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Wideband Communications

Wideband Communications . Lecture 10-11: DMT Aliazam Abbasfar. Outline. Synchronization PAPR Freq EQ Zero prefix. Synchronization issues. Timing acquisition and Coarse frequency offset estimation Pilot symbols Timing offset timing synchronization errors Data rotation

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Wideband Communications

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  1. Wideband Communications Lecture 10-11: DMT Aliazam Abbasfar

  2. Outline • Synchronization • PAPR • Freq EQ • Zero prefix

  3. Synchronization issues • Timing acquisition and Coarse frequency offset estimation • Pilot symbols • Timing offset • timing synchronization errors • Data rotation • Carrier phase offset • Data rotation • Carrier frequency offset • mismatched oscillators, Doppler frequency shifts • Causes attenuation and ICI • y = diag{wak}kQLX; a=Dw/w0 • Sampling frequency offset : x[k] = y( k(T’+dt)) • y = Q’L X; w’ = w(1+a); a=dt/NT’

  4. Peak Power/Amplitude • The linear range of TX/RX circuits • Non-linearity degrades performance • Extended linear range is more expensive • Peak amplitude • xmax = max( |x(t)| ) 0<t<T • Digital xmaxvs Analog xmax • Range of DAC/ADC • Range of PA • Peak power • Pmax = max( |x(t)|2 ) 0<t<T • Peak to Average Power Ratio (PAPR) • Pmax / Pavg = max( |x(t)|2 ) / E[ |x(t)|2 ] • Peak to Mean Envelope Power Ratio (PMEPR) • PAPR <= PMEPR

  5. PAPR distribution • E[ |x|2 ] = E[ |X|2 ] = EX = S En • x = Q* X • xk : Gaussian distribution when N is large • Large values happens rarely • PAPR is different for DMT/OFDM symbols • P( PAPR > a ) = (xk > sqrt(a) sx) = Q(sqrt(a)) • a = 18 dB  1e-15 • a = 14.2 dB  1e-7 • a = 12.5 dB  1e-5 • Worst case : All Xn are co-phase (PAPR = N)

  6. PAPR reduction techniques • Clipping • Error in all tones • Spectrum re-growth • Reduce the probability of high peaks • SLM/PTS • Low overhead/High complexity • Reserved tones • min max |x + Q*C| • Linear programming • Iterative algorithms • 5-20% is good enough • Tone injection • Add levels to some tones • Extra power ( 5%) • No extra tones • Coding • Add redundancy to reduce PAPR • Coding gain • Data rates are low

  7. Frequency domain EQ • x is single carrier data stream + cyclic prefix • y = P x + n • P is circulant : P = Q* L Q • FFT the received samples • Qy = LQx + Qn • Equalize • L-1Qy = Qx+ L-1Qn • Convert it to time domain (IFFT) • Q*L-1Qy = x+ Q*L-1Qn • Low PAPR • No bit loading • Noise enhancement • Good for COFDM

  8. Zero extension • No cyclic prefix • Zero is sent in guard time • Make P circulant in RX • Add the CP to the beginning of the symbol • No wasted power in CP • Added noise in CP

  9. Reading • Cioffi Ch. 4.10

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