Principles of Multicarrier Modulation and
OFDM a
Lie-Liang Yang
Tel:
a Main
Communications Research Group
Faculty of Physical and Applied Sciences,
University of Southampton, SO17 1BJ, UK.
+44 23 8059 3364, Fax: +44 23 8059 4508
Email: lly@ecs.soton.ac.uk
http://www-mobile.ecs.soton.ac.uk
reference: A. Goldsmith, Wireless Communications, Cambridge University Press, 2005.
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MC Modulation and OFDM - Summary
p Principles of multicarrier (MC) modulation;
p Principles of orthogonal frequency-division multiplexing (OFDM);
p Inter-symbol interference (ISI) suppression;
p Implementation challenges.
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Multicarrier Modulations - Introduction
p In multicarrier (MC) modulation, a transmitted bitstream is divided into many
different substreams, which are sent in parallel over many subchannels;
p The parallel subchannels are typically orthogonal under ideal propagation
conditions;
p The data rate on each of the subcarriers is much lower than the total data rate;
p The bandwidth of subchannels is usually much less than the coherence bandwidth of the wireless channel, so that the subchannels experience flat fading.
Thus, the ISI on each subchannel is small;
p MC modulation can be efficiently implemented digitally using the FFT (Fast
Fourier Transform) techniques, yielding the so-called orthogonal frequencydivision multiplexing (OFDM);
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Multicarrier Modulations - Application
Examples
p Digital audio and video broadcasting in Europe;
p Wireless local area networks (WLAN) - IEEE802.11a, g, n, ac,
ad, etc.;
p Fixed wireless broadband services;
p Mobile wireless broadband communications;
p Multiband OFDM for ultrawideband (UWB) communications;
p Main modulation scheme in the 4th generation cellular mobile
communications systems (uplink SC-FDMA, downlink OFDMA);
p A candidate for many future generations (802.11ax, 5th
generation cellular) of wireless communications systems.
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Multicarrier Modulations - Transmitter
R/N bps
R bps Serial-to- R/N bps
Parallel
Converter
Symbol
Mapper
s0
g(t)
×
cos(2πf0 t)
Symbol
Mapper
s1
g(t)
..........
R/N bps
s0 (t)
Symbol
Mapper
sN −1
s1 (t)
×
+
s(t)
cos(2πf1 t)
g(t)
sN −1 (t)
×
cos(2πfN −1 t)
Figure 1: Transmitter schematic diagram in general multicarrier modulations.
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Multicarrier Modulations - Principles
p Consider a linearly modulated system with data rate R and bandwidth B;
p The coherence bandwidth of the channel is assumed to be Bc < B, so
signals transmitted over this channel experience frequency-selective fading.
When employing the MC modulations:
l the bandwidth B is broken into N subbands, each of which has a bandwidth
BN = B/N for conveying a data rate RN = R/N ;
l Usually, it is designed to make BN << Bc , so that the subchannels
experience (frequency non-selective) flat fading.
l In the time-domain, the symbol duration TN ≈ 1/BN of the modulated signals
is much larger than the delay-spread Tm ≈ 1/Bc of the channel, which hence
yields small ISI.
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An example
Consider a MC system with a total passband bandwidth of 1 MHz.
Suppose the channel delay-spread is Tm = 20 µs. How many
subchannels are needed to obtain approximately flat fading in each
subchannel?
l The channel coherence bandwidth is
Bc = 1/Tm = 1/0.00002 = 50 KHz;
l To ensure flat fading on each subchannel, we take
BN = B/N = 0.1 × Bc << Bc ;
l Hence, N = B/(0.1 × Bc ) = 1000000/5000 = 200 subcarriers.
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Multicarrier Modulations - Transmitted
Signals
s(t) =
N
−1
X
si g(t) cos (2πfi t + φi )
(1)
i=0
where
4 si : complex data symbol (QAM, PSK, etc.) transmitted on the ith
subcarrier;
4 φi : phase offset of the ith subcarrier;
4 fi = f0 + i(BN ): central frequency of the ith subcarrier;
4 g(t): waveform-shaping pulse, such as raised cosine pulse.
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Amplitude
Time
0
T
Figure 2: Illustration of multicarrier modulated signals.
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Multicarrier Modulations - Receiver
s0 (t) + n0 (t)
f0
Demodulator
R/N bps
cos(2πf0 t)
s1 (t) + n1 (t)
s(t) + n(t)
f1
..........
sN −1 (t) + nN −1 (t)
fN −1
Demodulator
R/N bps
Parallelto-Serial
Converter
R bps
cos(2πf1 t)
Demodulator
R/N bps
cos(2πfN −1 t)
Figure 3: Receiver schematic diagram in general multicarrier modulations.
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Overlapping MC
f0
f1
f2
f3
f4
f5
f6
f7
The set of orthogonal subcarrier frequencies, f0 , f1 , . . . , fN −1 satisfy:

Z TN
 0.5, if i = j
1
cos(2πfi t + φi ) cos(2πfj t + φj )dt =
 0,
TN 0
else
(2)
The total system bandwidth required is:
B=
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≈ N/TN
TN
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(3)
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Overlapping MC - Detection
p Without considering fading and noise, the received MC signal can be
expressed as
r(t) =
N
−1
X
si g(t) cos (2πfi t + φi )
(4)
i=0
p Assuming that the detector knows {φi }, then, sj can be detected as
Z TN
ŝj =
r(t)g(t) cos (2πfj t + φj ) dt
0
Z
N
−1
X
TN
=
0
=
N
−1
X
si g(t) cos (2πfi t + φi ) g(t) cos (2πfj t + φj ) dt
i=0
TN
Z
g 2 (t) cos (2πfi t + φi ) cos (2πfj t + φj ) dt
si
0
i=0
=C ×
N
−1
X
i=0
si δ(i − j) = C × sj , j = 0, 1, . . . , N − 1
(5)
where C is a constant.
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Fading Mitigation Techniques in MC
Modulation
p Coding with interleaving over time and frequency to exploit the
frequency diversity provided by the subchannels experiencing
different fading;
p Frequency-domain equalization: When the received SNR is
αi2 Pi , the receiver processes it as αi2 Pi /α̂i2 ≈ Pi to reduce the
fading;
p Precoding: If the transmitter knows that the channel fading gain
is αi , it transmits the signals using power Pi /α̂i2 , so that the
received power is Pi ;
p Adaptive loading: Mitigating the channel fading by adaptively
varying the data rate and power assigned to each subchannel
according to its fading gain.
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Implementation of MC Modulation Using
DFT/IDFT
p Let x[n], 0 ≤ n ≤ N − 1, denote a discrete time sequence. The
N -point discrete Fourier transform (DFT) of {x[n]} is defined as
X[i] =DFT{x[n]}
N
−1
X
1
j2πni
,√
x[n] exp −
, 0≤i≤N −1
N
N n=0
(6)
p Correspondingly, given {X[i]}, the sequence {x[n]} can be
recovered by the inverse DFT (IDFT) defined as
x[n] =IDFT{X[i]}
1
,√
N
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N
−1
X
i=0
X[i] exp
j2πni
N
, 0≤n≤N −1
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(7)
Implementation of MC Modulation Using
DFT/IDFT
p When an input data stream {x[n]} is sent through a linear time-invariant
discrete-time channel having the channel impulse response (CIR) {h[n]}, the
output {y[n]} is given by the discrete-time convolution of the input and the
CIR, expressed as
X
y[n] = h[n] ∗ x[n] = x[n] ∗ h[n] =
h(k)x[n − k]
(8)
k
p Circular Convolution: when {x[n]} is a N -length periodic sequence, then the
N -point circular convolution of {x[n]} and {h[n]} is defined as
X
h(k)x[n − k]N
(9)
y[n] = h[n] ~ x[n] = x[n] ~ h[n] =
k
p which has the property
DFT{y[n] = h[n] ~ x[n]} = X[i]H[i], i = 0, 1, . . . , N − 1
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Implementation of MC Modulation: Cyclic
Prefix
Original Length N Sequence
Cyclic Prefix
x[N − µ], x[N − µ + 1], ..., x[N − 1]
x[0], x[1], ..., x[N − µ − 1]
x[N − µ], x[N − µ + 1], ..., x[N − 1]
Append Last µ Symbols to Beginning
Figure 4: Cyclic prefix of length µ.
p The original N -length data block is x[n] : x[0], . . . , x[N − 1];
p The µ-length cyclic prefix block is x[N − µ], . . . , x[N − 1], which
is constituted by the last µ symbols of the data block {x[n]};
p The actually transmitted data block is length N + µ, which is
x̃[n] : x[N − µ], . . . , x[N − 1], x[0], x[1], . . . , x[N − 1]
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Implementation of MC Modulation: Cyclic
Prefix
p Then, when {x̃[n]} is input to a discrete-time channel having the CIR
h[n] : h[0], . . . , h[L], the channel outputs are
y[n] =x̃[n] ∗ h[n] =
L
X
k=0
h[k]x̃[n − k] =
L
X
k=0
h[k]x[n − k]N
=x[n] ~ h[n], n = 0, 1, . . . , N − 1
(11)
p Therefore,
Y [i] = DFT{y[n] = x̃[n] ~ h[n]} = X[i]H[i], i = 0, 1, . . . , N − 1
(12)
p When {Y [i]} and {H[i]} are given, the transmitted sequence can be
recovered as
DFT{y[n]}
Y [i]
x[n] = IDFT X[i] =
= IDFT
, n = 0, 1, . . . , N − 1 (13)
H[i]
DFT{h[n]}
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OFDM Using Cyclic Prefixing - An Example
p Consider an OFDM system with total bandwidth B = 1 MHz and
using N = 128 subcarriers, 16QAM modulation, and length µ = 8
of cyclic prefix.
Then
l The subchannel bandwidth is BN = B/128 = 7.812 kHz;
l The symbol duration on each subchannel is
TN = 1/BN = 128 µs;
l The total transmission time of each OFDM block is
T = TN + 8/B = 136 µs;
l The overhead due to the cyclic prefix is 8/128 = 6.25%;
l The total data rate is
128 × log2 16 × 1/(T = 136 × 10−6 ) = 3.76 Mbps.
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OFDM - System Structure
Transmitter
X
N
x
N
IDFT
processing
P/S
CP
Signal shaping
g(t)
Channel
Receiver
processing
y
N
Y
N
DFT
S/P
CP removing
Matchedfiltering
g ∗ (−t)
Figure 5: Schematic block diagram of the transmitter/receiver for OFDM systems using IDFT/DFT assisted multicarrier modulation/demodulation and cyclicprefixing (CP).
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OFDM - Transmitter
R bps
X
QAM
Modulation
X[0]
x[0]
X[1]
x[1]
Serial-toParallel
Converter
IFFT
Add Cyclic
Prefix, and
Parallelto-Serial
Converter
D/A
x̃(t)
×
cos(2πf0 t)
X[N − 1]
x[N − 1]
Figure 6: Transmitter of OFDM with IFFT/FFT implementation.
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s(t)
OFDM - Receiver
R bps
QAM
Demod
Y
Y [0]
y[0]
Y [1]
y[1]
Parallelto-Serial
Converter
FFT
Remove
Prefix, and
y[n]
Serial-toParallel
Converter
LPF
and A/D
×
cos(2πf0 t)
Y [N − 1]
y[N − 1]
Figure 7: Receiver of OFDM with IFFT/FFT implementation.
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r(t)
OFDM - Transmitted Signal
l Let the N data symbols (thought as in the frequency-domain) to
be transmitted on the N subcarriers within a DFT period is given
by
X = [X0 , X1 , . . . , XN −1 ]T
(14)
l After the IDFT on X , it generates N time-domain coefficients
expressed as
N
−1
X
1
2πmn
xn = √
, n = 0, 1, . . . , N − 1
(15)
Xm exp j
N
N m=0
l Let F be a fast Fourier transform (FFT) matrix given by the next
slide. Then, we can express x = [x0 , x1 , . . . , xN −1 ]T as
x = F HX
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(16)
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FFT/IFFT Matrices
l FFT matrix:


1
1
1
···
1


N −1 
2
1
W
W
·
·
·
W
1 
N
N


N
F = √ .

.
.
.
.
..
..
..
..
..

N


2(N −1)
(N −1)2
N −1
1 WN
WN
· · · WN
(17)
where WN = e−j2π/N ;
l IFFT matrix is given by F H ;
l Main Properties: F H F = F F H = I N .
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OFDM - Transmitted Signal
x of length
l After adding the cyclic-prefix (CP) of length µ, x is modified to x̃
N + µ;
l The normalized transmitted base-band OFDM signal is formed as
s(t) =
N
−1
X
n=−µ
=A ×
x̃n ψTψ (t − nTψ )
N
−1
X
m=0
Xm exp(j2πfm t), − µTψ ≤ t < TN
(18)
where
4 A: Constant related to the transmit power;
4 ψTψ (t): time-domain waveform construction function, such as the
sinc(·)-function;
4 Tψ : chip-duration and Tψ ≈ 1/B.
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OFDM - Representation of Received Signals
p When the OFDM signal of (18) is transmitted over a frequencyselective fading channel with the CIR hn , 0 ≤ n ≤ L as well as
Gaussian noise, the discrete-time received observation samples
in correspondence to x0 , x1 , . . . , xN −1 are obtained from
sampling the received signal, which can be expressed as
yn =x̃n ∗ hn + vn =
L
X
k=0
hk x̃n−k + vn , n = 0, 1, . . . , N − 1
(19)
p Let y = [y0 , y1 , · · · , yN −1 ]T . Then, it can be shown that y can be
expressed as
y = H̃
H x̃
x+v
(20)
H.
p Here, it is very important to represent the matrix H̃
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OFDM - Representation of Received
Signals (Linear Convalution)
x−L
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x−1
x0
x1
x2
x3
x4
×
×
×
×
×
0
···
×
···
×
h1
h0
P
0
hL
h1
h0
P
0
0
···
h1
h0
P
0
0
0
···
hL
h1
h0
P
0
0
0
0
···
hL
h1
h0
+
+
···
+
+
+
v0
v1
v2
v3
v4
=
=
=
=
=
y0
y1
y2
y3
y4
P
Southampton
···
hL
···
hL
0
···
0
···
0
···
···
···
0
···
···
···
···
···
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OFDM - Representation of Received
Signals (Another Way)
x0
x1
x2
x3
x4
···
h0
h0 x0
h0 x1
h0 x2
h0 x3
h0 x4
h1
..
.
h1 x−1
..
.
h1 x0
..
.
h1 x1
..
.
h1 x2
..
.
h1 x3
..
.
···
hL
hL x−L
P
hL x−L+1
P
hL x−L+2
P
hL x−L+3
P
hL x−L+4
P
···
+v0
+v1
+v2
+v3
+v4
=
=
=
=
=
···
y0
y1
y2
y3
y4
x−L
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···
..
.
···
···
···
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OFDM - Representation of Received Signals
From the previous slide, we can see that

 
y0
hL x−L + hL−1 x−L+1 + · · · + h0 x0 + v0

 
 y  
hL x−L+1 + hL−1 x−L+2 + · · · + h1 x0 + h0 x1 + v1
 1  
 .  
..
 .  
 .  
.

=

 
hL xn−L + hL−1 xn−L+1 + · · · + h1 xn−1 + h0 xn + vn
 yn  

 
 ..  
..
 .  
.

 
yN −1
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
hL xN −L−1 + hL−1 xN −L + · · · + h1 xN −2 + h0 xN −1 + vN −1
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












(21)
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OFDM - Representation of Received Signals
When expressed in matrix form, (21) is



y
h
 0   L

 
 y1   0

 =
.
 .   ..
 .   .

 
yN −1
0
| {z } |

hL−1
···
h0
0
···
0
0
hL
..
.
hL−1
..
.
···
..
.
h0
..
.
···
..
.
0
..
.
0
..
.
0
0
···
0 ···
{z
hL
hL−1
y
H
H̃
···
···
..
.
···

x−L


 .. 
0  . 




0   x−1 


..  

 x0 
.


 .. 
h0  . 

}
xN −1
| {z }
x
x̃


v
 0 


 v1 

+
 .. 
 . 


vN −1
| {z }
(22)
v
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OFDM - Representation of Received Signals
Therefore, we have


hL hL−1 · · ·
h0 0 · · · 0
0
··· 0


0

h
h
·
·
·
h
·
·
·
0
0
·
·
·
0
L
L−1
0


H = .
H̃
..
..
..
. . . .. . . . ..
. . . .. 
 ..

.
.
.
.
.
.


0
0
0
· · · 0 · · · hL hL−1 · · · h0
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(23)
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OFDM - Representation of Received Signals
l In (22), if CP is used and set as x−i = xN −i , i = 1, . . . , L, then, (22) can be
represented as

h0


 h1

.

 
 ..

y0

 
hL

 

 y1   .


..
 ..  = 

 .  

 
0
yN −1
 .
..
| {z } 

y

0

0
|
0
···
0
···
0
h0
..
.
···
..
.
0
..
.
···
..
.
0
hL−1
..
.
···
..
.
h0
..
.
···
..
.
0
..
.
0
..
.
···
..
.
0
..
.
···
..
.
h0
..
.
..
0
···
0
···
hL−1
···
0
···
0
···
{z
H
0
hL
···
..
.
h2
..
.
···
0
0
..
.
···
..
.
0
···
..
.
.
···
h0
h1

h1
.. 

. 


 

hL 

  x 0   v0 
0
 


v
x



1 
1
.. 

+

.
.



. 
  ..   .. 





0
 xN −1
vN −1
.. 
} | {z }
. 
 | {z
x
v

0

h0
}
(24)
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31/ 49 ⇒|
OFDM - Representation of Received Signals

h0
0

h
 1 h0
 .
..
 ..
.


hL hL−1

 ..
..
H = .
.


0
0

..
 ..
.
 .

0
0

0
0
UNIVERSITY OF
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···
0
···
0
···
...
0
..
.
···
...
0
0
· · · h0 · · ·
.. . .
..
. .
.
0
..
.
···
...
0
..
.
···
...
h0
..
.
···
0
···
hL−1
···
0
···
hL
···
...
h2
..
.

h1
.. 
. 


· · · 0 hL 


0 ··· 0 

.. . .
.. 
. . 
.


0 ··· 0 

.
.
... .
.. 
.


· · · h0 0 

· · · h1 h0
School of ECS, Univ. of Southampton, UK. http://www-mobile.ecs.soton.ac.uk
(25)
32/ 49 ⇒|
An Example
p Let we assume x = [x0 , x1 , x2 , x3 ]T and L = 2.
p Then, we have




h2 h1 h0 0 0 0
h0 0 h2 h1




0 h h h 0 0
h h 0 h 
2
1
0
2


 1 0
H =
H̃
, H = 
 (26)
 0 0 h2 h1 h0 0 
h2 h1 h0 0 




0 0 0 h2 h1 h0
0 h2 h1 h0
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33/ 49 ⇒|
OFDM - Signal Detection
p In (24), H is a circulant channel matrix, which can be decomposed into
H = F H ΛF , where Λ = diag{H0 , H1 , · · · , HN −1 } is a (N × N ) diagonal
matrix, and Hn is in fact the fading gain of the nth subcarrier.
p Using x = F H X of (16), we can re-write (24) as
H
H
y = H F HX + v = F HΛ F
F
X
+
v
=
F
ΛX + v
| {z }
(27)
=II N
p Carrying out the FFT on y gives
0
H
Y = Fy = F
F
Λ
X
+
F
v
=
Λ
X
+
v
| {z }
(28)
=II N
p Therefore, for n = 0, 1, . . . , N − 1,
Yn = Hn Xn + vn0
(29)
based on which {Xn } can be detected.
p Explicitly, there is no ISI.
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34/ 49 ⇒|
OFDM - Peak-to-Average Power Ratio
p The peak-to-average power ratio (PAPR) is an important
attribute of a communication system;
p A low PAPR allows the transmit power amplifier to operate
efficiently, whereas a high PAPR forces the transmit power
amplifier to have a large backoff in order to ensure linear
amplification of the signal;
p A high PAPR requires high resolution for the receiver A/D
converter, since the dynamic range of the signal is much larger
for high-PAPR signals.
p High-resolution A/D conversion places a complexity and power
burden on the receiver front end.
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35/ 49 ⇒|
Amplitude
Time
0
T
Figure 8: Illustration of multicarrier modulated signals.
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36/ 49 ⇒|
OFDM - Peak-to-Average Power Ratio
p The PAPR of a continuous-time signal is given by
maxt {|x(t)|2 }
P AP R ,
Et [|x(t)|2 ]
(30)
p The PAPR of a discrete-time signal is given by
maxn {|x[n]|2 }
P AP R ,
En [|x[n]|2 ]
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(31)
37/ 49 ⇒|
OFDM - Peak-to-Average Power Ratio
p In OFDM, the transmitted signal is given by
1
x[n] = √
N
N
−1
X
i=0
X[i] exp
j2πni
N
, 0≤n≤N −1
(32)
2
p Given E |X[i]| = 1, the average power of x[n] is given by
N
−1
X
1
2
2
En |x[n]| =
E |X[i]| = 1
N i=0
(33)
p The maximum value occurs when all X[i]’s add coherently, yields

2  −1
 1 NX
 N 2
max{|x[n]|2 } = max √
= √ = N
X[i]
n
 N

N
i=0
(34)
p Therefore, in OFDM systems using N subcarriers, P AP R = N , which
linearly increases with the number of subcarriers.
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38/ 49 ⇒|
OFDM - Techniques for PAPR Mitigation
p Clipping: clip the parts of the signals that are outside the
allowed region;
p Coding: PAPR reduction can be achieved using coding at the
transmitter to reduce the occurrence probability of the same
phase of the N signals;
p Peak cancellation with a complementary signal;
p ···
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39/ 49 ⇒|
OFDM - Frequency and Time Offset
f0
f1
f2
f3
f4
f5
f6
f7
Figure 9: Spectrum of the OFDM signal, where the subcarrier signals are orthogonal to each other.
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40/ 49 ⇒|
OFDM - Frequency and Time Offset
p OFDM modulation encodes the data symbol {Xi } onto
orthogonal subcarriers, where orthogonality is assumed by the
subcarrier separation ∆f = 1/TN ;
p In practice, the frequency separation of subcarriers is imperfect
and so ∆f is not exactly equal to 1/TN ;
p This is generally caused by mismatched oscillators, Doppler
frequency shifts, or timing synchronization, etc.;
p Consequently, frequency offset generates inter-carrier
interference (ICI).
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41/ 49 ⇒|
OFDM - Frequency and Time Offset
p Let us assume that the signal transmitted on subcarrier i is
xi (t) = ej2πit/TN
(35)
where the data symbol and the main carrier frequency are suppressed;
p An ideal signal transmitted on subcarrier (i + m) would by xi+m (t). However,
due to the frequency offset of δ/TN , this signal becomes
xi+m+δ (t) = ej2π(i+m+δ)t/TN
(36)
p Then, the interference imposed by subcarrier (i + m) on subcarrier i is
Z TN
−j2πδ
−j2π(δ+m)
TN 1 − e
TN 1 − e
∗
xi (t)xi+m+δ (t)dt =
Im =
=
(37)
j2π(δ + m)
j2π(δ + m)
0
p Explicitly, when δ = 0, Im = 0.
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42/ 49 ⇒|
OFDM - Frequency and Time Offset
p It can be shown that the total ICI power on subcarrier i is given
by
X
ICIi =
|Im |2 ≈ C0 (TN δ)2
(38)
m6=i
where C0 is a certain constant.
p Observations
4 As TN increases, the subcarriers become narrower and
hence more closely spaced, which then results in more ICI;
4 As predicted, the ICI increases as the frequency offset δ
increases;
4 The ICI is not directly related to N , but larger N results in
larger TN and, hence, more ICI.
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43/ 49 ⇒|
OFDM - Frequency and Time Offset
p The effects from timing offset are generally less than those from
the frequency offset, as long as a full N -sample OFDM symbol
is used at the receiver without interference from the previous or
subsequent OFDM symbols;
p It can be shown that the ICI power on subcarrier i due to a
receiver timing offset τ can be approximated as 2(τ /TN )2 ;
p Since usually τ << TN , the effect from timing offset is typically
negligible.
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44/ 49 ⇒|
IEEE802.11 Wireless LAN Standard
p There are many IEEE802.11 (a,g,n,ac,ad) using OFDM;
p IEEE802.11a: Bandwidth= 300 MHz, operated in the 5 GHz
unlicensed band;
p IEEE802.11g: Virtually identical to the IEEE802.11a, but
operated in the 2.4 GHz unlicensed band.
p Main Parameters:
3 300 MHz bandwidth is divided into 20 MHz channels that can
be assigned to different users;
3 N = 64, µ = 16 samples;
3 Convolutional code with possible rate: r = 1/2, 2/3 or 3/4;
3 Adaptive modulation based on the modulation schemes:
BPSK, QPSK, 16-QAM and 64-QAM.
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45/ 49 ⇒|
OFDM - Summary
l No interference exists among the transmitted symbols;
l It is a transmission scheme achieving the highest spectral-efficiency;
l No diversity gain is achievable in frequency-selective fading channels;
l Sensitive to the frequency offset and timing jitter;
l The transmitted OFDM signals have a high dynamic range, resulting in the
high PAPR;
l The high PAPR requires that the OFDM transmitter has a high linear range
for signal amplification. Otherwise, the OFDM signals conflict non-linear
distortion, which results in out-of-band emissions and co-channel
interference, causing significant degradation of the system’s performance;
l The high PAPR has more harmful effect on the uplink communications than
on the downlink communications, due to the power limit of mobile terminals;
l When OFDM is used for uplink communications, the high PAPR may
generate severe inter-cell interference in cellular communications.
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46/ 49 ⇒|
Single-Carrier Frequency-Division
Multiple-Access
p In order to take the advantages of multicarrier communications
whereas circumventing simultaneously the high PAPR problem,
the single-carrier frequency-division multiple-access (SC-FDMA)
scheme has been proposed for supporting high-speed uplink
communications;
p In principle, the SC-FDMA can be viewed as a DFT-spread
multicarrier CDMA scheme, where time-domain data symbols
are transformed to frequency-domain by a DFT before carrying
out the multicarrier modulation;
p SC-FDMA is also capable of achieving certain diversity gain,
when communicating over frequency-selective fading channels.
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47/ 49 ⇒|
SC-FDMA - Transmitter
T-domain
F-domain
T-domain
{Xk0 , . . . , Xk(N −1) } {X̃k0 , . . . , X̃k(U −1) }
{xk0 , . . . , xk(N −1) }
DFT
(FFT)
Subcarrier
mapping
s(t)
{x̃k0 , . . . , x̃k(U −1) }
IDFT
(IFFT)
Add
CP
Low-pass
filter
Figure 10: Transmitter schematic for the kth user supported by the SC-FDMA
uplink.
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48/ 49 ⇒|
SC-FDMA - Receiver
T-domain
F-domain
{Yk0 , . . . , Yk(N −1) }
{x̂k0 , . . . , x̂k(N −1) }
IDFT
(IFFT)
Subcarrier
demapping
T-domain
{Ỹ0 , . . . , Ỹ(U −1) }
F-domain
processing
r(t)
{ỹ0 , . . . , ỹ(U −1) }
DFT
(FFT)
Remove
CP
Matchedfilter
Figure 11: Receiver schematic for the kth user supported by the SC-FDMA uplink.
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49/ 49 ⇒|