IEEE Wireless Communications • June 2007
34
OFDM
OFDM is essentially a discrete implementation
of multicarrier modulation, which divides the
transmitted bitstream into many different sub-
streams and sends them over many different
subchannels. Typically, the subchannels are
orthogonal and the number of subchannels are
chosen such that each subchannel has a band-
width much less than the coherence bandwidth
of the channel. Thus, intersymbol interference
(ISI) on each subchannel is very small. For this
reason, OFDM is widely used in many high data
rate wireless systems.
Figure 1a shows a simplified block diagram of
an
N-tone OFDM system. First, the incoming
bits are mapped to data symbols according to
some modulation scheme such as QPSK or
QAM. Then the serial data stream is converted
into a number of parallel blocks, and each of
them has length-
N. Then, each block of symbols
(including pilot symbols, which are used for
channel estimation or synchronization) will be
forwarded to the IFFT and transformed into an
OFDM signal. After that, the OFDM signal will
be appended with a cyclic prefix by copying the
last
N
cp
samples to the top of the current OFDM
block. By choosing the length of the cyclic prefix
larger than the maximum path delay of the chan
-
nel, ISI can be eliminated [11]. Afterward, the
OFDM blocks will be converted to serial signals
and sent out. At the receiver, assuming a perfect
timing and carrier frequency synchronization,
the received signals will be first converted to
parallel signals and then the cyclic prefix will be
removed. After going through the DFT block,
the data symbols are detected with the estimated
channel information. After demodulation, the
transmitted bit stream is recovered.
In broadband time-varying multipath fading
channels, OFDM has some of its own challeng-
ing issues, such as peak-to-average-power ratio
(PAPR) and carrier frequency offset (CFO).
However, much more unique merits of OFDM
make it widely used in wireless applications and
standards. The merits can be generally summa-
rized as follows [11]:
•
OFDM is easy to implement in the digital
domain thanks to the use of DFT.
• OFDM is bandwidth efficient, since the paral-
lel subcarriers are overlapping but orthogonal
to each other without causing interference.
• OFDM is robust to multipath fading thanks to
the use of a cyclic prefix.
• OFDM is insusceptible to most forms of
impulse noise thanks to the parallel transmis
-
sion.
•
OFDM provides a high flexibility in resource
allocation since it splits the broadband chan-
nel into a number of parallel subchannels.
Thus, various resources (data rate and power)
can be dynamically allocated to different sub-
channels.
MIMO-OFDM SYSTEM MODEL
Future broadband wireless systems should pro-
vide high data rate and high performance over
very challenging channels that may be time-
selective and frequency-selective. The combina-
tion of MIMO and OFDM has the potential of
meeting this stringent requirement since MIMO
can boost the capacity and the diversity and
OFDM can mitigate the detrimental effects due
to multipath fading.
A general MIMO-OFDM system is shown in
Fig. 1b, where
M
t
transmit antennas, M
r
receive
antennas, and
N-tone OFDM are used. First, the
incoming bit stream is mapped into a number of
data symbols via some modulation type such as
QAM. Then a block of
N
s
data symbols S = [s
1
,
s
2
, ⋅⋅⋅, s
Ns
] are encoded into a codeword matrix
C of size NT × M
t
, which will then be sent
through
M
t
antennas in T OFDM blocks, each
block consisting of
N subchannels. Specifically,
c
j
1
, c
j
2
, ⋅⋅⋅, c
j
T
will be transmitted from the jth
transmit antenna in OFDM blocks 1, 2, · · ·,
T,
respectively, where
c
j
n
denotes a vector of length-
N, for all j = 1, 2, · · ·, M
t
and n = 1, 2, · · ·, T.
The codeword matrix
C can be expressed as
(1)
After appending the cyclic prefix on each
OFDM block,
c
j
n
will be transmitted from the jth
transmit antenna in the
nth OFDM block.
After passing through the MIMO channels,
the received signals will be first sent to the
reverse OFDM block (cyclic prefix removal and
DFT) and then sent to the decoder. If the chan-
nel state information (CSI) is available at the
receiver, the optimal ML detection can be per-
formed.
CODE RATE
Since in Eq. 1 the total number of N
s
informa
-
tion symbols are sent over
NT channels where N
channels are used in T times, we can get the
C
cc
cc
=
1
11
1
L
MO M
L
M
T
M
T
t
t
.
■ Figure 1. A simplified block diagram of MIMO-OFDM system, where S =
[s
1
, s
2
, ⋅⋅⋅, s
Ns
] denotes a block of Ns data symbols.
^
S
1
OFDM
MOD
c
1
M
t
M
t
c
T
M
t
P/S
Fad
ing
channel
Pilot
insertion
Cyclic
prefix
S/P IFF
T
OFDM
MOD
c
1
1
c
T
1
Coding
(a) An OFDM transceiver
(b) A MIMO-O
FDM transceiver
S
Digital
modulation
Raw
data
Decoding
S/P
Channel
estimation
Remove
cyclic
prefix
P/S FF
T
Digital
demodulation
Output
1
OFDM
DEMOD
M
r
OFDM
DEMOD
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