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ECE637 : Fundamentals of Wireless Communications
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OFDM Aliazam Abbasfar * N ... and space Diversity MIMO OFDM Synchronization issues Timing acquisition and Coarse frequency offset estimation Pilot symbols Timing ... – PowerPoint PPT presentation
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Title: ECE637 : Fundamentals of Wireless Communications
1
ECE637 Fundamentals of Wireless Communications
- Lecture 13,14,15,16
- Multi-carrier Modulation
- OFDM
- Aliazam Abbasfar
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Outline
- Multi-carrier Modulation
- Digital Multi-tone (DMT)/OFDM
3
Multi-carrier Modulation
- Used in wideband systems
- Frequency selective fading
- B gtgt Wc
- Divide data stream into N sub stream, each
- transmitted over a sub-channel with BNB/N
bandwidth - If N is big enough
- Narrowband/flat fading modulation
- BN lt Wc
- TN (sub-channels) gtgt Tm (delay spread)
- FDM system
- Multiple carrier frequencies
- Guard bands
- Spectrally inefficient
- Roll-off factor
- Time-limited pulses
4
Orthogonal sub-channels
- Sinusoids with different frequencies (in a period
of T) - Df n/T
- N complex sinusoids
- Multiple Sinc functions in spectrum
- Overlapping spectrums
- Sub-channels are not band-limited
- Bigger guard band
- Time and frequency offset problems
- Early HF modems (1970)
- OFDM/DMT foundation
5
Band-limited sub-channels
- Orthonormal sets
- ISI free Nyquist functions
- Root raised cosine functions
- If g(t) is a Nyquist function,
- g(t-kT)k is an orthonormal set
- g(t-kT) cos(wct)k
- g(t-kT) cos(witfi)k,i
- ISI and ICI free
- QAM modulation possible
- Staggered I and Q
- Sensitive to delay and phase
- Spectrally efficient
6
Digital Multi-Tone (DMT)Orthogonal Frequency
Division Multiplexing (OFDM)
- Send N symbols dn over N orthogonal sinusoids
in a period of TN - OFDM symbol
- dn can be complex symbols
- x(t) is baseband signal
- x(k/N TN) is IDFT of dn
- Transmitted signal
7
Cyclic prefix
- Discrete channel response h0, h1, ,
hL-1 - Extended TX signal samples xN-LN-1,
x0N-1 - xN-L, , xN-1 is cyclic prefix
- Cyclic prefix changes linear convolution to
circular convolution - y(t) h(t) ? x(t) ? yn hn ? xn
n0, , N-1 - DFTyn DFThn . DFTxn Hn . dn
- The first L-1 samples of y(t) are discarded
- Eliminates ISI form previous OFDM symbol
- Cyclic prefix is a guard time between OFDM
symbols - CP overhead L
8
Zero prefix
- Sends nothing (zero) instead of cyclic prefix
- No ISI
- Less transmitted power
- Add the received tail of each symbol to its
beginning to make circular convolution work - Additional noise (NL)/N 1 L/N
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OFDM in matrix form
- y H W d n
- H is convolution matrix
- With cyclic prefix yN Hc W d n
- Hc is circulant matrix Hc W L WH
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Frequency equalization
- yN Hc (Wd) n W L d n
- Frequency domain equalization
- Y WH yN L d WH n
- L-1 WH Y d L-1 WH n
- Noise enhancement
- Pre-coding
- yN Hc (W L-1 d) n Wd n
- WH Y d WH n
- Channel response needed in the TX
- Power allocation and bit loading needed
11
OFDM system block diagram
- Transmitter
- Receiver
12
OFDM performance
- Independent sub-channels
- Pi signal power in ith sub-channel
- Ni0 noise power in ith sub-channel
- dmin is a function of Pi and the constellation
- in ith sub-channel
- (dmin/2)2 3 Pi /(M2-1) (M-ary PAM)
13
Power allocation
- Power allocation to sub-channels
- Maximize capacity subject to power constraint
- Lagrangian technique
- Water filling
- Bit loading
- Power and data rate allocation
- Adaptive in fading channels
- Commonly used in ADSL
14
Channel estimation
- Channel estimate when data is known
- Using preamble
- Frequency domain
- WH y L WH x n
- Time domain
- y X h n
- h (XHX)-1 XH y
- Time and Frequency domain
- Tracking
- Pilot tones
- Time and
- Frequency interpolation
15
OFDM in fading channels
- Flat fading for sub-channels
- Coding in time, frequency, and space
- Diversity
- MIMO OFDM
16
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
17
Windowing
- Mitigates frequency offset problem
- Raised cosine
- Gaussian
- Done after cyclic extension
- Power spectrum
18
Peak to average power ratio
- Linear operation is needed for
- OFDM symbols
- Average power N Ps N A2
- Assume the same power
- for sub-channels (Ps A2)
- Peak power (NA)2
- PAPR N
- Limiting when N is large
- Large back-off in power amps (PA)
- PAPR distribution
19
PAPR reduction
- Clipping
- distortion (increase Pe)
- Spectral regrowth
- Symbol selection
- Peak cancellation
- Coding
20
Case study 802.11a/11g
- Wireless LAN
- Band 5 GHz (11g operates in 2.4 GHz)
- B 20 MHz
- N 64
- 48 used for data
- 12 outer tones not used
- 4 used as pilot tones
- BN 20 MHz/64 312.5 KHz
- CP 16 samples (16/20 0.8 usec)
- Delay spread lt 0.8 usec
- OFDM symbols 80 samples (80/20 4 usec)
- CP overhead 20
- The same modulation and coding for all
sub-carriers - Modulations BPSK, QPSK, 16QAM, and 64 QAM
- Convolutional code Rates ½, 2/3, and ¾
21
Reading
- Ch. 12 Goldsmith
- Ch. 1, 2 Bahai
