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
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 Peak amplitude
Non-linearity degrades performance
Extended linear range is more expensive
Peak amplitude
xmax = max( |x(t)| ) <t<T
Digital xmax vs Analog xmax
Range of DAC/ADC
Range of PA
Peak power
Pmax = max( |x(t)|2 ) <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 = 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 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

9. Reading
Cioffi Ch. 4.10