Soft-decision Viterbi Decoding with Diversity Combining. T.Sakai, K.Kobayashi, S.Kubota, M.Morikura, S.Kato

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1 Softdecision Viterbi Decoding with Diversity Combining T.Ski, K.Kobyshi, S.Kubot, M.Morikur, S.Kto NTT Rdio Communiction Systems Lbortories 2356 Tke, Yokosukshi, Kngw, 2383 Jpn ABSTRACT Diversity combining methods for convolutionl coded nd softdecision Viterbi decoded chnnels in mobile stellite communiction systems re evluted. Computer simultions confirm tht the previterbidecoding mximl rtio combining method hs better performnce thn other methods in Ricin fding chnnels. Pe performnces derived from the nlysis model using the probbility density function of Ricin fding nd the bit error probbility performnce of Viterbi decoding in AWGN chnnels gree with the simultion results. This diversity method is pplied to trellis coded 8PSK modultion nd coherent detection differentil detection nd their performnces re compred with conventionl QPSK modultion nd coherent detection with high codingrte nd high codinggin Viterbi decoding. n consequence, QPSK with high codingrte Viterbi decoding cn be n ttrctive cndidte for mobile stellite systems s well s TC8PSK.. NTRODCTON n mobile stellite systems, rdio terminl must stbly operte in quite low C/N nd Ricin fding environments. To improve bit error probbility (Pe) in low C/N stellite links, soft decision Viterbi decoding hs been widely dopted s mximum likelihood decoding for convolutionl code in AWGN (dditive white Gussin noise) chnnels('). On the other hnd, to overcome fding in rdio chnnel, diversity combining hs been used for mobile communiction nd microwve trnsmission, nd recently it hs been considered for mobile stellite communiction systems(2). Therefore, more Pe performnce improvement is expected in Rich fding chnnel using softdecision Viterbi decoding together with diversity techniques. Previous studies on Viterbi decoding with diversity combining considered severl methods for vrious systems. For exmple, selection diversity in(3) or fted4) Viterbi decoding ws investigted for Ryleigh fding chnnels in portble rdio communiction systems, where Viterbi decoding used hrd decision signls. With softdecision Viterbi decoding, it is possible to dopt mximl rtio combining before decoding(5). n mobile stellite communiction systems, combining diversity is more promising thn selective diversity becuse the combining offers remrkble diversity improvements even in n AWGN chnnels in contrst to selective diversity which offers no improvement t ll. n this pper, the performnce of the three methods, ()post Viterbidecoding selection, (b)selection in ACS output of Viterbi lgorithm, (c)previterbidecoding mximl rtio combining, re evluted by computer simultion. t is clrified tht the third method shows more improvement in bit error probbility thn the others. Moreover, simultion results re pproximtely nlyzed using the probbility density function of Ricin fding nd the bit error probbility performnce of Viterbi decoding in AWGN chnnels. Furthermore, this diversity method is pplied to trellis coded 8PSK (TC8PSK) modultion nd coherent detection / differentil detection nd their performnces re compred with tht of conventionl QPSK modultion nd coherent detection with high codingrte nd high codinggin Viterbi decoding. 2. COMPARSON OF DVERSTY COMBNNG METHODS Three methods for softdecision Viterbi decoding with diversity combining re investigted nd their performnces re evluted by computer simultion. () PostViterbidecoding Selection n this method, ech diversity brnch signl received by diversity is individully demodulted nd Viterbidecoded s shown in Fig.l(). Decoded results re compred,nd selection is mde bsed on some likelihood informtion such s the pth metrics provided by Viterbi decoder. n this simultion, pth metrics of symbols equl to the pth memory length re dopted s the likelihood informtion to mke selection more ccurte. (b) Selection in ACS Output of Viterbi Algorithm n Viterbi lgorithm, the brnch memcs ssocited with the stte trnsitions re computed nd then dded to the previous pth metrics. The contending pth metrics re compred nd the pth with the lrgest metrics is selected s the survivor. n this diversity method, the pth metrics re computed for ech CH28274/9/27 $.OO 99 EEE 27

2 ~ selector DEM mximl rtio combiner Viterbi decoder / informtlon pth metric in the lst 2 symbols (equl to pth memory length) #2". pth metric pth select CS # (chnnel stte informtion) softdecision Viterbi softdecision decoder CS #2 (chnnel stte informtion) () PostViterbidecoding selection. diversity brnch, nd then simultneously compred to select the survivor s shown in Fig.l(b). Therefore, this method hs only one set of pthhistory storge. (c) PreViterbidecoding Combining n the lst method, shown in Fig.l(c), conventionl postdetection combining is pplied to softdecision Viterbi decoding. Softdecision demodulted signls from ech diversity brnch re weighted for mximl rtio combining in proportion to their signl to noise power rtio, nd then summed. After tht, they re decoded by the usul Viterbi lgorithm. The performnces of the bove three methods in Ricin fding chnnels re evluted for QPSK modultion nd coherent detection with convolutionl coding nd Viterbi decoding (r=/2,k=4) by computer simultion. Simulted bit error probbilities re shown in Fig.2. n this comprison, the Ricin prmeter C/M, tht is the rtio of direct pth signl power to diffused signl power, is set to lodb nd fdt (fd : mximum Doppler frequency, T : symbol period) is set to 5x 3. t is clrified tht method (c), previterbidecoding combining, hs the best performnce. Similr results re obtined with other Ricin prmeters. For prcticl use, novel combining circuit hs been relized using softdecision demodulted signls(@. 3. APPROXMATE ANALYSS () Method of Anlysis n this section, it is ssumed tht fding is much slower thn the bit rte, nmely fdt<<. Thus, the verge bit error probbility in Ricin fding chnnel is given(7) by Eq.( )..he=[ PAwcj,r(s).rice(s).ds () (b) Selection t ACS in Viterbi decoder. Fig. Combining methods under considertion. 2, (c) PreViterbidecoding combining.. QPSK, Viterbi r=/2,k=4 A method () 6; Eb/No [db] Fig.2 Comprison of combining methods with bit error probbility chnnel, nd rice(s) is the probbility density function of Ricin fding. (b) Approximte Clcultion of PAWGN The reltion of bit error probbility fter Viterbi decoding (Pout) to tht before decoding (Pi,) which is chnnel bit error probbility in AWGN, is shown in Fig.3. Since Pout nd Pi, hve liner reltion in logrithmic scle, Pout is given by Eq.(2). Pout= k.p i", (2) where k nd m re constnts, nd Pi, is given for theoreticl bit error probbility of QPSK modultion nd coherent detection by Eq43). Pi, = +rfc( m7k) (3) (c) pdf of Ricin fding with diversity The probbility density function (pdf) of received signls in Ricin fding chnnel is where PAWGN(S) is the bit error probbility in n AWGN

3 2 VTB r=?b,k=? 3 A TCBPSK l6sttes db 5dB brnch] db w ' 4 L 5 5dB brnch2 db 5dB Sclcctlve dlvsrslty 9 6 O 3 * Pin l Fig.3 Reltion between bit error probbilities before nd fter Viterbi decoding. where A2/22 is the Ricin fctor C/M, nd the distribution function is Rice(s)= rice(x)dx (5) When 2brnch selective diversity is dopted for Ricin fding chnnel, the pdf, p,,l(s) nd the distribution function, P,,l(s) re given by Eq.(6) nd (7). psei(s)=2.rice(s).rice(s) (6) Psel(s)={Rice(s)]* (7) nd in the cse of mximl rtio combining, the pdf, p(s) nd the distribution function, Pcom(s) is given by Eq.(8) nd (9). Pcom(S)= rice(x).rice(m).d x (8) Pcom(S)= Pcom(S).dX (9) These cumultive distribution functions, Rice(s), Psel( s), Pco,,,(s), nd n exmple of simulted fding in C/M=lOdB re illustrted in Fig.4. (d) Pe Performnce Clcultion Substituting p,,l(s), or pcom(s) for rice(s) in Eq.(l) yields bit error probbility when using 2brnch diversity. Clcultion results for QPSK modultion nd coherent detection with r=/2,k=4 Viterbi decoding re shown in Fig.5, nd previous simultion dt by diversity methods, (), (b), (c) re lso plotted in this grph. Clculted curves pproximtely fit the simultion dt except for diversity method (b), selection in ACS output of Viterbi lgorithm. n the diversity method (b), it is considered tht diversity improvement is obtined not only for fding but lso somewht for AWGN from the pth memcs selection in ACS output. n consequence, simultion dt of method (b) gets db 5dB rl.\* Y m +r c CZ 2 Mximl rtio comblnlng E Time Csl () Simultion exmple, C/M=lOdB, fd=lhz _ E Receive signl level (reltive) CdBl (b) Cumultive probbility distribution function. Fig.4 Probbility distribution of Ricin fding. P) simultion no diversity A method () i method (b) method (c) Eb/No CdBl Fig.5 Approximte nlyzed Pe performnce. \

4 , n lo; Eb/NO [db] Fig.6 Diversity improvement with correltion of fding s prmeter. better thn the model performnce of conventionl selective diversity. 4. EFFECT OF CORRELATON BETWEEN DVERSTY BRANCHES Prior to this section, the received signls from the two diversity brnches in Ricin fding chnnel re supposed to be uncorrelted. n prctice, however, there is no position t which the two diversity ntenns cn yield uncorrelted signls. n previous repod8) on se surfce reflection fding, coefficient of correltion ws found to be bout.3 when the two ntenns re seprted by few multiples of the wve length in the verticl direction. The diversity improvement in Pe performnce with correltion of fding s prmeter is shown in Fig.6, where the diversity method (c), previterbi decoding combining, is dopted nd other prmeters re the sme s in Fig.2. As seen from this figure, the improvement with diversity degrdes less thn db when the coefficient of correltion is less thn.3. Therefore, this diversity method is effective in prcticl situtions such s under se surfce reflection fding. 5. APPLCATON TO TRELLS CODED MODLATON () Appliction to TC8PSK The diversity method (c), previterbi decoding combining, is considered for trellis coded modultion. n conventionl convolutionl coding nd Viterbi decoding, brnch metrics re clculted bsed on the Hmming distnce. On the other hnd, in coded modultion, they re bsed on Eucliden distnce. Therefore, mximl rtio combining for coded modultion is relized by weighting the received signls in the signl stte spce. 3 (,,, combining (2brnch) 't os s : mu t i ion coh dif no diversity A method (c) O+ h:, \,,,,,, Eb/No CdBl Fig.7 Anlyzed nd simulted Pe performnce of 6sttes TCSPSK with diversity. Simultion results of trellis coded 8PSK modultion nd coherent detection / differentil detection using 6 sttes ngerboeck code(9) with the diversity method (c) re shown in Fig.7, where C/M=lOdB, f~t=8xlo~. As in the previous pproximte nlysis, clculted Pe performnces re shown using the reltion of Pe before nd fter decoding in Fig.3, where Pi, is 8PSK demodulted bit error performnce. n this simultion, idel CS (chnnel stte informtion) is ssumed. The improvement of required Eb/No t Pe=4 with the proposed diversity scheme is 7dB over tht with no diversity in both coherent detection nd differentil detection. Furthermore, the Pe performnce of differentil detection with the diversity scheme is superior to tht of coherent detection without it. (b) Comprison of TCSPSK nd QPSK with High Codingrte Viterbi Decoder Above mentioned, TC8PSK with predecoding combining diversity shows significnt improvement in Pe performnce in the simultion results. Especilly, TC8PSK modultion nd coherent detection hs both efficient frequency use nd good Pe performnce in Ricin fding chnnels. An 8PSK coherent demodultor, which is ssumed to be idel in the simultion, is, however, quite difficult to operte stbly in low C/N nd Ricin fding environments. Therefore, differentil detection tends to be dopted for mobile stellite systems(). For QPSK, new coherent demodultion techniques(lw*) hve been proposed for mobile stellite systems nd stisfctory performnces were reported in Ricin fding chnnel with C/M=lOdB. Consequently, QPSK coherent detection nd conventionl Viterbi decoding with high codingrte nd high codinggin, for exmple, r=7/8, K=7('), cn be cndidte for mobile stellite systems

5 2 4 Ebl'No CdB () D/=OdB. Fig.8 Pe performnce comprison of A bit error probbility performnce comprison of TC8PSK (6sttes) nd QPSK coherent detection with r=7/8, K=7 Viterbi decoding by the previous pproximte nlysis is shown in Fig.8 for Ricin fding chnnel with C/M=lOdB. n this comprison, supposing the following system prmeters; voice codec is 4.8kbps, chnnel spce is SlrHz, nd frequency stbility in mobile sttion is 5~.~ in Lbnd, thus, the TC8PSK system opertes in.4bpshz frequency efficiency nd for the QPSK system, djcent chnnel interference (AC) with.6bps/hz is considered becuse in QPSK with r=7/8 Viterbi decoding, required frequency bnd is 87 times s wide s TC8PSK which hs no bnd expnsion. n clcultion of AC effect, =.5 roll off bnd limited nd liner chnnel is ssumed. Even in the cse of D/=SdB, which is desired signl level difference from djcent chnnel signls, Pe performnce of QPSK coherent detection with r=7/8 Viterbi is degrded only db from TC8PSK coherent detection nd it hs n dvntge of 2dB over TC8PSK differentil detection. Considering difficulty of stble opertion, or degrdtion cused by phse error of 8PSK coherent demodultion in Ricin fding chnnel, it is not wrong to select QPSK modultion nd coherent detection with r=7/8 Viterbi decoding for mobile stellite communiction systems. 6. CONCLSON n this pper, diversity combining methods for convolutionl coded nd softdecision Viterbi decoded chnnels in mobile stellite communiction systems re evluted. t is clrified tht the previterbidecoding mximl rtio combining hs the best performnce in Ricin fding chnnels by computer simultion, nd Pe performnces derived from the nlysis model using the probbility density function of Ricin fding nd the bit error Q 2 Eb/No CdBl (b) D/=SdB. TCSPSK nd QPSK with r=7/8 Viterbi decoding. probbility performnce of Viterbi decoding in AWGN chnnels gree with the simultion results. Furthermore, this diversity method is pplied to TC8PSK nd QPSK with high codingrte Viterbi decoding. n consequence, QPSK modultion nd coherent detection with high codingrte Viterbi decoding cn be n ttrctive cndidte for mobile stellite systems s well s TC 8PSK. ACKNOWLEDGMENT The uthors wish to thnk Dr. H.Ymmoto nd Mr. K.Morit for their encourgement nd helpful guidnce, nd Mr. T.Dohi for his ssistnce during the computer simultion runs. REFERENCES () S.Kubot, et l. : "Generl purpose highspeed convolutionl encoder / Viterbi decoder.", The trnsction of ECE, Jpn. J72B, pp (2) S.Hr, et l. : "Postdetection combining diversity improvement of 4 phse DPSK system in mobile stellite communictions.", The trnsction of ECE, Jpn. 572B2, pp (3) L.F.Chng, et l.: "Diversity selection using convolutionl coding in portble rdio communictions chnnel.", GCOM87, 2.3. Tokyo.987. (4) T.Kohri, et l. : "Mximum likelihood receiver for building block bse sttion structure.", Ntionl Conf. of ECE, Jpn. B (5) K.Kog, et l. : "Signl combining method using FEC technique in diversity stellite communiction.", The trnsction of XECE, Jpn. 68B. pp , (6) TSki, et l., : "Softdecision Viterbi decoding with diversity combining.", MSC'9, Ottw, pp.224, 99. (7) C.Loo, : "Digitl trnsmission through lnd mobile stellite chnnel.", EEE Trnsction on Communiction, COM38, pp ,99. (8) S.Kozono, et l. : "Switch nd sty diversity effect on mritime mobile stellite communiction.", The trnsction of ECE, Jpn. J64B. pp (9) G.ngerboeck, : "Chnnel coding with multilevel/phse signls.", EEE Trnsction on nformtion Theory. T28. pp () T.C.Jedrey, et l. : "The MSATX MARECS B2 stellite experiment : grnd segment results.", GCOM89, Dlls, pp , 989. () S.Yoshid, et l. : "A new coherent demodultion technique for lndmobile stellite communictions.", MSC9, Ottw, pp , 99. (2) K.Kobyshi, et l. : "DCF reverse modultion type crrier recovery circuit crrier recovery circuit for Ricin fding chnnel.", Report of Tech. Group, ECE, Jpn, SAT92, pp.924,