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关于DVB-S2系统的64,128,256APSK的软解调算法
EFFICIENT SOFT DEMODULATION SCHEMES FOR THE DVB-SZX SYSTEM 2.2. Hard decision threshold-based soft demodulation It was proved that for BPSK, the SDBi using the ml soft estimation can be described as the weighted schemes, the SDBI for the ith bit, L(bilr), can be represented as follow. s ideato higher modulation distance between the detected symbol and the hdt line [lo]. Extending thi L(bier)=pbi where p=2 h 2/o is a weighing factor and bi is the distance between the detected synbol, s rh/hl and the corresponding HDT line. This method is called the HDT-based soft demodulation scheme For conventional quadrature amplitude modulation(QAM) and phase shift keying modulation schemes, the hDT-based scheme requires only a single distance calculation per bit, so its complexity is O(1). In addition, the performance of the hdT-based scheme approximates that of the ml,even with higher-order modulation schemes up to 256-QAM [91 However. for the apsk schemes defined in the dvb-s2. the hdt-based method shows non negligible performance degradation. The performance degradation of the hdT-based scheme has been shown to be mainly because of over-estimation of the SDBI, and the application of a proper scaling actor contributed to enhance the performance [10]. The scaled HIT-based method can be represented by the following L(bir)=pbi where p'=2 hl/0/m is a weighting factor 3. DERIVATION OF SDBI USING THE HDT-BASED SOFT DEMODULATION SCHEME 3.1. 64-amplitude and phase shift keying Three different 64-APSK constellations are specified in the DVB-S2X and are referred to as 4+12+20+28-APSK,8+16+20+20-APSK, and 16+16+16+16-APSK, respectively [3]. For example, 4+12+20+28-APSK is the modulation scheme with four rings, and 4, 12, 20, and 28 sym bols are allocated in the first to the fourth rings, respectively. In the following sub-sections, we illustrate the hDt lines for all six bits in a symbol using the constellation diagram specified in the dvB-s2X and derive the mathematical expressions to estimate the sdbi for each bit 000110|000100 010110 010110 010100 010010 000010 100110 100100 100000 110110 100 10010 101010 10L1C0 l0I010 l01000 11 1010 40100 111100 001010 01110011:10 0111003011 010110119 011001 事001(01 001011 101·011 秀011l010 4001001 111011 IN1 111001 101 111101 101011 10111 101001 110001 101001 II00l1要 10011 11000 100011 10111 10:101 fied 00001l 000011 Simplified 0/011 Origina) 010111 HIDT lines 010l1 0011000101 010101 H 11001 HDT lines (a)b1 (b)b2 Figure 1. Hard decision threshold (HDT) lines for bI and b2 of 4+12 +20+28-amplitude and phase shift keyin Copyright C 2015 John Wiley Sons, Ltd Int J. Satell. Commun. Network (2015) DOI:10.1002/sat M. ZHANG AND S. KIM 3.1..4+12+20+28-amplitude and phase shift keying. The constellation diagram of the 4+12 +20+28-APSK defined in the dvB-S2X is shown in Figures 1-3 3, where Ri indicates the radius of the ith ring from the center. In Figure 1, the hdt lines for b1 and b2 are presented as in(a) and(b), respectively. We note that the HDT lines, HI and H2 for b1 and b2, are simplified in order to avoid excess discontinuous points in the middle, as indicated in Figure 1(a), where the original hDT line for b, is denoted with a dotted line Using the hdt-based method, the SDBl, L(b:), is estimated by(3), and thus the distance between the detected symbol and the corresponding HDT line, bi, should be estimated. Referring to the hDT lines in Figure 1, b1 and b2 can be written as follows if|s(s)≤L1 min136-L1,2/}-8l}, else if≤m2,0≤ min{3()-L1,| s sin(江-θ)}, else if|$‖>rl3 14 (5) min{rza3-1|,(G)-L1}, else if 5|≤ra3,0>证, ax{ra3-||.|sin(汪-0)} else if‖S‖>ra3,6> 00010000100 010110 0]0100 iOI 010010 01000 00000 000010 U30000 100100 100110 0U01 10UU10 11110 100003 110010 110310 101010 10000 l01110 10100 l11010 111000 11010 l11000 1.1110r l1100 001010011010au10/9011000 01190110费 0010011010 0011l0ou 0C,01100 01000 0001901oM1o °01110·011001 001011101l 010100 1101011 10100 11 夏l1111 111001 /inn 1011 101101 11001】 101011 110011 110001 l000l1 110111 110101 100011 100111100101 11 000011 00001 000011 Simplified 〔1001 Simplified C10001 IDT lines C10011 010001 HDT lines 010111 0001010101 004c1 (b)b4 Figure 2. Hard decision threshold (HdT) lines for b3 and b4 of 4+12+20+28-amplitude and phase shift keying 00011000010 0010000 010110 010100 010110 010100 U1UOIO 010000 010010 010000 000000 000010 000000 100100 l00110 100130 l10l10 l10100 100010 110110 10100 10010夏 101010 霄110000 101000 101010/ 110C10. 10000 101000 01010110001181110 l11010 1110 111110 b“…·S 11001110 100b 00100 0111001004901000c0101 01100110010109 011100 0]000 00010190110 Toon>oll10010000101. o1111i\ 00. 111 our,0101100 4001001 11011l x1111 01111) l11101 111001 101011 101111 0110t 110001 10100 10101 /10111110101 110011 l100l 101001 10)011 110111 n1001 1101110 100101 11 000011 000011 010011 一010001 HDT lines 010011联 010001 HDT line 0101 l0101 o0111000101 00110010101001 (b)b6 Figure 3. Hard decision threshold (HDt) lines for bs and b6 of 4+12+20+28-amplitude and phase shift keying Copyright C 2015 John Wiley Sons, Ltd Int.. Satell Commun. Network(2015) DOI:10.1002/sat EFFICIENT SOFT DEMODULATION SCHEMES FOR THE DVB-SZX SYSTEM where (S)and S(s) are the real and imaginary parts of S, respectively, and 6= tan (S(S)/S(S)) LI is the average distance of the symbols in the set $t from the real axis, that is, LI setl ((s)/8, where 51 =(58, $12, $24, 528, 540, 544, $56, S60 and si is a symbol with the decimal value of i, for example, a symbol with a binary mapping of 001000 is denoted by sg. Id; is the average radius of Ri and Ri+1, that is, rd,=(Ri+Ri+1)/2 9(s)|-L2 if9(s)≤L2, min {9(G)-L2,ra3-‖1}, else if|s≤ra3,0≤2 62=max{ra3=1|3si=2 else if|ls‖>rd3,b≤分 (6) min19()|-L IISl j0 else if|s‖≤ra,>2 min{9()-L2,|剑‖sin(-2)}, else if 5>rd3,b>, where L2 is the average distance of the symbols in the set cl from the imaginary axis that is, L2 s∈(9t( )/8and3={s4,s12,s20,528,s36.4,.2,6 In Figure 2, the HDt lines for b3 and b4 are presented in(a)and(b), respectively. Similar to H1 and H2, we simplified HDT lines for b3 and b4, which are denoted as H3 and H4, respectively. Referring to these hdT lines, b3 and b4 can be written as follows L3-|3(S), There L3 is the average distance of the symbols in the set sl from the real axis, that is,L3 e((s)/8andi={832,s36,540,44,s4,.92,56,560) b4=L4-19H(3) where L4 is the average distance of the symbols in the set sa from the imaginary axis, that is, L4 ∑se((s)/8and={16,520,524,528,S48,52,56,560 In Figure 3, the HDT lines for bs and b6 are presented as Hs and H6 in(a) and(b), respectively Referring to these hdt lines, bs and b6 can be written as follows b5=-9(3) 10J100 1010 R 0010l L00l01 x/20 101001 101I0 10010 LUOUO⊥ 01110 100110 0000l 101111 R10011 101111 11 10100100g1o00-0y100 11101101011 0100 a1000l1 l11001 011夏 100000 110001 101010 01010 111011 lloo鬥 l111011 1010101101 0101101010102001001 110111010110 101000101100101l 10101010010000 °ouo.ol01101 01010 0110001000 010101 ●l0011 001010 00010 001010 001000 a000011 o11c0 1011 00060y101 10001 001I 1 inal 60011l HDT lin 00110 00010l 001101 000101 HDT lines 001100 Figure 4. Hard decision threshold (HDT) lines for bI and b2 of 8+16+20+20-amplitude and phase shift keying Copyright C 2015 John Wiley Sons, Ltd Int J. Satell. Commun. Network (2015) DOI:10.1002/sat M. ZHANG AND S. KIM Even with the simplified HDT lines for b1 to b4, many discontinuous points exist in Hi to H4 which will incur computational complexity for comparison operations and will eventually degrade the performance 3. 1.2. 8+16+20+20-amplitude and phase shift keying. The constellation diagram of 8+16 +20+20-APSk as defined in the dvB-S2X is shown in Figures 4-6[3]. In Figure 4, the HDT lines for b1 and b2 are presented as Hi and H2 in(a) and(b), respectively, where H2 is a simplified hdt line. Referring to the hdt lines in Figure 4, b1 and b2 can be written as follows: b1=、(), 72-|3(s) if|sl≤rad s sin( else if e≤ (12) 0), else if 0> where T2=s(rd,es)=rd, sin(5) 10110 100101 「R 01110 100110 1011l l00110 10000l 0111 00111 1111101011 77 10001 1101000×d 100 10001S11000 101010 11101 10010 111101 10000o01o011+ 11010u00109 100010 0010101001 丌/151 10100°01010·01011o10l01 0111101110 0101000101109010111 u·Q00、010o000 00001 010010 U01010 Cl0310 010011 010011 0010 0000 00101 0110001)X 005000 0000 o1100 00100000000 000l 00001 00111 000111 001001 0c0110 Original 00 001001 Simplified HDT lines O0OIDT Ii nes C01101 00l0l 00l100 003100 001100 0001C0 b Figure 5. Hard decision threshold(HDT) lines for b3 and b4 of 8+16+20+ 20-amplitude and phase shift keying 101100 l00100 l01100 10000 1011 100101 101101 0111 100001 01001 l00001 10011 10111 100111 111001 01011 1000 11C001 10 11090110100010 l01010 100011 110011 111010 111101 1111011 b101010)1101011110 1111101100 01011+011010c×R. 00010110·oo1 o01011001110o+0n1o0 15z≠米R00y10o100l 011010 1101y00100500 0100) 001011 00100 01000I 11001 00010001000 00111 00111 0010010 00:100010 OooooPriginal Original HDT lines IDT lines 001101 000101 0011010 000101 10 H6 (a)b5 Figure 6. Hard decision threshold (HDt) lines for bs and b6 of 8+16+20+20-amplitude and phase shift keying Copyright C 2015 John Wiley Sons, Ltd Int.. Satell Commun. Network(2015) DOI:10.1002/sat EFFICIENT SOFT DEMODULATION SCHEMES FOR THE DVB-S2X SYSTEM In Figure 5, the HDt lines for b3 and b4 are presented as H3 and H4 in(a) and(b), respec tively, where H4 is a simplified HDT line. Referring to these HDT lines, b3 and b4 can be written as follows (13) Sin ifs(s)≤T4,(3)≤T4 74-|3(3 if3($)≤T4,沉(3)>4, max 74-1G),-1e-11. Ise if ss rd2,6 (14) max ( -Tda -rd,: -ll le l, else if Td2, 6>10 max{si(O-语,74-13(3)}, lse if s‖ 6≤ |S‖ ),|3-ra2 Ise if‖Ss‖ where T4 =s(rdi e4)=rdi sin(4) In Figure 6, the HDT lines for bs and b6 are presented as lIs and 16 in(a)and(b), respectively Referring to these hdt lines, bs and b6 can be written as follows: if|s‖≤ra1,≤ rd,e. if|"≤ra1,6>3 min di, SIn 8)) if S≤ra2,6≤ maX (S -ra2,|ssin(3-b),ifa1<|剑‖≤ra2,0>3, (15) n(ra3-|s‖,ra2e 2<‖S≤ra3,6≤ nn(a3-1|S‖,|S‖-ra2) if s if < 6≤ if|s‖≤ra2,b (16) min{lsin(3-6),|s-ra2},if|s‖>ra2,0≤3 S‖sin(2x-0) if|s‖>ra2,6>3 L00010 100110 100010 1101010010 10110 110010 110011 0111 100L0 3 100001 010110 110101 Q111100 010111 010101 1001009110100 0y6100000 10010000 01000 0000 010100 00l100 101100 111100 1101 01010· 14011001 I1l101 11001 101101 111111 l1011 lI 101001 1011010 11111010 1011l1 d101011 Original 101011 Original HDT lines HDT lines 10111 l01010 101110 01010 Figure 7. Hard decision threshold(HDT) lines for b1 and b2 of 16+16+16+16-amplitude and phase shift kcving Copyright C 2015 John Wiley Sons, Ltd Int J. Satell. Commun. Network (2015) DOI:10.1002/sat M. ZHANG AND S. KIM We applied the simplified HDT lines for b2 and 64. Like 4+12+20+28-APSK, even with simplified HDT lines, there are still many discontinuous points in the hDT lines, which will incur computational complexity for comparison operations and will eventually degrade the performance. 3.1.3. 16+16+16+16-amplitude and phase shift keying. The constellation diagram of 16+16+16+ 16-APSK as defined in the dvB-S2X is shown in Figures 7-9 [3]. In Figure 7, the hDT lines for b1 and b2 are presented as Hi and H2 in(a)and(b), respectively. Referring to the HDT lines in Figure 7, b1 and b2 can be written as follows 17 rd3 (18) 100010 100:10 100010 10011 RA C00l1 10011 R 110110 110010 11010 110010 100101 l10111 R l00 100001 110111 R11001 100001 010l 110101 1100 11010 010l11 01001110 010101 ●B001010 0:0101B b 100100110100 000101 000001 410000 000001 110000·100000 01010000 100100◆110100 010000 01009000 010000 01010 l00100 0l1100 011000 01100 01000● 0:1c04110 001l01 100om00 l11000a101 011101·00 001011011001 01100◆11100 011101Q00l 011·011001 111101 6101111 111101 1to t o1 11010 1111 111011 01001 o16 l010 111011 01001 l111l 111010 111110 101111 dolo Original original 10111 010ll HINT lines HDT lines 101010 Figure 8. Hard decision threshold(HDt) lines for b3 and b4 of 16+16+16+16-amplitude and phase shift key 1001:1 R 100011 1001:1 R 100011 110110 010 100101 R 100 10010 101yo01000 10101/0101 010011110y 01010 01000l 0l01p 10100●10100 0000C1 110000·100 100100●110100 oo10000Q 010100(00XLZi 1100001000 E010 001100 1011011 00110l 1100010100 011101. 0 10110·1110 ·e\0010 11000·101000 011,011 11110 610N110 11100o 6 111001 011lr 101101 l1010 ↑10No 01101 l111 ll1010 1011110 To1o11 Original 101111 Origina HDT lines HDT lines 0l110 0010 10110 10010 ×H 米B6 Figure 9. Hard decision threshold (HDT) lines for bs and b6 of 16+16+16+16-amplitude and phase shift keying Copyright C 2015 John Wiley Sons, Ltd Int.. Satell Commun. Network(2015) DOI:10.1002/sat EFFICIENT SOFT DEMODULATION SCHEMES FOR THE DVB-SZX SYSTEM In Figure 8, the HDT lines for b3 and b4 are presented as H3 and H4 in(a) and(b), respectively Referring to these hDt lines, b3 and b4 can be written as follows (19) 9() (20) In Figure 9, the HDT lines for bs and b6 are presented as H5 and H6 in(a) and(b), respectively Referring to these hdt lines, bs and b6 can be written as follows: sin d- 兀 We note that all of the hdt lines for this 16+16+16+16-apsK are continuous. so the sdbi can be estimated using a single distance calculation per bit. Because of these compact HDT lines, the performance of the HDT-based scheme for this 16+16+16+16-APSK more closely approximates that of the ml scheme than do the 4+12+20+2 8-apsk and 8+16+20+ 20-apsk this will be confirmed later in the simulation results 3. 2. 128-amplitude and phase shift keying The constellation diagram of 128-APSK as defined in the dvB-s2X is shown in Figures 10-13 3 For simplicity, not all of the details of the binary mappings are presented in the constellation diagram Instead, we only indicate the parts allocated for 0 and 1 in the corresponding bit and the HDt lines In Figure 10, the HDt lines for bI and b2 are presented as Hi and H2 in(a) and(b), respectively Referring to the hdt lines in Figure 10, b1 and b2 can be written as follows 23) 9() 24 R2 RA b1 R Original Original e HdT lines HDT lines (a)b1 (b) b2 igurc 10. Hard dccision threshold(HDT) lincs for b and b2 of 128-amplitudc and phasc shift keying Copyright C 2015 John Wiley Sons, Ltd Int J. Satell. Commun. Network (2015) DOI:10.1002/sat M. ZHANG AND S. KIM 0 0 Original original HDT lir nes .HDT lines 米 Figure 11. Hard decision threshold (HDT) lines for b3 and b4 of 128-amplitude and phase shift keying 0 R W Original HDT lines IDT lines 0 (b)b6 Figure 12. Hard decision threshold (HDT) lines for bs and b6 of 128-amplitude and phase shift keying In Figure ll, the hdt lines for b3 and b4 are presented as H3 and Ha in(a)and (b), respectively Referring to these HDT lines, b3 and b4 can be written as follows 兀 sin (25) sin (26) In Figure 12, the HDt lines for bs and b6 are presented as Hs and h6 in(a)and(b), respectively. Referring to these hdt lines, bs and b can be written as follows b d5 rds t (27) Copyright C 2015 John Wiley Sons, Ltd Int.. Satell Commun. Network(2015) DOI:10.1002/sat

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