Multicarrier Digital Pre-distortion/ Equalization Techniques for Non-linear Satellite Channels

Transcription

1 Multicarrier Digital Pre-ditortion/ Equalization Technique for Non-linear Satellite Channel R. Piazza 1 and M. R. Bhavani Shankar 2 SnT, Univerity of Luxembourg, Luxembourg, Luxembourg, L-1359 E. Zenteno 3 and D. Rönnow 4 Univerity of Gävle, Gävle, Sweden, J. Grotz 5 and F.Zimmer 6 SES, Betzdorf, Luxembourg, 6815 M. Gralin 7 and F.Heckmann 8 Steinbei Tranfer Centre for Space, Gäufelden, Germany, and S. Cioni 9 ESA/ESTEC, Noordwijk, Netherland, 2200 AG Two key advance are enviaged for future miion: (a) pectrally efficient tranmiion to meet the increaing demand and (b) haring of atellite capacity among different link to meet power/ma requirement. Joint amplification of multiple-carrier DVB-S2 ignal uing a ingle High-Power Amplifier (HPA) i a particular application of atellite reource haring. However, effect pecific to uch a cenario that degrade power and pectral efficiencie include (a) an increaed Adjacent Channel Interference caued by non-linear characteritic of the HPA and (b) increaed peak to average power ratio. The paper tudie ignal proceing technique digital pre-ditortion (DPD) at the gateway and equalization (EQ) at the Uer Terminal to mitigate the non-linear effect and improve power a well a pectral efficiencie. While the algorithm for DPD and EQ are decribed in literature, their ue in multi-carrier cenario i novel and poe new challenge that are invetigated in the paper Nomenclature ACI = Adjacent Channel Interference ACM = Adaptive Coding and Modulation APSK = Amplitude Phae Shift Key BER = Bit Error Rate DPD = Digital PreDitortion DTH = Direct To Home Doctoral Student, SnT, roberto.piazza@uni.lu, non-member Reearch Aociate, SnT, Bhavani.Shankar@uni.lu, non-member Doctoral Student, Univerity of Gävle, Efrain.Zenteno@hig.e, non-member Profeor, Univerity of Gävle, Daniel.Ronnow@hig.e, non-member Senior Sytem Engineer, SES, Joel.Grotz@e.com, non-member Senior Manager, SES, Frank.Zimmer@e.com, non-member Senior Scientit, TZR, graelin@tz-raumfahrt.de, non-member PhD, TZR, heckmann@tz-raumfahrt.de, non-member Communication Sytem Engineer, TEC-ETC, tefano.cioni@ea.int, non-member

2 EQ = EQualization FIR = Finite Impule Repone GW = Gate Way HPA = High Power Amplifier IBO = Input Back-Off IMUX = Input IRD = Integrated Receiver Decoder ISI = Inter-Symbol Interference L-TWTA = Linearized Travelling Wave Tube Amplifier LS = Leat Square OBO = Output Back-Off OMUX = Output SINR = Signal to Interference plu Noie Ratio SNR = Signal to Noie Ratio TWTA = Travelling Wave Tube Amplifier I. Introduction In the arena of atellite communication, there i an increaing demand for higher data rate and bandwidth efficiency. A recent example of thi trend i Viaat-1 that reache a total throughput of 140 Gbp being the highet capacity broadcat atellite ever launched. In atellite broadcat ytem, the data tream goe through the forward link, where we have, in general, three actor: the gateway, the atellite tranponder and the end-receiver. The gateway collect the data and tranmit the ignal to one or more atellite. Each atellite tranponder receive the data ignal from one or more gateway and it then redirect it to the ground receiver. In widepread direct to home (DTH) ervice, the end receiver are fixed integrated receiver decoder (IRD) for motly TV application. Tranparent payload, where the uplink data i mainly amplified and forwarded to uer, are by far the mot common telecom atellite architecture due to their competitive cot and technological flexibility ince the ignal proceing carried out on the ground can be updated with the technological advancement in the coure of the lifetime of the atellite. To enure that the amplification i power-efficient, the High Power Amplifier (HPA) are operated cloe to the aturation point. However, the on-board HPA uffer from non-linear effect when driven cloe to aturation leading to undeired component being introduced into the ignal of interet 1. High order ignalling/modulation technique, uch a 16/32 amplitude and phae-hift keying modulation (APSK), are often ued to increae pectral efficiency in DVB-S2 ytem 2. However, they are very enitive to the non-linear ditortion introduced by the on board HPA. Thi lead to a trade-off between power efficiency and ignal degradation. Compenation technique at the tranmitter (known a pre-ditortion) and at receiver (equalization) have been conidered to mitigate the non-linear effect of the channel 1, 3, 4. Typical technique include Look-up Table 1 and Volterra function for pre-ditortion 3 and Volterra equalizer for equalization 4. An overview of thee technique i provided in Ref. 5. The non-linear effect become even more prominent when multiple carrier are amplified uing a ingle HPA. Such a ituation arie very often, when different carrier hare the ame on-board HPA due to power/ma and flexibility requirement. Thi lead to puriou term ariing due to the inter-modulation product caued by the HPA nonlinearity. A large guard-band between the carrier may be needed in order to avoid inter-modulation product or adjacent channel interference (ACI). Additionally, ue of multiple carrier lead to the well-known high peak to average power ratio, and thi increae the back-off ued in the power amplification, leading to lo in amplification efficiency. Thee effect manifet a pectrum-inefficient frequency carrier egregation and power lo depending on the pectral efficiencie of the individual carrier. Apart from amplification, the payload forward or channelize the data from gateway to the repective uer. Thi involve filtering caue inter ymbol interference (ISI) which further degrade the performance. Compenation technique for uch a multi-carrier cenario are being only recently conidered, for e. g., dual carrier preditortion, 6,7, dual carrier Volterra equalizer 8 and multiple carrier turbo-baed equalizer 9. However, the preditortion focue on two carrier per HPA only and i decribed in a terretrial ytem context. On the other hand, the equalization technique, though conidered for atellite, aume joint proceing of all carrier at the receiver. Thi requirement may not alway be feaible, epecially when focuing on low complexity receiver. Thee motivate the tudy and deign of pre-ditortion and equalization technique that can be applied to any number of carrier through a HPA, without the poibility of joint decoding. Thi paper i baed on

3 the on-going European Space Agency ARTES 5 activity titled, On Ground Multicarrier Digital Equalization/Preditortion Technique for Single or Multi Gateway Application. In the paper we decribe: the cenario upporting multiple carrier per HPA, the non-linear channel model and it implication to multiple carrier tranmiion in Section II, mitigation technique in Section III and their performance analyi in Section IV. Concluion are drawn in Section V. II. Multiple Carrier Tranmiion: Scenario and Channel model A. Scenario Recently launched wideband atellite tranponder perform joint filtering and amplification of multiple carrier ignal and the trend i enviaged for future ytem a well. In uch application, different carrier are uually independent and dedicated to different uer terminal or application. Joint onboard filtering and amplification of the tream of carrier, allow ignificant aving in hardware complexity and weight. Improved pectral and power efficiencie i thi etting motivate the target cenario where a atellite broadcat tranmiion from a ingle gateway to many receiver with a tranparent atellite tranponder i conidered. Each carrier channel i aumed to be compliant with DVB-S2 tandard 2. Preent multicarrier tranponder have typical bandwidth of 33 and 72 MHz, carrier throughput varying from 10MSp to 45 MSp and a linearized TWTA with typical OBO in the range of db. From a ytem perpective, the preditortion need be deigned under the aumption of a full knowledge of the channel characteritic in term of filter, amplifier etc at the gateway prior to launch, but no real time data on a loop back ignal will be aumed available. Poible feedback from the receiver (dedicated receiver tation) can be conidered available, at regular interval, for channel reconfiguration. Concerning uer terminal equalization, although the on-board joint amplification of multiple carrier can often occur, mot of the current uer receiver uually upport demodulation and decoding only for a ingle carrier ignal. The compenation of poible channel variation, e.g. TWTA parameter drift, will be delegated to the end receiver that have to track fat channel variation. B. Non-Linear Satellite Channel Model The typical model of the path between the tranmitter and the receiver in a tranparent atellite communication i hown in Figure 1. The ignal from the GW are channelized to the atellite HPA through the IMUX filter whoe amplitude and group delay repone i depicted in Figure 2. Thi wideband filter can be approximated a a linear ytem with memory (FIR filter) whoe parameter are obtained from the repone of Figure 1: A typical Satellite Non-linear Channel TWTA contitute the commercially ued onboard HPA and are intrinically non-linear. Further, the TWTA ued in Ku-band can be aumed to have a tranfer characteritic largely independent of the frequency. Such memoryle ytem are characterized by the AM/AM and AM/ PM curve depicted in Figure 3.

4 Figure 2: Ku band IMUX and OMUX filter characteritic Figure 3: Ku band TWTA AM/AM and AM/PM characteritic Eentially, the atellite channel can be abtracted a a non-linear ytem with memory. Such a channel lead to the following ditortion: Contellation Warping caued by memoryle non-linearity Inter-Symbol Interference caued by o Firt order due to linear memory o Higher order due to non-linearity coupled with the filter Adjacent Channel interference due to non-linearity Thee ditortion are hown in Fig. 4, where in a three carrier ytem i imulated. Further, the ditortion for a ingle carrier channel are alo hown for reference. C. Volterra Analyi Being a nonlinear dynamic ytem, the atellite tranponder i decribed by Volterra theory 4, 10, where complex baeband input ignal, x(n) and output ignal, y(n) are related a: p k y(n) = h k (n 1, n 2, n k ) x(n n r ) x(n n q ) k=1 n 1 n k r=1 q=p+1 (1)

5 Figure 4: Scatter plot of received 16 APSK contellation: Single Carrier (left), Multicarrier (right) Tranmiion where h k (n 1, n 2, n k ) are the Volterra kernel. Auming M equi-paced carrier (eparation of f) with m (n) denoting the baeband ignal tranmitted on the m th carrier, we have, x(n) = M m (n)e j[2πm( f)+ φ m] m=0 (2) where i an arbitrary phae difference. Volterra erie can be ued to analye the variou ditortion 8,9 and Table 1 ummarize thi analyi by preenting the different term contributing to ISI and ACI for the cae of three carrier (dependence on time index n- i dropped for eae of comprehenion). For each carrier f i all the third order in band interference term atify the following condition: where we have by the cenario f 1 = f, f 2 = 0 and f 3 = f. f i = f k1 + f k2 f k3 (3) Table 1: Term contributing to ICI and ACI for three carrier Nonlinear order Carrier #1 Carrier #2 Carrier #3 Bandwidth Interference 1 t 1 2 f ISI 3 3 rd rd rd rd f ISI+ACI f ACI f ACI f ACI 221

6 III. Mitigation Technique A. Preditortion The functionality of the preditorter i to modify the tranmitted ignal o a to reduce or eliminate non-linear effect. Thei can be done in everal way 5, leading to variou clae of equalizer. We now preent the mot relevant of thee claification below; the intereted reader i referred to Ref. 5 for detail. 2. Claification of Preditortion Technique Data and Signal Preditortion: The preditorter achieve it functionality of inverting the channel either operating on the baeband data ymbol (data preditorter) or on the baeband analog ignal (ignal preditorter). Digital and Analog Preditortion: Thi claification i baed on the technology ued to implement the preditorter: analog technique provide for ignal preditortion while digital implementation are eential for data preditortion Lookup Table and Model baed Preditortion: Baed on their architecture, DPD algorithm are commonly claified a model baed or look-up table baed method. For each contellation ymbol, a tranmitted ymbol i generated uing a pre-determined table in the LUT method 1. Thi method ha been ued for ingle carrier tranmiion with non-linearity and memory effect 1. On the other hand, a model of the nonlinear dynamic tranfer function of the HPA i derived and the pre-ditorter i obtained a an invere of thi characteritic in model baed mechanim. The Volterra erie decribed earlier i widely ued to decribe the non-linearity a well a invere 5, Algorithm for Preditortion Several algorithm for preditortion have been conidered in literature for ingle carrier cae 1, 3, 11, 12, 13. To adapt ome of thee method to multiple carrier cenario, we retrict ourelve to model baed digital preditortion. Data preditortion modifie the contellation ymbol before the pule haping filter and doe not caue out of band interference on the uplink. Moreover, the digital technique are eay to implement and adapt. On the other hand, LUT 1 i not feaible in multiple carrier cenario due to the increaed number of entrie on account of ACI. A nonlinear dynamic ytem with memory can be decribed a Volterra model. Further, it invere i alo a nonlinear dynamic ytem and can alo be decribed by a Volterra model 10. Thu, a Volterra model i the firt choice for a DPD algorithm. However, the Volterra erie converge lowly, and in practice variou memory polynomial 13 are ued. Thee are reduced Volterra model and have the advantage that they have fewer coefficient and are fater in convergence. Ue of memory polynomial ha been conidered in a cenario involving two or more RF ignal are amplified by the HPA imultaneouly 6,7. Thee motivate the ue of preditortion baed on memory polynomial in thi paper and the ame i decribed next. 4. Memory polynomial and their identification The Volterra erie relating the input and output of a non-linear ytem i given in Eq. (1). A imilar model i ued at the Volterra DPD where y(n) i now the preditorted ymbol while x(n) denote the contellation ymbol. Dependence of y(n) on x(n k), k > 0, indicate a nonlinearity with memory (due to IMUX and OMUX) and the preditorter i dynamic in nature 5. The kernel, {h k (n 1, n 2, n k )}, i alo known a the coefficient of the Volterra DPD. Motivated by thi, a third order memory polynomial multicarrier DPD algorithm without ACI (cro talk) relate the pre-ditorted ignal u k (n) on the k th channel to the input according to P u k (n) = 1,k (1) P m=0 h k (m) k (n m) + 3,k (3) m=0 h k (m) k (n m) k (n m) 2 M k=1 (4) (m) Here, h k denote the model coefficient of order m and k denote the ymbol on k th carrier.,k denote the memory depth of the order l and channel k. It i clear that the number of co-efficient, are much lower than that in Eq. (1) for a given order leading to the complexity advantage of memory polynomial. If cro talk i included, the third order memory polynomial preditorter take the general form,

7 P 1,k (1) P 3,k, (m) k (n m) + u p (n) = M k=1 m=0 h p,k, M k 1 =1 M k 2 =k 1 M k 3 =1 m=0 h p,k1,k 2,k 3 (m) k1 (n m) k2 (n m) k3 (n m) +.. (5) (3) Apart from h (1) (3) p,k, additional co-efficient indicating ACI alo appear in the form of h p,k1,k 2,k 3 (m). Again, the reduction of co-efficient with repect to Volterra can be oberved. It hould be noted that ymbol on all carrier are ued to generate the pre-ditorted ignal of a particular carrier. Central to DPD i the identification of neceary coefficient. While direct and indirect learning method are ued in identification, we focu on the indirect learning method. Thi tem from the fact that indirect learning method i eay to implement and it doe not require any real time feedback 13. The indirect learning method i baed on the fundamental pth order theorem that tate that the pot invere and pre invere of a nonlinear dynamic ytem are identical and that the nonlinear order (p) of the ytem invere i the ame a the nonlinear order of the ytem itelf 10. In thi method, the coefficient in the algorithm for the invere of the nonlinear ytem are identified in a firt tep uing an etimation of the preditorter output error, and in a econd tep copied to the preditorter function itelf. When the input and output in Eq. (4) or (5) are known, the model co-efficient atify a linear relation and it form for three carrier i given in Eq. (6) below. [ ] = [ (x) (x) ] [ ] ( ) (x) Here, i = [u (1), u ( ), u ( )], i the et of received ymbol, i = [h (1) 1 (0), h (1) (1) 1 (1),, h ( 1,1 1), h (1) (1) (0),, h ( 1, 1), h (1) (1) (1),, h ( 1, 1), h (3) 1,1,1 (0),, h (3) 1,1,2 (0),, h (3) 1,1,2 (0),, h (3) 3,3,3 (0), ] denote all the model coefficient tacked into a vector, i(x) i the regreion matrix that decribe previou equation and T repreent the tranpoition operator. Clearly, Eq.(6) allow for ue of linear method to identify the coefficient. B. Equalization 1. Motivation While multicarrier digital preditortion i implemented at the tranmitter ide, in reality, it cannot fully compenate the non-linear effect of the channel. The limited model degree and memory a well a the not-invertible nature of the HPA function, do not allow perfect compenation. Hence, without particular aumption, the reulting channel till poee the characteritic of a non-linear dynamic ytem. Hence, non-linear equalization i alo conidered a a poible enhanced receiver technique. Non-linear equalization would compenate for the reidual non linearity and interference. Further, the ytem cenario mandate ingle carrier equalization where tranmiion from other carrier are merely conidered a interference. 2. Non-linear equalizer Equalization i performed on the ymbol level after the pule-haping filter. Since the cacade of the DPD and the atellite channel i till non-linear due to incomplete compenation, it can be modelled uing the Volterra erie. Hence, imilar to DPD, Volterra equalizer are widely ued in atellite literature 3,4,5. The equalized output of any carrier, denoted by y(n), i obtained from it input x(n k), k 0, uing the following equation y[n] = h 1 [k 1 ]x[n k 1 ] + h 3 [k 1, k 2, k 3 ]x[n k 1 ]x[n k 2 ]x[n k 3 ] +... ( ) k 1 =0 k 1 =0 k 2 =0 k 3 =0 where the h [ ] are the channel/ Volterra coefficient. Since ingle carrier equalization i ued, x(n k) i the ignal on the deired carrier and that the adjacent channel information i not ued. A mentioned earlier, memory polynomial and their orthogonal verion, have found wide application a DPD mechanim in terretrial ytem. Due to the exponential growth of complexity in Volterra equalizer with increae

8 in degree, we alo conider memory polynomial. Baed on Eq. (7), the memory polynomial function i take the form y[n] = h 1 [k 1 ]x[n k 1 ] + h 3 [k 3 ]x[n k 3 ]x[n k 3 ]x[n k 3 ] +... k 1 =0 k 3 =0 ( ) Clearly, intead of coefficient h 3 [k 1, k 2, k 3 ] in the Volterra, we only have h 3 [k 1 ] and hence it complexity grow linearly with degree. In many application, numerical iue become important in addition to limited computational complexity. The accuracy in etimating the equalizer parameter need to be optimized and the complexity need to be reduced. Orthogonal polynomial repreent a tailoring of memory polynomial, in which the bae function are defined to improve numerical tability and accuracy 15. Orthogonality uually guarantee thee apect and bae function are defined to enure orthogonality in the tatitical ene among different degree term. In particular, the equalizer take the form in equation (8), where () denote the bae function: y[n] = h 1 [k 1 ] 1(x[n k 1 ]) + h 3 [k 3 ] 3(x[n k 3 ])+... k 1 =0 k 3 =0 ( ) Further, ψ i are defined auming a known input ditribution of the variable x uch that: E[ k(x) (x) ]=0 k l (10) In thi work, we chooe the bae function derived in Ref. 15. Since orthogonal memory polynomial have the ame property and complexity characteritic of memory polynomial, they will alo be conidered for ingle carrier equalization. 3. Identification For a given order and memory, etimation of the kernel co-effcient can be formulated a a Linear Leat Square problem In thi paper, a tandard Recurive Leat Square implementation i conidered to reduce the complexity and to be able to track channel change 8,9. In all equalization cae, RLS technique i employed to iteratively adapt the kernel coefficient to channel change according to the following et of equation: x( ) x( 1) u( ) = x( )x( )x( ) x( 1)x( 1)x( 1) [ ] e( ) = d( ) u( ) T h( 1) ( 1)u( ) g( ) = γ + u( ) T ( 1)u( ) ( ) = γ ( 1) g( ) u( ) T γ ( 1) h( ) = h( 1) + e( )g( ) where u( ) i the vector of all the linear and non-linear term included by the equalization function (number of term and form depend on the type of model, degree and memory depth), h( ) = [h 1 (0), h 1 ( 1), h (0), h ( 1), ], i the vector coniting of the kernel coefficient during the i th intance, d( ) i the deired ymbol and γ the forgetting factor.

9 For all the conider equalization technique identification i baed on training ymbol. Each frame i aumed to have a dedicated code_eg 1 of 90 training ymbol in the target modulation. Thi allow upporting Adaptive Code Modulation operation mode foreeen by the tandard, a well a channel parameter drift. From imulation reult the forgetting factor ha been et to IV. Performance Analyi of Mitigation Technique A. Simulation Set-up The imulation et-up i illutrated in Figure 5 and the imulation parameter are ummarized in Table 1. Simulation were performed by chooing the repreentative cae of three carrier, each of 8 MHz (excluding raied coine bandwidth exce) with the eparation between their centre frequencie being 10 MHz. Thee carrier ue a quare root raied coine pule haping with an exce bandwidth of 2MHz (roll-off of 0.25). A a reult, the adjacent channel are cloe to each other without any channel pacing. In order to correctly repreent the ignal at the output of the HPA, a imulation frequency even time the IMUX bandwidth wa ued. Thi account the pectral regrowth correponding to a non-linear order of eventh degree. Figure 5: Schematic diagram of the imulation chain Table 2: Simulation Parameter Number of carrier 3 Sytem Symbol Rate Carrier Frequency Spacing Modulation Code Rate 8 Mbaud 1.25 R APSK ¾ - 2/3 - ¾ Roll-off factor (all carrier) 0.25 Channel IMUX pa-band (3 db) OMUX pa-band (3 db) HPA type / model 29 MHz 30 MHz Linearized Ku-band / Saleh E/N0 (db) Noie power, choen according to E/N0, i added at the output of OMUX. Thi tem from the fact that noie power at the receiver i fixed. Hence, the actual SNR at the receiver i not contant, but varie with the ignal power a dictated by the operating point of HPA.

10 1. Channel Model The well-known Saleh model 5 i ued to model HPA. Such model i defined by : F a ( x(n) ) = a 0 x(n) 1 + a 1 x(n) 2, F P ( x(n) ) = b 0 x(n) b 1 x(n) 2 (11) HereF a ( x(n) ), denote the AM/ AM ditortion while F P ( x(n) ) denote the phae ditortion (AM/PM ditortion). With the input to the HPA being x(n) = x(n) e j, the output take the form, y(n) = F a ( x(n) )e j( +P p( x(n) )) The IMUX and OMUX filter are modelled a FIR function.the traightforward implementation of the FIR filter model i directly in the up-ampled imulation frequency domain. Thu the ampling frequency of the FIR will correpond to the imulation frequency F. Sampling frequency and number of tap control both accuracy and complexity. The FIR filter coefficient (h(t k ), k = 0,, M 1) are obtained from frequency domain meaurement ( (f k ), k = 0,, 1) uing the well-known over-determined (or averaged) Frequency ampling method. In thi method, the coefficient are obtained a the LS olution of the following overdetermined (N > M) et of equation: [ (f 0 ) ] = [ e j2πf 0t 0 e j2πf 0t M h(t 0 ) ] [ ] (12) (f N ) e j2πf Nt 0 e j2πf Nt M h(t M ) The obtained FIR will be the optimum in the minimum quared ene with repect to the provided meaurement. A. Performance 1. Figure of Merit The widely ued FoM to characterize performance on the nonlinear atellite channel i the total degradation defined a D = E b 0 NL E b 0 Idea + OBO. (1 ) The term E b N 0 NL E b reflect the lo in SNR of a practical HPA compared to ideal HPA for achieving the ame N 0 Idea BER at the ame OBO level. Thi term i penalized by OBO to reflect on the lo in power efficiency with high OBO. A OBO increae, the practical HPA i puhed more and more into the linear region and E b N 0 NL E b N 0 Idea reduce. Thu one could ee a trade-off between the two component and an optimum OBO minimizing the TD i uually een. Evaluating the TD in the framework of DVB-S2 requrie implementation of the LDPC and the enuing imulation are time conuming (a it involve Decoding of LDPC code). Since the entire chain i not imulated currently, we ue SINR a an alternative metric ince i 1. Show a behaviour conitent with TD 2. Fater to compute ince it work on uncoded ytem To reflect on the imilaritie between TD and SINR, we ee that the OBO affect the SINR a follow: Low OBO lead to high interference (non-linear region) but higher SNR (higher amplification of the ignal) High OBO lead to low interference (linear region) but low SNR (lower amplification) Thi define an optimum OBO where SINR how it maximum. Thi maximum repreent the compromie between noie and interference.

11 When the tranmitted ymbol (n) i received a y(n) after appropriate proceing (DPD->IMUX->HPA->OMUX>EQ), the SINR i evaluated a ρ= E[ (n) 2 ] E[ y(n) (n) 2 ] (14) In Eq. 14, we aume, without lo of generality, that the reulting path gain on the ignal of interet i unity. In practice, DPD/ EQ deign trive to enure that the received ignal ha a unity gain for the ueful component and the aforementioned ignal model i deemed appropriate. Finally caling of the received ignal doe not alter the SINR. 2. Preditortion only Scenario A preliminary analyi we conider the cae in which only preditortion i applied and o no equalization i performed at the receiver ide. Multicarrier DPD with and without cro-term a it i decribed in ection III i hereafter conidered. Notice that DPD without cro-term baically correpond to tandard ingle carrier DPD applied eparately to each channel (thi latter verion in the figure i labelled NC that tand for No Cro-term included). 32APSK External Channel 16APSK Internal Channel 2 2 no DPD DPD(NC) DPD 16APSK Q Q I no DPD DPD(NC) DPD 32APSK I Figure 6: Channel output catter plot for different DPD, Noie le cae In Figure 6, we ee the noiele catter plot of the received ymbol for the external and internal channel, repectively. The catter plot give an idea on how the clutering and warping effect are reduced by the applied technique. In particular we can ee how DPD improve the hape of received ample compared to the cae in which DPD i not including cro term or i not applied at all. In Fig. 7 we ee the SNIR performance, when only preditortion i applied, for the channel configuration of Table 2. Oberving Fig. 7 we notice that, for the internal carrier, the application of preditortion not including cro term actually degrade the performance. In the internal channel memory effect are negligible and ACI are dominant. Therefore applying a preditortion function that doe not include cro term bring to a model mimatch. On the other hand, in the external channel, where the dominant impairment are related to ISI, we have a ignificant gain between the two technique. In fact the external channel, poitioned on the filter bandwidth edge, uffer of ignificant memory effect leading to trong linear and non-linear ISI. On the other hand they experience lower ACI being external in frequency.

12 SNIR [db] SNIR [db] SNIR [db] 18 SNIR Internal Channel 16APSK 18 SNIR Internal Channel 16APSK only DPD No DPD only DPD (NC) only DPD No DPD only DPD (NC) OBO [db] OBO [db] Figure 7: SNIR of Preditortion only applied: Internal Channel (left) and External Channel (right) 3. Equalization only Scenario A a further tep in the analyi, we now conider the ituation where only equalization i applied. Recall that we implement a ingle carrier equalizer that i capable of compenating both linear and non-linear ISI while it fail to cancel ACI ince it doe not proce ymbol of the other carrier (unlike multicarrier equalization in Ref. 8-9). Some reult of the equalization only approach with channel configuration of Table 2 are preented below. 18 SNIR External 32APSK only ingle tap EQ only Mem.Poly EQ only Orth Mem.Poly EQ only Volterra EQ only Linear EQ OBO [db] Figure 8: SINR for different Equalizer: External Channel Figure 8 how the ignificant gain between the olution without equalization (a ingle tap filter compenating only warping) and other architecture for the external channel (the two external channel have imilar behaviour and only one i reproduced). Thi i related to the preence of trong linear ISI coming from the filtering effect preent at the edge of the tranponder bandwidth. The relative gain between linear and non-linear equalization technique i intead limited ince both non-linear ISI and ACI are, rather, negligible compared to linear ISI effect. On the other hand, a depicted in Figure 9, memory effect (ISI) are negligible for the internal carrier and a ignificant SNIR gain i achieved by non-linear equalization. Further SINR improvement in thi cae cannot be achieved becaue ACI cannot be effectively cancelled with ingle carrier equalization. Thi jutifie the definition of multicarrier (joint) DPD at the GW to in order to pre-compenate at bet ACI

13 SNIR [db] 17 SNIR Internal 16APSK only ingle tap EQ only Mem.Poly EQ only Orth Mem.Poly EQ only Volterra EQ only Linear EQ OBO [db] Figure 9: SINR for different Equalizer: Central Channel Comparing the only preditortion approach with the only equalization one, we can notice a major degradation in the internal channel in the only equalization cae. The internal channel uffer predominantly from ACI and ingle carrier equalization cannot effectively compenate for that. On the other hand, DPD with cro term ha the wherewithal to cancel ACI. 4. Combined Preditortion and Equalization In the following we illutrate the conolidate gain of the mitigation technique in which we combine preditortion and equalization together in order to achieve the bet performance. In the external channel multicarrier preditortion i fairly effective in compenating both ISI and ACI and o no additional gain i achievable with ingle carrier equalization technique. Thi i clearly een from Fig. 10. Single carrier preditortion (no cro term) provide ignificant gain compenating for linear and non-linear ISI. A already highlighted in the only preditortion cae (Fig. 9), on the internal channel, being ACI the dominant impairment, the olution applying DPD without cro term produce a modelling mimatch reulting in performance degradation (kindly refer to Fig. 11). With multicarrier DPD (cro-term included), we have intead a ignificant SINR gain, epecially in the aturation region. However, differently from the external channel cae, ome reidual memory effect and non-linear interference are till preent in the ignal and equalization provide ome further improvement in SNIR. In thi combined DPD and EQ cae of tudy, Orthogonal polynomial and Volterra equalization, in conjunction with multicarrier DPD, eem to provide the bet performance in the optimum OBO region. In the region cloe to aturation all the non-linear equalization technique have imilar performance gain. Thee repreentative reult how the SINR improvement in uing non-linear mitigation technique at either end, a compared to ituation without DPD and EQ. Thi gain i available not only at the optimum OBO, but alo cloer to aturation. Although maximum SNIR would repreent the maximum capacity region with repect to OBO, we are alo intereted in the SINR gain cloer to the aturation region where power efficiency i higher. In thi region, coding technique could be applied in order to achieve the optimum compromie between throughput and power efficiency. The plot alo corroborate the fact that non-linear equalizer can give gain, both with and without the ue of DPD.

14 SNIR [db] SNIR [db] 20 SNIR External Channel 32APSK Mem.Poly EQ Orth. Mem.Poly EQ Volterra EQ Linear EQ Mem.Poly EQ(NC) Orth. Mem.Poly EQ (NC) Volterra EQ(NC) Linear EQ(NC) no DPD no EQ OBO [db] Figure 10: SINR of Combined Preditortion and Equalization Technique: External Channel 18 SNIR Internal Channel 16APSK Mem.Poly EQ Orth. Mem.Poly EQ Volterra EQ Linear EQ Mem.Poly EQ(NC) Orth. Mem.Poly EQ (NC) Volterra EQ(NC) Linear EQ(NC) no DPD no EQ OBO [db] Figure 11: SINR of Combined Preditortion and Equalization Technique: Central Channel V. Concluion The paper tudied the ue of non-linear mitigation technique to the ituation where multiple carrier were amplified by a ingle HPA. The tranmitter proceing (preditortion) i privy to the data on the multiple carrier while the receive proceing (equalization) ha only acce to deired carrier. Several algorithm are conidered and the ue of proceing at either end how ignificant SINR gain at low OBO region (2-3 db). Thi SNIR gain can be exploited by coding technique to further reduce the OBO and improve power efficiency. A final confirmation of thi i awaited, pending Total Degradation and overall ytem efficiency evaluation, to ae the achievable gain with repect to actual benchmark for multicarrier ytem. The tudy alo provide a firt undertanding of the gain obtained by ue of preditortion only/ equalization only and can be ueful in ytem deign.

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