SOFT ESTIMATES FOR DOUBLY ITERATIVE DECODING FOR 16 QAM AND 64 QAM MODULATION

BULETINUL INSTITUTULUI POLITEHNIC DIN IAŞI Publica de Universiaea Tehnică Gheorghe Asachi din Iaşi Volumul 62 (66), Numărul 2, 2016 Secţia ELECTROTEHNICĂ. ENERGETICĂ. ELECTRONICĂ SOFT ESTIMATES FOR DOUBLY ITERATIVE DECODING FOR 16 QAM AND 64 QAM MODULATION BY ANA-MIRELA ROTOPĂNESCU *, LUCIAN TRIFINA and DANIELA TĂRNICERIU Gheorghe Asachi Technical Universiy of Iaşi Faculy of Elecronics, Telecommunicaions and Informaion Technology Received: June 6, 2016 Acceped for publicaion: June 30, 2016 Absrac. In order o increase he specral efficiency, a bi inerleaved coded modulaion can be combined wih a high order modulaion scheme like Phase Shif Keying (PSK) and Quadraure Ampliude Modulaion (QAM), improving he communicaion sysem s performance. In his paper, we derive and explain he sof esimaes for a doubly ieraive decoder using space-ime urbo codes and a large number of ransmi and receive anennas for 16 QAM and 64 QAM modulaion used in a mobile communicaion sysem. Key words: space-ime urbo codes; doubly ieraive decoder; sof esimaes; QAM; FER performances. 1. Inroducion The use of muliple anenna ransmission echniques increases he specral efficiency of wireless sysems. (Biglieri e al., 2005) presened a block scheme for a doubly ieraive receiver, based on he minimum mean square error (MMSE) crieria (Biglieri e al., 2003). A new scheme has been presened wih a significanly reduced complexiy for a large number of ransmi and receive anennas, compared o previous scheme proposed by Sefanov and Duman (Sefanov & Duman, 2001). Since he large number of anennas * Corresponding auhor: e-mail: mroopanescu@ei.uiasi.ro

32 Ana-Mirela Roopănescu, Lucian Trifina and Daniela Tărniceriu increases he receiver complexiy, a spaial inerference canceling scheme is used, ensuring a good compromise beween complexiy and performance. A higher order modulaion scheme gives he advanage ha larger daa raes and beer specral efficiency for radio communicaions sysems are obained. The disadvanage is ha he performance of he ieraive receivers depends criically on he size of he signal consellaion and a high order modulaion scheme is less robus o noise and inerference. This leads o performance degradaion. In Secion 2 we recall he sysem model consising of he ransmier and he receiver block scheme. In Secion 3 we analyze 16 QAM and 64 QAM modulaion schemes, specifying heir characerisics, advanages and disadvanages. In Secion 4, we derive he sof esimaes for 16 QAM and 64 QAM modulaions. In Secion 5 we analyze he simulaion resuls and Secion 6 concludes he paper. 2. Sysem Model We consider he same mobile communicaion sysem as in (Roopanescu e al., 2012) wih N ransmi and N r receive anennas. The informaion bis are urbo-coded wih coding rae R c and block size of N N symbols, where N is he number of successive ransmissions from he ransmi anennas, corresponding o a codeword. The inpu signal from he modulaor oupu, is ransmied by anenna i, 1 i N, a each ime insan. The specral efficiency refers o he informaion rae ha can be ransmied over a given bandwidh in a specific communicaion sysem. The specral efficiency is equal o R c MN, where R c is he coding rae of he urbo code. The ransmier block scheme is presened in Fig. 1 and performs a coded modulaion wih bi inerleaving and anenna diversiy as described in (Caire e al., 1998). The receiver block scheme (Trifina e al., 2011) uses MMSE ieraive algorihm and a linear MMSE inerface (Roopanescu e al., 2012) and i is given in Fig. 2. The used urbo decoding algorihm is he Max- Log-APP. Fig. 1 Transmier block scheme. Fig. 2 Receiver block scheme.

Bul. Ins. Poli. Iaşi, Vol. 62 (66), Nr. 2, 2016 33 The linear MMSE inerface used by he receiver consiss in a linear filer modeled by a marix ha minimizes he mean square error. The filered signal is ransmied o he inerference canceling block. The exrinsic sof esimaes of ransmied bis are provided by he urbo decoder as a logarihm likelihood raio (i.e. he logarihm of he raio of he probabiliies ha he bi is eiher 1 or 0): Pci, 1 Lci, ln (1) Pci, 0 and knowing ha P c 0 1 P c 1, (2) i, i, we have Lc 2Pci, 1 1 anh 2 where x x e e anh( x) x x e e is he hyperbolic angen funcion. 3. QAM Consellaion i,, (3) QAM is exensively used as a modulaion scheme for digial elecommunicaion sysems. Arbirarily high specral efficiencies can be achieved wih QAM by seing a suiable consellaion size, limied only by he noise level and lineariy of he communicaions channel. A moivaion for he use of QAM comes from he fac ha QAM schemes are more bandwidh efficien. Considering a higher-order QAM consellaion, i is possible o ransmi more bis per symbol. However, if he mean energy of he consellaion remains he same, he poins mus be closer o each oher and hus hey are more suscepible o noise and oher corrupion. The QAM consellaion poins are normally arranged in a square grid wih equal verical and horizonal spacing, so ha he mos commonly used QAM consellaions have a number of poins equal o a power of 4, such as 4 QAM, 16 QAM, 64 QAM, 256 QAM, and so on. In general, he number of poins of he QAM modulaion is 4 m = 2 2m, where he number of he bis in each consellaion symbol is M = 2m (m is an ineger). In his paper, we use he 4 QAM modulaion, hus he number of ransmied bis per symbol is M = 2 (m = 1), 16 QAM, hus M = 4 (m = 2), and 64 QAM, wih M = 6 (m = 3). The poins are represened in a complex plane having he in-phase componen on he real axis and he quadraure componen on he imaginary axis. For a general QAM consellaion he used alphabe symbols are chosen of he form: (4)

34 Ana-Mirela Roopănescu, Lucian Trifina and Daniela Tărniceriu QAM M M 2 2 2 p 1 2q 1 j, where p 1,..., and q 1,...,. (5) 2 2 For 16 QAM, he symbols used are chosen from he se 16 QAM 1 j, 13 j, 3 j, 3 3 j and he average energy is E 16 QAM = 10. Fig. 3 presens he signal consellaion for 16 QAM modulaion using he Gray coded bi-mapping. Fig. 3 Bi mapping for 16 QAM signal consellaion. 64 QAM is ofen used in digial cable elevision and cable modem applicaions. In he Unied Saes, 64 QAM is one of he mandaed modulaion schemes for digial cable. In he UK, 64 QAM is used for digial erresrial elevision. For 64 QAM, he symbols used are chosen from he se 1 j, 13 j, 15 j, 17 j, 3 j, 3 3 j, 3 5 j, 3 7 j, 64 QAM 5 j, 5 3 j, 5 5 j, 5 7 j, 7 j, 7 3 j, 7 5 j, 7 7 j and he average energy is E 16 QAM = 42. Fig. 4 presens he signal consellaion for 64 QAM modulaion using he Gray coded bi-mapping.

Bul. Ins. Poli. Iaşi, Vol. 62 (66), Nr. 2, 2016 35 Fig. 4 Bi mapping for 64 QAM signal consellaion. Knowing his and having a 1/2 global rae, he specral efficiency is 32 bis/s/hz for 16 QAM modulaion and 48 bis/s/hz for 64 QAM modulaion, in he case of 16 ransmi anennas. 4. Sof Esimaes for 16 QAM and 64 QAM In (Trifina e al., 2011) he associaions beween he hree and four bi sequences from he consellaion and he complex values of symbols are given for 8 PSK and 16 PSK modulaion, respecively. Here, we presen he four and six bi sequences from he consellaion and he complex values of symbols for 16 QAM and 64 QAM modulaion. From he above explanaions, i is reasonably inuiive o guess ha he scaling facor of 1 10 and 1 42 will be used in 16 QAM and 64 QAM consellaions, respecively, for normalizing he average ransmi power.

36 Ana-Mirela Roopănescu, Lucian Trifina and Daniela Tărniceriu For 16 QAM he associaions beween he consellaion bi sequences and he complex values of he symbols are: 0000, 1000 Amp 1 j 0001, 1001 Amp 3 j 0010, 1010 Amp 13 j 0011, 1011 Amp 3 3 j 0100, 1100 Amp 1 j 0101, 1101 Amp 3 j 0110, 1110 Amp 13 j 0111, 1111 Amp 3 3 j where: Amp 1 10. We assume ha c2i 1,, c 2 i,, c2i 1,, c2i 2, are he four bis in he sequence associaed o he symbol. c2i 1, is he firs bi and gives he sign of he real par of he complex number represening he sof esimaes. If his bi is 0, hen he sign of he real par is posiive, and if he bi is equal o 1, he sign of he real par is negaive. The second bi c 2 i,, gives he sign of he imaginary par of he complex number. If he bi is 0, hen he sign of he imaginary par is posiive, and if he bi is 1, he sign of he imaginary par is negaive. The sign of he real and he imaginary pars of he sof esimaes is esimaed by he quaniy 1 2Pc2i 1, 1 and 1 2P c2 i, 1, respecively. If one of hese bis is 1, he probabiliy of ha bi o be 1 is equal o 1 and if he bi is 0, hen, he probabiliy of ha bi o be 1 is equal o 0. For example, if c2i 1, = 0, hen Pc2i 1, 1 0 and he sign of real par is given by he sign of he expression 1 2P c2i 1, 1 = 1. Also, if 2 i, P c2 i, 1 1 and he sign of he c = 1, hen imaginary par is given by he sign of 1 2Pc2 i, 1 = -1. c2i 1, is he hird bi and gives he ampliude of he imaginary par of he sof esimaes. If he bi is 0, he ampliude of he imaginary par is equal o 1. Oherwise, if he bi is 1, he ampliude is 3. In he same way, he fourh bi, c2i 2,, gives he ampliude of he real par of he sof esimaes. If he bi is 0, he ampliude of he real par is equal o 1 and if he bi is 1, he ampliude is 3. The ampliude of he imaginary par and he ampliude of he real par are 1 2P c2i 1, 1 1 2P c2i 2, 1, esimaed by he quaniies and respecively. For example, if c2i 1, = 1, hen 2i 1, 1 1 P c, meaning ha he

Bul. Ins. Poli. Iaşi, Vol. 62 (66), Nr. 2, 2016 37 ampliude of he imaginary par is 1 2Pc2i 1, 1 3 c i Pc2i 2, 1 0 and he ampliude of he real par is Pc2i 2,. Also, if 2 2, = 0 hen 1 2 1 1. In his example, for c2i 1, c 2 i, c2i 1, c 2i 2, = 0110, he complex value is 11 1 3 j 1 3 j. According o he above consideraions and using eq. (3), he sof esimaes for 16 QAM are given in he nex formula: x, Amp 1 2 2 1, 1 1 2 2 2, 1 1 2 2, 1 1 2 2 1, 1 i P c i P c j P c P c i i i 2 1, 2 2, 2, 2 1, i i i i L c L c L c L c Amp anh anh 2 j anh anh 2 2 2 2 2 For 64 QAM, he associaions beween he consellaion bi sequences and he complex values of he symbols are: 000000, 100000 Amp 1 j 010000, 110000 Amp 1 j 000001, 100001 Amp3 j 000010, 100010 Amp 7 j 000011, 100011 Amp5 j 000100, 100100 Amp 1 3 j 000101, 100101 Amp3 3 j 000110, 100110 Amp 7 3 j 000111, 100111 Amp5 3 j 001000, 101000 Amp 1 7 j 001001, 101001 Amp 3 7 j 001010, 101010 Amp 7 7 j 001011, 101011 Amp 5 7 j 001100, 101100 Amp 1 5 j 001101, 101101 Amp 3 5 j 001110, 101110 Amp 7 5 j 001111, 101111 Amp 5 5 j 010001, 110001 Amp3 j 010010, 110010 Amp 7 j 010011, 110011 Amp5 j 010100, 110100 Amp 1 3 j 010101, 110101 Amp3 3 j 010110, 110110 Amp 7 3 j 010111, 110111 Amp5 3 j 011000, 111000 Amp 17 j 011001, 111001 Amp 3 7 j 011010, 111010 Amp 7 7 j 011011, 111011 Amp 5 7 j 011100, 111100 Amp 15 j 011101, 111101 Amp 3 5 j 011110, 111110 Amp 7 5 j 0101111, 111111 Amp 5 5 j where: Amp 1 42. We assume ha c2i 1,, c 2 i,, c2i 1,, c2i 2,, c2i 3, and c2i 4, are he six bis in he sequence associaed o he symbol. c2i 1, is he firs bi and gives he sign of he real par of he complex number. If his bi is 0, he sign of he real par is posiive and if he bi is 1, he sign of he real par is negaive. The second bi c 2 i,, gives he sign of he (6)

38 Ana-Mirela Roopănescu, Lucian Trifina and Daniela Tărniceriu imaginary par of he complex number. If his bi is 0, he sign of he imaginary par is posiive, oherwise, if he bi is 1, he sign of he imaginary par is negaive. The sign of he real par is esimaed by he sign of he quaniy 1 2P c2i 1, 1 and he sign of he imaginary par is esimaed by he sign of he expression 1 2Pc2 i, 1. If one of hese bis is 1, he probabiliy of ha bi o be 1 is equal o 1 and if he bi is 0, he probabiliy of ha bi o be 1 is equal o 0. For example, if 2i 1, P c2i 1, 1 1 and c = 1, hen 1 2P c2i 1, 1 1, hus he sign of he real par is negaive. Through he same analogy, if c 2 i, = 1, he sign of he imaginary par is also negaive. The ampliude of he real and imaginary par is given by a group of wo bis. Thus, he hird and fourh bi, c2i 1, and c2i 2,, give he ampliude of he imaginary par, and he fifh bi ogeher wih he sixh bi, c2i 3, and c2i 4,, give he ampliude of he real par. We denoe he firs and he second bi, respecively, from a group of wo bis, by b 1 and b 2, respecively. Then, he ampliude value is given by he nex formula: 1 0 A 1 2 2 Pb1 1 2 Pb1 b2 1. (7) The XOR of wo bis is 1 only when one of hem is 0 and he oher one is 1. Thus, he probabiliy ha XOR of he wo bis is 1 is given by: 1 2 1 1 0 2 1 1 1 2 0 Pb1 0Pb2 1 P b1 1 Pb2 0 1 Pb1 1 Pb2 1 P b1 11 Pb2 1 Pb 1 Pb 1 2Pb 1 P b 1. P b b P b b P b b 1 2 1 2 In (8) we assumed ha he wo bis, b 1 and b 2, are independen. This assumpion is valid, aking ino accoun ha he codeword a he urbo encoder oupu is inerleaved by a random inerleaver wih large enough lengh. Wih (8), he ampliude in (7) becomes: 1 0 A 1 2 2 Pb1 1 2 Pb1 1 Pb2 1 2Pb1 1 Pb2 1 4 1 4Pb1 1 2Pb1 1 2Pb2 1 4P b1 1 Pb2 1 9) 1 6Pb 1 2Pb 1 4P b 1 Pb 1. 1 2 1 2 As i was menioned above, he hird and fourh bi, c2i 1, and c2i 2,, give he ampliude of he imaginary par. If c2i 1, is 0 and c2i 2, is 0, hen he ampliude of he imaginary par is equal o 1, bu if c2i 1, is equal o 0 and c2i 2, o 1, he ampliude of he imaginary par is equal o 3. Also, if c2i 1, is 1 and c2i 2, is 0, hen he ampliude of he imaginary par is equal o 7 and if c2i 1, (8)

Bul. Ins. Poli. Iaşi, Vol. 62 (66), Nr. 2, 2016 39 is 1 and c2i 2, is 1, he ampliude of he imaginary par is equal o 5. The ampliude of he imaginary par is esimaed by he quaniy 1 6 P c 1 2 P c 1 4 P c 1 P c 1. For example, for 2i1, 2i2, 2i1, 2i 2, c i = 0, he probabiliies P c2i 1, 1 1 and i c2i 1, = 1 and 2 2, P c2 2, 1 0, so ha he ampliude of he imaginary par is 1 61 20 410 7. In he same way, he fifh bi ogeher wih he sixh bi, c2i 3, and c2i 4,, give he ampliude of he real par. If c2i 3, is equal o 0 and c2i 4, o 0, hen he ampliude of he real par is equal o 1 and if c2i 3, is 0 and c2i 4, is 1 hen he ampliude of he real par is equal o 3. If c2i 3, is equal o 1 and c2i 4, is 0, hen he ampliude of he real par is equal o 7 and if c2i 3, is 1 and c2i 4, is 1, hen he ampliude of he real par is equal o 5. The ampliude of he real par is esimaed by he quaniy 1 6Pc2i3, 1 2Pc2i 4, 1 4P c2i3, 1 P c2i4, 1. For example, for c2i 3, = 0 and 2i 4, probabiliies P c2i 3, 1 0 and 2i 4, 1 1 c = 1, he P c, so ha he ampliude of he real par is 1 6 0 21 401 3. For he given example, for c2i 1, c 2 i, c2i 1, c 2i 2, c 2i 3, c 2i 4, = 111001, he complex number is 13 1 5 j 3 7 j. According o he above consideraions and using equaion (8), he sof esimaes for 64 - QAM are given in he nex formula: x i, Amp 1 2P c2 1, 1 i 1 6Pc2 i3, 1 2Pc2 i4, 1 4Pc2 i3, 1 Pc2 i4, 1 j1 2 Pc2, 1 i 1 6Pc2 i1, 1 2Pc2 i2, 1 4Pc2 i1, 1 Pc2 i2, 1 2i1, 2i3, 2i4, L c L c L c Amp anh 4 anh 2 anh 2 2 2 2 i, 2i1, 2i2, L c L c L c j anh 4 anh 2 anh. 2 2 2 5. Simulaion Resuls (10) In his paper, he simulaions were performed for 4 QAM (M = 2), 16 QAM (M = 4) and 64 QAM (M = 6), considering he same scenario as in (Roopanescu e al., 2012). The urbo encoder uses a random inerleaver of lengh Len = 2,080 for 4 QAM and 16 QAM modulaions and of lengh 2,112 for 64 QAM modulaion. The global rae of he urbo code is 1/2 (wih alernaive puncuring of

40 Ana-Mirela Roopănescu, Lucian Trifina and Daniela Tărniceriu pariy bis), he forward and feedback generaor polynomials are (5, 7) in ocal form, and he inerleaver beween he urbo encoder and he serial o parallel converer is a random one. We considered a number of 16 ransmi and 16 receive anennas. The space-ime codeword is a marix wih 16 rows (he number of ransmi anennas) and 130 columns for 4 QAM, 65 columns for 16 QAM, and 44 columns for 64 QAM. The number of disinc blocks wih consan fading, F, is equal o 1. In all hree cases, he urbo decoder uses he Max-Log-APP algorihm, described in (Trifina e al., 2011), and performs maximum 10 ieraions. The sop crierion is genie sopper. To cancel spaial inerference, here was used a number of k = 0, k = 1 and k = 4 ieraions. In (Trifina e al., 2011), an analysis was performed o evaluae he influence of he exrinsic informaion scaling coefficien denoed by s on he BER/FER performance of he sysem wih QPSK modulaion. I ranges from 0.6 o 1 wih he sep 0.05. As in (Roopanescu e al., 2012), we consider he same exrinsic informaion scaling coefficien ha performs he bes FER and BER performance. For k = 0, we have considered he scaling coefficien s = 0.9, for k = 1, s = 0.8 and for k = 4, s = 0.75. The Mone Carlo simulaion resuls are given in Figs. 5,,7 for 4 QAM, 16 QAM, 64 QAM, respecively, using k = 0, 1 and 4. These figures show he performance of he MMSE receiver hrough FER, versus signal-onoise raio per bi ( Eb N 0 ). For every modulaion, we observe from simulaions ha he coding gain increases proporionally wih he number of double ieraions k, as we will analyze furher. Increasing he ieraion number of he MMSE ieraive decoder up o 4, leads o improved performances. In (Biglieri e al., 2005) i was shown ha furher increasing he number of ieraions does no lead o addiional performance improvemen. Also, we observe from simulaion resuls ha for k = 4, he double ieraions inroduce relaively more errors compared o k = 1, and he supplemenary coding gain obained for k = 4 is smaller han he one achieved when k = 1. From simulaion resuls, we observe he performance degradaion. We can see ha i is a grea difference in FER performances beween all hree modulaions. There is a coding gain up o 6.44 db for 4 QAM compared o 16 QAM and up o 9.68 db for 16 QAM compared o 64 QAM. For he same FER value, equal o 2 10 4, we analyze all hree modulaions for differen number of ieraions. From Table 1 we can see ha for 4 QAM he supplemenary coding gain is 3.31 db for k =1 compared o k = 0 and 0.05 db for k = 1 compared o k = 4. The coding gain is beer for k = 1 compared o k = 4 a FER = 2 10 4 since he error floor phenomenon is more pronounced for k = 4 han for k = 1. However a FER = 2 10 3, a 0.4 db supplemenary coding gain is achieved for k = 4, compared o he performance when k = 1, as i was shown in

Bul. Ins. Poli. Iaşi, Vol. 62 (66), Nr. 2, 2016 41 (Roopanescu e al., 2012) for QPSK modulaion (which is he same wih 4 QAM). For 16 QAM, he coding gain is 3.61 db for k = 1 compared o k = 0 and 0.32 db for k = 4 compared o k = 1. Thus, he oal coding gain achieved for 16 QAM is 3.93 db. For 64 QAM, for he proposed FER value, he resuling coding gain is 3.30 db for k = 1 compared o k = 0 and 0.55 db for k = 4 compared o k = 1, and he oal coding gain for 64 QAM is 3.85 db. Table 1 SNR Values (db), for a Given Value FER = 2 10 4 SNR, [db] k = 0 k = 1 k = 4 4 QAM 2.29 5.60 5.55 16 QAM 4.15 0.54 0.22 64 QAM 13.52 10.22 9.67 Because 4 QAM modulaion is he same as QPSK, he FER performances for his modulaion and differen number of ieraions are he same as by Roopanescu e al., (2012), Fig. 6. Therefore, we do no give hem separaely in his paper. In Fig. 8 we analyze he FER performances for differen number of ieraions and 16 PSK and 16 QAM modulaions. The resuls expressed in SNR are given in Table 2. The used number of ieraions is k = 0, k = 1 and k = 4, in order o see he performance difference beween hem. Table 2 SNR Values (db), for a Given Value FER = 2 10 4 SNR, [db] k = 0 k = 1 k = 4 16 PSK 7.10 3.42 2.95 16 QAM 4.15 0.54 0.22 Assuming a value FER = 2 10 4, for k = 0, he obained coding gain is 2.95 db for 16 QAM compared o 16 PSK. When k increases he supplemenary coding gain slighly decreases. Thus, for he same FER value and k = 1 he coding gain is 2.88 db for 16 QAM compared o 16 PSK. Also, for k = 4, for he proposed FER value he supplemenary coding gain is 2.73 db for 16 QAM compared o 16 PSK. Also, comparing he resuls obained for he same modulaions bu differen number of ieraions, we see ha for 16 PSK he supplemenary coding gain is 3.68 db for k = 1 compared o k = 0 and 0.47 db for k = 4 compared o k = 1. As i was shown above, for 16 QAM he obained coding gain is 3.61 db for k = 1 compared o k = 0 and 0.32 db for k = 4 compared o k = 1. In Fig. 9 we analyze he FER performances for 64 QAM and for

42 Ana-Mirela Roopănescu, Lucian Trifina and Daniela Tărniceriu differen number of ieraions. The resuls are given in he las line of Table 1. We consider he same value, FER = 2 10 4. The coding gain obained for k = 1 compared o k = 0 is 3.30 db and is larger han ha obained for k = 4 compared o k = 1, which is 0.55 db. This means ha he supplemenary coding gain obained for k = 4 is smaller han he one achieved when k = 1, explained by he fac ha for k = 4, he double ieraions inroduce relaively more errors compared o k = 1. Fig. 5 FER performances for 4 QAM, 16 QAM and 64 QAM when k = 0. Fig. 6 FER performances for 4 QAM, 16 QAM and 64 QAM when k = 1.

Bul. Ins. Poli. Iaşi, Vol. 62 (66), Nr. 2, 2016 43 Fig. 7 FER performances for 4 QAM, 16 QAM and 64 QAM when k = 4. Fig. 8 FER performances for 16 PSK and 16 QAM for k = 0, 1, 4.

44 Ana-Mirela Roopănescu, Lucian Trifina and Daniela Tărniceriu Fig. 9 FER performances for 64 QAM for k = 0, 1, 4. 6. Conclusions In his paper we deermined and explained he sof esimaes needed for a doubly ieraive decoder for space-ime urbo codes on a quasi-saic fading channel, considering 16 QAM and 64 QAM modulaions, respecively. Transmiing more bis per symbol is possible if he order of modulaion is increased. In his way, much higher daa raes and beer specral efficiency are obained for ransmission communicaion sysems. Hence, for 16 ransmi anennas, he specral efficiency is increased, from 16 bis/s/hz for 4 QAM modulaion o 32 bis/s/hz for 16 QAM and o 48 bis/s/hz for 64 QAM modulaion. A disadvanage is ha he increased order of QAM modulaion inroduces a degradaion of he FER performances. The simulaions were performed for a Max-Log-APP urbo decoding algorihm in a sysem using a spaial inerference canceling inerface (ieraive MMSE receiver). We used a doubly-ieraive decoding process, scaling boh he exrinsic informaion of he urbo decoder and he informaion a he inpu of he inerference canceling block. The number of ieraions are k = 0, k= 1 or k = 4 used o cancel spaial inerference. The scaling coefficien used for performing he simulaions is s = 0.9 for k = 0, s = 0.8 for k = 1, and s = 0.75 for k = 4. Increasing he number of ieraions he FER performances are improved. So, for 4 QAM a supplemenary coding gain up o 3.31 db can be achieved, for

Bul. Ins. Poli. Iaşi, Vol. 62 (66), Nr. 2, 2016 45 16 QAM up o 3.93 db and for 64 QAM up o 3.85 db. The degradaion of he FER performances is shown in simulaion resuls, as we can see a large difference in coding gain beween modulaions, up o 6.44 db for 4 QAM compared o 16 QAM and up o 9.68 db for 16 QAM compared o 64 QAM. REFERENCES Benedeo S., Divsalar D., Monorsy G., Pollara F., A Sof-Inpu Sof-Oupu APP Module for Ieraive Decoding of Concaenaed Codes, IEEE Communicaions Leers, 1, 1, 22-24 (1997) Biglieri E., Nordio A., Taricco G., Subopimum Receiver Inerfaces And Space-Time Codes. IEEE Transacions on Communicaions, IEEE Transacions on Signal Processing, 53, 5, 773-779 (2003). Biglieri E., Nordio A., aricco G., Doubly Ieraive Decoding of Space Time Turbo Codes wih a Large Number of Anennas, IEEE Trans. on Communicaions, 53, 5, 773-779 (2005). Caire G., Taricco G., Biglieri E., Bi-Inerleaved Coded Modulaion, IEEE Trans. on Informaion Theory, 44, 3, 927-946 (1998). Roopănescu A.-M., Trifina L., Tărniceriu D., Sof Esimaes for Doubly Ieraive Decoding wih 8-PSK and 16-PSK Modulaions, Frequenz, 66, 3-4, 101-107 (2012). Trifina L., Tărniceriu D., Roopănescu A.-M., Influence of Exrinsec Informaion Scaling Coefficien on Doubly-Ieraive Decoding Algorihm for Space-Time Turbo Codes wih Large Number of Anennas, Advances in Elecrical and Compuer Engineering, 11, 1, 85-90 (2011). Sefanov A., Duman T. M., Turbo-Coded Modulaion for Sysems wih Transmi and Receive Anenna Diversiy over Block Fading Channels: Sysem Model, Decoding Approaches, and Pracical Consideraions, IEEE J. on Seleced Areas in Communicaions, 19, 5, 958-968 (2001). ESTIMAŢII SOFT PENTRU DECODARE DUBLU ITERATIVĂ PENTRU MODULAŢIA 16 QAM ŞI 64 QAM (Rezuma) În scopul creşerii eficienţei specrale, o modulaţie codaă cu inercalarea biţilor poae fi combinaă cu o modulaţie de ordin ridica cum ar fi Phase Shif Keying (PSK) şi Quadraure Ampliude Modulaion (QAM), îmbunăăţind asfel performanţa sisemului. În aces aricol, derivăm şi explicăm esimaţii sof a decodorului dublu ieraiv folosind codurile urbo spaţio emporale şi un număr mare de anene de ransmisie şi recepţie penru modulaţia 16 QAM şi 64 QAM uilizaă înr-un sisem de comunicaţii mobile.