10GBASE-T T PAM Scheme: Fixed Precoder for all Cable Types and Lengths
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1 10GBASE- PAM Scheme: Fixed Precoder or all Cable ypes and Lengths IEEE P80.3an ask Force Portland, July 1-16, 004 Gottried Ungerboeck 1
2 Key points One ixed precoding response, h (D), suices or all cable types & lengths. h (D (D)) is designed or worst case conditions: maximum cable length + ANEX + AWGN. Decision-point SNR increases rapidly with shorter cable length despite precoder mismatch causing non-minimum colored noise.
3 Contents Assumed modulation and coding 10GBASE- cable model extensions One pair model o PAM transmission scheme Choice o ixed precoding response h (D) SNR vs cable length with optimum precoding and with ixed h (D), assuming ideal X and RCV ilters Practical X and RCV ilters SNR vs cable length with practical X and RCV ilters Feed-orward equalizer (FFE): required span Precoder simulation Conclusions 3
4 Assumed modulation and coding 1. RS(55,39) + 8-PAM 4d 16st CM 39/55 x 11/4 =.5775 bit/sym x Mbaud =.5 Gbit/s per pair Minimal decision-point SNR required or BER 10-1 : SNR req 0 db. RS(55,39) + 1-PAM 4d 16st CM 39/55 x 13*/4 = bit/sym x 80.7 Mbaud =.5 Gbit/s per pair Minimal decision-point SNR required or BER 10-1 : SNR req 3 db 3. RS(55,39) + 16-PAM 4d 16st CM 39/55 x 15/4 = bit/sym x Mbaud =.5 Gbit/s per pair Minimal decision-point SNR required or BER 10-1 : SNR req 6 db Interleaving: NxI row-column interleaving o RS bytes + periodic interleaving o J CM encoded symbol streams (N = 55, I = 4-8; J = 4-8). * 13 = loor( log (1 4 /) ) 4
5 10GBASE- cable models variable-length length cable models Complex-valued cable-transer unction G C ( [Hz], l j / 6 lγ( ) /10 / 0 s s [m]) = e 10 ; γ( ) = 4 connectors Rd + 1/ jπc propagation constant dielectric loss R skin eect s = 00MHz; L= 0.5mH/m,C= 50pF/m: Z0 L/C = 100Ω, v = 1/ LC = jπl 6 m/s Expected alien-nex squared magnitude unction G A ( [Hz], l [m] ) = 10 8 X1+.5 S log10 /10 /10 NEX attenuation [db] ( ) 4 1 G (, l) ; S = C dependence on length 10, 15, Model #1 (Cat 7, shielded), 100 m cabtyp ClassF : R s =9.48 Ω/m, R d =1.7 mω/m, X1=60 db Model # (Cat 6, unshielded), 55 m cabtyp ClassEu :R s =9.85 Ω/m, R d =3.5 mω/m, X1=47 db Model #3 (Cat 6, shielded), 100 m cabtyp ClassEs :R s =9.85 Ω/m, R d =3.5 mω/m, X1=6 db 5
6 Fitting cable Model # R R s j / s s s = 00 MHz L = 0.5µ H / m R d = 9.85 Ω / m = 3.5 mω / m C = 50pF/ m Cable model #3, in MHz : IL = 1.05 (1.8 Average PS-ANEX + 0.5/ ) F db
7 10GBASE- PAM transmission model (one pair) a(d) + M k(d) = b(d) kn Z s.t. M xn < M modulation symbols in expanded constellation Encoding a(d) M -PAM M k(d) h(d)-1 x(d)= b(d)/h(d) D A C ransmit ilter (F) H () (t) x h(d) = l 0 h D,h 0 = 1 l l h(d) n (Sel NEX & FEX) Alien NEX AWGN ( N0) n(t) PSD : N( ) Cable G C (,l ) Decoding z(d) = b(d)+ e(d) -spaced equalizer (FFE) g E (D) y(d) A D C Receive ilter (RF) G R () x R (t) n + τ 7
8 ransmit power spectral density (X PSD) Modulation rate = 80.7 Mbaud, P = 5 dbm X PSD rom ideal F: S (; 0.05,0.5,0.5) 1 x 10-8 spectral null at dc, zero excess bandwith ( = /) = 0.05 = 0.50 = = 0.5 MHz = MHz = MHz Area : P 3.16 = mw cosine roll- o sin roll-o x = / 8
9 Signal-to to-noise ratio unction SNR() = 80.7 Mbaud, P = 5 dbm, ideal F S (; 0.05,0.5,0.5) cabtyp ClassEs, cablen = 100m, ANEX + AWGN (N 0 = -140 dbm/hz) SNR() = N 0 S + S () G C () G (, l) A (, l) x 10 8 / 9
10 Optimal precoding response (=FBF coes o ideal DFE) = 80.7 Mbaud, P = 5 dbm, ideal F S (; 0.05,0.5,0.5) cabtyp ClassEs, cablen = 100m, ANEX + AWGN (N 0 = -140 dbm/hz) Optimal precoding response h(d) = 1+ h1d + h D L... optimal in MMSE sense or assumed X ilter, cable, noise... obtained by spectral actorization SNR A * () + 1= h(d = SNR -1 )A mmse wm h(d) 10 log 10 h(d) D= exp( jπn ) 10
11 Fixed rational precoding response h (D) (D) h = (1 D)(1+ D) ( D)(1 0.75D)(1 0.5D) zeroes: α 1 = + 1 α = 1 Fixed rational precoding response h (D) 10 log 10 h (D) D= exp( jπn ) poles: β 1 = + 15/16 β = + 3/4 β 3 = + 1/ 11
12 Precoder or rational precoding response h (D) h (D) = ( (1 D)(1+ D) 3 D)(1 D)(1 4 1 = D) D 99 D+ D D 3 h (D) 1 = D D+ D D D 3 D 3 3 b1d + bd + b D = 3 1 a D a D a D a(d) + mod M b 1 x b x b 3 x D x(d) b b b 1 3 = = = = = = D + D + D a 1 x a x a3 x a a a 1 3 = = = = = =
13 Results on SNR vs cable length: next 5 slides Common assumptions Ideal F S (; 0.05,0.5,0.5) P = 5 dbm; alien NEX + AWGN (-140 dbm/hz) receiver equalization: MF + mmse FFE (-spaced). Each slide showing two curves a) optimum h(d) or each cable length b) ixed h (D) 1. Cable type = ClassF, = 80.7 Mbaud (1-PAM). Cable type = ClassEu, = 80.7 Mbaud (1-PAM) 3. Cable type = ClassEs, = 80.7 Mbaud (1-PAM) 4. Cable type = ClassEs, = Mbaud ( 8-PAM) 5. Cable type = ClassEs, = Mbaud (16-PAM) 13
14 SNR vs cable length: optimal h(d) ) and ixed h (D) Cable type = "ClassF"; = 80.7MBaud (1- PAM) ; ideal F S (; 0.05, 0.5, 0.5); P = 5 dbm; alien NEX + AWGN (-140dBm/Hz) SNR mmseffe [db]: MF+ optimum h(d) ( MF + mmseffe = mmsewmf) or each length SNR MF+mmseFFE [db]: ixed h (D) 5 SNR req 3 db 6.07 db 5.46 db
15 SNR vs cable length: optimal h(d) ) and ixed h (D) Cable type = "ClassEu"; = 80.7MBaud (1- PAM) ; ideal F S (; 0.05, 0.5, 0.5); P = 5 dbm; alien NEX + AWGN (-140dBm/Hz) SNR mmseffe [db]: MF+ optimum ( MF + mmseffe = mmsewmf) h(d) or each length SNR MF+mmseFFE [db]: ixed h (D) 30 5 SNR req 3 db 8.6 db 6.81dB
16 SNR vs cable length: optimal h(d) ) and ixed h (D) Cable type = "ClassEs"; = 80.7MBaud (1- PAM) ; ideal F S (; 0.05, 0.5, 0.5); P = 5 dbm; alien NEX + AWGN (-140dBm/Hz) SNR mmseffe [db]: MF+ optimum h(d) ( MF + mmseffe = mmsewmf) or each length SNR MF+mmseFFE [db]: ixed h (D) 5 SNR req 3 db 5.50 db 4.95 db
17 SNR vs cable length: optimal h(d) ) and ixed h (D) Cable type = "ClassEs"; = MBaud (8- PAM) ; ideal F S (; 0.05, 0.5, 0.5); P = 5 dbm; alien NEX + AWGN (-140dBm/Hz) SNR mmseffe [db]: MF+ optimum h(d) ( MF + mmseffe = mmsewmf) or each length SNR MF+mmseFFE [db]: ixed h (D) 5 SNR req 0 db db 1.4 db 17
18 SNR vs cable length: optimal h(d) ) and ixed h (D) Cable type = "ClassEs"; = MBaud (16- PAM) ; ideal F S (; 0.05, 0.5, 0.5); P = 5 dbm; alien NEX + AWGN (-140dBm/Hz) SNR mmseffe [db]: MF+ optimum h(d) or each length 50 ( MF + mmseffe = mmsewmf) SNR MF+mmseFFE [db]: ixed h (D) 30 5 SNR req 6 db 8.35 db 7.84 db
19 Practical continuous-time time transmit ilter (F) Modulation rate = 80.7 Mbaud, P = 5 dbm Modiied 5th-order Butterworth ilter with spectral null at dc +0.5 ( /) 1 x j Area : P = 3.16 mw s N -plane Zeroes in sn-plane: b1= j x 10 8 Poles in sn-plane: a1= j a= j a3= j a4= j a5= j a6= j / 19
20 Practical continuous-time time receive ilter (prf( prf) Receive ilter: G R () G C (,l = 50m) o ClassEs cable U i R11 R 1 R 1 C 1 R C R 3 U o preliminary choice : R R R C = R = R = 100Ω = C 1 = 8Ω = 0.5Ω = 150pF 0 G ( ) = U R o / U i -10 0log10 G R ( ) [db] G R ( ) [rad] π / = MHz x 10 8 π 0
21 Results on SNR vs cable length: next slides Common assumptions F = modiied 5-th order Butterworth ilter with dc null P = 5 dbm; alien NEX + AWGN (-140 dbm/hz) Each slide showing three curves a) optimum h(d) or each cable length; MF + mmse FFE = mmse WMF b) ixed h (D); MF + mmse FFE c) ixed h (D); prf + mmse FFE with worst-case sampling phase 1. Cable type = ClassEs, = 80.7 Mbaud (1-PAM). Cable type = ClassEu, = 80.7 Mbaud (1-PAM) 1
22 SNR vs cable length: optimal h(d) ) and ixed h (D) Cable type = "ClassEs" ; = 80.7 MBaud (1 - PAM) ; F = modiied BW ilter with dc null; P = 5 dbm; alien NEX + AWGN (-140 dbm/hz) SNR mmseffe [db] : MF+ optimum h(d) ( MF + mmseffe = mmsewmf) or each length 45 SNR MF+mmseFFE [db]: ixed h (D) SNR + prf mmseffe [db]: ixed (worst - case sampling phase) SNR req 3 db h (D) 5.85 db 4.9 db 4.53 db
23 SNR vs cable length: optimal h(d) ) and ixed h (D) Cable type = "ClassEu" ; = 80.7 MBaud (1 - PAM) ; F = modiied BW ilter with dc null; P = 5 dbm; alien NEX + AWGN (-140 dbm/hz) SNR mmseffe [db] : MF+ ( MF + mmseffe = mmsewmf) optimum h(d) or each length 45 SNR MF+mmseFFE [db]: ixed h (D) SNR + prf mmseffe [db]: ixed (worst - case sampling phase) h (D) 30 5 SNR req 3 db db db db
24 Feed-orward equalizer (FFE): the only variable ilter Cable type = "ClassE s"; = 80.7 MBaud (1 - PAM) ; alien NEX + AWGN (-140 dbm/hz); practical transmit and Cable length 0 m 50 m P = 5 dbm; receive ilters 100 m scaled coes magnitude spectrum[db] 4
25 Precoder simulation: 8-PAM 8 using h (D) 8 - PAM symbols a n Precoder outputs x n Extended 8- PAM symbols bn : b(d) = x(d)h (D) 5
26 Precoder simulation: 8-PAM 8 using h (D) 0.15 a n 8-PAM; b n = a n + 8k n, k n Ζ such that -8 x k < 8, Empirical distributions rom 100'000 modulation intervals 0.15 Histogram o 8 - PAM symbols a n Distribution o precoder outputs x n k n = 3 = = 1 k n = 0 k n = + 1 k n = + k n = + 3 k n k n 0.05 Histogram o extended 8 - PAMsymbols b n
27 Conclusions One ixed precoding polynomial is suicient or all cable types and length. Perormance loss due to practical continuous-time X and RCV ilters is < 1 db. Further optimization o initial ilter designs may result only in small improvements. he only variable ilter is the eed-orward equalizer (FFE), which requires a time span o 3 to compensate or m variations in cable length (or one pair). Additional FFE span will be needed to cope with delay skew and FEX in a our-pair matrix FFE. 7
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