Trellis Shaping Techniques for Satellite Telecommunication Systems

Transcription

1 > 1 Trelli Technique for Satellite Telecommunication Sytem M. Álvarez-Díaz 1, M. Neri, C. Moquera 1 and G. E. Corazza 1 Dept. Signal Theory and Communication (TSC), Univerity of Vigo Campu Univeritario Vigo (Pontevedra), Spain Dept. of Electronic, Computer Science and Sytem (DEIS), Univerity of Bologna, Viale Riorgimento, Bologna, 4016 Italy 1 {malvarez,moquera}@gt.tc.uvigo.e, {mneri,gecorazza}@dei.unibo.it Abtract In recent year, atellite overlay network have hown their potential for delivering multimedia content both to rural and urban environment. In the latter cae, the adoption of terretrial Intermediate Module Repeater (IMR) i in order to cloe the link in Non-Line-of-Sight propagation condition, cauing a evere increae of multipath propagation and conequent linear ditortion, adding to the intrinic non linear ditortion of atellite link. Whenever the propagation channel for the uer receiving the data can be known with good approximation at the tranmitter, the application of precoding technique can be conidered a a feaible olution to counter channel diperion. In thi paper, trelli haping (the combination of Tomlinon-Harahima precoding and ignal haping) i ued along with preditortion technique to increae the reilience to channel diperion and non-linear ditortion. Numerical imulation allow u to ae the robutne to nonlinear ditortion of trelli-haped ignal. Different optimization goal are purued by mean of different trelli haping metric, including everal novel one. Improvement in performance are achieved with repect to the unhaped cae. Index Term Fractional Preditortion, Satellite Communication, Tomlinon-Harahima Precoding, Trelli Precoding I I. INTRODUCTION N RECENT year, atellite overlay network have hown their potential for delivering multimedia content both to rural and urban environment. In the latter cae, the adoption of Intermediate Module Repeater (IMR) i in order to cloe the link in Non-Line-of-Sight propagation condition. The introduction of IMR increae diverity, but involve alo trong time diperion, which mut be properly taken into account. In parallel, the wide adoption of precoding technique in terretrial wireline ytem ha purred the interet for the application of thee technique to other field uch a Multi- Antenna and Multi-Uer communication [1]. Whenever the propagation channel a een from the receiver can be known with good approximation at the tranmitter, the application of Thi work ha been upported in part by the IST FP6 SatNEx project. M. Álvarez-Díaz and C. Moquera' work ha alo been funded by the Spanih MEC project TEC precoding technique can be conidered a a feaible olution to counter channel diperion. In practice, thi may retrict the range of application to tationary or nomadic uer terminal. In thi paper, we focu on a well known precoding technique, namely Tomlinon-Harahima Precoding (THP) [], which can be een a an alternative to tandard Deciion- Feedback Equalization (DFE). It avoid two drawback of the latter: no error propagation occur and application of channel coding i traightforward. However, THP ha it own diadvantage a well, the main being that the ymbol equence entering the pule haping filter no longer belong to a finite et of dicrete ymbol; intead, it ditribution approximate a continuou uniform with a lightly larger dynamic range than in the unprecoded cae. Thi i certainly undeirable if we conider the characteritic of atellite tranmiion, where trong nonlinear ditortion i introduced into the amplified ignal by on-board High Power Amplifier (HPA), which are puhed to operate cloe to aturation for cot and efficiency reaon. Indeed, the higher the dynamic range of the ignal to be amplified, the higher it enitivity to nonlinear ditortion. A natural way to control the dynamic of the tranmitted ignal i the ue of ignal haping. The combination of THP and ignal haping i known a trelli precoding. By mean of trelli precoding, the characteritic of the precoded ignal can be accommodated to different deired goal. In thi tudy we focu on the reduction of the dynamic range and the average energy of the tranmitted equence, ince our goal i the robutne to nonlinear ditortion. We propoe a et of trelli precoding technique ome of them novel which will provide an improvement in performance with repect to unhaped THP tranmiion. While trelli precoding take care of canceling the linear ditortion introduced by the channel, the nonlinear ditortion caued by the HPA i dealt with by mean of fractional preditortion. The combination of trelli precoding and fractional preditortion will offer an improvement with repect to the equivalent unhaped cae. In Section II, we offer a complete decription of the ytem we propoe. Special attention i given to the operation of the ignal haping and preditortion block. In Section III we

2 > AWGN Sampling TH Decoder Source Pule Whitened bit QAM TH Trelli Complex Decided bit Preditorter HPA Channel Matched Slicer Demapper Mapping Modulo Filter Filter Fig. 1. Block diagram of the propoed ytem model, including Trelli and Preditortion technique dicu the different ignal haping alternative we are conidering for evaluation of the propoed tranmiion cheme. In Section IV we preent the reult offered by imulation and extract the relevant concluion. Finally, in Section V we ummarize the main outcome of our reearch. II. SYSTEM DESCRIPTION Fig. 1 how the main block of the propoed tranmiion cheme. The QAM equence enter the TH Precoder-Shaper, whoe output i converted to waveform by the pule haping filter (a quare-root raied coine). Preditortion i applied to the waveform before the HPA block, which i the lat tage at the tranmitter ide. The channel i a tapped delay line introducing coniderable ISI, according to a typical model of IMR channel power-delay profile (PDP), and AWG noie. Fig. how the PDP we have ued throughout our tudy. The receiver front-end filter i the Whitened-Matched Filter (WMF) [], which i the optimum receive filter yielding a ignal compoed of ISI ditorted ymbol in AWGN. It output i ampled at ymbol rate before the TH-decoder eliminate the remaining ISI and yield the etimated ymbol equence. Signal Power (dbm) IMR Channel - Power Delay Profile Delay/T (ymbol period) Fig.. Power Delay Profile of the IMR channel ued for evaluation A. Tomlinon-Harahima Precoding and Signal THP can be een a a way of performing pre-equalization at the tranmitter ide, with the exception that a (nonlinear) modulo operation i performed on the pre-equalized ignal. By doing thi, the likely increae in power of the pre-equalized ignal i avoided at the cot of introducing the nonlinearity. Like pre-equalization, THP require the channel repone to be etimated. The tranmitted ignal can be recovered at receiver ide by mean of the ame modulo operation ued at the tranmitter. The underlying principle in precoded tranmiion i that, thank to the modulo operation, intead of uing the original QAM ymbol we can ue a modulocongruent replica of it, i.e., a complex ymbol which i converted after the modulo operation into the original one. The et of replica of the original ymbol can be grouped in replica of the original contellation whoe location follow a regular fahion, preenting the propertie of a lattice. For a more detailed decription of THP, the reader i referred to []. Signal haping [] i achieved by introducing redundancy in the tranmitted ignal. In plain THP, only precoded ymbol are tranmitted that belong to the contellation replica with le average energy. Here, only one ymbol replica among the et of modulo-congruent ymbol caue the precoded ymbol to lie within the allowed tranmiion region. However, in ignal haping, the allowed tranmiion region i enlarged (uually by a factor of two, a i our cae). Now, two ymbol replica are allowed intead of jut one. A wie election of the tranmitted replica will allow u to effectively hape the tranmitted ignal, i.e., to drive it propertie toward a deired goal. Uually, the main application of haping i to reduce the average tranmitted power. Neverthele, other aim can be achieved by mean of haping, uch a reducing the Peak-to- Average Power Ratio (PAPR) or reducing the dynamic of the tranmitted or received ignal. While ignal haping can be relatively eaily applied to unprecoded QAM tranmiion, the combination with precoding i not traightforward at all. Thi i due to the fact that the precoding operation itelf affect trongly the hape of the tranmitted ignal. A a matter of fact, the TH-precoded ignal under typical condition i almot uniformly ditributed within the region defined by the modulo operation. The only way to achieve haping on a precoded ignal i to perform both operation jointly, by mean of a technique called trelli precoding. In particular, we will ue a variation of it called haping without crambling []. Both technique ue a Viterbi decoder within the precoder, which actually elect (decode) the equence to be tranmitted a the one offering the lowet accumulated metric. The metric i choen according to the deired goal, and thu, a variety of metric i available depending on the characteritic we demand from the haped ignal. In Section III we decribe the metric we have conidered for our tudy. Fig. 3 illutrate the functioning of the trelli haping block. (Viterbi decoder) Replica election Complex Modulo H(z) - 1 Fig. 3. Block diagram of the Trelli block All the benefit offered by haping come at ome cot. One of the drawback i that, in general, the PAPR of the haped ignal i increaed with repect to the unhaped precoded cae. Another one, a we have already aid, i the 1 bit redundancy

3 > 3 needed for haping, which i accommodated by increaing the contellation ize entering the pule haping filter. In other word, the haped ignal pan twice the area of the ignal in the unhaped precoding cae. Thu, if we want to hape a 16- QAM equence, we will be uing a 3-ymbol contellation after the haping operation. Though it may initially eem that one bit redundancy would not be enough to achieve haping it can be demontrated that no practical improvement are gained by adding more redundancy. While the extra bit i unavoidable, the increae in PAPR can be kept low performing a wie haping, a we will ee in the next ection. B. Fractional Preditortion A the precoded and haped ignal i proceed through the atellite channel, it propertie are changed by the non linear ditortion that i introduced by the on-board HPA. In order to counteract thee effect, fractional preditortion technique are conidered in the gateway tranmitter [3]. The principle of preditortion i to proce the ignal at ome point before entering the HPA o a to compenate in advance the nonlinear ditortion that the HPA will introduce, aiming to obtain an overall linear characteritic between the input of the preditorter and the output of the HPA. Other method exit, for example nonlinear equalization at the receiver ide, but preditortion ha the advantage of reducing adjacent channel interference, ince it i applied at the tranmitter ide. Fractional preditortion work at waveform level, operating on the ignal ample at the output of the pule haping filter, by inverting the amplifier characteritic according to a given model of the HPA. In thi tudy, we conidered an on-board traveling wave tube (TWT) amplifier whoe AM/AM and AM/PM ditortion characteritic are hown in Fig. 4. OB O [d B] IBO [db] Fig. 4. TWTA AM/AM and AM/PM Characteritic ,00-15,00-10,00-5,00 0,00 5,00 10,00 15,00 IBO [db] The HPA characteritic are modeled through a rational polynomial model enviaging 5 parameter for each of the two characteritic. The fitted characteritic are then inverted and ued to preditort the proceed ignal. For the implementation of the preditorter we have choen an approach baed on a Look-Up-Table (LUT), which tore the inverted HPA gain value that are computed off-line [4]. A block diagram of a fractional preditorter i hown in Fig. 5. Phae [deg] b n Pule haping x m Gain baed LUT fractional preditorter Amplitude Phae. LUT (F) g m HPA Fig. 5. Block diagram of the gain-baed LUT fractional preditorter. Thi approach allow reducing the computational burden in the gateway, a only one LUT acce plu one multiplication are needed to proce each ample, and doe not hinder the poibility to periodically update the preditortion characteritic after a calibration/meaurement of the HPA characteritic that may have changed due to ageing. III. METRIC SELECTION The election of the metric ued in the Viterbi algorithm of the haper mut be driven by the improvement we deire to achieve through haping. Standard objective uch a minimizing the average tranmitted power can be mapped into well-known metric, a we will next ee. However, ome other group of objective do not offer a imple tranlation into a metric formula, thu requiring reearch effort in order to find a uitable working metric. In thi ection we decribe the et of improvement we have purued by mean of haping and their correponding metric. A. Minimization of average energy Thi i the mot common ue of haping. The goal i to achieve a reduction in the energy of the precoded equence in comparion to the unhaped ignal. The ave in energy i called haping gain (G S ). A natural way to build the metric i thu to accumulate the intantaneou energy of each of the equence ample. The metric for each tranition k of the trelli read λ k = x k, (1) being x k the (candidate to) precoded ymbol. B. Joint minimization of average energy and Peak-to- Average Energy Ratio The quadratic order of the metric (1) minimize the average energy of the precoded ignal. However, it i poible to ubtitute the power by a generic power : x k λ k =. () If we chooe >, the optimal reduction of energy will not be fully achieved, but we will be able to reduce the PAR. Thi i o becaue the metric penalize the highet energie in the haped ignal, thu reducing the PAR in comparion to the cae =. A trade-off mut be found between the minimization of the average energy ( = ) and the maximum reduction of the PAR ( ). We have done thi empirically. The reult are hown in ection IV. Metric () admit a refinement. By etting a given amplitude threhold ρ we could differentiate between two region: if the amplitude of the precoded ymbol i below the threhold normal energy minimization could be applied ( low = y m

4 > 4 ); intead, when the amplitude i over the threhold we could apply ome other value high > : xk, if xk ρ λ( k ) =. (3) high xk, if xk > ρ Again, the election of the pair (ρ, high ) mut be done empirically. C. Minimization of the diperion of the haped ignal with repect to a given radiu ρ Conidering the preence of the HPA, it would be deirable to adapt the characteritic of it input ignal to prevent a much ditortion a poible. One poibility i to try to concentrate around a circle of fixed radiu ρ a much of the haped ignal a poible. In thi way we would be (a) making our haped ignal reemble a PSK ignal (circular contellation are accepted a the mot appropriate modulation for atellite tranmiion) and (b) reducing it PAR at the ame time. The metric we propoe for doing thi i λ ( k) x k m m = ρ, (4) where, imilarly to metric () can be tuned in thi cae to penalize the diperion around the circle of radiu ρ, and m allow exploration of a wide range of poibilitie. The election of the bet pair (m,) eem to be bound to an empirical earch. In Section IV we preent the value we have obtained. D. Minimizing the perturbation between conecutive ymbol Another way to avoid the ditortion introduced by the HPA can be to prevent large tranition between conecutive ymbol of the precoded equence. If the equence to be tranmitted preent few of uch variation, it i likely that the HPA will introduce le ditortion. We propoe the following tranition metric: m m k = x k xk 1 λ. (5) A in the previou cae, a theoretical election of the mot appropriate pair (m,) eem complicated, and one mut revert to empirical earch. We how our reult in the next ection. IV. NUMERICAL RESULTS In order to earch for the bet et of parameter for each metric, we have conducted a number of numerical imulation, teting a large variety of parameter combination. In Table I we how one cae of interet for each of the metric preented in Section III. The metric of Table I have either proved to perform well in term of BER or offer an intereting trade-off between G S and PAR. A a meaure of PAR we ue the peak to average energy ratio of the imulated equence conidering it peak to be the 99% percentile of the empiric cumulative denity function of the equence. Thi i repreented by PAR 99. For the ake of comparion, we have included the performance of THP when no haping i applied. Metric (1) achieve the maximum G S (0.4 db) a well a a high PAR (5 db). The ret of eleceted metric are able to reduce the 5 db PAR while avoiding haping lo or even maintaining part of it. TABLE I COMPARISON OF THE PROPOSED METRICS Metric Parameter G S (db) PAR 99 (db) THP (1) = () = (3) ρ = 0.6, high = (4) m = 1, = 4, ρ = (5) m = 5, = The performance i compared in term of G S and PAR 99. Plain THP (no haping) i included for reference. The performance in term of BER i hown in Fig. 6 and Fig. 7. We include here the performance of all cae of Table I except metric (5), becaue thi metric doe not achieve an acceptable performance in term of BER, depite offering a good trade-off between G S and PAR. Fig. 6 contain the performance of the metric when no preditortion i applied. The cae for linear HPA, IBO = 10 db and IBO = db are hown. Firt of all, the improvement in performance of haping i clear, ince a viible gap in performance can be een between unhaped THP and for the linear cae and for IBO = 10 db. In the linear cae, the gap amount cloe to 1 db, which i coniderable. For IBO = 10 db, a performance floor i found. Thi i certainly due to the fact that nonlinear ditortion trongly affect the precoded and haped ignal. However, it can be een that THP i more everely affected than trelli haping. For IBO = db, the performance floor i even more evere and no difference are noticeable between THP and trelli haping. Fig. 7 how the performance when preditortion i ued for counteracting the effect of the HPA. The cae for IBO = 10 db and IBO = db are hown (the linear cae i not hown ince no preditortion i needed in thi cae). The main reult that can be extracted from the comparion between Fig. 6 and Fig. 7 i that the introduction of preditortion greatly improve the performance of the ytem. In fact, the performance floor for IBO = 10 db that i preent in Fig. 6 i completely removed by preditortion, and the performance reache the ame level a in the linear cae. A great improvement i alo achieved for the IBO = db cae, reducing the BER floor almot one order of magnitude. Another intereting effect can be een in Fig. 7. While when no preditortion i applied THP perform wore than trelli haping, when preditortion i ued it happen the ame, but now the performance gap i even larger. Thi i clearly een for the cae IBO = 10 db, where the improvement reache almot db. V. CONCLUSIONS We have hown that the introduction of ignal haping in the form of trelli precoding improve the performance of a atellite ytem uing unhaped THP. Trelli precoding allow a reduction in the average energy of the tranmitted equence (haping gain) in comparion with unhaped THP tranmiion. Thi i certainly of interet conidering the power retriction that are preent in atellite tranmiion due to the preence of the HPA. One drawback of ignal haping i that the PAR of the tranmitted ignal i increaed. However, we have hown that the ue of wie trelli precoding cheme

5 > 5 can keep the PAR at the ame level a in unhaped THP tranmiion, while till providing ome haping gain. In term of BER, trelli precoding perform better than unhaped THP. If no nonlinearitie are preent the gap in performance can be around 1 db. The introduction of preditortion lead to a great improvement in the performance of the propoed ytem. In thi regard, the trelli-precoded ignal get more benefit from preditortion than the unhaped ignal: the gap in performance can reach db for IBO = 10 db. [3] P. Salmi, M. Neri, and G.E. Corazza, Deign and Performance of Preditortion Technique in Ka-band Satellite Network, AIAA, Twenty-econd International Communication Satellite Sytem Conference (ICSSC), May 004, Monterey [4] P. Salmi, M. Neri, and G.E. Corazza, Fractional Preditortion Technique with Robut Modulation Scheme for Fixed and Mobile Broadcating, IST Mobile Summit 004, Lion, May 004 [5] M. Álvarez-Díaz, M. Neri, C. Moquera and G. E. Corazza, Joint precoding and preditortion technique for atellite telecommunication ytem, preented at IWSSC 005, Siena, Italy, September 8-9, Performance without Preditortion IBO=dB 10-1 BER THP Fiher ClaicPower Threhold Diperion IBO=10dB Linear E b /N 0 (db) Fig. 6. Performance in term of BER of the propoed ytem when no preditortion i ued 10 0 Performance uing Preditortion IBO=dB 10-1 BER THP Fiher ClaicPower Threhold Diperion IBO=10dB E b /N 0 (db) Fig. 7. Performance in term of BER of the propoed ytem when preditortion i added REFERENCES [1] C. Windpainger, R. F. H. Ficher, T. Vencel, and J. B. Huber, Precoding in multi-antenna and multi-uer communication, IEEE Tran. on Wirele Comm., Vol. 3, No. 4, pp , July 004. [] R. F. H. Ficher, Precoding and Signal for Digital Tranmiion, New York, John Wiley & Son, 00.