Markov mode-multiplexing mode in OFDM outphasing transmitters

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1 Crro et l. EURASIP Journl on Wireless Communictions nd Networking 18 18:36 RESEARCH Open Access Mrkov mode-multiplexing mode in OFDM outphsing trnsmitters Pedro L. Crro *, Plom Grci-Ducr, Jesus de Mingo nd Antonio Vldovinos Astrct Outphsing trnsmitters hve een explored to study the trde-off etween linerity nd efficiency. The outphsing technique enhnces efficiency y operting two mplifiers t lower output mplitudes, using two constnt envelope signls. Their mjor drwck is the inherent sensitivity to gin nd phse imlnces etween the two mplifier rnches. Another importnt issue is relted to the degrdtion of efficiency, especilly in isolted cominers. This pper presents Sttisticl Mrkov-Chin Mode-Multiplexing MM trnsmitter which comines fetures of the MM nd Reverse MM-LINC. Commercil nlog devices nd digitl pltform for signl processing purposes re used to test the performnce with n orthogonl frequency multiplexing modultion OFDM, which is one of the most used modultion schemes in wireless communiction systems. Keywords: PAPR, OFDM, Outphsing 1 Introduction Rdio frequency power mplifiers PAs re the most criticl components in the design of spectrl nd power efficient wireless trnsmitters. Mny trnsmitted signls in the new stndrds, such s long-term evolution LTE, nd the future 5G multicrrier-sed modultion schemes such s Filtered Bnd Multicrrier FBMC nd Generlized Frequency Division Multiplexing GFDM hve high pek-to-verge power rtio PAPR cused y complex modultion schemes. The use of high PAPR signls requires lrge enough ck-off in the power mplifier operting to stisfy the stringent linerity requirement, ut this region shows very low PA efficiency. Recent trends in efficient nd liner PA reserch re minly focusing on the use of two-rnch mplifier systems nd moving wy from the clssicl single-ended mplifier topology comined with the use of digitl predistortion techniques. Among these dul-rnch systems, the most populr re the Doherty mplifier, the envelope elimintion nd restortion EER techniques, the liner mplifiction with nonliner components LINC, nd the modified implementtion of the LINC MILC technique [1 3]. *Correspondence: plcrro@unizr.es Deprtment of Electronic Engineering nd Communictions, Argon Institute of Engineering Reserch I3A, University of Zrgoz, sttus=mrino Esquillor,, 518 Zrgoz, Spin This pper presents complete design nd experimentl implementtion of new Mode-Multiplexing LINC technique [4, 5] in order to enhnce the efficiency with reduced spectrl regrowth. The pper is outlined s follows. In Section, we introduce the previous mode multiplexing methods pplied in the context of the LINC. The novel Mrkov mode multiplexing method is explined in Section 3. The simultions, which hve een ccomplished to nlyze the proposed technique, re shown in Section 4. The proposed lgorithm is vlidted y mens of n experimentl setup nd the min results re discussed in Section 5. Finlly, some conclusions out this work re provided in Section 6. Mode-multiplexed LINC methods There re some issues which decrese the overll performnce in LINC trnsmitter implementtion, nmely the power gin nd phse imlnce etween the two RF pths. These re typiclly due to PAs, mixers, pth length differences, qudrture modultors errors, quntiztion noise, nd smpling rte error [6 9]. A LINC scheme which is implemented with n isolted cominer shows n efficiency which is the product of those correspondingtoothpandcominer[, 1, 11]. Although PA efficiency is mximized, the whole performnce is drmticlly reduced in LINC structure if the cominer TheAuthors. 18Open Access This rticle is distriuted under the terms of the Cretive Commons Attriution 4. Interntionl License which permits unrestricted use, distriution, nd reproduction in ny medium, provided you give pproprite credit to the originl uthors nd the source, provide link to the Cretive Commons license, nd indicte if chnges were mde.

2 Crro et l. EURASIP Journl on Wireless Communictions nd Networking 18 18:36 Pge of 11 efficiency is tken into ccount. Therefore, some techniques, like the Mode-Multiplexing method MM-LINC, hve een proposed either to improve cominer efficiency or linerity Reverse Mode, RM-LINC [4]. Figure 1 shows schemtic digrm of the Mode- Multiplexing LINC structure MM-LINC. The source signl sn we use sn = st t=n Tm,eingT m the smpling period to descrie its discrete version is split into two constnt envelope signls of LINC trnsmitter y Signl Component Seprtor lock SCS. The MM-LINC nd the RM-LINC technique re pplied t the signl component seprtor stge. In clssicl implementtion, the constnt envelope signls re computed y mens of { } [ s1 n 1 je n = s n 1 je n ]{ } s n / s n / where jen is signl which is in qudrture to the source signl, sn = cne jρn,nditisevluteds 1 c en = mx s n 1 < cn <c mx where c mx is the mximum of the signl envelope cn.if the LINC decomposition is expressed in mtrix form, s LINC n = nsn 3 the MM-LINC nd the RM-LINC re esily introduced sustituting the mtrix y [ ] 1 jen sn <γ 1 jen MM LINC = [ ] 1 sn γ 1 The MM-LINC switches etween the so-clled outphsing constnt envelope, here denoted y O nd lnced modes originl envelope with 3-dB ckoff, denoted y B, shown in Fig. 1 s stte digrm. The MM- LINC decomposition improves the LINC trnsmitter efficiency ecuse the outphsing ngle is reduced compred to the stndrd LINC solution. The reverse mode is otined y inverting the inequlities in 4, chieving etter lineriztion insted of n efficiency improvement. The threshold γ must e optimized for every desired trnsmitted wveform, nd thus, the method performnce depends on the signl proility density function. Authors propose novel switching method Mrkov mode-multiplexing which llows to trnsmit ny prticulr envelope vlue in certin time step s outphsing mode ut s lnced mode lter. 3 Mrkov chin MM-LINC technique 3.1 Algorithm principles The MM-LINC structure is modified through the signl component seprtion lock, which is proposed to e 4 s MARKOV MM LINC n = nsn 5 Fig. 1 Generl mode-multiplexing LINC rchitecture. The digitl domin is crried out in FPGA test-ench, wheres the remining prts re nlog components

3 Crro et l. EURASIP Journl on Wireless Communictions nd Networking 18 18:36 Pge 3 of 11 where the mtrix is driven through Mrkov chin nd is defined s [ ] 1 jen πn = 1 jen n = [ ] 1 π n = 1 1 where πn isthemrkovstte.thesequenceofinryvlued rndom smples π, π1,...πn cn e esily generted in digitl pltform DSP or FPGA or cn e offline creted nd stored in RAM or ROM if desired to reduce the computtionl cost [1]. In ddition, it should fulfill the so-clled Mrkov property [13], nd echinry vlue, i.e., the stte vlue, controls the trnsmitting mode OUTPHASING O, BALANCED B. Figure shows the rchitecture corresponding to the novel policy in comprison to the MM-LINC. The signl component seprtor for oth schemes crries out the decomposition s 1, = 1 αn sn 1 ± jen + αn sn where α is inry sequence which controls the sttisticl properties of the PA input signls, nd consequently the trde-off etween efficiency nd linerity. The MM- LINC sequence is sed on the input smples 1, if the instntneous envelope is greter thn the threshold, otherwise, nd in our proposl, it is sed on the mthemticl properties of Mrkov process. 6 7 The new switching policy is descried y using the vlues of the conditionl proilities: P πn + 1 = B /πn = O = P πn + 1 = O /πn = B = 8 where nd re vlues specified y the designer. These re the proilities of going from stte BALANCED to OUTPHASING or the opposite, in one time step. Besides, the sum of ll the proilities leving stte must e one. Under this lossless chin ssumption, the rndom stte is modeled with the id of trnsition proility mtrix which is given y 1 M = 9 1 Furthermore, we study two mgnitudes so tht the effects of nd cn e investigted nd the opertive principles cn e properly understood: i Percentge of outphsing or lnced smples: the greter the numer of LINC-trnsmitted smples, the higher the PA efficiency nd the lower the isolted cominer efficiency. Those re estimted y mens of the stedy stte proilities, which re computed using 9 nd P π = + Pπ = 1 = P O + P B = 1 1 where P O is the proility of smple of eing trnsmitted in outphsing mode nd P B of the lnced mode. Fig. Proposed Mrkov-multiplexed LINC rchitecture. The switching is controlled y sequence which cn e rel-time generted or stored in ROM using stte digrm

4 Crro et l. EURASIP Journl on Wireless Communictions nd Networking 18 18:36 Pge 4 of 11 Fig. 3 PAPR nd sttistics prmeters. Input signl PAPR in terms of the policy prmeters from closed-form expressions. Exmple of pdfs for specific policy prmeters According to Mrkov theory, 1 [P O P B ] = [P O P B ] 1 Solving 1with11, P B = + P O = ii The verged time of eing in outphsing lnced mode efore chnging to lnced outphsing mode: This property is relted to how mny smples re consecutively trnsmitted in the sme mode neglecting instntneous envelope vlues. It quntifies the correltion properties of the signl nd the switching rte etween modes. According to Mrkov chin theory, the numer of verge smples for ech stte N O, N B is computed s 1 N O = P πn + 1 = B /πn = O = 1 1 N B = P πn + 1 = O /πn = B = 1 13 The importnce of these equtions will e ddressed with the simultions nd with nlysis of the theoreticl PAPR. Theory nd results will e focused on OFDM-like modultions due to the widespred use in ctul wireless communiction systems, ut the technique is pplicle to other modultion formts such s WCDMA. Mrkov LINC reduces the PAPR of the decomposed signl in comprison to the mode multiplexing method, nd consequently, there will e noticele difference etween oth with high PAPR wveforms. 3. PAPR theoricl performnce In order to show tht the proposed lgorithm outperforms the existing multiplexing methods in OFDM, we present novel theoreticl nlysis of the PAPR not only for the Mrkov multiplexed rchitecture ut lso for the MM- LINC. The PAPR of the trnsmitted signl, s n is defined s [14, 15] PAPR = 1 log mx s n E [ s n ] db 14 where E [ s n ] is its verged power. As fr s generic OFDM signl is concerned, it is ssumed tht the symptotic proility distriution pdf follows Ryleigh sttistics since the inphse nd qudrture components pproximte to Gussin processes, f s ρ = R ρ e ρ /R R = σ ρ> 15 eing σ the inphse or qudrture vrince. On the other hnd, LINC wveform envelopes re constnt regrdless the input signl vlues. Thus, it is esy to write the envelope sttistics tking into ccount tht LINC signls hve n envelope mplitude of vlue c mx /s f sn ρ = δρ c mx / 16 eing δ the Dirc distriution. Notice tht in the cse of the clssicl LINC, PAPR = 1. The terms in 14 cn e evluted in oth multiplexing schemes y mens of proper envelope sttistics closed-form expression. Let F e the proility function corresponding to the originl input signl. Integrting 15, we otin F α = P s <α = α f s ρ dρ 17 Tle 1 Input envelope sttisticl vlues nd PAPR Bndwidth c mx E[ ρ] Vr[ ρ] PAPR db 1.4 MHz MHz

5 Crro et l. EURASIP Journl on Wireless Communictions nd Networking 18 18:36 Pge 5 of 11 Tle Multiplexing-Mode LINC theoreticl nd rel PAPR vlues Bndwidth Policy Rel PAPR db Pred. PAPR db 1.4 MHz Reverse MM Mrkov MHz Reverse MM Mrkov F OFDM α = 1 e α /R MM-LINC PAPR In the MM-LINC, the modes re switched using the γ threshold. Thus, the proility distriution is computed in the lnced mode y constrining the envelope distriution to γ, which leds to F s /B ρ = F s /B ρ s <γ = = P s <ρ, s <γ P s <γ = { P s <ρ P s <γ if ρ < γ 1 ρ>γ 19 Therefore, the proility density function should e f s /B ρ = f S ρ u γ ρ F s γ eing ux the Heviside function. Finlly, it is importnt to relize tht the envelope is trnsmitted in the lnced mode with 3 db ckoff. Using 15, 18, nd nd chnge of vrile, it is found tht g s /B ρ = f s /B ρ = 8ρe 4ρ /R γ R 1 e γ /R u ρ 1 The MM-LINC pdf is otined pplying the totl proility theorem with the conditionl proility in the LINC mode in 16 f s ρ = g s /B ρ P s γ + f s /O ρ 1 P s γ Using the results from 16, 18, nd 1, f s ρ = 8ρe 4ρ /R R γ u ρ + δ ρ c mx e γ /R 3 If some smples re trnsmitted in outphsing mode, which is resonle if the threshold γ is properly selected, the numertor in 14 comes from the LINC constnt envelope property, which yields to mx s = c mx 4 The denomintor in 14 iscomputedusing3, s summrized in 35 intheappendix. Finlly, the closed-form PAPR expression in MM-LINC scheme is c mx PAPR = R e γ /R R + γ + c mx e γ /R Mrkov-multiplexed LINC PAPR The novel Mrkov scheme PAPR estimtion is nlogous to the MM-LINC mode with certin differences such s the pdf in the cse of the lnced mode nd the proilities of ech mode, which re now those in 1. In ddition, the mximum envelope is limited in the lnced stte to c mx / insted of γ, which is usully less thn c mx /. This stems from the fct tht the switching policy is precisely independent from the signl mplitude nd consequently 8ρe 4ρ /R g s B ρ = R 1 e c mx /R u cmx ρ 6 The conditionl proility corresponding to the outphsing mode still remins. Thus, Fig. 4 Mrkovsimultion elements. AM-AM Cree PA-mesured nd PM-identified model. 1.4 MHz Mrkov-LINC ACPR performnce in terms of trnsition proilities

6 Crro et l. EURASIP Journl on Wireless Communictions nd Networking 18 18:36 Pge 6 of 11 Fig. 5 Mrkovsimultion elements. AM-AM Cree PA-mesured nd PM-identified model. 5 MHz Mrkov-LINC ACPR Performnce in terms of trnsition proilities f s ρ = g s /B ρ P B + f s /O ρ P 7 Replcing 1, 16, nd 6in7, 8ρe 4ρ /R f s ρ = R 1 e c mx /R u cmx + δ ρ c mx + ρ + 8 The PAPR numertor is c mx /4 in the Mrkov mode, nd the verged power is estimted in the Appendix in 37. According to those results, PAPR = R c mx e cmx /R 1 c mx + + c mx + 9 The PAPR Eqs. 5 nd9 my forecst suitle vlues for γ nd the reltion / in order to fix specified PAPR fter estimting the input originl OFDM signl sttisticl moments. Two prcticl wveforms test the proposed eqution vlidity in this work, QPSK OFDM downlink signl with 1.4 nd 5 MHz ndwidth. The decomposition process is ccomplished y mens of the Mtl pltform. Equtions 5 nd9 re studied under threshold vritions, γ, nd the stedy-stte proility τ = P B. According to Fig. 3, oth methods cn chieve PAPR vlues etween db fully LINC mode nd the PAPR of theoriginlsignl.however,themrkovdecomposedsignl PAPR is lower for wider rnge of nd vlues nd increses quickly when τ pproches the complete lnced stte. As expected, oth policies gree in the limiting cses LINC nd lnced limits. Tle 1 shows their sttisticl theoreticl nd estimted vlueswithselectedfixedprmetersγ = E[ sn ]nd = =.1. The prediction Tle greeswiththose numericlly clculted, ut there is smll difference in the Mrkov cse. This is due to fct tht the estimted vlue is single reliztion of the process, wheres 9 computes verged vlues. Figure 3 shows the proility density functions not only of the OFDM signl envelopes, which re well pproximted using the Ryleigh distriution, ut lso of Fig. 6 Simultion results with LINC, MM-LINC, Mrkov-LINC, nd direct mplifiction. OFDM with 1.4 MHz ndwidth. OFDM with 5 MHz ndwidth

7 Crro et l. EURASIP Journl on Wireless Communictions nd Networking 18 18:36 Pge 7 of 11 Tle 3 Estimted efficiency ounds % OFDM 1 MHz ndwidth Conf. Clss A Clss B Com. Totl A Totl B LINC MMLINC Mrkov the clssicl multiplexing mode nd the Mrkov mode envelopes. Their pdfs hve strong peks in the c mx / envelope vlue, which re clerly outphsed LINC smples. According to Fig. 3, there re strong differences in the lnce mode sttistics which leds to different performnce in terms of efficiency nd linerity. 4 Simultion Anlysis The importnce of the Mrkov chin prmeters nd hs een shown in previous sections. On the one hnd, PAPR cn e selected ccording to the percentge of outphsed signl smples. On the other hnd, this llows us to properly set the rtio / ut not to fix numericl vlues for nd. Distortion nlysis cn e helpful in order to finlly choose suitle vlues which im t otining good performnce in terms of linerity nd efficiency. Mrkov LINC simultions re crried out to study the performnce nd to compre to the MM-LINC nd clssicl LINC. Firstly, PA model is extrcted from rel mesurements using polynomil model PM with n OFDM signl source. Secondly, n ACPR nlysis is ddressed using the PA models to drw some conclusions out nd independently. Finlly, the LINC structure is evluted in n idel scenrio oth rnches do not hve imlnces. Figures 4 nd 5 show the mesurement nd the simple model corresponding to rel power mplifier. Polynomil models re very populr clss of ehviorl power mplifier mthemticl representtions for widend pplictions nd or high-power mplifiers nd re shown to e good chrcteriztion of nonliner PAs [16 18]. If the send input nd output re xt, yt respectively, φ p is sis function with terms in the form of xt p xt, α p re complex coefficients, N is the nonlinery order, the PM: yn = N N α p φ p n = xn α p xn p 3 p= p= In this work, the rel modeled PA is the CREE CGH46P, which hs 1-dB compression round 9.9 dbm nd is mesured round.6 GHz using multicrrier modultion with two different signl ndwidths, 1.4 nd 5 MHz. Finlly, the PM model hs een trined up to order 7. Trnsition proilities re the key prmeters which my e nlyzed to minimize spectrl regrowth. Some Monte Crlo simultions hve een crried out to study their effects on ACPR nd efficiency. Figures 4 nd 5 show tht etter efficiencies re chieved when the trnsition proilities nd re reltively close. Intuitively, if cominer nd PA efficiencies would increse/decrese t the sme rte, then 5% would e the optiml vlue in terms of efficiency nd distortion. The efficiency rte depends on the is of the PAs nd is different from tht of the cominer. Thus, the trde-off solution is not exctly t this point ut close. As conclusion, some optimiztion lgorithm should e crried to choose the ccurte proportion etween outphsing nd lnced smples in order to fulfill stndrd specifiction. In ddition, the higher vlues of trnsition proilities, the fster the modes switch N B, N O, re smller due to the time vriility of the signls. The Mrkov sequence multiplies the smples, nd nd must fulfill the smpling theorem. Therefore, the signl ndwidth plys n importnt role so tht the trnsition proilities do not cuse lising in the signl component seprtion process. Figure 6 shows the simultion results otined for LINC structure in three cses, LINC, MM-LINC, nd Mrkov LINC. The signl sources re the previous OFDM signls nd re decomposed using the three schemes keeping the sme input power. The MM-LINC threshold nd trnsition proilities re set using the PAPR nd ACPR studies γ =.18, = =.1 just to check if the proposed technique works. These vlues hve een chosen so tht the output power with oth multiplexing schemes were similr in order to hve n efficiency which is comprle. Alterntively, those vlues could hve een chosen to provide similr ACPR nd then verify if the Mrkov technique provides etter efficiency. Nevertheless, proper optimiztion lgorithm should e investigted or utility function should e defined in order to choose the est trde-off ccording to the needs nd requirements of specific wireless scenrio. As expected, the Mrkov MM-LINC outperforms the stndrd mode multiplexing method ecuse its signls hve etter PAPR, leding to identicl output power ut less djcent chnnel interference. Tle 4 Estimted efficiency ounds % OFDM 5 MHz ndwidth Conf Clss A Clss B Com. Totl A Totl B LINC MMLINC Mrkov

8 Crro et l. EURASIP Journl on Wireless Communictions nd Networking 18 18:36 Pge 8 of 11 Fig. 7 Experimentl setup. Hrdwre implementtion. Equivlent lck-ox digrm corresponding to experimentl test Furthermore, efficiency ounds showed in Tles 3 nd 4 hve een estimted in oth cses, using results from [1, 11, 14] under the hypothesis tht the mplifier could e either clss A ised or clss B nd with n isolted cominer. Actul vlues will e experimentlly evluted, ut this shows tht with the proposed vlues, the Mrkov method my led to comprle efficiency vlues with etter ACPR ehvior. The use of clss B mplifiers could improve the efficiency ut mode multiplexing schemes would e more sensitive to nonliner effects. 5 Experimentl evlution 5.1 Implementtion Three mode-multiplexing lgorithms hve een tested on LINC prototype to verify the rel improvement nd to find out if the trends predicted through simultions re ccurte. The complete experimentl test ench is shown in Fig. 7 together with n equivlent lock digrm including the rel RF elements Fig. 7. The digitl development pltform used for the implementtion of signl component seprtor, digitl signl processes, nd the digitl I/Q modultor nd demodultor consists of min ord ZedBord feturing Zynq 7 All-Progrmmle SoC connected to PC, which controls high-speed nlog module with n integrted RF gile trnsceiver, the AD-FMCOMMS-EBZ. It comprises RF trnsceiver with integrted 1-it DACs nd ADCs nd hs tunle chnnel ndwidth from khz to 56 MHz nd RX gin control. The output signls of the DACs re premplified nd upconverted to RF frequency of. 6 GHz. Finlly, two power stges ZHL-44 Minicircuits driver nd CGH46P power mplifier mplify oth signls. The operting input power levels ensure tht the driver is working linerly in ck-off with the tested OFDM signls. Both rnch outputs re comined y mens of power cominer ZNPD-5-S+. The experimentl evlution egins with clirtion process, estimting the imlnce in mgnitude nd phse for ech rnch of the LINC trnsmitter. The imlnce correction lgorithm uses the feedck loop nd the RX AD-FMCOMMS-EBZ input, nd only two complex Fig. 8 Experimentl performnce results. Mesured power spectrum densities in LINC, MM-LINC, nd proposed pproch red. OFDM 1.4 MHz nd OFDM 5 MHz

9 Crro et l. EURASIP Journl on Wireless Communictions nd Networking 18 18:36 Pge 9 of 11 Tle 5 Experimentl LINC nd mode-multiplexing results BW = 1.4 MHz BW = 1.4 MHZ Pout dbm ACPR dbc P DC,1 P DC, Eff % FoM EVM % LINC MM-LINC Mrkov coefficients thus, it is only ccurte in nrrownd context nd not pplicle to widend wveforms. The trnsmitted signls, ŝ 1 n nd ŝ n re corrected version in mplitude k i nd phse φ i of the outphsing signls s 1 n nd s n through two complex coefficients ŝ 1 n = k 1 e jφ 1s 1 n ŝ n = k e jφ 31 s n Those coefficients re computed y minimizing the ACPR using the Nelder-Med lgorithm which voids to compute derivtives nd cn e dptively performed. Therefore, the ACPR is function f of the correction coefficients, ACPR y = f k 1, φ 1, k, φ 3 nd the optiml solution is opt k1, φ opt 1, k opt opt, φ = rg min ACPR { y } 33 where yn is n ttenuted version t the cominer output. Once they re compensted, the signls corresponding to the different signl seprtion component methods re trnsmitted. It must e pointed out tht simultions do not include either memory effects or imlnces in the whole RF chin; hence, simulted nd experimentl figures re not directly comprle. Simultions re used in this cse for designing the lgorithms nd the rel setup is used for confirming the proposed pproch. In order to ensure tht linerity is chieved without decresingefficiency,weproposetousefigureofmerit sed on DC power P DC nd output power P out, which re mesured using the power supply nd spectrum nlyzer EXA N91A. The totl LINC efficiency PA nd cominer cn e evluted s P out η LINC = 34 P DC,1 + P DC, where suscripts 1 nd denote the DC power used y ech power mplifier. This expression is lso vlid in the cse of the mode-multiplexed policies. Therefore, the metric FoM = η Mrkov η LINC = PMrkov out Pout LINC PDC,1 LINC + PLINC DC, P Mrkov DC,1 + P Mrkov DC, 35 tkes into ccount the improvement or degrdtion in efficiency. 5. Results The experimentl setup hs een tested with the sme simulted OFDM signls nd smpling frequency of MHz. Figure 8 shows the power spectrl density of the output trnsmitter signl in stndrd LINC, MM- LINC, nd our proposed method. From qulittive point of view, the stndrd LINC chieves good ACPR with the lowest output power s Tles 5 nd 6 show. Better efficiency is otined with MM-LINC policy, ecuse the output power is incresed nd DC power is decresed. However, the enhncement in output power is chieved t the sme time tht nonlinerity effects re incresed. ACPR is incresed compred to the stndrd LINC. The novel pproch improves glol efficiency s well nd my provide the mximum output power compred to the other methods db for the 1.4 MHz signls nd.9 db for 5 MHz, with higher rchitecture efficiency thn the stndrd LINC. However, like in the MM-LINC policy, the EVM is incresed in comprison to the stndrd LINC. Furthermore, the ACPR is the sme thn the stndrd LINC or even is improved.9 db, nd the spectrl regrowth is less severe in the Mrkov policy if it is compred to the MM-LINC scheme. Although impirments re not studied in simultions, experimentl results show their effects on the 5 MHz OFDM signl. It should require more roust memory mismtch correction lgorithm to improve out-of-nd cncelltion, nd in contrst, Mrkov MM-LINC wveforms seem to e less sensitive to RF chin imlnces, s the ACPR is etter thn in the stndrd LINC. The Mrkov-outphsed signls do not hve such gret signl ndwidth compred to the LINC signls, nd therefore, impirments due to memory effects re smll in comprison with the stndrd LINC nd esier out-of nd cncelltion cn e crried out. To sum up, the proposed method cn comprtively chieve similr results thn the MM-LINC method ut with etter ACPR, which is one of the chrcteristics of the reverse MM-LINC. 6 Conclusion In this work, novel mode multiplexing method for LINC trnsmitters is presented, implemented, nd verified. A mthemticl nlysis of the PAPR proves tht the new policy ehves etter in terms of spectrl Tle 6 Experimentl LINC nd mode-multiplexing results BW = 5 MHz BW = 5 MHz Pout dbm ACPR dbc P DC,1 P DC, Eff % FoM EVM % LINC MM-LINC Mrkov

10 Crro et l. EURASIP Journl on Wireless Communictions nd Networking 18 18:36 Pge 1 of 11 regrowth compred to other proposed multiplexing policies, which hs een verified y mens of simultion. The experimentl LINC trnsmitter hs een implemented nd tested with OFDM signls, otining good performnce with low complexity. Experimentl results demonstrte tht it is possile to reduce the ACPR up to 4.5 db in system with multicrrier modultion without decresing the output men power, compred to stndrd MM methods, nd improving efficiency y pproximtely compred to the clssicl LINC technique. Appendix According to 14, PAPR derivtion requires to compute the quntity P v = E [ s n ] = ρ f s ρ dρ 36 The MM-LINC PAPR uses the density given in 3. Then Pv MM LINC = ρ f MM LINC s ρ dρ = = γ/ + 8 R ρ3 e 4ρ /R dρ ρ e γ /R δ ρ c mx = 1 4 e 4ρ /R R + 4ρ γ/ + dρ cmx e γ /R 37 Simplifying Pv MM LINC = 1 [ R e γ /R R + γ ] cmx e γ + /R 4 38 The Mrkov-multiplexed LINC PAPR uses the density givenin8. Then Pv Mrkov = ρ f Mrkov s ρ dρ = = cmx / + Computing the integrls, Pv Mrkov = 1 R 4 8ρ 3 e 4ρ /R R 1 e c mx /R + dρ ρ δ ρ c mx + dρ c mx e c mx /R cmx + 4 Arevitions ACPR: Adjcent chnnel power rtio; ADC: Anlog digitl converter; DAC: Digitl nlog converter; DSP: Digitl signl processor; EER: Envelope elimintion nd restortion; FBMC: Filtered nd multicrrier; FPGA: Field progrmmle gte rry; GFDM: Generlized frequency division multiplexing; LINC: Liner mplifiction with non-liner components; LTE: Long-term evolution; MILC: Modified implementtion of LINC; MM-LINC: Modemultiplexing LINC; OFDM: Orthogonl frequency multiplexing modultion; PA: Power mplifier; PAPR: Pek-to-verge power rtio; PC : Personl computer; PDF: Proility density function; QPSK: Qudrture phse-shift keying; RAM: Rndom ccess memory; RF: Rndiofrequency; RM-LINC: Reverse mode LINC; ROM: Red-only memory; SCS: Signl component seprtor Funding This work ws supported y the spnish Government Project TEC C4--R from MICINN nd FEDER nd the Argón Government nd FSE GCM T97. Authors contriutions PLC contriuted to the mesurements, result nlysis, nd rticle writing. PG-D contriuted to the result nlysis nd rticle writing. JdeM contriuted to the result nlysis nd rticle writing. AV contriuted to the rticle writing. All uthors red nd pproved the finl mnuscript. Competing interests The uthors declre tht they hve no competing interests. Pulisher s Note Springer Nture remins neutrl with regrd to jurisdictionl clims in pulished mps nd institutionl ffilitions. Received: 31 My 17 Accepted: Jnury 18 References 1. PM Lvrdor, TR Cunh, PM Crl, JC Pedro, The linerity efficiency compromise. IEEE Microw. Mg. 115, A Birfne, M El-Asmr, AB Kouki, M Heloui, FM Ghnnouchy, Anlyzing LINC systems. IEEE Microw. Mg. 115, B Kim, J Moon, I Kim, Efficiently Amplified. IEEE Microw. Mg. 115, M Heloui, FM Ghnnouchi, Lineriztion of power mplifiers using the reverse MM-LINC technique. IEEE Trns. Circuits Syst. II, Exp. Briefs. 571, M Heloui, S Boumiz, FM Ghnnouchi, AB Kouki, A Ghzel, A new modemultiplexing LINC rchitecture to oost the efficiency of WiMAX up-link trnsmitters. IEEE Trns. Microw. Theory Techniques. 55, P Grci-Ducr, A Orteg, J de Mingo, A Vldovinos, Nonliner distortion cncelltion using LINC trnsmitters in OFDM system. IEEE Trns. Brodcst. 511, P Grci-Ducr, J de Mingo, PL Crro, A Vldovinos, Design nd experimentl evlution of LINC trnsmitter for OFDM systems. IEEE Trns. Wirel. Commun. 91, T Hwnq, K Azdet, RS Wilson, J Lin, Lineriztion nd imlnce correction techniques for rodnd outphsing power mplifiers. IEEE Trns. Microw. Theory Tech. 637, AF Aref, TM Hone, R Negr, A study of the impct of dely mismtch on linerity of outphsing trnsmitters. IEEE Trns. Circ. Syst. I. 61, FH R, Efficiency of outphsing RF power-mplifier systems. IEEE Trns. Commun. 331, T Hwnq, K Azdet, RS Wilson, J Lin, On the linerity nd efficiency of outphsing microwve mplifiers. IEEE Trns. Microw. Theory Tech. 57, PL Gilert, A Cesri, G Montoro, E Bertrnd, J Dilhc, Multi-lookup tle FPGA implementtion of n dptive digitl predistorter for linerizing RF power mplifiers with memory effects. IEEE Trns. Microw. Theory Tech. 56, H Yng, M Alouini, Mrkov chins nd performnce comprison of switched diversity systems. IEEE Trns. Commun. 57, H Ochii, H imi, On the distriution of the pek-to-verge power rtio in OFDM signls. IEEE Trns. Commun. 49, H Ochii, An nlysis of nd-limited communiction systems from mplifier efficiency nd distortion perspective. IEEE Trns. Commun. 614,

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