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OFDM Overview Divides high-speed serial information signal into multiple
lower-speed sub-signals: Transmits simultaneously at different frequencies in parallel.
Modulation ( BPSK, PSK,QPSK,16QAM, …). Pilot sub-carriers used to prevent frequency and phase shift
errors. Usage of cyclic prefix for lower multi-path distortion Controlled overlapping of bands in one channel Max spectral efficiency (Nyquist rate) Easy implementation using inverse FFTs Easy time-freq. Synchronization Modulate by switching between time and frequency domain
Some Assumptions Usage of cyclic Prefix Impulse response of the channel shorter
than Cyclic Prefix Slow fading effects so that the channel is
time-invariant over the symbol interval Rectangular Windowing of the transmitted
pulses Perfect Synchronization of transmitter and
receiver Additive, white, Gaussian channel noise
System Architecture (cont’d)1. Input to time domain2. Guard Interval 3. Channel4. Guard Removal5. Output to frequency
domain
6. Output
7. Channel Estimation
1,...,2,1,0 NnkXIDFTnx
1,...,1,0,
1,...,1,,NnnxNNnnNx
nx ggf
nwnhnxy ff
1,...,1,0 Nnnyny f
1,...,2,1,0 NknyDFTkY
1,...,1,0
Nk
kWkIkHkXkY
ICI AWGNChannel
1,...,1,0 NkkHkYkXe
e
Estimated Channel
Pilot for Channel EstimationTi
me
Carriers
Tim
e
Carriers
Comb Type: Part of the sub-
carriers are always reserved as pilot for each symbol
Block Type: All sub-carriers is
used as pilot in a specific period
Block-type Channel Estimation LS: Least Square Estimation
1
0
110
1
.
.
.
,...,,
N
N
LS
y
y
y
xxxdiagXwhereyXh
Comb-type Estimation
0,
1,...,1,.inflmpx
Lldata
lmLXkXNp pilot signals uniformly inserted in X(k)L=Number of Carriers/Np
xp(m) is the mth pilot carrier value
{Hp(k) k=0,1,…,Np} , channel at pilot sub-carriersXp input at the kth pilot sub-carrierYp output at the kth pilot sub-carrier
LS Estimate
1,...,1,0 pp
pp Nk
kXkY
kH
LMS Estimate
Xp(k) LMS + e(k)-
Yp(k)
Interpolation for Comb-type Linear Interpolation
Second Order Interpolation
Ll
mHLlmHmH
lmLHkH
ppp
ee
0
1
Nl
mpHcmpHcmpHc
c
c
c
where
lmLHkH ee
/
11011
,2
11
,110
,2
11
Simulation ParametersParameter Specifications
FFT Size 64Number of Carriers 64
Pilot Ratio 1/16
Guard Length 16
Guard Type Cyclic Extension
data rate of OFDM signal 1Mbps/sub-carrier
Signal Constellation 16QAM
Comb-LS Estimation Combating multipath rayleigh fading with RLS adaptive
equalization A detail simulation with MATLAB 20 multipath, random phase, and weibull distribution of
amplitutde
Sym
bol E
rror
Rat
e
Filter length .vs. Sample Rate
1. Keep the ratio of F/S, increase S2. Keep S, increase F.
Observed Symbol error rate with F ( filter length ) and S ( samples per symbol)
Conclusion OFDM System Introduction Block Type
Direct or Decision Feedback Comb Type
LS or LMS estimation at pilot frequencies Interpolation Techniques
Linear Second Order Time Domain
Modulation BPSK,QPSK,16QAM,DQPSK
Some Results: Comb Type performs better since it tracks fast fading channels. RLS algorithm vs. LMS algorithm