International Journal on Electrical Engineering and Informatics ‐ Volume 4, Number 3, October 2012 

Practical Evaluation of Power Control Performance for Multipath Mitigation in Wireless Mobile Communication

Adit Kurniawan

School of Electrical Engineering and Informatics

ITB, Bandung, Indonesia adit@ltrgm.ee.itb.ac.id

Abstract: In this paper, practical evaluation of power control technique to combat multipath fading in wireless mobile communications is performed using computer simulation. We consider two types of power control algorithm in Code Division Multiple Access (CDMA) system in this paper, namely fixed-step and variable step algorithms. Practical aspects of power control investigated in this paper are focused on the effect of power update step size, fading rates, and feedback transmission error on the power control performance. The results show that the fixed-step power control algorithm exhibits only a slightly lower performance than that of the variable step algorithm, and therefore is more desirable in practice to minimize the signaling bandwidth. The effect of fading rates on power control performance also shows that variable step algorithm outperforms the fixed step algorithm during high fading rates but gives a comparable performance when fading rates are low. Finally when feedback information is subject to transmission errors, the performance of variable-step algorithm degrades more significantly because it is more sensitive to command error than that of fixed-step algorithm. Keywords: Fixed step; multipath fading; power control; variable step.

1. Introduction The most serious problem in mobile wireless communication systems is the signal distortion due to multipath fading channels. When a moving terminal, e.g. a mobile user transmits information to a base station, the signal received at the base station will experience severe fluctuations as well as possible intersymbol interference due to multipath propagation experienced by a moving vehicle. To overcome the problem of intersymbol interference due to frequency selective fading condition when transmitting high speed data, several techniques have been developed using orthogonal frequency division modulation or multicarrier communication schemes [1]-[2]. The effect of severe signal fluctuation, however, remains to be overcome despite the fact that multicarrier techniques can mitigate the frequency selectivity of wireless channel. The signal-to-noise ratio SNR in a flat or Rayleigh fading channel varies according to the channels’ response, and in CDMA systems the required SNR, or more precisely called the signal-to-interference ratio, SIR, to achieve a certain level of BER depends on its distribution as a result of fading channel [3]. To keep the SIR nearly constant at the desired level, power control can be used [4]. There are two types of power control algorithms: open-loop and closed-loop power control algorithms. The open-loop power control is designed to overcome the near-far problem, while the closed-loop power control aims at reducing the effect of Rayleigh fading. In this paper, we focus on the evaluation of closed loop power control, particularly the effect of mobility rate of the user and also the effect of power update step size on practical situation of power control algorithm.

Received: December 27th, 2011.  Accepted: October 4th, 2012 

435

  

The rest of the paper is organized as follows. Section II presents the wireless channel as well as the CDMA signal and mathematical models. Section III describes power control algorithm, Section IV provides computer simulation and numerical results. Finally, Section V concludes the paper. 2. Wireless Channel and CDMA Signal Models A. Wireless Channel Model In a mobile communication system, a signal transmitted through a wireless channel will undergo a complicated propagation process that involves diffraction, multiple reflections, and scattering mechanisms. In most cases, a line-of-sight path (LOS) between the mobile and the basestation is hardly in existence due to a very dense propagation environment between the mobile and the basestation. Figure 1 shows the near-far distance problem and also describes the signal fluctuation due to multipath fading. To overcome the near-far problem, an open-loop power control can be used [5]. The open-loop power control is designed to ensure that the received powers from all users are equal in average at the basestation. In the open-loop algorithm, the mobile user can compute the required transmit power by using an estimate from the downlink signal (no feedback information is needed). This is because the large-scale propagation loss is reciprocal between uplink and downlink channels [6].

Figure 1. Channel Modelling in Wireless Mobile Communications

In contrast to the large-scale propagation loss, the small-scale propagation loss is uncorrelated between uplink and downlink. A mathematical model to describe the received multipath signal can be determined as follows. Let the transmitted signal be x(t) which can be expressed as

 

(b) Mu ltipath fading  

    

Location 2    

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      2   

  

    

  

  Pt1 

Pr1 

Pr2 

Pt2 

d1 d2 

Receive  

transmit  

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(a)  Near ‐far distance  

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Practical Evaluation of Power Control Performance for Multipath

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Practical Evaluation of Power Control Performance for Multipath

439

  

chips per symbol M is called the processing gain or spreading factor of a DS-CDMA system. It reflects the ratio of the signal bandwidth after spreading to that of the unspread data symbol. A PN spreading sequence can be used to approximate the random spreading sequence and can be easily generated using a feedback shift register, and thus has widespread applications. Although a rectangular chip waveform can be easily generated, it has a considerable frequency spectral component beyond the spectral null at 1/Tc, where Tc is the chip period. Therefore, a smooth chip waveform such as a sync chip waveform is usually used for the sake of spectral efficiency. Since the uplink is considered in this study, a random spreading sequence is assumed and will be used for simulations. The correlation property of a random spreading sequence can be expressed as follows

⎪⎩

⎪⎨⎧

≠==

=∑=

=jk

jkmjcmkc

M

mMkjEfor0

0andfor1)(*)(

1

1)]([

ττρ . (3)

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of cj, and M is the number of chips (spreading sequence) per symbol or the spreading factor. In (3.1), m is the chip index in every symbol period. The second moment of the crosscorrelation function of a random sequence with rectangular chip waveform can be expressed as [87].

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⎪⎨

⎧

≠≠=≠==

=0,for3/10,for/1

0,for1)](2[

τττ

τρjkMjkM

jk

kjE . (4)

For the real systems using PN spreading sequence, the synchronous correlation property of a PN spreading sequence can be expressed as

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≠−

==

=∑= jk

M

jkmcmc

M

mjkkj

Mfor1for1

)()(

1

*1

ρ . (5)

We can see that the crosscorrelation of PN spreading sequence differs only by -1 from that of the pure random sequence. In the simulations, we normalise the amplitude of the quadrature spreading sequence, so that the magnitude of its complex form is unity and can be expressed as

)(

21)(

21)( )()( mcjmcmc Q

kI

kk += . (6)

The superscripts (I) and (Q) in Figure 5 represent, respectively, the in-phase and the quadrature components of the QPSK modulation. In a QPSK modulation scheme, the transmitted symbols sequence bk(n) from the kth user can be expressed as

}...,,2,1{,)()( BnjenAnb kn

kk ∈= θ . (7) Here Ak(n) is the scale factor of symbol amplitude, θkn ∈{± π/4, ± 3π/4} is the modulation phase, and B is the number of the transmitted symbols. If Ak(n) = 1 (the transmission power is normalised to unity), the spread sequence of the transmitted symbol expressed in a chip index m can be written as

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ΔpTp

Integrator

Step size

+

+

+ _

+

-γ t

γest

PCC bit error

e(i) PCC bits

MAI andAWGN

Mobile station

DT pLoop delayU

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k

chan

nel β

(t)

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nlink channel

Basestation

}...,,2,1{),(

21)(

21)( )()( MBmmbjmbmb Q

kI

kk ∈+= , (8)

where bk

(I)(m), bk(Q)(m) ∈{+1,-1}. The spread sequence is modulated by a carrier and then

filtered before transmission through the channel. For SIR estimation purposes, we assume perfect carrier modulation/demodulation and filtering, so that we can simplify the model by only considering the signal at the baseband level. In a fading channel situation, the received baseband signal from all K users at demodulator can be expressed as

)()()( tncbttr kkkk

kσβ +∑= (9)

Here βk(t) is the fading channel coefficient and n(t) is the additive white Gaussian noise (AWGN) with unit power spectral density (σk is the standard deviation of the AWGN, experienced by the kth user. After carrier demodulation and filtering in a QPSK CDMA scheme, the received baseband signal is despread by the conjugate of the kth user’s spreading sequence ck

* and then integrated over one symbol period (over M chips) to obtain the decision variable, yk(n). For a slow fading channel (βk(t) is constant over one symbol period), the SIR of the kth user computed during one symbol period can be expressed as follows

∑≠

+=

kjkjj

kkk

nnAM

nAn22

2

)(|)(|1|)(|)(σβ

βγ . (10)

The factor 1/M (crosscorrelation between spreading sequences) in the denominator of (10) is the result of despreading user j by the kth user’s spreading sequence. The first term of the denominator represents the multi access interference from the other K-1 users due to non-zero crosscorrelations between users’ spreading sequences, and the second term represents the thermal noise. In the following sections, we will use the SIR as the control parameter of the CDMA power control algorithm. 3. CDMA Power Control Algorithms For power control based on SIR, the mechanism of uplink power control algorithm is shown in Figure 6.

Figure 6. Power Control Model of Uplink Wireless Channel

Practical Evaluation of Power Control Performance for Multipath

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The power control algorithm proceeds as follows. First, the SIR for each user, γest is estimated at the basestation for the ith time slot. Then the estimated SIR γest(i) is compared with the target SIR γt to produce the error signal e(i). The error signal e(i) is then quantised using a binary representation, so it can be transmitted via the downlink channel to the mobile station. The quantised form of error signal is called the power control command (PCC) bits, which can be implemented using a pulse code modulation (PCM) realisation of mode q, where q is the number of PCC bits required in each power control interval. The PCC bits are transmitted to a mobile station via the downlink channel. However, the PCC bits are subject to high bit error rates because they are not coded or interleaved in order to minimise signalling bandwidth on the downlink channel and to avoid the corresponding delays due to the interleaving [13]-[14]. The feedback loop delay, however, is unavoidable for at least one measurement interval. Therefore, transmission of the PCC bits on the downlink channel suffers from two major impairments: PCC bit errors and feedback delay. The PCC bits error is represented as a multiplicative disturbance on the PCC bits, while feedback delay is represented by a delay operator of DTp, which represents a multiple integer D of power control interval Tp. After the PCC bits are received by a mobile station, the mobile station computes

⎪⎪⎪⎪⎪⎪

⎩

⎪⎪⎪⎪⎪⎪

⎨

⎧

−≥−−−<≤−−−

<≤−

+−<≤+−−+−<−

=−

−−

−−−

−−−

−−

2/12index),12(2/12index2/32),22(

..

..2/1index2/1,0

..

..2/32index2/12,22

2/12index,12

)(

11

111

111

11

qq

qqq

qqq

qq

qDie

(11)

where index is the difference between the estimated SIR (γest) and the desired SIR (γt). The difference between the estimated and the desired SIR is quantified to yield e(i-D)q, which is sent to the mobile to adjust the mobile’s transmit power by Δp. e(i-D)q dB. The loop delay DTp accounts for the delays due to SIR estimation process and transmission time of the PCC bit on the forward link expressed as a multiple, D, of the time slot unit, Tp. In the absence of PCC bit errors, the transmit power at the next interval is p(i+1) = p(i) - Δp . e(i-D)q, (12) where e(i-D)q is expressed in (1). For the fixed step algorithm (q=1) the PCC bit can be expressed as

⎩⎨⎧

≥<−+

=−= = 0 D)-(i1-0 )(1

])([ bit PCC 1 eDie

Diesign q , (13)

where e(i-D) is the power control error at the (i-D)th power control interval designating DTp loop delay from the ith control interval. In this work, the power control performance is evaluated when the PCC bits received by a mobile are subjerct to transmission error due to the impairment of the downlink (feedback) channel. If the PCC bits are received in error, a mobile will experience incorrect power adjustments. If the downlink channel error has a BER of Ppcc, the probability that the mobile transmit power will be reduced is P’d[γest] = (1- Ppcc) Pd[γest] + PpccPu[γes], (14)

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and the probability that the mobile transmit power will be increased is P’u [γest] = (1-P’d[γest] ) = (1-Ppcc) – (1-2Ppcc) Pd[γest], (15) where Pd[γest] = P[γest > γt] and Pu[γest] = P[γest < γt], γest is the estimated SIR to which the power control algorithm is based on, and γt is the target SIR level. 4. Computer Simulation and Numerical Results A. Simulation Procedure In the simulation, a single-cell CDMA system with the number of users K = 10 is considered. To reflect a practical situation, all users are considered in motion with different vehicle’s speeds and thus have different maximum Doppler spreads. We model this situation by varying the users’ vehicle speeds from 10 to 100 km/h at 10 km/h interval (i.e., the speed of the kth user is vk = 10 k km/h for k = 1, 2 , …, 10. Carrier frequency fc = 1.8 GHz is used, so that the corresponding maximum Doppler spreads, fD for the users are approximately ranging from 17 to 170 Hz at 17 Hz interval. The DS-CDMA processing gain is M = 64 and the modulation scheme is QPSK with a data rate Rb = 120 kbps (symbol rate Rs = 60 ksps in QPSK scheme). The power-update rate of 1.5 kHz is considered, which corresponds to the power control interval Tp = 0.667 ms [16]. SIR estimation/measurement is performed in every time slot that corresponds to one power control interval Tp = 0.667 ms. All data symbols in the time slot are utilised by SIR estimator to estimate the SIR. The chip rate Rc = 3.84 Mcps as given in the 3G specification for uplink data channel [14] is assumed in the simulation, resulting in each time slot to contain 2560 chips. Therefore, 40 binary symbols per time slot are available for SIR estimation. Feedback delay is assumed to be one measurement interval (D=1) in that the mobile user can adjust its transmit power as soon as the measurement of each time slot (equal to Tp) is completed. The simulation parameters is summarized in Table 1.

Table 1. Simulation parameters Parameter Notation and value Number of users K = 10 Carrier frequency fc = 1.8 GHz Vehicle’s speed vk = 10.k km/h, k = 1, 2, …, K Maximum Doppler spread fD = 1.67 vk Hz Processing gain M = 64 Chip rate Rc = 3.84 Mcps Power control interval Tp = 0.667 ms Data rate Rb = 120 kbps Power update step size Δp = 1 dB

A Gaussian distribution of the feedback channel error is assumed. To model the downlink transmission error, a Gaussian distributed random number consisting of {+1, -1} is generated according to the BER of PCC bits required for simulation. Then they are multiplied with the actual PCC bits generated by the power control algorithm. Performance evaluation is performed for both fixed-step and variable-step algorithms when the transmission of the PCC bits is subject to error with BER = 0.001, 0.01, and 0.1. The simulation is conducted for fDTp = 0.01, and the performance is evaluated in terms of bit error rate (BER) as a function of bit energy-to-interference power density ratio (Eb/I0).. B. Numerical Results In this section, the BER performance of a fixed-step and a variable-step algorithm are compared. The variable-step algorithm is implemented using a PCM realisation described in

Practical Evaluation of Power Control Performance for Multipath

443

  

[15] with modes q = 2, 3, and 4. In the variable-step algorithm with mode q = 4, the quantised error signal can be derived from (11) as follows

(16)

where the index is defined as e(i-D)/Δp. It is clear from (16) that the required number of bits for PCC is 4 for each power control interval. The mapping of PCC bits is shown in Table II. The first bit of the PCC bits sequence represents the sign of the command, i.e. 0 represents the positive sign and 1 represents the negative sign. The remaining bits represent the value of step size in a multiple of Δp for the mobile to increase or decrease its transmit power. The first four rows in Table 4.3 reflect the instructions to decrease the mobile transmit power, the fifth line indicates the instruction for the mobile to keep the same transmit power as in the previous interval, and the last four lines are instructions to increase the transmit power. The mobile will change its transmit power with variable step sizes of Δp.e(i-D)q=4 as expressed in (4). For PCM realization with modes q = 2 and q = 3, the mapping technique is the same with that shown in (3) and Table 1, with the index quantity of error signal e(i-D) /Δp are mapped to integer numbers of between –2 and 2 for q =2 and between –3 and 3 for q = 3. Therefore, the number of PCC bits required for PCM realization of modes q = 2 and q = 3 are 2 and 3 bits, respectively. To see the effect of fading rates, we introduce the parameter fDTp, which is defined as the ratio of the fading rate to the power-updating rate. Since the power-updating rate is standardised at 1.5 kHz, the parameter fDTp will only depend on the fading rate fD, which is directly proportional to the vehicle’s speed. For 1.8 GHz carrier frequency, the vehicles’ speed of 10, 30, and 60 km/h correspond, respectively, to the maximum Doppler spread of 16.7, 50, and 100 Hz. With a power control interval of Tp = 0.667 ms (standardized power-updating rate is 1.5 kHz for 3G system) and for a mobile travelling at 10 km/h, the parameter fDTp equals 0.01, which means that the mobile transmit power is updated 100 times faster than the fading rate. For mobile speeds of 30 and 60 km/h, the parameter fDTp are 0.033 and 0.067, which correspond to the transmit power updating rates of 30 and 15 times faster than the fading rates, respectively. In the fixed step power control algorithm (q = 1), only the sign of the error signal e(i-D) is needed by the mobile to either increase or decrease its power by a fixed step size. In the fixed step size algorithm the algorithm is now simplified as follows. If the estimated SIR, γest(i) is less than the target SIR, γt, the PCC bit -1 is sent to the mobile to increase its transmit power by Δp dB. While if γest is higher than γt, the PCC bit +1 is sent to the mobile to decrease its transmit power by Δp dB. Note that with one PCC bit, the power control algorithm will still increase or decrease the mobile transmit power by Δp even when the target SIR has been achieved.

⎪⎪⎪⎪⎪⎪

⎩

⎪⎪⎪⎪⎪⎪

⎨

⎧

≥−<≤−<≤−<≤−<≤−−<≤−−<≤−−<≤−−<

=− =

5.3index,45.3index5.2,35.2index5.1,25.1index5.0,15.0index5.0,05.0index5.1,15.1index5.2,25.2index5.3,3

5.3index,4

)( 4qDie

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Table 2. PCC bits with PCM realisation (q = 4). e(i-D)q = 4 PCC bits

4 3 2 1 0 -1 -2 -3 -4

0100 0011 0010 0001

0000 or 1000 1001 1010 1011 1100

To see the effect of different modes of variable-step algorithm, the BER performance is evaluated for the same channel condition with the parameter fDTp = 0.01. The BER performance is shown in Figure 7. The top curve is the BER for fading channel without power control, while the bottom curve is the BER for AWGN channel (perfectly power-controlled)

Figure 7. BER performance of power control with PCM realisation (fDTp = 0.01).

We can see in Figure 7 that variable-step power control algorithm outperforms the fixed-step algorithm. This is because with variable-step algorithm, power control can track the fading slope more quickly by using a higher step size and can reduce the oscillation when the target SIR has been achieved by using a smaller step size. Note that the performance improvement by using a higher mode (higher number of PCC bits) is obtained at the expense of a higher signaling bandwidth on the downlink channel. This is not desirable because the downlink channel capacity in third generation systems is crucial for internet downlink traffic, and thus needs to be preserved. Moreover, as we can see from Figure 7, the performance improvement at a voice quality BER of 10-3 is not significant when the quantisation mode is increased from q = 1 (fixed step size with 1 PCC bit) to q = 4 (variable step size with 4 PCC bits). Yet the required signaling bandwidth for power control updates is four times higher. This result can answer the question why most practical power control schemes rely on a fixed-step algorithm, because the gains offered by the variable-step algorithm over the fixed-step algorithm may not be justified. To evaluate the effect of fading rates on the power control performance, we perform simulations using a fixed step algorithm and variable step algorithm with mode q = 4. The simulation results are presented in Figure 8 (a) and (b), respectively. From Figure 8 (a) we can see that the fixed step power control is less effective at higher fading rates with fDTp greater

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-7

10-6

10-5

10-4

10-3

10-2

10-1

100

Bit

erro

r ra

te, B

ER

Eb/Io (dB)

Fading channel Fixed step (q=1) Variable step (q=2)Variable step (q=3)Variable step (q=4)AWGN channel

Practical Evaluation of Power Control Performance for Multipath

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