2.
OFDM Origins
•
•
•
•
OFDM is a modulation type whereby the information coming from a
single source is intentionally split up into many carriers (subcarriers) to
combat multipath effects and to add a dimension of “diversity” to the
transmit signal
Initial work in 1960s for military applications
OFDM stands for “Orthogonal Frequency Division Multiplexing”
– “Orthogonal” in the sense that each information-bearing subcarrier
may be demodulated without interference from adjacent
subcarriers
– “Frequency Division” in the sense that the subcarriers are
generated as frequency-disjoint coupled carriers with fixed spacing
and modulation type
– “Multiplexed” in the sense they are synthesized into a single
channel
Error-correction coding essential because some subcarriers may be in
deep fades so encoding of all information bits with interleaving
necessary
2
3.
OFDM-BASED SYSTEMS
•
•
•
IEEE 802.11a was the first wireless networking standard with
widespread usage in unlicensed 5 GHz band providing up to 54 Mbps
16.67 MHz wide channel containing 52 subcarriers with BPSK,
QPSK, 16-QAM, 64-QAM modulation on each subcarrier
OFDM “symbol rate” of 250 ksym/sec and up to 288 bits/symbol of
encoded information
IEEE 802.11g is a dual mode system fusing 802.11b WiFi and 802.11a
except at a lower frequency band (unlicensed 2.4 GHz)
UWB- Multiband OFDM is the leading contender for ultra-wideband
communications (>100 Mbps)
Hopped OFDM over three bands to spread energy for short range
high-speed communications
• Spatially diverse Vector OFDM (VOFDM)
•
•
•
Multiple Input/Multiple Output (MIMO) diversity to combat flat fading
Wideband Networking Waveform for military communications
4-G Cellular
IEEE 802.16 Metropolitan Area Networking--OFDMA
3
5.
Why Use OFDM?
• There are a few ways to cope with multipath channels:
Use spread spectrum techniques to allow separation of paths
Direct Sequence Spreading (CDMA/DSSS)—Low bps/Hz
Use Frequency Hopping (Bluetooth, GSM)—MAC inefficiencies/complex
Use high bandwidth single-carrier signal —Large delay spread vs Tsym
Use lower data rates to allow channel to be flat over signal bandwidth
• The problem is that the signal bandwidth needs to be as narrow as possible to
mitigate multipath (the symbol period needs to be as long as possible), Unless…
The signal is made bandwidth-inefficient in order to perform combining of
dispersed rays (e.g., RAKE combining)
The optimal signal would be one which has high bandwidth efficiency and
immunity to channel variations due to multipath
• Lower complexity equalization for given delay spread than single-carrier modulation
OFDM allows tightly packed carriers to convey information orthogonally
and with high bandwidth efficiency
5
6.
Equalization Complexity
• Let’s compare equalization complexity of a single carrier (SC) system with the same
total bandwidth as an OFDM system subject to similar channel conditions
Frequency domain equalization (via FFT) for OFDM Rx
Decision feedback equalization for SC Rx
• OFDM complexity grows slightly greater than linear with BW*Delay Spread product
• Single carrier complexity grows quadratically with BW*Delay Spread product
•Single Carrier Case
GMSK or OQPSK 24 Mbps
Delay Spread = 250 nsec
Requires 20 FF, 20 FB taps
•OFDM Case
QAM 52-OFDM 24 Mbps (QAM 16)
Delay Spread = 250 nsec
64 Point FFT
52 Subcarriers
Guard Interval = 800 nsec
Rsym = 250 kHz
FEEDFORWARD FILTER (FFF)
Cmplex
Data In
D
Tap 0
D
Tap 1
D
Tap 2
D
FEEDBACK FILTER (FBF)
Tap 3
D
[ . ]*
X
X
Tap FB2
+
X
From other Taps FFF
D
+
X
+
From FBF Taps
µLMS
+
Tap FB3
1 SPS
Error
Eq. Output
Slicer
Decisions
+
+
D(k) {Training,
Demod Decisions}
Tap FB1
Tap FB0
[ . ]*
µ4
6
Single Carrier DFE is 10 times as complex!!!
D
X
D
+
Adj Proc.
• GMSK Eq (LMS) = 2*20*24*10 (960E6) rmult/sec
• OFDM (radix 4)= 96*106 = (96E6) cmult/4µsec
= 96E6 rmult/sec
D
Tap 4
Peamble Sequence
6
Error
X
8.
Indoor Channels (Cont)
Small Room Fading (amb. Motion)
Tunnel Fading (amb. Motion)
k = 0 → Gaussian, k = ∞ → Rayleigh
k is the ratio of power of the direct path to the scattered paths
8
9.
Outdoor Channels
Tx Height=15 m, 3.5 GHz/Outdoor Vs Antenna Height—12 &15dBi antennas 3km Separation
9
16.
OFDM Channel Estimation
• Each subcarrier corrected by a single tap (complex) equalizer
• Typically have training symbols with to train frequency domain equalizer
• Sometimes have embedded pilot subcarriers that are used to estimate channel
Uniformly spaced throughout symbol to allow interpolation between
pilots to correct data-bearing subcarriers
• Data subcarriers corrected post-FFT in frequency domain
• Additional performance by weighting soft decisions based on channel estimates
16
18.
Insert
Short Train
Standard (52-Carrier) Mode Spectrum For Various Output Backoffs
10
0
-10
-20
-30
10 dB OBO
-40
12 dB OBO
-50
-60
Linear PA
-70
-80
-2.0E+7
-1.5E+7
-1.0E+7
-5.0E+6
0.0E+0
5.0E+6
Frequency (MHz)
1.0E+7
1.5E+7
-8 -6 -4 -2 0 2 4 6 8
-8 -6 -4 -2 0 2 4 6 8
-8 -6 -4 -2 0 2 4 6 8
I
1
I
Conv.
Encode
PN Data
0
Interleave
Subcarrier
Mapper
QAM Map Q
Add Cyclic
Prefix
IFFT
Spectral
Window
Digital
To
Analog
Polyphase
Interpolate
Oscillator
Phase Noise
Effects
PA
Nonlinearity
Effects
To Channel
10
0
-10
Normalized Pout Vs Pin GaAsTEK ITT6401FM
-20
DAC
Compensate
Insert
Long Train
1.2
-30
-40
Phase PSD
Sxx(f)
-50
A0cos(2π f1t+Φ 1 (t))
-60
-70
-80
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1
A1cos(2π f2t+Φ 2(t))
A3cos(2π f3t+Φ 3(t))
0.8
Y=1 for (X>2.0)
0.6
0.4
Y = 0.0781X^3-0.5285X^2+1.245X for (0<X<2)
0.2
-f3 -f2 -f1
f1
f2 f3
0
Freq.
0
0.5
1
1.5
2
2.5
Pin (Normalized : 1dB compression Pt=1.0) --Real Units
α 1 exp( jφ1 ) S( t − τ1 )
α 0 exp( jφ 0 ) S( t − τ 0 )
α 2 exp( jφ 2 ) S( t − τ 2 )
QAM 64 Uncoded BER Performance {Enhanced 105-Carrier Mode}
1.0E-2
1.0E-3
10
0
Channel
Sample Output Of H0-H15 Under Severe Multipath
1200
1000
-10
1.0E-4
Peak
Multipath
Peaks
800
1.0E-5
Right Adjacent
Left Adjacent
600
-20
400
1.0E-6
Multipath peak > 0
(1) Theory
(2) Simulation
200
-30
0
1.0E-7
-200
-40
-400
-50
-60
-512
Additive Noise
+
AGC
-600
7400
-312
-112
88
288
I
DQM
Decimate Q
Filter
Analog To
Digital
Fs = 40,80M
Short
Train
Correl
Noise
Average
Decimate By 2 Filter Frequenc y Respons e
10
RADIX
2
STAGE
128-Points
Multipath
Resistant
Detection
RADIX
8
FFT A
STAGE 1
{64-Points}
Orthogonalizer
RADIX
8
FFT B
STAGE 1
{64-Points}
Mag
0
By 2
-10
-20
-40
7550
7600
7650
7700
7750
7800
20
21
22
23
24
Ecarr/No (dB)
RADIX
8
FFT A
STAGE 2
{64-Points}
RADIX
8
FFT B
STAGE 2
{64-Points}
Channel
Inverter
Unscramble
64-pt
Transform
-50
-60
UNSCRAMBLE
128-pt
Transform
Phase Noise
Reduction
Algorithm
Slicer
Adaptive
Filters
-70
-80
-90
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Frequency (1.0 = Ny quist)
0.8
0.9
1
Decimate By 4 Filter Frequenc y Respons e
20
By 4
0
-20
250
-40
200
-60
150
-80
-100
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Frequency (1.0 = Ny quist)
0.8
0.9
1
100
50
0
-50
-100
0
500
1000
1500
25
26
27
28
Equalization
Tap
Update
AGC
-30
7500
Programmable
FFT
Mag
Gen Test
Statistic
1.0E-8
7450
488
Burst Detector/Orthogonalizer/Synchronizer
Amplitude Spectrum (dB)
Q
8
6
4
2
0
-2
-4
-6
-8
Pilot
Carriers
Amplitude Spec trum (dB)
Su
bca
rrie
r#
8
6
4
2
0
-2
-4
-6
-8
8
6
4
2
0
-2
-4
-6
-8
10
0
-10
-20
-30
-40
-50
-60
-70
-80
Real System
Up to 64 QAM
Per Carrier
2000
2500
Time (Samples)
3000
3500
4000
18
De-Interleave
And Decode
PN
Data
Out
3
2.0E+7
19.
OFDM Waveform/Receiver
• 802.11a/g uses training symbols that can be used to estimate/correct gain
frequency offsets and to equalize the channel and Pilot carriers to correct
phase offsets during the data symbols
• VOFDM uses dense training structure in the data symbols to allow for
interpolation between pilots to equalize data-bearing carriers
19
20.
The Peak to Average Power (PAPR) Problem
• 802.11a/g consists of 52 subcarriers which are modulated using Digital
rather than analog techniques forcing output PA backoffs of ~5-9 dB from P1
• The peak signal envelope is the vector sum of the instantaneous amplitude
and phases of the 52 subcarriers rotating at n∆F where n ranges from –26
to +26 (in the case of 802.11a)
• The PAPR is more dependent on the number of subcarriers than the
modulation on each subcarrier when the #subcarriers grow
QAM 64 52-Carrier OFDM W/Shaping
Crest Factor PDF
4E-2
4E-2
3E-2
3E-2
2E-2
2E-2
1E-2
99.9 % =9.5 dB
5E-3
0E+0
-25
-20
-15
-10
-5
0
5
Amplitude Relative To Mean Amplitude (dB) (mean=0 dB)
10
15
20
21.
The Phase Noise and AFC Problem
• Since the subcarriers are packed closely (at the 1st Null of Sinx/x) frequency
errors in the Rx will cause signal leakage and Inter-carrier interference
• Phase Jitter will cause the carriers to leak as well
• However, for 802.11a/g 64 QAM-OFDM the single carrier phase noise spec.
is adequate to supress LOT (loss of orthogonality)
• Low OFDM symbol rate (250 Ksym/sec) implies low loop bandwidth which
may allow a lot of Flicker Noise through
QAM 64 -OFDM Loss Vs Jitter
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
0.2
0.4
0.6 0.8
1
1.2 1.4
RMS Phase Jitter (Degrees)
1.6
1.8
2
21
22.
OFDM Waveform Design
• The parameters to design are function of channel characteristics
Number of subcarriers
Efficiency, delay spread of channel
Subcarrier bandwidth
Mobility/Time variation of channel, coherence BW of channel
Guard period
Delay spread of channel, modulation order
• Fundamental Design criterion of OFDM is that the channel must appear
flat across one subcarrier bandwidth
• Coherence BW determines subcarrier bandwidth to ensure flatness
• Cyclic prefix period must be > delay spread of channel
For BPSK/QPSK-OFDM cyclic prefix should be > 1 x Delay Spread
For QAM 16 cyclic prefix should be > 2 x Delay Spread
For QAM 64 cyclic prefix should be > 3.5 x Delay Spread
• For efficiency want guard period to be less than 50% or so of total symbol
period—determines # subcarriers/symbol
22
23.
Non-Idealities / Mitigation /Modem Design
• Peak-Average Power Problem
The signal band consists of many closely-spaced subcarriers (in fact,
overlapped by 50%)
With large modulation orders, the signal behaves like
bandlimited Gaussian noise
The signal envelope exhibits a Rayleigh density—different than
SC modulations
Mitigate by either clipping signal or by modifying data or adding
sacrificial subcarriers to reduce PAPR
Low order modulations can be improved by phase whitening
the BPSK or QPSK subcarriers
Data symbols may be multiplied by one of N stored sequences
—Sequence with lowest PAPR is transmitted along with best
sequence index
Peak Cancellation
Coding Techniques—Golay complementary codes etc.
Sacrifice subcarriers to cancel biggest peaks (need about 50%
for canceling to limit PAPR < 3 dB)
23
24.
Non-Idealities / Mitigation /Modem Design Cont.
{PAPR}
Shaped Amplitude PDF Vs Quadrature Gaussian Noise Model
8E-1
fm ( m) =
7E-1
6E-1
π
σ 2 = 2 − σ 2
m
n
2
(1) Simul. Signal
5E-1
m2
m
exp − 2
2σ
σ2
n
n
(2) Quadrature Noise Model
4E-1
3E-1
µm =
2E-1
1E-1
πσ 2
n
2
σ 2 (equiv) = σ 2 (equiv) ≅ 0.811 •
nI
nQ
0E+0
-1
0
1
2
Normalized Amplitude
3
4
ES
2
5
• The signal envelope has nearly identical statistics to BL Gaussian Noise (52 Subcarriers)
24
25.
Non-Idealities / Mitigation /Modem Design Cont.
• Phase Noise & Frequency Errors
The symbol rate of OFDM is slow (equal to the BW of a single
subcarrier + 1/Guard Period thus close-in phase noise more critical
Zero IF (Direct Conversion) designs will admit a Flicker noise
component
Frequency control very important to keep the subcarriers orthogonal
relative to FFT Rx Bin reference. SinX/X leakage will cause InterCarrier Interference
Phase noise will jitter subcarriers (SCs) into each other and a given
SC will interfere with all other SCs resulting in a maximum attainable
SNR
Phase tracking via pilots or decision-directed techniques allow
tracking of so-called “Common Phase Error”
Error Power =
2
R ee ( 0 ) = σe =
ESig
N
N −1
∑ S ( k − m)
k =0
φφ
Where S( ) = Phase noise PSD, N = # subcarriers
25
26.
Non-Idealities / Mitigation /Modem Design Cont.
Phase Jitter Max SNR (52 Subcarriers)
Maxim um Attainable SNR Vs Phas e Jitter St Dev
45
40
35
30
25
20
15
10
5
0
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
Phase Jitter Standard Deviation (Radians)
0.08
0.09
26
0.1
27.
Non-Idealities / Mitigation /Modem Design Cont.
{Phase, Frequency Recovery}
Phase may be recovered by Noting common phase shift of pilot symbols and constructing a loop
With this information
Frequency information may exploit cyclic prefix since same time waveform is at start & end
Of OFDM symbols—Use Lag Product Correlation
Symbol Length Less Cyc prefix
r ( t − T ) r ( t ) = exp( j2πf d T )
*
TCP
∫ h ( τ ) s( t - τ )
2
2
dτ + n ( t ) n * ( t − T )
I In
To Phase Rotator/NCO/FFT
Q In
0
(
ARG r * ( t − T ) r ( t )
fd ≅
2πT
FIFO
)
( • )∗
Conjugate
X
+
Freq Est
Z -1
ARG ( . )
0
Switch
Select
27
28.
Non-Idealities / Mitigation /Modem Design Cont.
{Fine Timing Adjust & Tracking}
Because each subcarrier is narrowband and typically the OFDM access scheme is TDMA,
We can correct spectrally any time offset or residual sampling errors
Typically the RF reference is used as the sampling reference so a frequency error may be
translated into a ppm error for the sampling frequency error as well –bursts must be short
enough so that the total timing slew is << cyclic prefix or guard period
ω
Can correct timing drift using FT time scaling property ℑ{ f ( at )} ↔ a F a
1
SCs will rotate at a speed linearly related to their distance from DC subcarrier—rotation in opposite
directions for positive vs negative subcarriers—delta phase between subcarrier and its negative
frequency complement provides timing frequency error signal—can rotate each subcarrier in
direction and rate to stop spinning
slow
DC
fast
28
29.
Non-Idealities / Mitigation /Modem Design Cont.
{DC Offsets, I/Q Imbalance}
• DC Offsets
Zero-IF designs may suffer from large DC offsets
Analog cancellation on I/Q arms
Digital DC offset detection and cancellation feedback to analog
Progressive notch filter near DC
Low-IF improves
Zero (DC) subcarrier not used for data in waveform design
• I/Q imbalances
I/Q Imbalance causes positive/negative frequency aliasing
I/Q mismatch will introduce crosstalk between I, Q branches
May be mitigated digitally in Rx to eliminate crosstalk
Isolation of imbalance to one side of link desirable due to multiusers each of which may have different Tx imbalances
Low-IF rather than Zero-IF eliminates problem to a large extent
Double complex-mixing mitigates phantom image products
29
30.
Soft Symbol/LLR Generation
• Typically every bit is encoded in OFDM to provide full time/frequency
diversity—for QAM constellations the optimum approach is “Bit/Slice”
decisioning—based on bit qualities of symbol.
QAM 16 LSB Unweighted Soft Decision Mapping
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
-4
-3
-2
-1
0
1
I or Q Input (To Slicer)
2
3
4
QAM 16 MSB Unweighted Soft Decision Mapping
16
14
12
10
8
6
4
Gray-Coded Square QAM
2
0
-8
-6
-4
-2
0
2
I or Q Input (To Slicer)
4
6
8
30
31.
MIMO (Multiple-Antenna OFDM)
• OFDM is very amenable to space-time diversity
Each subcarrier easy to combine from different antenna
Channel flat over a single subcarrier
Huge BER gains possible with just dual Tx/Rx diversity
Transmitter signal sent to two antennas/Tx chains
Receiver uses two antennas/Rx chains
• Strict Line-of-Sight (LOS) not required
Channel
31
32.
MIMO System (2 Antenna Rx, 2 Antenna Tx—Delay Diversity)
Chan Est #1
(Data)
Antenna
#1 Channel
Estimates
Via FFT
(Training)
Antenna
#2 Channel
Estimates
Via FFT
(Training)
FFT Out #1
FFT Out #2
Chan Est #1
(Data)
32
33.
Cross Correlation From Rx Antennas
• WT1 & WT2 are the training tone channel estimates HT1, HT2 with delay compensation
for antenna 1 and 2 respectively to compute Covariance Matrix R
• Channel Estimates are then used with R to form a weighted channel estimate
33
35.
Diversity Advantage
• Dual Tx/Rx up to 23 dB advantage for 1E-3 Uncoded for flat fading channel
over single antenna OFDM
35
36.
OFDM for multiple access (OFDMA)
• IEEE 802.16.3 uses OFDM as a multiple access scheme for fixed wireless
access
36
37.
Multicarrier CDMA
•Multi-Carrier CDMA is a combination of OFDM & CDMA:
First an OFDM system is used to provide orthogonal carriers, free from ISI.
Second each carrier is modulated by an individual code chip, to provide a
spread spectrum system
• The main advantage of doing this is that when the multiple-access interference becomes
a problem, the resulting linear detectors are much simpler to implement as only a single tap
equalizer is required for each channel.
• Rake reception can also be employed to exploit the channel diversity by channel matching in
the frequency domain allowing optimal reception for a single user.
• In the uplink another advantage of MC-CDMA can be exploited. If the signals can be synchronized
to arrive within a small fraction of the symbol time ( e.g. indoor, or very small cell environment)
then this asynchronism can be overcome by cyclically-extending the signal further allowing
synchronous reception of all signals, with no ISI from other users
• Makes multiple-access easier with ability to correlate out interfering users
37
38.
Spread
De-Spread
• Transmitter Multiplies symbols by spreading
sequence (Walsh etc.) prior to IFFT
• Receiver Multiplies symbols by same seq. as
was used to transmit after FFT
38
39.
Further Reading
•
•
•
OFDM for Wireless Multimedia Communications, Van Nee & Prasad,
Artech House Publishers, 2000, Boston, MA
OFDM Wireless LANs: A Theoretical and Practical Guide, Heiskala &
Terry, SAMS Publishers, 2002, Indianapolis, IN
“Supplement To Standard For Information TechnologyTelecommunications and Information Exchange Between SystemsLocal And Metropolitan Area Networks-Part 11: Wireless LAN Medium
Access Control(MAC) and Physical Layer (PHY) Specifications: High
Speed Physical Layer In The 5 GHz Band {IEEE 802.11a}”
39