Synchronization with DMT Modulation

1. Synchronization with DMT Modulation Milos Milosevic The University of Texas at Austin ESPL October 1, 1999

2. S/P FFT IFFT P/S FEQ DAC h(t) ADC s(t) s(t) fs fs Discrete Multitone Modulation Symbol DMT Transceiver 2N samples n Cyclic prefix

3. Delay D Delay D = integer partD + fractional parte • sample synchronization • frequency alignment of RX and TX sampling clocks • estimates D • symbol synchronization • insures that proper symbols are fed to the FFT

4. Tone k n * n T h(t) w The Effect of D • ideal synchronizer delays RX symbol clock 2 samples w/r to TX symbol clock

5. p/8 Transmitted symbol e=.5T p/4 n To FFT p/4 The Effect of e • sample phase shift 0 e  T => rotation of FFT outputs • delay-rotor property

6. The Effect of Frequency Offset D Df < 0 +T mth symbol m + 1 Time -T Df > 0 • RX clockfs -TX clockfsDf 0 => frequency offset • timing error increases linearly, intercarrier interference (ICI) is generated • longer DMT symbols are more sensitive to Df • if Df not minimized the TX and RX clocks will desynchronize

7. Basic PLL Operation + + a cos(wlokT+qk) fk= qk- qk Phase detector b cos(wlokT+qk) Z-1 VCO qk+1= qk+ kvcofkfk Dfk = Dfk+1+ bfk - frequency offset qk+1= qk+ afk + Dfk - phase increment fk - phase error

8. Single Pilot Synchronization SNR spectrum 1 se2 pilot << 4p2fn2SNR wlo w • pilot - sinusoid of a known mid-band frequency (ADSL ~ 64KHz) • bandpass filtering achieved using the FFT • gives a very accurate PLL reference input signal • RX modem samples at expected zero-crossings => phase error fk • the variance of the timing error can be estimated using • clock accuracy from 1-2% for ISDN down to 0.1% for ADSL

9. Phase Offset Correction • PLL produces a sampling phase offset f • The signal with timing error v( t+f ) => V( f ) e-j2p ff • single complex rotation of (2p/n)fn radiansper carrier • simple, but not correct entirely; Df => all samples have different phase offset (wide-band signal) • f ~ average of all fn ; more accurate for a shorter symbol

10. Frequency Offset Correction Duplicated sample Duplicate process 2N samples n n-1 2N samples 2N samples n Skip process n 2N samples n+1 2N samples n 2N samples Skipped sample • if Df so that the induced delay  to one sample period T a sample is skipped/duplicated in the cyclic prefix • Df is adjusted accordingly

11. Ad Hoc Symbol Synchronization D h(t) w(n) w(n) n 2N 2N+n n n Window for ad-hoc low-complexity estimation Window for min ICI+ISI w(n) n n n Window for NDA ML estimator • ML criterion not optimal; optimal max. capacity criterion - complex • try minimizing average ICI + ISI power V(D)  n w(n)h2[(n+D)T] • choose a window w(n) that will satisfy the desired criterion • estimate D • requires the knowledge of h(n)

12. Maximum Likelihood Symbol Synchronization RX 2N+n 2N+n 2N+n n X X X S D • maximizing an AWGN likelihood function • search for D that produces the function maximum • not useful for e estimation

13. Sync Symbols • known symbols embedded in the signal • used to determine the symbol being transmitted • in ADSL they occur every 69th frame (T1.413) • generated by pseudorandom binary signals mapped to 4-bit constellation • location determined using correlation maximum