Orthogonal Frequency Division Multiple-Access, The approach that made LTE possible

1. Orthogonal Frequency
Division Multiple-Access
Dr.Ayman Elezabi
Yasser Monier
900062323

2. Orthogonal Multiplexing Principle and structure of
OFDM symbols in practical standards
 An OFDM signal consists of orthogonal subcarriers modulated
by parallel data streams. Each baseband subcarrier is of the form
 , (1)
 where is the frequency of the th subcarrier. One baseband OFDM
symbol (without a cyclic prefix) multiplexes modulated
subcarriers:
 (2)
 where is the th complex data symbol (typically taken from a PSK
or QAM symbol constellation) and is the length of the OFDM
symbol. The subcarrier frequencies are equally spaced
 (3)

3. Orthogonal Multiplexing Principle and structure of
OFDM symbols in practical standards
 The OFDM symbol (2) could typically be received using a
bank of matched filters. However, an alternative
demodulation is used in practice. T-spaced sampling of the
in-phase and quadrature components of the OFDM symbol
yields (ignoring channel impairments such as additive noise
or dispersion)
 , (4)

4. Effect of Carrier Frequency Offset and Sampling Time
offset
 At the front-end of the receiver OFDM signals are subject to
synchronization errors due to oscillator impairments and sample
clock differences. The demodulation of the received radio signal to
baseband, possibly via an intermediate frequency, involves
oscillators whose frequencies may not be perfectly aligned with the
transmitter frequencies. This results in a carrier frequency offset.
Figure 6 illustrates the front end of an OFDM receiver where these
errors can occur. Also, demodulation (in particular the radio
frequency demodulation) usually introduces phase noise acting as
an unwanted phase modulation of the carrier wave. Carrier
frequency offset and phase noise degrade the performance of an
OFDM system.

5. Effect of Carrier Frequency Offset and Sampling Time
offset
 When the baseband signal is sampled at the A/D, the sample
clock frequency at the receiver may not be the same as that
at the transmitter. Not only may this sample clock offset
cause errors, it may also cause the duration of an OFDM
symbol at the receiver to be different from that at the
transmitter. If the symbol clock is derived from the sample
clock this generates variations in the symbol clock. Since the
receiver needs to determine when the OFDM symbol begins
for proper demodulation with the FFT, a symbol
synchronization algorithm at the receiver is usually
necessary. Symbol synchronization also compensates for
delay changes in the channel.

6. Channel Estimation Algorithms
 System Architecture

7. System Architecture

8. System Architecture (cont’d)
1. Input to time domain
2. Guard Interval
3. Channel
4. Guard Removal
5. Output to frequency domain
6. Output
7. Channel Estimation
xn  IDFTXk n  0,1,2,...,N 1
 
 
  


x N n n N N
     
, , 1,..., 1
x n g g
x n n N
 

, 0,1,..., 1
f
y x n hn wn f f   
yn  y n n  0,1,..., N 1 f
Yk  DFTynk  0,1,2,...,N 1
Channel ICI AWGN
         
Y k  X k H k  I k 
W k
k N
 0,1,..., 1
 
 
 
Y k
 k  0,1,..., N 1
H k
X k
e
e
Estimated
Channel

9. Pilot for Channel Estimation
Time
Carriers
Time
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

10. Block-type Channel Estimation
 LS: Least Square Estimation
 
h X y
where X diag x x x




















1
0
0 1 1
1
y
.
.
.
, ,...,
N
N
LS
y
y

11. Comb-type Estimation
   
X k  X mL 
l
xp m l
, 0
 





 
data l L
inf . , 1,..., 1
Np 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-carriers
Xp input at the kth pilot sub-carrier
Yp output at the kth pilot sub-carrier
LS Estimate
 
 
 
Y k
p
p k N
  0,1,..., 1 p
X k
p
H k
LMS Estimate
Yp(k)
Xp(k) LMS + - e(k)

12. Interpolation for Comb-type
 Linear Interpolation
H k H mL l e e
 Second Order Interpolation
   
l
H k  H mL 
l
      
   
l L
H m
L
H m H m
p p p
e e
 
0
1
    

     
 
  
 




c

c



c H p m c H p m c H p m



  
 
 





   
l N
c
where
/
1
0 1
1
1
,
2
1
1
1 1 ,
0
,
2
1
1

 

13. OFDMA, the multi user communication system.
 The main motivation for adaptive subcarrier allocation
in OFDMA systems is to exploit multiuser diversity.
Although OFDMA systems have a number of
subcarriers, we will focus temporarily on the allocation
for a single subcarrier amongst multiple users for
illustrative purposes.

14. principles that enable high performance in OFDMA: multiuser diversity and adaptive modulation. Multiuser
diversity describes the gains available by selecting a user of subset of users that have “good” conditions.
Adaptive modulation is the means by which good channels can be exploited to achieve higher data rates.
OFDMA, the multi user communication system.
Multiuser Diversity
main motivation for adaptive subcarrier allocation in OFDMA systems is to exploit multiuser diversity.
Although OFDMA systems have a number of subcarriers, we will focus temporarily on the allocation for a
 Consider a K-user system, where the subcarrier of interest
subcarrier amongst multiple users for illustrative purposes.
experiences i.i.d. Rayleigh fading, that is, each user’s channel gain
is independent of the others, and is denoted by hk. The probability
density function (pdf) of user k’s channel gain p(hk) is given by
Consider a K -user system, where the subcarrier of interest experiences i.i.d. Rayleigh fading, that is,
user’s channel gain is independent of the others, and is denoted by hk . The probability density function
user k’s channel gain p(hk ) is given by
p(hk) =
(
2hke− h2
k if hk ≥ 0
0 if hk < 0.
(6.1)
suppose the base station only transmit to the user with the highest channel gain, denoted as hmax =
h1, h2, · · · , hK } . It is easy to verify that the pdf of hmax is
p(hmax) = 2K hmax
⇣
1 − e− h2
m ax
⌘K− 1
e− h2
m ax . (6.2)
8

15. channel gain p(hk ) is given by
(
2hke− h2
k if hk ≥ 0
OFDMA, the multi user communication system.
p(hk) =
0 if hk < 0.
 Now suppose the base station only transmit to the user with
base station only transmit to the user with the highest channel gain, hK the highest channel gain, denoted as hmax = max{h1,h2,···
,hK}. It is easy to verify that the pdf of hmax is
} . It is easy to verify that the pdf of hmax is
p(hmax) = 2K hmax
⇣
1 − e− h2
m ax
⌘K− 1
e− h2
m ax . 8

16. THANKS