Abstract—This paper first presents an outer-loop power

control (OLPC) optimization analysis in the EVDO Rev. A (DOrA) system where we focus on the limitations of the power control in different channel fading conditions. Based on the analysis, a new OLPC framework is proposed and simulated in DOrA link-level simulation testbed. It is shown that the new algorithms could bring 1.5%-2% power saving in slow fading channels and only 0.5% enhancement in fast fading scenarios while maintaining a similar or better convergence speed and static state than the conventional approach. Tradeoffs could also be made between convergence speed and power consumption. Also, in order to identify the channels, a channel classification algorithm is introduced which can be implemented at BTS and provide slow/fast/stationary /transition channel information to BSC via Abis message.

I. INTRODUCTION In CDMA system, for inner-loop power control (ILPC), BTS

commands the mobile to adjust its transmission power based on the received signal to interference ratio from the reverse link where the target SIR or power control threshold (PCT) is assumed known to the BTS. The outer-loop is then responsible to further adjust this target SIR to guarantee certain quality of service (usually would be FER) with a lower frequency. Outer-loop power control has been in the literature for a long time [4] and the conventional OLPC algorithm [5] works as follows: If CRC fails for a received and decoded frame, the SIR target is increased by Dup and a good frame will result a decreased SIR target by Ddn. In order to maintain a target FER in the static state, based on some simple Markov relationship, the following condition should be satisfied,

target

target

1up dn

FERFER−

∆ = ∆ ⋅ (1)

Although the algorithm was first proposed for IS-95 system, it is also proved [6] to be suitable for the system with Hybrid ARQ (HARQ) and subframes involved, where in 1xEVDO, the common setting is Dup=0.5dB and Ddn=0.0045dB in order to achieve 1% target frame error rate. Although the algorithm has been shown as a robust one, there are some problems to be addressed,

a. The conventional method does not differentiate various channel conditions, such as slow fading, fast fading, stationary,

or transition period in its algorithm which could impact the effectiveness of the algorithm.

b. By adjusting the PCT with a fixed step size, it is impossible to balance between the convergence speed and static state. Since some times we may care about how fast the algorithm converges (e.g., at the call setup or channel changes) and some times we may care more about the variance of the FER (e.g., when the channel is relatively stable during the call), conventional algorithm does not really let us control anything in such cases.

c. Starting from DOrA, HARQ and subframes are introduced to the reverse link transmission. However, conventional algorithm does not cognize subframe early termination scenarios which could lose the potential side information with higher-frequency “quantization” of the channel.

In this work, we show that outer-loop power control should be closely tied to the channel fading conditions in the analysis and an OLPC framework should be proposed for various channels along with a channel classifier. In Section II, a power control model is proposed and analyzed to show the fading impact to the effectiveness of the OLPC. In Section III, both conventional and existing OLPC algorithms are introduced. Our proposed OLPC framework is then introduced and simulated in Section IV. Section V concludes the paper.

II. STATE OF THE ART IN OLPC ENHANCEMENT To address the problems of conventional OLPC method,

many enhancements are proposed. Some approaches focus on introducing subframe side information in OLPC PCT update. It is shown in [7] that individual subframe transmission success rate can be specified and controlled to enhance the QoS via OLPC algorithm. Therefore, not only FER but also frame delay can be somehow guaranteed by OLPC. A Markov process based approach is proposed in the paper while convergence still seems to be a problem and need to be further enhanced.

Some enhancement approaches focus on the variable step size settings based on the channel variation. Adaptive up and down step sizes is applied in [8] where a filtered PCT up/down history is used to determine the increase or decrease of both step sizes. However, the impact of the fading conditions to the algorithm is highly neglected. In order to balance between the OLPC reaction time and FER standard deviation, a proportional regulator is introduced in [9] where relationship between short-term FER and PCT step sizes are piece-wise linear. In

Outer-loop Power Control Optimization Analysis and a new algorithm

Bo Wei, Lin Ma and Mazin Al-ShalashHuawei Technologies,

Plano, TX 75025 {wbo, linma, mshalash}@huawei.com

1-4244-0264-6/07/$25.00 ©2007 IEEE 1484

other words, step sizes are not a fixed value and depend on currently measured FER (or error counting). In extreme case, if step size is adjusted as frequent as for every frame, it actually converges to the conventional OLPC. Bursting error is also shown to be smoothed by a leaky-bucket based algorithm with variable up/down step sizes [10].

Some other works do realize the OLPC performance impact caused by the channel fading conditions. For example, in [11], static and dynamic channels are differentiated by comparing the powers of the first and second strongest paths so that special treatment could be applied in OLPC for the channel transition period. Algorithm convergence speed during this period of time is highly enhanced although power consumption is definitely increased at the same time. More refined channel classification, however, is neglected in the work.

III. MODEL ANALYSIS OF DO REV A POWER CONTROL

A. An analytical model for power control Some inner-loop power control models have been existing in

the literature for some time [1][2][3]. In our model, as shown in Figure 1, measured signal to inference ratio (SIR) Y(z) is compared with the power control threshold (PCT, which is determined via outer-loop) X(z) in order to make power control command decision D(z). The command will experience k subframe of delay which incorporates SIR measurement, transmission and processing delay. Since in DOrA, SIR measurements are performed to the entire last subframes and the power control up/down decision will be applied until the beginning of next subframe, a reasonable value of k should be 2. Delayed decision is then aggregated by an integrator on top of the current transmission power. Please note that the model is simplified by neglecting the constant power adjustment factor block in Figure 1 based the fact that power up/down step in DoRA is happen to be 1dB. Also, we ignore any forgetting factor maybe needed in the model and directly assume its stability. By adding channel component L(z), we obtain the measured SIR and finish the loop.

+ +z-k

z-1

+

PCTX(z)

Measured SIRY(z)

ChannelL(z)

+-

Power ControlCommand Decision D(z)

Figure 1. Power control model

Furthermore, to obtain the transfer function of this linear system, the command decision making process (more like a delta quantizer) need to be linearized as an additive quantization error E(z). With some simple derivation, the z-transform of the system becomes,

( ) ( ) ( )( ) ( )

( ) ( ) ( )( ) ( ) ( )

1

-1 - -1 -

1

1- 1-

k

k k

z zY z X z E z L z

z z z zA z X z E z B z L z

− −−= + −

+ += ⋅ + − ⋅

(1)

Where ( )-1 -1 -

k

k

zA z

z z

−

=+

and ( )1

-1 -

1

1 - k

zB z

z z

−−=

+ with k=2

are illustrated in Figure 2 (not in scale though, for illustration purpose only). Clearly, received SIR Y(z) is the summation of a low-pass filtered version of the power control threshold X(z) and a high-pass filtered (from 25Hz to 75Hz) version of the channel L(z).

2 5 H z 7 5 H z f

B( z )

A( z )

Figure 2. Illustration of filters A(z) and B(z)

B. Analysis for inner-loop power control

From Eq. (1), we can get the following:

a. Due to the low frequency of DOrA power control (150Hz), power control is reasonable at fairly low mobile moving speed, i.e., Doppler frequency less or equal than 75Hz or about 45km/h for 1900MHz band. Inner-loop power control is not effective at all above that frequency. b. Let’s assume cases where outer-loop power control does not exist and PCT X(z) is simply a constant. The channel L(z) can only be tracked by the ILPC algorithm and attenuated by B(z) where clearly, 0-25Hz will be most effective region.

C. Analysis for outer-loop power control

From above, we know that even with inner-loop power control, channel effect can not be fully cancelled and some “leftover” remains. This is where OLPC comes into play. Now, let’s recall Eq.(1), with OLPC enabled, power control threshold X(z) is not a constant anymore, rather tracking the channel leftover and further subtracting fading impact from the received signal Y(z) and further reduce the AT transmission power. However, since PCT X(z) is low passed by A(z) as shown in the model, retuning X(z) does not provide much impact at speed higher than 15km/h or 25Hz Doppler frequency. For channel with 75Hz Doppler frequency or higher, since even inner-loop power control does not work to combat the channel fading as we discussed before, it is obvious that adjusting ILPC SIR target (i.e. OLPC) will not help at all. Therefore, although OLPC still works for maintaining 1% FER QoS-wise, it is not helpful anymore on suppressing channel fading and on AT transmission power saving for the fast fading case.

IV. PROPOSED OLPC METHOD We illustrate the traditional fixed step size based “jump”

method as that in Eq. (1) in Figure 3. Let us assume there exits a virtual frame error SIR threshold. Whenever this virtual threshold is reached, frame error happens and PCT threshold

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jumps up by Dup. In the “ideal” channel case, this threshold is flat as shown in the figure and every Dup is followed by exactly ( )

target target1 FER FER− number of Ddn, i.e., good frames. In the

slow fading case, this virtual threshold goes up and down with low frequency and we notice that the number of good frames between consecutive errors could somehow reflect the up and down slope of the virtual threshold. In fast fading case, since the virtual threshold has mainly high frequency component, guessing the slope from the number of good frames between errors could be misleading. We can think of OLPC as some delta quantization process which tries to track the channel with very low frequency and could not reconstruct the fast fading channel because of that.

virtual frameerror

SIR threshold

Ideal Case

Number of good frames between consecutive errors

Slow Fading Case

Fast Fading Case

Figure 3. Illustration of the traditional fixed stepsize based “jump” algorithm

working for different channels

The OLPC enhancement ideas are then as follows:

For slow fading channels, based on the knowledge of the virtual SIR threshold slope, we can compensate the channel effect by adapting the Dup (without changing Ddn) to erase the “jitter” between errors, and therefore, to “flatten” the virtual threshold as that in “ideal” channel case. In another point of view, increase the Delta up during the upward slope and decrease the Delta up during the downward slope will also speed up the PCT tracking when channel changes.

For fast fading channels, even ILPC does not work any more, there is no point to adjust PCT except to maintain the 1% FER. So, as long as we guaranty

( )target target

1up dn

FER FER∆ ∆ = − , reduce both up and down stepsizes will save power without impacting the convergence.

At the channel transition period, either because of the bias due to the PCT initial value setting or because of the mobile speed change, both Dup or Ddn should be increased so that the convergence speed could be enhanced despite the possible increment of the AT transmission power at that period of time.

We also need a mechanism to classify the channel status so that above schemes could be applied accordingly.

A. Proposed New OLPC Framework

1) For slow fading channels

For users experiencing slow fading channel, the algorithm is shown in Figure 4 where 1% target FER is assumed. Whenever

a good frame received, PCT is reduced by a fixed Ddn which is consistent with the conventional. PCT increment Dup due to the mth error frame, however, is a variable need to be updated all the time. The adaptation depends on the number of good frames between previous consecutive errors. If the number of good frames between mth and (m-1)th error frame, i.e., GoodFrameCnt(m) is greater than 99, our virtual SIR is assumed to be in an down slope in this period of time. To eliminate the possible noise from the decision, a margin α (with a value between 20 and 30) is considered. If this happens twice in a row, we update the Dup as

( ) ( ) ( ) - 991 +

99up up

GoodFrameCnt mm m

β∆ = ∆ − (2)

where β is the scaling factor with a value somewhere between 0.1-0.3. In other words, we reduce the PCT up step size when we are “confident” that the virtual SIR curve is currently in the down slope from the history. The same methodology applies to the up slope case as shown in the right hand side of the block diagram. For any other cases, the observations are treated to be too noisy to be used and Dup rather kept unchanged.

Please note that similar algorithm is proposed in [8]where the relative PCT value between two consecutive errors instead of simple good frame count is used. Main difference between this work and the proposal in [8], however, is that although it is assumed to be universal applied in [8], we claim here that similar algorithms are only a subset of a complete OLPC framework. In other words, this algorithm should be limited for slow fading channel only, especially when the AT speed less or equal to 15km/h according to the analysis.

nth packet info from BTS

Yes

No

PCT(n+1) =PCT(n)-Ddown

GoodFrameCnt(m) =GoodFrameCnt(m) + 1

CompareGoodFrameCnt(m)

with 99

(GoodFrameCnt(m) - 99)>Alpha

(GoodFrameCnt(m) - 99)< -Alpha

else

CompareGoodFrameCnt(m-1)

with 99

CompareGoodFrameCnt(m-1)

with 99

(GoodFrameCnt(m-1) - 99)< -Alpha

(GoodFrameCnt(m-1) - 99)>Alpha Dup(m)=Dup(m-1)

PCT(n+1) =PCT(n)+Dup(m)

(GoodFrameCnt(m-1)-99)< -Alpha

(GoodFrameCnt(m-1)-99)>Alpha

Dup(m)=Dup(m-1) +Alpha*|GoodFrameCnt(m)-99|/99PCT(n+1) = PCT(n) + Dup(m) In these cases, observation

may be too noisy to be used,so keep the Dup unchanged

CRC check pass?

Dup(m)=Dup(m-1) -Alpha*|GoodFrameCnt(m)-99|/99PCT(n+1) = PCT(n) + Dup(m)

Virtual SIRthreshold going up,

so reduce Dup!

Virtual SIRthreshold going down,

so increase Dup!

mth error coming

Figure 4. New OLPC algorithm for slow fading channels

2) Utilizing the subframe side information

In DOrA, at which subframe the good packet succeeds could also be traced out with callbacks, but how to use it to enhance the OLPC algorithm is still under investigation. In this work, we would like to provide some initial investigation on this topic. Unlike [7], in this work, subframe transmission success rates are not used to directly determine the step sizes rather being used to further “de-noisying” the step size adaptation decision described in previous section.

Let us look at an illustration of the basic idea here in Figure 5. Figure 5(a) shows the conventional scheme, i.e., no matter

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which subframe early termination each frame experienced (1st, 2nd, 3rd or 4th as shown in the plot), the Ddn is always a fixed value. In this case, although the virtual SIR threshold may have some high frequency component, due to the low sampling rate of OLPC, this virtual SIR can only be constructed to be something like the dash line. In our approach (see Figure 5(b)), we think the subframe early termination does reflect the channel high frequency variation information and would like to assign different amount of PCT drop to each cases. For example, for frames successfully transmitted within the 1st, 2nd, 3rd and 4th subframe, PCT drops 4D′, 2D′, 4D′/3 and D′ respectively and the following equation has to be hold for the static state,

1 2 3 4 target4

4 23 upp p p p FER′ ′ ′ ′∆ + ∆ + ∆ + ∆ = ∆ (3)

where p1, p2, p3, p4 are the probabilities of each subframe early termination happens and p1, p2, p3, p4 are estimated with a moving-average window for the lth frame

( )( ) ( )

( )1 1 1 Succeed in kth subframe

1 otherwise

k

k

k

p lp l

p l

θ θ

θ

− + − ⋅=

−

(4)

From the plot, we see that slope is actually revised with these subframe information so that the slope will reflect the “medium” line of the actual channel. This revised slope is then used to retune the scaling factor β in Eq. (2).

11

23

34

44

1

1

23

34

4 4

Revi sed sl ope wi t hsubframe i nf ormat i on

∆

∆

∆

4∆’2∆’

4/3∆’∆’

(b)(a)

∆

Figure 5. Illustration of subframe aided OLPC enhancement

3) Algorithm for other channel conditions

For fast fading channel or static channel, as we discussed before, we intend to reduce both originally fixed Dup and Ddn by a factor γ to save AT power, i.e.,

_

_ where <1up fast up

dn fast dn

γ

γ γ

∆ = ∆

∆ = ∆ (5)

For channel transition period, however, power saving may not be a concern while the convergence speed is a major issue to solve. In these cases, an increased stepsize is set for fast convergence, i.e.

_

_ where 1up trans up

dn trans dn

γ

γ γ

∆ = ∆

∆ = ∆ > (6)

Please note that in both (5) and (6), we maintain the ratio

up dn∆ ∆ unchanged in order to guarantee the OLPC algorithm convergence to the target FER in the static state.

4) Fading channel estimation

From above, our OLPC framework in this work does need a channel estimator or classifier to identify the channel type in order to perform different algorithms accordingly. Here, we borrow the ideas in [2] and [11] to estimate the channel fading conditions.

In [2], power control bits are used to classify the slow fading, fast fading and static channels. We claim here that using power control bits to estimate the channel is a reasonable approach firstly because power control bits are logged and easy to be obtained at the BTS. Secondly, power control bits do reflect the channel fading conditions. Let us recall the model we proposed in Figure 1 with power control bits shown as D(z). We can easily get

( ) ( ) ( ) ( )( )1

-1 -

1

1- kz

zD X z E z L z

z z

−−= + +

+ (7)

We can see from (7) that D(z) is actually a high-pass filtered version of channel L(z). In other words, D(z) does preserve some of the channel information. Also, we plot out PC bits spectrum from the DOrA link-level simulation for Channel model A, B & D in 3GPP Evaluation Methodology [12] in Figure 6. Clearly, peak of the spectrum move from the low to high frequency when the channel moves from slow fading to fast fading scenarios. Therefore, we would like to borrow the scheme in [2] into our framework where PC bits level-crossing rate, excursion depth and excursion times are jointly used to identify the slow fading, fast fading and stationary channels.

0 10 20 30 40 50 60 70 800

0.5

1

1.5

2

2.5

3

Frequency (Hz)

PSD

Channel A (3km/h)Channel B (10km/h)Channel D (120km/h)

Figure 6. PC bit spectrum for channels with different velocity

Channel transition, on the other hand, can be detected via a sliding window like scheme and this idea is somehow similar to the one in [11]. The sliding window is shown in Figure 7. Instead of using path gain difference between the left window and right window to detect channel change between only static and dynamic in [11], we can compare the PC bits information to detect any transition among slow fading, fast fading and stationary channels.

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Left Side Window(Previous Channel PC Bits

Information)

Right Side Window(Current Channel PC B its

Inform ation)

Gap(Transi tion Period)

1 second 0. 5 second 1 second

Figure 7. Sliding window approach to detect channel transitions

B. Simulation Results

The proposed OLPC algorithms are simulated in a DOrA link-level simulation testbed although we should note that system level simulator is also capable of such OLPC evaluations. Channel A model (3km/h) in [12] is used to simulate the slow fading channel and the simulation results are shown in Figure 8. In Figure 8(a), we can clearly see the new algorithm lead to about 1500 frames faster convergence and roughly the same static state FER which is very close to 1%. At the same time, average AT transmission power can be saved about 1.5%-2% over the time in Figure 8(b). An interesting observation is that average power used for the new algorithm is actually a bit higher than the conventional algorithm at the beginning (from 100-1000 frames) to achieve the fast convergence. This is where we can see the tradeoffs between the convergence speed and power consumption.

0 2000 4000 6000 8000 100000.01

0.012

0.014

0.016

0.018

0.02

0.022

0.024

0.026

0.028

0.03

Number of Frames

FER

Conventional OLPCNew Scheme

(a)

0 2000 4000 6000 8000 100001

1.05

1.1

1.15

1.2

1.25

1.3

1.35

Number of Frames

Ave

rage

Tra

nsm

ission

Pow

er

Conventional OLPCNew Scheme

(b)

Figure 8. (a) FER convergence and (b) average power consumption comparison for slow fading channel

Channel D model (120km/h) is a typical fast fading channel model which is applied here to test the scheme in Section IV.A.3. In Figure 9, we reduce both the Dup and Ddn by setting γ =0.9, 0.8, 0.7,…, resulting Dup=0.45, 0.4, 0.35… and so on. We can see that starting from 0.4, 0.5% power saving is obtained while convergence time start to increase significantly. Therefore, 0.9γ = should be set in the algorithm.

V. CONCLUSIONS In this work, we provide some power control analysis to

show the limitations of outer-loop power control in different channel fading conditions. We propose that BTS should classify the AT’s speed status using power control bits as that in Section IV.A.4 in order to perform OLPC accordingly. BSC will decide for every period of time:

If AT is in slow fading static state, use the algorithm in Section IV.A.1 and IV.A.2 to benefit from the faster convergence and 1.5% to 2% power saving.

If AT is in fast fading static state or stationary, lower both Dup or Ddn as that in Section IV.A.3 for 0.5% power saving.

If AT is in transition state, increase both Dup or Ddn for fast convergence, i.e., faster channel tracking.

Figure 9. Power consumption and converge time with different stepsizes

REFERENCES [1] Ariyavisitakul and L.F. Chang, "Signal and interference statistics of a

CDMA system with feedback power control," IEEE Trans. Commun., vol.41, no.11, pp.1626–1634, Nov. 1993.

[2] S. Sarkar and Y-C. Jou, “Adaptive Control of the Reverse Link in cdma2000,” International Journal of Wireless Information Networks, Volume 9, no. 1, pp.55-70, January 2002.

[3] Lei Song and Narayan B. Mandayam and Zoran Gajic, “Analysis of an Up/Down Power Control Algorithm for the CDMA Reverse Link under Fading,” IEEE JSAC Wireless Series, vol. 19, No. 2, pp. 277-286, February 2001.

[4] A. J. Viterbi, CDMA: Principles of Spread Spectrum Communication, Addison-Wesley, 1995.

[5] A. Sampath, P.S. Kumar and J.M. Holtzman, “On Setting Reverse LinkTarget SIR in a CDMA System”, IEEE VTC, pp. 929-933, 1997.

[6] A. Zhdanov, “Methods of hybrid ARQ and outer loop power control for the CDMA uplink,” IEEE-Siberian Conference on Control and Communications (SIBCON) pp.119-122, 2003.

[7] J. Gu, X. Che, S. Nie and D. Wang, „“QoS based outer loop power control for enhanced reverse links of CDMA systems,” Electronics Letters, Vol. 41, No. 11, pp.659-661, May 2005.

[8] Seok Ho Won, Whan Woo Kim, and In Myoung Jeong, "Performance Improvement of CDMA Power Control in Variable Fading Environment," IEEE SECON '97 Proceedings, pp. 241-243, Blacksburg, Virginia, Apr. 12-14, 1997

[9] H. Silfvernagel, Outer Loop Power Control in a Wideband CDMA System, Master Thesis, Lulea University of Technology, August 1999.

[10] N. T. Hai and S-M. Shin, “Burst error smoothing by using the outer loop power control in DS-CDMA systems,” The 6th International Conference on Advanced Communication Technology, pp. 38-41, 2004.

[11] Chang-Soo Koo, Sung-Hyuk Shin, Robert A. DiFazio, Donald Grieco, and Ariela Zeira, “Outer Loop Power Control Using Channel-Adaptive Processing for 3G WCDMA,” IEEE VTC, vol. 1, pp. 490-494, April 2003.

[12] 3GPP2 C.R1002-0, CDMA2000 Evaluation Methodology, December 2004.

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1

1.01

1.02

1.03

1.04

1.05

1.06

1.07

1.08

1.09

OLPC Stepsize (dB)

AT Tranmission Power

Convergence Time

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