Body

INTRODUCTION
WIRELESS SYSTEMS with multiple
antennas at
the transmitter and receiver
(multiple-input–multiple-output, MIMO) have
much larger capacity in fading channels
than standard wireless systems . The
appropriate
use
of
space-time
(ST)
processing and ST codes allows us to
achieve, or at least approach, these
capacities in practical systems.
When generated OFDM signal is transmitted
through a number of antennas in order to achieve
diversity or cap any gain (higher transmission rate) then
it is known as MIMO-OFDM
For frequency-selective channels, a
combination of MIMO with OFDM (orthogonal
frequency
division
multiplexing)
is
promising . The simplest way
to perform ST coding in a MIMO-OFDM
system would be to apply the ST-codes for
the frequency-flat channels to each tone
separately. However, a recent paper has
pointed out that this is suboptimum, as the
inherent
frequency
diversity
of
the
frequency-selective channel is not exploited.
It was also stated that construction of codes
that code across tones would be difficult. In
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this paper, we show by a very simple
observation how we can extend ST code
design rules to frequency selective channels
without sacrificing performance. We will also
develop further simplifications and illustrate
the performance-com- trade off.
BASIC OF MIMO OFDM SYSTEM
OFDM converts a frequency-selective
channel into a parallel collection of
frequency flat sub-channels. The subcarriers
have the minimum frequency separation
required to maintain orthogonality of their
corresponding time domain waveforms, yet
the signal spectra corresponding to the
different subcarriers overlap in frequency.
Hence, the available bandwidth is used very
efficiently. If knowledge of the channel is
available at the transmitter, then the OFDM
transmitter can adapt its signalling strategy
to match the channel. Due to the fact that
OFDM uses a large collection of narrowly
spaced
sub-channels,
these
adaptive
strategies
can approach the ideal water pouring
capacity of a frequency-selective channel. In
practice this is achieved by using adaptive
bit loading techniques, where different sized
signal constellations are transmitted on the
subcarriers.
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OFDM is a block modulation scheme
where a block of information symbols is
transmitted in parallel on subcarriers. The
time duration of an OFDM symbol is times
larger than that of a single-carrier system.
An OFDM modulator can be implemented as
an inverse discrete Fourier transform (IDFT)
on a block of information symbols followed
by an analog-to-digital converter (ADC). To
mitigate the effects of inter symbol
interference (ISI) caused by channel time
spread, each block of IDFT coefficients is
typically
preceded by a cyclic prefix (CP) or a guard
interval consisting of samples, such that the
length of the CP is at least equal to the
channel length. Under this condition, a
linear convolution of the transmitted
sequence and the channel is converted to a
circular convolution. As a result, the effects
of the ISI are easily and completely
eliminated. Moreover, the approach enables
the receiver
to
use
fast
signal
processing
transforms such as a fast Fourier transform
(FFT) for OFDM implementation . Similar
techniques can be employed in singlecarrier systems as well, by preceding each
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transmitted data block of length by a CP of
length , while using frequency- domain
equalization at the receiver.

Fig. 1.1 Q _ L MIMO-OFDM system, where Q and L are the

numbers of inputs and outputs, respectively.

Multiple antennas can be used at the
transmitter and
receiver, an arrangement called a multipleinput multiple-output (MIMO) system. A
MIMO system takes advantage of the spatial
diversity that is obtained by spatially
separated antennas in a dense multipath
scattering environment. MIMO systems may
be implemented in a number of different
ways to obtain either a diversity gain to
combat signal fading or to obtain a capacity
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gain. Generally, there are three categories
of MIMO techniques. The first aims to
improve the power efficiency by maximizing
spatial diversity. Such techniques include
delay diversity, space–time block codes
(STBC) [4], [5] and space–time
trellis codes (STTC) [6]. The second class
uses a layered approach to increase
capacity. One popular example of such a
system is V-BLAST suggested by Foschini et
al. [7] where full spatial diversity is usually
not achieved. Finally, the third type exploits
the knowledge of channel at the transmitter.
It decomposes the channel coefficient
matrix using singular value decomposition
(SVD) and uses these decomposed unitary
matrices as pre- and post-filters at the
transmitter and the receiver to achieve near
capacity [8].
OFDM has been adopted in the IEEE802.11a
LAN and
IEEE802.16a LAN/MAN standards. OFDM is
also being considered in IEEE802.20a, a
standard in the making for maintaining highbandwidth connections to users moving at
speeds up to 60 mph. The IEEE802.11a LAN
standard operates at raw data rates up to
54 Mb/s (channel conditions permitting) with
a 20-MHz channel spacing, thus yielding a
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bandwidth efficiency of 2.7 b/s/Hz. The
actual throughput is highly dependent on
the medium access control (MAC) protocol.
Likewise, IEEE802.16a operates in many
modes depending on channel conditions
with a data rate ranging from 4.20 to 22.91
Mb/s in a typical bandwidth of 6 MHz,
translating into a bandwidth efficiency of 0.7
to 3.82 bits/s/Hz. Recent developments in
MIMO techniques promise a significant boost
in
performance
for
OFDM
systems.
Broadband
MIMO-OFDM
systems
with
bandwidth efficiencies on the order of 10
b/s/Hz
are
feasible
for
LAN/MAN
environments. The physical (PHY) layer
techniques described in this paper are
intended to approach 10b/s/Hz bandwidth
efficiency. This paper discuss several PHY
layer
aspects
broadband
MIMO-OFDM
systems. Section II describes the basic.
MIMO-OFDM system model. All MIMO-OFDM
receivers
must
perform
time
synchronization,
frequency
offset
estimation, and correction and parameter
estimation. This is generally carried out
using a preamble consisting of one or more
training sequences. Once the acquisition
phase is over, receiver goes into the
tracking mode. Section III provides an
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overview of the signal acquisition process
and investigates sampling frequency offset
estimation and correction in Section IV. The
issue of channel estimation is treated in
Section V. Section VI considers space–time
coding techniques for MIMO-OFDM, while
Section VII discusses coding approaches.
Adaptive analog beam forming approaches
can be used to provide the best possible
MIMO link.
Section VIII discusses various strategies for
beam forming. Section IX very briefly
considers medium access control issues.
Section X discusses a software radio
implementation for MIMO-OFDM. Finally,
Section XI wraps up with some open issues
concluding remarks.

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Fig. 1.2. Frame structure for the Q _ L OFDM
system

CHAPTER 2
SPACE TIME CODING
Space-time codes (STC) provide transmits
diversity for the Multi-Input Multi-Output fading
channel. There are two main types of STC’s namely
space-time block codes (STBC) and space-time trellis
codes (STTC). Space time block codes operate on a
block of input symbols, producing a matrix output
whose columns represent time and rows represent
antennas. Their main feature is the provision of full
diversity with a very simple decoding scheme. On the
other hand, Space-time trellis codes operate on one
symbol at a time, producing a sequence of vector
symbols whose length represents antennas. Like
traditional TCM (Trellis Coded Modulation) for a
single- antenna channel, Space-time trellis codes
provide coding gain. Since they also provide full
diversity gain, their key advantage over space-time
block codes is the provision of coding gain [3]. Their
disadvantage is that they are extremely hard to design
and generally require high complexity encoders and
decoders. An STBC is defined by a p x n transmission
matrix G, whose entries are linear combinations of x1,
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…xk and their conjugates x, and whose columns are
pair wise – orthogonal. When p = n and {xi } are real, G
is a linear processing orthogonal design which satisfies
the condition that GT G = D, where D is the diagonal
matrix with the (i,i)^th diagonal element of the form .
Without loss of generality, the first row of G contains
entries with positive signs. If not, one can always
negate certain columns of G to arrive at a positive row.
We assume that transmission at the base-band
employs a signal constellation A with 2b elements. At
the first time slot, nb bits arrive at the encoder and
select constellation signals c1,…, cn. Setting xi = ci for
i = 1…., n in G yields a matrix C whose entries are
linear combinations of the ci and their conjugates.
While G contains the in determinates x1,…, xn, C
contains specific c constellation symbols (or linear
combinations of them), which are transmitted from the
n antennas as follows: At time t, the entries of row t of
C are simultaneously transmitted from the n antennas,
with the ith antenna sending the ith entry of the row. So
each row of C gives the symbols sent at a certain time,
while each column of C gives the symbols sent by a
certain antenna.

SPACE FREQUENCY CODING
In this section we design a fixed space-frequency
codes providing high diversity gain and manageable
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decoding complexity. Choosing any unitary matrix as ¨
yields the same mutual information, but it has
significant impact on error performance. It can be seen
from the fact that without spreading source symbols
across space and frequency (i.e. ¨ = I), the diversity gain
is only NR which is significantly less than the
maximum diversity gain min(NNR;NPNTNR) [1], [2].
In order to maintain a manageable level of complexity
for maximum-likelihood decoding, we divide the NNT
source symbols into G = N=Q groups of NTQ symbols
each. Then we code source symbols in each group
across space and frequency applying threaded algebraic
space-time (TAST) block codes since they possess the
best or close to best error performance among spacetime block codes [12]. As an example, a modified TAST
code for the NT = Q = 4 case is shown below [9] where
[z1(n) z2(n) z3(n) z4(n)]T = ©s(n), n = 1; 2; 3; 4, is the
rotated symbol vector, and µ is a unit-norm scaling
parameter for ensuring full-diversity of the TAST code.
The unitary matrix ¡ ensures that each source symbol
interacts with every channel coefficient even when the
power allocation matrix DW(n) or ^D(n) mutes some
spatial streams or rows (see [9] for details on ¡). It is
convenient to write (4) in a vector form as where G
generator matrix for TAST codes incorporating the
rotation matrix © and scaling parameter µ. Finally, the
coded symbols are fed to the permutation matrix ¦,
whose role is to place symbol vectors belonging to the
same group far apart in the subcarrier domain as shown
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in, so that each symbol experiences independent subchannels instead of highly correlated ones.

SPACE TIME FREQUENCY CODING
In signal processing, time–frequency analysis is a
body of techniques and methods used for characterizing
and manipulating signals whose statistics vary in time,
such as transient signals. It is a generalization and
refinement of Fourier analysis, for the case when the
signal frequency characteristics are varying with time.
Since many signals of interest – such as speech, music,
images, and medical signals – have changing frequency
characteristics, time–frequency analysis has broad
scope of applications. Whereas the technique of
the Fourier transform can be extended to obtain the
frequency spectrum of any slowly growing locally
integrable signal, this approach requires a complete
description of the signal's behaviour over all time.
Indeed, one can think of points in the (spectral)
frequency domain as smearing together information
from across the entire time domain. While
mathematically elegant, such a technique is not
appropriate for analyzing a signal with indeterminate
future behaviour. For instance, one must presuppose
some degree of indeterminate future behaviour in any
telecommunications systems to achieve non-zero
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entropy (if one already knows what the other person
will say one cannot learn anything).
To harness the power of a frequency representation
without the need of a complete characterization in the
time domain, one first obtains a time–frequency
distribution of the signal, which represents the signal in
both the time and frequency domains simultaneously. In
such a representation the frequency domain will only
reflect the behavior of a temporally localized version of
the signal. This enables one to talk sensibly about
signals whose component frequencies vary in time.
For instance rather than using tempered
distributions to globally transform the following
function into the frequency domain one could instead
use these methods to describe it as a signal with a time
varying frequency.
Once such a representation has been generated
other techniques in time–frequency analysis may then
be applied to the signal in order to extract information
from the signal, to separate the signal from noise or
interfering signals, etc.
MODELING OF OFDM SYSTEM
Orthogonal frequency-division Multiplexing

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(OFDM) is a method of encoding digital data on
multiple carrier frequencies. OFDM has developed into
a popular scheme
wideband communication
whether wireless or over copper wires, used in
applications such as digital television and audio
broadcasting, DSL broadband internet access, wireless
networks, and 4G mobile communications. OFDM is
essentially identical to coded OFDM (COFDM)
and discrete multi-tone modulation (DMT), and is
a frequency-division multiplexing (FDM) scheme used
as a digital multi-carrier modulation method. A large
number of closely spaced orthogonal sub-carrier
signals are used to carry data. The data is divided into
several parallel data streams or channels, one for each
sub-carrier. Each sub-carrier is modulated with a
conventional modulation scheme (such as quadrature
amplitude modulation or phase-shift keying) at a
low symbol rate, maintaining total data rates similar to
conventional single-carrier modulation schemes in the
same bandwidth.
The primary advantage of OFDM over single-carrier
schemes
is
its
ability
to
cope
with
severe channel conditions (for example, attenuation of
high frequencies in a long copper wire,
narrowband interference and frequency selective fading
due to multipath) without complex equalization filters.
Channel equalization is simplified because OFDM may
be viewed as using many slowly modulated
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narrowband signals
rather
than
one
rapidly
modulated wideband signal. The low symbol rate makes
the use of a guard interval between symbols affordable,
making
it
possible
to
eliminate intersymbol
interference (ISI) and utilize echoes and time-spreading
(that shows up as ghosting on analogue TV) to achieve
a diversity gain, i.e.a signal-to-noise ratio improvement.
This mechanism also facilitates the design of single
frequency networks (SFNs), where several adjacent
transmitters send the same signal simultaneously at the
same frequency, as the signals from multiple distant
transmitters may be combined constructively, rather
than interfering as would typically occur in a traditional
single-carrier system.

(Figure-2.1)

ADVANTAGES & DISADVANTAGES OF
OFDM
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Advantages:The advantages using OFDM are listed below.
 Makes efficient use of the spectrum by allowing
overlap.
 By dividing the channel into narrowband flat
fading sub channels, OFDM is more resistant to
frequency selective fading than single carrier
systems.


OFDM is an efficient way to deal with
multipath; for a given delay spread, the
implementation complexity is significantly
lower than that of a single-carrier system with
an equalizer.

 Eliminates ISI and ICI through use of a cyclic
prefix.


Using adequate channel coding and interleaving
one can recover symbols lost due to the
frequency selectivity of the channel.

 Channel equalization becomes simpler than by
using adaptive equalization techniques with
single carrier systems.


It is possible to use maximum likelihood
decoding with reasonable complexity.
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 OFDM is computationally efficient by using
FFT techniques to implement the modulation
and demodulation functions.
 It is less sensitive to sample timing offsets than
single carrier systems are.
 Provides good protection against co-channel
interference and impulsive parasitic noise.
Disadvantages:The disadvantages of OFDM are as follows:
 OFDM has a relatively large peak-to-averagepower ratio, which tends to reduce the power
efficiency of the radio frequency (RF) amplifier.
 The OFDM signal has a noise like amplitude
with a very large dynamic range; therefore it
requires RF power amplifiers with a high peak to
average power ratio.


It is more sensitive to carrier frequency offset and
drift than single carrier systems are due toleakage
of the DFT.

 Adding a guard period lowers the symbol rate
and hence lowers the overall spectral efficiency
of the system.
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APPLICATIONS OF OFDM

 DAB - OFDM forms the basis for the Digital
Audio Broadcasting (DAB) standard in the
European market.
 ADSL - OFDM forms the basis for the global
ADSL (asymmetric digital subscriber line)
standard.
 Wireless Local Area Networks - development is
ongoing for wireless point-to-point and point-tomultipoint configurations using OFDM
technology.


In a supplement to the IEEE 802.11 standard,
the IEEE 802.11 working group published
IEEE 802.11a, which outlines the use of
OFDM in the 5GHz band.

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CONCLUSION
We have investigated STF codes for MIMO-OFDM.
Starting from the premise that coding across the tones must be
done in a systematic way, we have pointed out the basic
mathematical analogy between antennas (or spatial eigen
modes) and tones, and explained how this similarity allows to
reuse the concepts of ST coding for space-time-frequency
(STF) coding required for OFDM. We then proposed a
reduced-complexity scheme that codes only across tones that
are separated by about one coherence bandwidth. A logical
next step would be to use real-world codes on that scheme and
investigate performance with full- and reduced-complexity
schemes. In this paper we proposed a joint detection-

estimation scheme for MIMO-OFDM systems. The
scheme consists of linked iterations of a turbo-decoder and
an efficient channel estimator. The joint-detector estimator
demonstrates good performance over time varying
channels even at relatively high Doppler frequencies. It is
shown by numerical simulation that for a 4T4R
configuration with a data rate of 4 Mb/s over a 1.25 MHz
channel and over a channel with Doppler as high as 200
Hz, 1% PER performance is achieved at an SNR of 16 dB.
When the number of receive antenna is increased to 6, the
same performance can be achieved at an SNR of only 6
dB. While there is moderate complexity increase due to
turbo decoding, the proposed scheme has the advantage of
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avoiding high complexity interference suppression
techniques.
Meanwhile, the moderate complexity increase is
justified by significant performance improvement over
previously proposed schemes.

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