G(n) to interference power I(n), given by
Ch(n) =
G(n)
I(n). (1)
Fig. 1. Structure of Q-learning-based multirate transmission control (Q-MRTC) scheme.
Fig. 2. PRNN structure.
As shown in the figure, at time nTp, the mobile updates its
transmission power P (n); the base station measures the link gain G(n) and the interference I(n) for each user. The link gain can be measured from the signal strength of the com-mon pilot channel. The channel effect Ch(n) is then
deter-mined from G(n)− I(n) in the decibel domain and fed into the PRNN/ERLS predictor for the next-cycle prediction. The PRNN/ERLS will yield a one-step predicted value of the chan-nel effect Ch(n + 1). Furthermore, the measured transmission
power P (n) is determined by subtracting the received signal power from the link gain. The received SIR at the next time (n + 1)Tp, SIR(n + 1), defined as the product of the measured
transmission power P (n) and the predicted channel effect
Ch(n + 1), can then be obtained. Comparing SIR(n + 1) with
the desired SIR level D yields an error value. If the error is nonnegative, then the power control command cmd is set to 1; otherwise, it is−1. The base station sends this command to the mobile. After a loop delay of Tp, the mobile detects
the command cmd and adjusts the transmission power by an amount of ∆P× cmd dB.
B. PRNN Predictor
Consider a general sampled process of channel effect
{Ch(n), n = kTp, 0≤ k ≤ ∞}. According to the nonlinear
autoregressive-moving average (NARMA) model of this process, with one-step prediction, the prediction value of the sample Ch(n + 1) at time n + 1 can be determined from p
previous measured samples Ch(i), n− p + 1 ≤ i ≤ n, and q
prediction errors ˆe(j), n− q + 1 ≤ j ≤ n. It is expressed as
Ch(n + 1) = h (Ch(i); ˆe(j))
= h (Ch(n), . . . , Ch(n− p + 1)
ˆ
e(n), . . . , ˆe(n− q + 1)) (2) where h(·) is an unknown nonlinear function to be determined and ˆe(j) = Ch(j)− Ch(j).
The recurrent neural network (RNN) is an approach well suited to fit the NARMA model [8]. Equation (2) should be reformulated as a new function H to enable RNN to be adopted with real-time recurrent learning algorithm (RTRL) to approxi-mate h(·), given by Ch(n + 1) = H Ch(n), . . . , Ch(n− p + 1) Ch(n), . . . , Ch(n− q + 1) . (3)
In the implementation of the NARMA (p, q) prediction model, a fully connected RNN structure with M neurons and
p + q + M input nodes can be adopted. Several kinds of RNN
have been applied to the power control prediction problem, such as the modified Elman neural network [9]; however, their computational complexities are pretty high. Instead, the PRNN structure is here considered for its computation efficiency. As depicted in Fig. 2, PRNN refers to the NARMA-based RNN
IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 5, NO. 1, JANUARY 2006 25
predictor with a pipelined structure. PRNN divides the RNN structure into q small RNN modules [6], [7], whose structures are similar to that of the RNN. In our design, the ith small RNN consists of Mneurons and (d + M+ 1) input nodes, where
q× M= M and d = p− q + 1. The first d input nodes are the external inputs, which are the delayed signals from Ch(n−
i + 1) to Ch(n− d − i + 2); the (d + 1)th input node is
con-stantly set to unity; the (d + 2)th input node is the output of the first neuron in the (i + 1)th module, yi+1,1(n), if i = q, or it
is the feedback signal from the first neuron’s output of module
q in time ((n− 1)Tp), yq,1(n− 1), if i = q; and the
remain-ing (M− 1) input nodes are feedbacked from 2 ∼ M neu-rons’ output of the same module, yi,2(n− 1) ∼ yi,M(n− 1).
The weight of the connection from the jth input node to the kth neuron is given by wkj(n), 1≤ j ≤ d + M+ 1, 1≤ k ≤ M.
The PRNN predictor yields Ch(n + 1), which is the first
output of the first module y1,1(n), given by
Ch(n + 1) = φ d j=1 wi,j(n)Ch(n− j + 1) + w1,d+1 + w1,d+2(n)y2,1(n) + d+M+1 j=d+3 w1,j(n)y1,j−d−1(n− 1) (4) where φ(·) is a sigmoid function of each neuron, expressed as
φ(x) = 1
1 + exp(−x). (5) Ignoring the dependency of the updated weight matrix and recursively iterating yi,1(n) from i = 2 to (q− 1) yields
ˆ Ch(n + 1) as Ch(n + 1) = ˆH Ch(n), . . . , Ch(n− p + 1) Ch(n), . . . , Ch(n− q + 1) (6)
where ˆH(·) has a nested nonlinear property. ˆH(·) can accu-rately approximate the nonlinear function of H(·), which the NARMA-based RNN can provide.
C. ERLS LearningAlgorithm
Here, the ERLS is applied as the learning algorithm for PRNN. The prediction errors for each module ei(n) and the
PRNN predictor E(n) are, respectively, defined as
ei(n) = Ch(n− i + 1) − yi,1 (7) and E(n) = M i=1 ξi−1e2i(n) (8)
where ξ∈ (0, 1] is the forgetting factor. The term ξi−1 is an approximate measure of the memory of the individual modules in the PRNN. The cost function of ERLS is defined as
εERLS(n) =
n
k=1
ξn−kE(k). (9)
The ERLS algorithm minimizes the cost function (9) and then updates the weights of the neurons in the modules accordingly. For a detailed description of the learning algorithm, please see [6]. ERLS considers present and previous errors, so it outper-forms the gradient decent algorithm which considers only the present error.
The PRNN with ERLS is well suited for prediction in a nonlinear and nonstationary radio channel environment because of the distributed nonlinearity built into its design and the capability of the neural network learning from the environment.
III. SIMULATIONRESULTS ANDDISCUSSIONS
In the simulations, the DS-CDMA cellular mobile system is considered in a 19-cell hexagonal-grid configuration. The link gain G(n) of the channel is determined by the long-term fading (free space loss and log-normal shadowing) and the short-term fading (Rayleigh fading). The data traffic is modeled as an ON–OFFsource, which consists of two major parameter sets—the distributions ofON–OFFperiods and the distribution
of packet arrivals during an ON period. For simplicity, the transmission is assumed to be continuous during theONperiod. The Pareto distribution is used, where the typical mean ON
period is 7.2 s with a “heaviness” of ρ = 1.7 and the typical mean OFFperiod is 10.5 s with a “heaviness” of ρ = 1.2 [10]. Furthermore, the simulations ignore the effects of sectorization, handoff, branch diversity, and voice activity.
Every simulation result includes 100 simulation cycles, and each of which contains 1000 updating periods. Mobiles are randomly located at the beginning of each cycle and assumed to be fixed. As for the PRNN predictor, parameters are selected as: M = 4; N = 2; p = 4; and ξ = 0.99 [6].
The system performance measure considered herein is the average outage probability P0, which is given by
P0= Pr{SIRr< SIR0} (10)
where SIRris the received SIR and SIR0is the minimum SIR
required to achieve a desired bit error rate. Eb/N0= SIR0×
PG, where PG is the processing gain, so the value of SIR0 for
a service can be determined by the service’s required Eb/N0
and PG. For voice services, SIR0=−18 dB is obtained if
PG = 256 and the required Eb/N0= 6 dB. For multirate data
services, the required Eb/N0is assumed to be 9 dB, the PG is
assumed to be varied from 256 to 32, and then the SIR0is set
accordingly. The desired level D is set to be 4 dB higher than SIR0in the simulation. In addition, the step size ∆P is set to
2 dB, and the number of mobile users in each cell is K = 8. The proposed channel effect prediction-based power con-trol scheme and the conventional SIR prediction-based power
Fig. 3. Outage probabilities of power control schemes versus fDTpfor eight
voice users in a cell.
control scheme are simulated for performance comparison. Both the PRNN/ERLS and the grey methods are adopted by these two schemes as a predictor. Hence, four schemes are investigated, namely: 1) the channel effect prediction-based scheme with PRNN/ERLS (CE-PRNN/ERLS); 2) the channel effect prediction-based scheme with grey (CE-Grey); 3) the SIR prediction-based scheme with PRNN/ERLS (SIR-PRNN/ERLS); and 4) the SIR prediction-based scheme with grey (SIR-Grey) [4].
Fig. 3 plots the outage probabilities versus the normalized Doppler frequency shift fDTp. The channel effect
prediction-based power control schemes (CE-PRNN/ERLS and CE-Grey) outperform the conventional SIR prediction-based ones (SIR-PRNN/ERLS and SIR-Grey). This is due to the fact that the channel effect prediction-based scheme is related to the channel gain and the interference but is independent of the transmission power, especially for high-speed users. As mentioned above, if the transmission power is both the control objective and a component of the prediction objective, the situation could confuse the predictor regarding the real status of the radio channel. As a result, the SIR prediction-based power control scheme slowly converges to the desired SIR value D. Furthermore, PRNN/ERLS outperforms the grey method, given a prediction-based power control scheme. This is due to the fact that the PRNN/ERLS can capture the signal correlation more accurately than the grey method. The PRNN is basically a RNN and has an infinite memory of past signals. Moreover, the ERLS algorithm introduces the forgetting factor that assigns higher weights to recently received signals. This feature helps the PRNN/ERLS predictor to deal with nonstationary signals. On the contrary, the grey method only performs well in shorter learning windows (of three to six time intervals) [5].
Fig. 4 plots the outage probabilities versus the number of voice-only mobile users in each cell with fDTp= 0.05. The
CE-PRNN/ERLS scheme outperforms the other schemes. If the quality of service (QoS) required outage probability for voice service is set to 1%, then the proposed CE-PRNN/ERLS can serve seven users in each cell, while the SIR-Grey
Fig. 4. Outage probabilities of power control schemes versus the number of voice-only mobile users in each cell with fDTp= 0.05.
Fig. 5. Outage probabilities of power control schemes versus the number of mobile users in a cell with fDTp= 0.05.
scheme can only serve about five users. The CE-PRNN/ERLS yields a system capacity 40% higher than that given by the SIR-Grey. Fig. 5 plots the outage probabilities versus the num-ber of voice and/or data users in each cell with fDTp= 0.05.
It can be seen that the system performance deteriorates as the ratio of data users increases. The reasons are as follows: Data services require higher transmission rates and higher quality of communications; so the transmission power of data users must be increased. Furthermore, the traffic flows of data services are intermittent, corresponding to a relatively higher transmission variation. Hence, data services suffer a larger interference vari-ation. The CE-PRNN/ERLS scheme, with the aid of channel effect prediction, can eliminate the interference associated with power control adjustment itself. Thus, it still can outperform the SIR-Grey scheme by an amount of 8% in a mixed mode scenario and 6.5% in a pure data scenario, given with a 2% outage probability requirement.
IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 5, NO. 1, JANUARY 2006 27
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