2007 IEEE International Conference on Signal Processing and Communications (ICSPC 2007), 24-27 November 2007, Dubai, United Arab Emirates

Improving the Processing Power Efficiency of Minimum Selection GSCwith Adaptive Modulation and Post-Combini'ng Power Control*

Zied Bouida, Mohamed-Slim Alouini, Khalid A. QaraqeDept. of Electrical Eng.

Texas A&M University at QatarEducation City, Doha, Qatar

Email: {zied.bouida, alouini, khalid.qaraqe}@qatar.tamu.edu

Abstract Many joint adaptive modulation and diversity com-bining (JAMDC) schemes have been recently proposed to im-prove the performance and efficiency of wireless communicationsystems. Considering the problem of finding low-complexity,bandwidth-efficient, and processing-power efficient transmissionschemes for a downlink scenario and capitalizing on one of theserecently proposed JAMDC schemes, we propose and analyzein this paper a JAMDC scheme using post combining powercontrol and finger deactivation. More specifically, the modulationconstellation size and the number of combined diversity pathsare jointly determined to achieve the highest spectral efficiencywith the lowest possible combining complexity, given the fadingchannel conditions and the required error rate performance.Selected numerical examples show that the newly proposedscheme considerably reduces the processing power consumptionwith a slight increase in the radiated power while maintaininghigh average spectral efficiency and compliance with bit errorrate constraints.

Index Terms-Diversity Techniques, Adaptive Modulation,Power Control, Finger Deactivation, and Performance Analysis.

I. INTRODUCTION

Future wireless communication systems which will pro-vide multimedia services to the power/size limited mobileterminals are characterized by limited bandwidth and powerresources. These systems should be able to support highspectral efficiency with good link reliability. This need forhigher bandwidth efficiency motivates further optimization ofthe use of wireless resources. Due to user mobility and highlytime-variant propagation environments, resource managementin wireless communications becomes a difficult task whichimplies adaptive solutions. Key adaptive solutions are thoseof adaptive modulation [1], [2], power control [3], [4], andadaptive combining [5]-[8].

Based on multiple thresholds, adaptive modulation canachieve high spectral efficiency over wireless channels. Thekey idea of adaptive modulation is to adapt the modulationparameters, such as constellation size, to fading channel con-ditions while respecting the bit error rate (BER) requirements.Diversity combining, on the other hand, improves the reli-ability of wireless fading channels by adapting the combinerstructure to fading channel conditions. Adaptive power control

* This work was supported in part by the Qatar Foundation for Education,Science, and Community Development, Qatar, and in part by Qatar Telecom(Qtel) Qatar.

schemes, unlike schemes using a constant-power variable-rate setup, adapt the transmitted power to fading channelsconditions while fulfilling the BER constraint. These schemesreduce the radiated power, and thus the potential interferenceto other systems/users which implies a significant networkcapacity improvements.

These adaptive solutions have been originally studied sep-arately. Recently, joint adaptive solutions have been proposedand studied. For instance, while joint adaptive modulation andcombining schemes were introduced in [9], [10], joint adaptivecombining and power control were studied for constant-ratetransmission in [fl]-[13]. In addition, in [14] and for thepurpose of interference reduction, Gjendemsjo et. al. extendedthe schemes discussed in [9]-[ 13] by looking at joint adaptivemodulation, diversity combining, and power control. Cap-italizing on this most recent work, and in order to havemore processing power efficiency, we propose in this paper amodified bandwidth-efficient scheme using finger deactivation(BES-FD). We analyze this newly proposed scheme in termof average spectral efficiency (ASE) (in bits/s/Hz), averageBER, diversity combining complexity, and transmit powergain and compare its performance to that of the bandwidth-efficient scheme (BES JAMDC) proposed in [14]. Selectednumerical examples show that the BES-FD scheme reducesthe processing power consumption of the BES scheme witha slight increase in the radiated power, while keeping a highASE and compliance with BER constraints.

The remainder of the paper is organized as follows. SectionII presents first the system and channel models then gives thedetails behind the adaptive transmission system, the mode ofoperation of the proposed scheme, and power control. Next,the performance analysis of the proposed scheme is given insection III. Section IV offers some selected numerical exam-ples illustrating the performance of BES-FD and comparingit to that of BES JAMDC. Finally, section V concludes thepaper.

II. MODELS AND MODE OF OPERATIONA. System and Channel ModelWe consider a generic diversity system with L available

diversity paths and we assume that the proposed BES-FDscheme has a reliable feedback path between the receiverand the transmitter and are implemented in a discrete-timefashion. More specifically, short guard periods are periodi-cally inserted into the transmitted signal. During these guard

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periods, the receiver performs a series of operation, including(i) path estimation, (ii) decision on a diversity structure andsignal constellation, and (iii) selection of the power to beused for transmission. Once the suitable paths for combiningand constellation size are selected and once the appropriatetransmitted power is fixed, the combiner and the demodulator(at the receiver end) and the high power amplifier (HPA) andthe modulator (at the transmitter) are configured accordinglyand these settings are used throughout the subsequent databurst. Under the assumption of frequency fiat fading, we usea block-fading model assuming that different diversity pathsexperience roughly the same fading conditions (or equivalentlythe same SNR) during the data burst and its preceding guardperiod. For our study, we assume that the received signalon each diversity branch experiences independent identicallydistributed (i.i.d.) Rayleigh fading.

B. Adaptive Transmission SystemWe consider the constant-power variable-rate JVI-ary QAM

[1] as an adaptive modulation system for our proposed adap-tive transceiver. With this adaptive modulator, the SNR rangeis divided into N + 1 fading regions and the constellationsize I = 2" (where n is the number of bits per symbol)is assigned to the nth region (n= 0, 1 ... N). The selectionof a constellation size is based on the fading channel state.Specifically, we partition the range of the SNR after diversitycombining into N+ 1 regions, which are defined by the switch-ing thresholds {yTr}f=IN, and transmit using constellation nif the combined SNR is in the interval [7T,,, 7Tn+ 1).The BER of 2"-QAM constellations with SNR of y is given

in [1 ] by

BER,(k) = xexp ( 3 1) (1)ny-5 eP 2 (2n - 1)Given a target instantaneous BER equal to BERO, the regionboundaries (or adaptive modulator switching thresholds) Tfor n- 0,1,... N are given in this case by

2tYTn =-- ln(BERo) (2' - 1); n = 0, 1, ... N. (2)7n 3

CMode of OperationThe mode of operation of the BES-FD is summarized in a

flowchart given in Fig. 1. In the beginning of each data burst,the base station transmits a training sequence using the highestpower level. After estimating and ranking the L availablepaths, the combiner in the mobile's side tries to increase theoutput SNR above the threshold for the highest constella-tion size by performing the minimum selection generalizedselection combining (MS-GSC) scheme, proposed in [5] andfurther studied and analyzed in [6]-[8], with aTN as outputthreshold. Whenever the combined SNR is larger than 7TN,the receiver selects the highest constellation size (N) and asksthe transmitter to use the lowest possible power level such thatthe highest modulation mode (2N-QAM) is still usable. If thecombined SNR of all available branches is still below TN,the mobile determines the highest feasible constellation size bycomparing the combined SNR to different switching thresholds

{7T N-1 The modulation mode n is selected by the mobileif the combined SNR is smaller than -YTn+1 but greaterthan -T . The mobile will then start the finger deactivationprocess by selecting the minimum number of paths that areneeded such that the output SNR is still greater than Tn (i.etuming off the weakest branches while conserving the samemodulation mode). The deactivation process is continued untiltuming off a further diversity path leads to an output SNRbelow aTn After this, the base station reduces its power levelsuch that the selected constellation is still usable. If even thelowest constellation size is not feasible, data is buffered, andthere is no transmission for the next time interval.

D. Power Control

We use for the BES-FD scheme the same power adaptationvariants used for the BES JAMDC with post combining powercontrol of [14]. It means that we analyze both continuous anddiscrete power adaptation.

The post-adaptation power control is defined by -where F is the combined SNR with BES-FD before powercontrol and f3 is the power control parameter. While forcontinuous adaptation 13 [1, xoD), for the discrete poweradaptation there are M power parameters: /31 =1 < ,2 <

< /3M}. If the modulation mode n is selected then theSNR after continuous power control is reduced to Tn. Forthe discrete adaptation the SNR will be reduced by 13i, where13AI must verify the constraint given in [14] by

ITV7-n+ll<n<N 7Tn_3. mm nY~ (3)

III. PERFORMANCE ANALYSIS

A. Transmit Power Gains

1) Continuous Power Control. Using [14, Eq. (6)] and themode of operation of BES-FD, the average dB transmit powergain can be shown to be given by

GdB= J 10 log ) fr(x) d>cn=l<T-t-11 n/

N-= 10 log1o (-'c) fr(x) dcYc (4)

n=2 TYrw

- r 10 log10 .C (Fr (7Tn+l) -Fr (7TJ) )

n=l \7~Tnh/\where Fr (.) and fr (.) are the cumulative distribution function(CDF) and the probability density function (PDF) of thecombined SNR with BES-FD, respectively, and are the sameas those of the bandwidth efficient and power greedy schemeproposed in [10].

2) Discrete Power Control: The average dB transmit powergain for discrete adaptation is derived from [14, Eq. (8)] and

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is given by

GdB=EZ J IO1 log1(IO fp-(x) dky,

N M

10 log10(/3rn)n=1 m=l

X (FF (YTn 3rn+) -FF (rYTn Om) (5)where T7Tnj13MI+1 = Tn+1 -

B. Spectral and Processing Power EfficiencyThe BES-FD has the same spectral efficiency as the BES

JAMDC scheme and the average spectral efficiency is givenby

N

ru=N- " FmSC(TN)N a (6)n=1

The average number of combined branches is given byL N

Nc L= EEl Pi,n (7)1=1 n=1

where Pl,n is given in [10, Eqs. (25), (26), (27)].

C. Bit Error RateThe average BER of the BES-FD scheme can be calculated

as [1, Eq. (35)]N

BER-- n BERn) (8)-i n:1nl=1

where BERn is the average BER for constellation size n as

BERn- BERn (9)T ?).

where fjy (.) is the PDF of the combined SNR with BES-FDafter power control and which is obtained for continuous anddiscrete power control by [14] Eqs. (1L2) and (17), respectively,and by replacing the statistics of the combined SNR with BESJAMDC by the statistics of the combined SNR with BES-FD.Using Eq. (9) in Eq. (8) we can write

ZN fT -T 1 BER ) p (7BER= . (10)

IV. NUMERICAL EXAMPLES

For these examples, we set the number of available diversitybranches L = 3, the number of signal constellations N = 4,and the bit error rate constraint as BERo = 10-3.

While we can see from Fig. 2 that the BES-FD schemeconserves the same spectral efficiency as the BES JAMDCscheme, Fig. 3 shows that the proposed scheme considerablyreduces the average number of combined branches (i.e offerssome processing power savings) in the 0-20 dB SNR range.

These results are explained by the fact that the finger deactiva-tion process tums off the weakest branches while conservingthe same constellation size. For an average SNR above 20dB, we can see that for both schemes one diversity path isenough to utilize the highest constellation size (i.e 16-QAMmodulation).

In Fig. 4, we depict the average transmit power gain versusthe average SNR per branch for the BES-FD scheme forboth, continuous and discrete, adaptations. The shape of thegraphs in this figure is the same as in [14, Fig. (6)], but withlower values for the average transmit gain. This shows thatthe BES-FD scheme has lower average transmit power gain,or equivalently higher average radiated power, than the BBSJAMDC scheme.

According to the constraint given in (3), the maximumreduction for discrete level transmit power control is limitedby the length of the shortest interval. This explains whythe average transmit power gain saturates in different valuesdepending on the used power control step size.

In Fig. 5, we show the bit error performance of the proposedscheme and compare it to this of the BES JAMDC scheme.For continuous power control adaptation the proposed BES-FD has the same BER performance as the BES JAMDCscheme. For this case , the BER is constant and is equalto BERO, since the combined SNR after finger deactivationand continuous power control will be set to the switchingthreshold corresponding to the used constellation. For discretepower control adaptation we show that the BES-FD schemehas poorer error performance than the BES JAMDC scheme.For reference, we also compare the BER performances of theBES-FD and the BES JAMDC schemes using constant fullpower.

V. CONCLUSIONWe have proposed in this paper a variant of the existent BES

JAMDC scheme by the introduction of the finger deactivationprocess. Selected numerical examples show that the proposedscheme conserves the same spectral efficiency as the BESJAMDC scheme. On the other hand, the BES-FD schemeoffers better power efficiency at the cost of a slightly higherradiated power and slightly poorer BER. In conclusion, whileBES JAMDC gives higher average transmit power gains BES-FD offers considerable processing power savings.

REFERENCES[1] M.-S. Alouini and A. J. Goldsmith, "Adaptive modulation over Nak-

agami fading channels," Kluwer J. Wireletss Communications, vol. 13,pp. 119-143, May 2000.

[2] K. J. Hole, H. Holm, and G. E. Oien, "Adaptive multidimensional codedmoduLlation over flat fading channels," IEEE J Select. Areas Commurn.,vol. 18, no. 7, pp. 1153-1 158, July 2000.

[3] A. Gjendemsjo, G. E. Oien, and H. Holm, "Optimal power control fordiscrete-rate link adaptation schemes with capacity-approaching cod-ing," in Proc. IEEE Global Telecommunications Conference (GLOBE-COM'05), St. Louis, MO, Nov.-Dec. 2005, pp. 3498-3502.

[4] A. Gjendemsjo, G. E. Oien, and P. Orten, "Optimal discrete-levelpower control for adaptive coded modulation schemes with capacityapproaching component codes," in Proc. IEEE Interinational Co/ferenceon Communications (ICC'06), Istanbul, Turkey, March 2007.

[5] S. W. Kim, D. S. Ha, and J. H. Reed, "Minimum selection GSC andadaptive low-power RAKE combining scheme," in Proc. IEEE Int. Symp.on Circoita-nd Sy cm (ISCAS'03), Banlgkok ThailanAd May 2003.

31Authorized licensed use limited to: Texas A M University. Downloaded on January 30, 2010 at 15:55 from IEEE Xplore. Restrictions apply.

[6] P Gupta N. Bansal and R. K. Mallik "Analysis of minimum selectionH-S/MRC in Rayleigh fading" IEEE Trans. Commun. vol. 53 pp. 780-784 May 2005.

[7] R. K. Mallik P. Gupta and Q. T. Zhang "Minimum selection GSC inindependent Rayleigh fading" IEEE Trans. Veh. Technol. vol. 54 no. 3pp. 1013-1021 May2005.

[8] H.-C. Yang, "New results on ordered statitics and analysis of minimumselection generalized selection combining (GSC)," IEEE Trans. WirelessCommun. vol. 5 no. 7, pp. 1876-1885 July 2006.

[9] N. Belhaj, N. Hamdi, M.-S. Alouini, and A. Bouallegue, "Low-powerminimum estimation and combining with adaptive modulation" in Pro.IEEE Int. Symp. on Signal Processing and its App/ications Sydney,Australia August 2005 pp. 687- 690.

[10] H-C. Yang N. Belhaj and M.-S. Alouini "Performance analysis ofjointadaptive modulation and diversity combining over fading channels" inProc. International Wireless Communications and Mobile ComputingConference, Vancouver, BC, Canada, July 2006.

[11] N. Belhaj M.-S. Alouini and K. Qaraqe "Minimum selection GSCwith down-link power control," in Proc. IEEE Vehicular Tech. Conf(VTC'06-Spring), Melbourne, Australia, May 2006.

[12] S. S. Nam, M.-S. Alouini, and K. Qaraqe, "Diversity combining withup-link power control," in Proc. IEEE International Symposium on

Personal Indoor and Mobile Radio Communications Helsinki FinlandSeptember 2006.

[13] Z. Bouida M.-S. Alouini and K. Qaraqe "Joint minimum selectionGSC and down-link power control" in Signal Processing for WirelessCommunications Workshop London England June 2007,

[14] A. Gjendemsjo, H. C. Yang, G. E. Oien, and M.-S. Alouini, "Minimumselection GSC with adaptive moduLlation and post-combining powercontrol," in Proc. of IEEE Wireless Communications and NetworkingConference (WCNC 2007), Hong Kong, China, March 2007.

Fig. 3. Average number of combined paths versus the average SNR per

branch, -y, with BES JAMDC and BES-FD when L = 3 and N = 4.

Ea 2.5

z3 2

_a

0.5

0 5 1A01N5 20Average SNR per branch (dB)

Fig. 4. Average transmit power for the BES-FD scheme versus the averageSNR per branch, 7y, when L = 3 and N = 4.

Fig. 1. Mode of operation of the BES-FD scheme.

3.5

-I- 3

2 .5

a5

<,, 1.5

<D 1

0.5

Fig. 2. Average spectral efficiency versus the average SNR per branch, -y,with BES JAMDC and BES-FD when L = 3 and N = 4.

Average SNR per branch (dB)

Fig. 5. Average bit error rate versus the average SNR per branch, -, withBES JAMDC and BES-FD when L = 3, N = 4, and a BER constraintBERo = 10-3.

32

ContinuousStepsize: 1/4 dB

Stepsize: 1/2 dB

-Sttepsize: 1 dB..................... .............

Contin. power (Both shemes)If S- FD stepsize: dB--- BES JAMDC, stepsize: 1 dB

S-FD, fullpow er

1 BES JAMDC, full power

i~~~~~~~~~~~W£ O-

BES JAMDC S.h.BES-FD S.h

I§

- o

p

.?C

5 10 15Avera.ge SNR per branc.h (dB)

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