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 Carrier phase offset 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’

Peak Power/Amplitude The linear range of TX/RX circuits Peak amplitude Non-linearity degrades performance Extended linear range is more expensive Peak amplitude xmax = max( |x(t)| ) 0<t<T Digital xmax vs 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

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)

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

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

Zero extension No cyclic prefix Make P circulant in RX 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

Reading Cioffi Ch. 4.10