Fully Joint Diversity Combining, Adaptive Modulation, and Power Control

Transcription

1 Fully Joint Diversity Combining, Adaptive Modulation, and Power Control Zied Bouida, Khalid A. Qaraqe, and Mohamed-Slim Alouini Dept. of Eletrial and Computer Eng. Texas A&M University at Qatar Eduation City, Doha, Qatar {alouini, Abstrat Adaptive modulation and diversity ombining represent very important adaptive solutions for the future generations of ommuniation systems. In order to improve the performane and the effiieny of wireless ommuniation systems these two tehniques have been reently used jointly in new shemes named joint adaptive modulation and diversity ombining (JAMDC) shemes. Considering the problem of finding low-omplexity, bandwidth-effiient, and proessing-power effiient transmission shemes for a downlink senario and apitalizing on one of these reently proposed JAMDC shemes, we propose and analyze in this paper two fully joint adaptive modulation, diversity ombining, and power ontrol (FJAMDC) shemes. More speifially, the modulation onstellation size, the number of ombined diversity paths, and the needed power level are jointly determined to ahieve the highest spetral effiieny with the lowest possible ombining omplexity, given the fading hannel onditions and the required error rate performane. Seleted numerial examples show that the newly proposed shemes onsiderably inrease the spetral effiieny with a slight inrease in the average number of ombined path for the low signal to noise ratio (SNR) range while maintaining ompliane with the bit error rate (BER) performane and a low radiated power whih yields to a substantial derease in interferene to o-existing systems/users. Index Terms Diversity Tehniques, Adaptive Modulation, and Power Control. I. INTRODUCTION More and more importane is aorded to adaptive modulation [], [], adaptive diversity ombining tehniques [], [], and power ontrol [5], [6]. Many reasons are behind the use of these key adaptive solutions. Indeed, future wireless ommuniation systems whih will provide multimedia servies to the power/size limited mobile terminals are haraterized by limited bandwidth and power resoures. These systems should be able to support high spetral effiieny with good link reliability. This need for higher bandwidth effiieny motivates further optimization of the use of wireless resoures. Due to user mobility and highly time-variant propagation environments, resoure management in wireless ommuniations beomes a diffiult task. In order to failitate the management of these resoures adaptive tehniques seem to be one of the best solution. Based on multiple thresholds, adaptive modulation an ahieve high spetral effiieny over wireless hannels. The * This work was supported by Qatar National Researh Fund (QNRF), Doha, Qatar. key idea of adaptive modulation is to adapt the modulation parameters, suh as onstellation size, to fading hannel onditions while respeting the bit error rate (BER) requirements. Diversity ombining, on the other hand, improves the reliability of wireless fading hannels by adapting the ombiner struture to fading hannel onditions. Adaptive power ontrol shemes, unlike shemes using a onstant-power variablerate setup, adapt the transmitted power to fading hannels onditions while fulfilling the BER onstraint. These shemes onsiderably redue the radiated power, and thus the potential interferene to other systems/users whih implies a signifiant network apaity improvements. Generalized seletion ombining (GSC) is one of diversity ombining shemes that reeived a great deal of attention over the last deade (e.g. [7] [9]). Minimum seletion GSC (MS- GSC) was proposed in [] as a power-saving implementation of GSC. With MS-GSC the reeiver ranks the SNR of all available paths and then ombines the minimum number of branhes in order to make the ombined SNR exeed a ertain predetermined threshold. On average MS-GSC ombines less branhes, and hene uses less proessing power [], [], making it ideal for a downlink senario, where the mobile unit is power and size limited. These adaptive solutions have been originally studied separately. Reently, joint adaptive solutions have been proposed and studied. For instane, while joint adaptive modulation and ombining shemes were introdued in [], [], joint adaptive ombining and power ontrol were studied for onstantrate transmission in [], []. In addition, in [] and for the purpose of interferene redution, Gjendemsjø et. al. extended the shemes disussed in [] [] by looking at joint adaptive modulation, diversity ombining, and post-ombining power ontrol (JAMDC). Capitalizing on this reent work, and in order to have better spetral effiieny, better bit error rate performane, and less radiated power, we propose in this paper two fully joint adaptive modulation, diversity ombining, and power ontrol (FJAMDC) shemes, namely (i) a proessing power effiient (PES-FJAMDC) sheme and (ii) a bandwidth effiient (BES-FJAMDC) sheme. We analyze these newly proposed shemes in term of average spetral effiieny (ASE) (in bits/s/hz), average BER, diversity ombining omplexity, and transmit power gain and ompare their performane to that of the PES-JAMDC and the BES-JAMDC shemes proposed in []. Seleted numerial examples, obtained by Monte- Carlo simulations and onfirmed by analytial results, show /9/$. 9 IEEE Authorized liensed use limited to: Texas A M University. Downloaded on January 6, at 6:5 from IEEE Xplore. Restritions apply.

2 that both FJAMDC shemes inrease the ASE with a slight inrease in the average number of ombined paths, improve the bit error rate performane, and maintain a low average radiated power. The remainder of the paper is organized as follows. Setion II presents first the system and hannel models then gives the details behind the adaptive transmission system, the mode of operation of the proposed shemes, and power ontrol. While setion III analyzes the spetral and the proessing power performane of the proposed shemes, setion IV offers some seleted numerial examples illustrating this performane and omparing it to that of the JAMDC shemes. Finally, setion V onludes the paper. II. MODELS AND MODE OF OPERATION A. System and Channel Model We onsider a generi diversity system with L available diversity paths and we assume that the proposed FJAMDC shemes have a reliable feedbak path between the reeiver and the transmitter and are implemented in a disrete-time fashion. More speifially, short guard periods are periodially inserted into the transmitted signal. During these guard periods, the reeiver performs a series of operation, inluding (i) path estimation, (ii) deision on a diversity struture and signal onstellation, and (iii) seletion of the power to be used for transmission. One the suitable paths for ombining and onstellation size are seleted and one the appropriate transmitted power is fixed, the ombiner and the demodulator (at the reeiver end) and the high power amplifier (HPA) and the modulator (at the transmitter) are onfigured aordingly and these settings are used throughout the subsequent data burst. Under the assumption of frequeny flat fading, we use a blok-fading model assuming that different diversity paths experiene roughly the same fading onditions (or equivalently the same SNR) during the data burst and its preeding guard period. For our study, we assume that the reeived signal on eah diversity branh experienes independent identially distributed (i.i.d.) Rayleigh fading. As suh, the faded SNR, denoted by γ l (l =,,...,L), follows an exponential distribution, with ommon probability density funtion (PDF) and umulative distribution funtion (CDF) given by and f γi (x) = γ exp ( x γ ), x () ( F γi (x) = exp x ), x, () γ respetively, where γ is the ommon average faded SNR. B. Adaptive Transmission System We onsider the onstant-power variable-rate M-ary QAM [] as an adaptive modulation system for our proposed adaptive transeiver. With this adaptive modulator, the SNR range is divided into N + fading regions and the onstellation size M = n (where n is the number of bits per symbol) is assigned to the nth region (n =,,...N). The seletion of a onstellation size is based on the fading hannel state. Speifially, we partition the range of the SNR after diversity ombining into N + regions, whih are defined by the swithing thresholds {γ T n } N n=, and transmit using onstellation n if the ombined SNR is in the interval [γ T n,γ T n+ ). The BER of n -QAM onstellations with SNR of γ is given in [] by BER n (γ) = ( ) γ 5 exp ( n. () ) Given a target instantaneous BER equal to BER, the region boundaries (or adaptive modulator swithing thresholds) γ T n for n =,,...N are given in this ase by γ T n = ln(ber )( n ) ; n =,,...N. () C. Proessing-Power Effiient FJAMDC Sheme The aim of the PES-FJAMDC sheme is to redue the proessing power onsumption, by ombining the fewest branhes possible, while improving the spetral effiieny of the PES-JAMDC sheme. The mode of operation of the PES-FJAMDC sheme is summarized in a flowhart given in Fig.. In the beginning of eah data burst, the base station transmits a training sequene using the nominal power level β nom. After estimating and ranking the L available paths, the ombiner in the mobile s side tries to inrease the output SNR above the threshold for the lowest onstellation size by performing MS-GSC with γ T as output threshold. Whenever the ombined SNR γ is larger than γ T, the mobile stops ombining and determines the highest feasible onstellation index n for the given γ by omparing the ombined SNR to different swithing thresholds {γ T n } N n=. Ifγ is greater than γ T n but smaller than γ T n+ /G max, where G max is the transmitter gain saturation, the mobile selets the onstellation size n ( n -QAM) and asks the base station to use the lowest possible power level suh that the modulation mode n is still usable. If, on the other hand, γ is greater than γ T n+ /G max then the base station inreases its power till reahing the onstellation size n+ ( n+ -QAM). If, even after ombining all L paths, the lowest onstellation size is not reahed (i.e γ <γ T /G max ), the base station buffers the data and will not transmit for the next time interval. D. Bandwidth Effiient FJAMDC Sheme The BES-FJAMDC sheme is designed to maximize the spetral effiieny by, (i) performing all the the neessary diversity ombining aiming for the highest signal onstellation, and (ii) inreasing the power level that both allows to reah the next onstellation and obeys to the power onstraint. The mode of operation of the BES-FJAMDC is summarized in a flowhart given in Fig.. In the beginning of eah data burst, the base station transmits a training sequene using he nominal power level β nom. After estimating and ranking the L available paths, the ombiner in the mobile s side tries to inrease the output SNR above the threshold for the highest onstellation size by performing MS-GSC with γ T N as output threshold. Whenever the ombined SNR is larger than γ T N, the reeiver selets the highest onstellation size (N) and asks Authorized liensed use limited to: Texas A M University. Downloaded on January 6, at 6:5 from IEEE Xplore. Restritions apply.

3 the transmitter to use the lowest possible power level suh that the highest modulation mode ( N -QAM) is still usable. If the ombined SNR of all available branhes is still below γ T N, the mobile determines the highest feasible onstellation size. The modulation mode n is seleted by the mobile if the ombined SNR is smaller than γ T n+ /G max but greater than γ T n /G max. If even the lowest onstellation size is not feasible, data is buffered, and there is no transmission for the next time interval. E. Power Control In an ideal adaptive power ontrol system, we an assume that the transmitter power an be varied ontinuously to aurately follow the hannel variations. In the FJAMDC shemes, in addition to the ontinuous power adaptation, we also onsider power ontrol adaptations aounting for pratial implementation onstraints inluding disrete power levels (G δ ) and a transmitter gain saturation (G max ). In the beginning of eah data burst the transmitter db gain G db is initially set to db with respet to the nominal transmitted power. The ombined SNR after power ontrol is defined by Γ = Γ G, where Γ is the ombined SNR before power ontrol and G is the value of the gain. We assume that the maximal value of the additional gain G maxdb is a multiple of the power ontrol step size (G δdb ) (i.e, G maxdb = k G δdb where k Z ). While for ontinuous adaptation G [/G max, ), for the disrete power adaptation there are M + k power parameters: {β k =/G max <β k+ <β <...β =<β <...<β M }. If the modulation mode n is seleted and the mobile requests the base station to redue its power then the SNR after ontinuous power ontrol is redued to γ T n. For the disrete adaptation the SNR will be redued by β i, where β M must verify the onstraint given in [] by β M min n N γ T n+ γ T n. (5) III. PROCESSING POWER AND SPECTRAL ANALYSIS A. Average Number of Combined Paths We quantify the power onsumption for diversity ombining in terms of the average number of ombined paths. For the PES-FJAMDC sheme, it an be shown that the average number of ombined paths is given by L N =+ Fγ L/i GSC (γ T ) LFγ L MRC (γ T /G max), (6) i= where Fγ L/i GSC (.) is the CDF of the ombined SNR with L/i-GSC sheme (whih is given in losed-form for i.i.d. (.) is the CDF of the ombined SNR with L-branh maximum ratio ombining (MRC) sheme (whih is given in losed-form for i.i.d. Rayleigh fading as [9, Eq. (5)].) Similarly, it an be shown that the average number of ombined paths for the BES-FJAMDC is given by Rayleigh fading as [9, Eq. ()].) and F L MRC γ L N =+ Fγ L/i GSC (γ T N ) LFγ L MRC (γ T /G max), (7) i= B. Average Spetral Effiieny The probability that the nth onstellation is used for the proposed shemes based on MS-GSC is given by p n = F MSC(γ T ) ( ) MSC(γ γ γt n+/g max F T ) γ (γ T n/g max), PES FJAMDC; F MSC(γ T N γ ) ( ) MSC(γ γt n+/g max F T N ) (8) γ (γ T n/g max), BES FJAMDC; MSC(γT where F ) γ (.) and Fγ MSC(γT N ) (.) denote the CDF s of the ombined SNR with L-branh MS-GSC and using γ T and γ T N as output thresholds, respetively, and whih are given for the i.i.d. Rayleigh fading environment in [, Eq. ()]. Using the above expressions of p n and [, Eq. ()] we obtain the following expressions of the average spetral effiieny of both proposed shemes η = { N N (γ T n /Gmax), PES FJAMDC; γ (γ T n/g max), BES FJAMDC; (9) n= F MSC(γ T γ ) N N n= F MSC(γ T N ) In the partiular ase of G max =, the spetral and the proessing power performane of the FJAMDC shemes studied in this setion redues to the performane of the JAMDC shemes given by Yang et. al. in []. IV. NUMERICAL EXAMPLES The performane of the FJAMDC shemes is illustrated in this setion with some seleted numerial results. For these examples we set the number of available diversity branhes L =, the number of signal onstellations N =, the maximum value of the db additional gain G maxdb =db, and the bit error rate onstraint as BER =. Fig. illustrates the spetral effiieny improvement that is offered by the the proposed FJAMDC shemes over the JAMDC shemes. This improvement omes at the expense of a higher number of ombined paths in the low SNR range as shown in Fig.. These results are explained by the fat that the transmitter in the JAMDC shemes used to buffer the data whenever the ombined SNR does not reah the lowest onstellation size after ombining all the available L paths, but in the FJAMDC shemes if the ombined SNR is higher than γ T /G max the transmitter will transmit using the lowest onstellation size and ombining all the L available paths. For an average SNR above db, we an see that for both JAMDC and FJAMDC shemes one diversity path is enough to utilize the highest onstellation size (i.e 6 QAM modulation). Fig. 5 ompares the average transmitted power gain for BES-JAMDC and BES-FJAMDC for different values of G maxdb. We an see from this figure that when we set G maxdb =dbthe FJAMDC shemes redue to the ase of JAMDC shemes. When G maxdb inreases we obtain lower average transmit power gain, or equivalently higher average radiated power. The negative values of the gain are explained by the fat that the transmitter is sending with a higher level than its nominal power. In Figs. 6 and 7, we depit the average transmit power gain versus the average SNR per branh for the PES-FJAMDC and Authorized liensed use limited to: Texas A M University. Downloaded on January 6, at 6:5 from IEEE Xplore. Restritions apply.

4 the BES-FJAMDC shemes for both, ontinuous and disrete adaptations. We an see from these figures that reduing the power ontrol step size redues the average radiated power by inreasing the power gain. Aording to the onstraint given in (5), the maximum redution for disrete level transmit power ontrol is limited by the length of the shortest interval. This explains why the average transmit power gain saturates in different values depending on the used power ontrol step size. In Fig. 8 we show the bit error performane of the proposed shemes. For ontinuous power ontrol adaptation both shemes have the same BER performane. For this ase, the BER is onstant and is equal to BER, sine the ombined SNR after ontinuous power ontrol will be set to the swithing threshold orresponding to the used onstellation. For disrete power ontrol adaptation we show that the BES- FJAMDC sheme has slightly better error performane than the PES-FJAMDC sheme. The reason behind this is that in the low SNR range the BES-FJAMDC sheme needs to ombine more branhes than the PES-FJAMDC. For referene, we also ompare the BER performanes of the BES-FJAMDC and the PES-FJAMDC shemes using onstant full power. [9] M.-S. Alouini and M. K. Simon, An MGF-based performane analysis of generalized seletion ombining over Rayleigh fading hannels, IEEE Trans. Commun., vol. 8, no., pp. 5, Mar.. [] N. Belhaj, N. Hamdi, M.-S. Alouini, and A. Bouallegue, Low-power minimum estimation and ombining with adaptive modulation, in Pro. IEEE Int. Symp. on Signal Proessing and its Appliations, Sydney, Australia, August 5, pp [] H.-C. Yang, N. Belhaj, and M.-S. Alouini, Performane analysis of joint adaptive modulation and diversity ombining over fading hannels, in Pro. International Wireless Communiations and Mobile Computing Conferene, Vanouver, BC, Canada, July 6. [] N. Belhaj, M.-S. Alouini, and K. Qaraqe, Minimum seletion GSC with down-link power ontrol, in Pro. IEEE Vehiular Teh. Conf. (VTC 6-Spring), Melbourne, Australia, May 6. [] Z. Bouida, M.-S. Alouini, and K. Qaraqe, Joint minimum seletion GSC and down-link power ontrol, in Signal Proessing for Wireless Communiations Workshop, London, England, June 7. [] A. Gjendemsjø, H. C. Yang, G. E. Øien, and M.-S. Alouini, Minimum seletion GSC with adaptive modulation and post-ombining power ontrol, in Pro. of IEEE Wireless Communiations and Networking Conferene (WCNC 7), Hong Kong, China, Marh 7. V. CONCLUSION We have proposed in this paper, two new shemes using a fully joint adaptive modulation, diversity ombining, and downlink power ontrol. These shemes an be viewed as a general variant of the existent JAMDC shemes by the introdution of a joint power ontrol proess that an both inrease and derease the power level. Seleted numerial examples show that the newly proposed shemes onsiderably inrease the spetral effiieny with a slight inrease in the average number of ombined path for the low SNR range while maintaining ompliane with the BER performane and a low radiated power whih yields to a substantial derease in interferene to o-existing systems/users. Fig.. Mode of operation of the PES-FJAMDC sheme. REFERENCES [] M.-S. Alouini and A. J. Goldsmith, Adaptive modulation over Nakagami fading hannels, Kluwer J. Wireless Communiations, vol., pp. 9, May. [] K. J. Hole, H. Holm, and G. E. Øien, Adaptive multidimensional oded modulation over flat fading hannels, IEEE J. Selet. Areas Commun., vol. 8, no. 7, pp. 5 58, Jul.. [] S. W. Kim, D. S. Ha, and J. H. Reed, Minimum seletion GSC and adaptive low-power RAKE ombining sheme, in Pro. IEEE Int. Symp. on Ciruit and Systems (ISCAS ), Bangkok, Thailand, May. [] H.-C. Yang, New results on ordered statitis and analysis of minimum seletion generalized seletion ombining (GSC), IEEE Trans. Wireless Commun., vol. 5, no. 7, pp , July 6. [5] A. Gjendemsjø, G. E. Øien, and H. Holm, Optimal power ontrol for disrete-rate link adaptation shemes with apaity-approahing oding, in Pro. IEEE Global Teleommuniations Conferene (GLOBE- COM 5), St. Louis, MO, Nov.-De. 5, pp [6] A. Gjendemsjø, G. E. Øien, and P. Orten, Optimal disrete-level power ontrol for adaptive oded modulation shemes with apaity approahing omponent odes, in Pro. IEEE International Conferene on Communiations (ICC 6), Istanbul, Turkey, Marh 7. [7] N. Kong, T. Eng, and L. B. Milstein, A seletion ombining sheme for rake reeivers, in Pro. IEEE Int. Conf. Univ.Personnal Comm.(ICUPC 95), Tokyo, Japan, Nov. 995, pp [8] M. Z. Win and Z. A. Kosti, Virtual path analysis of seletive RAKE reeiver in dense multipath hannels, IEEE Commun. Lett., vol., pp. 8, Nov Fig.. Mode of operation of the BES-FJAMDC sheme. Authorized liensed use limited to: Texas A M University. Downloaded on January 6, at 6:5 from IEEE Xplore. Restritions apply.

5 Average spetral effieny (bits/s/hz) BES FJAMDC Sheme BES JAMDC Sheme PES FJAMDC Sheme PES JAMDC Sheme Average SNR per branh (db) Fig.. Average spetral effiieny versus the average SNR per branh, γ, omparison between the JAMDC and FJAMDC shemes Continuous PES FJAMDC Stepsize: / db Stepsize: / db Stepsize: db Average SNR per branh (db) Fig. 6. Average transmit power for the PES-FJAMDC sheme versus the average SNR per branh..5 Average no. ombined branhes BES FJAMDC Sheme BES JAMDC Sheme PES FJAMDC Sheme PES JAMDC Sheme Continuous BES FJAMDC Stepsize: / db Stepsize: / db Stepsize: db Average SNR per branh (db) Average SNR per branh (db) Fig.. Average number of ombined paths versus the average SNR per branh, γ, omparison between the JAMDC and FJAMDC shemes. Fig. 7. Average transmit power for the BES-FJAMDC sheme versus the average SNR per branh, γ. BES JAMDC (G maxdb = db) BES FJAMDC G maxdb = db BES FJAMDC G maxdb = db Average SNR per branh (db) Fig. 5. Average transmit power for ontinuous adaptation versus the average SNR per branh, γ, with BES-JAMDC and BES-FJAMDC for different G maxdb. Average bit error rate Continuous power (Both Shemes) PES FJAMDC: Stepsize db BES FJAMDC: Stepsize db PES FJAMDC, full power BES FJAMDC, full power Average SNR per branh (db) Fig. 8. Average bit error rate versus the average SNR per branh, γ, with PES-FJAMDC and BES-FJAMDC when L =,N =,and a BER onstraint BER =. 5 Authorized liensed use limited to: Texas A M University. Downloaded on January 6, at 6:5 from IEEE Xplore. Restritions apply.