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Abstract—This paper gives an overview of multiple-input-
multiple-output orthogonal frequency division multiplexing
(MIMO-OFDM) in wireless systems. For achieving high data rate
wireless communication OFDM is combined with MIMO
technology to enhance system capacity and to increase the
diversity gain.
Index Terms—Multiple-input-multiple-output(MIMO), Space
time coding, beamforming, multipath, Orthogonal frequency
division multiplexing(OFDM), spectrum efficiency, wireless
systems, diversity.
1.INTRODUCTION
HE growing demand in multimedia devices and internet
data content lead to extensive improvement of wireless
communication. The need for high bandwidth and more
efficiency over the communication channel has always been a
challenge as it requires very high flexibility to communicate
through a constantly changing wireless channel. While
propagation the signal looses power because of basically two
reasons: fading and path loss. The MIMO system exploits the
scattering typical for indoor and urban environments and allow
a very high gain in spectral efficiency [1], thus allowing
transmission at high data rates. With the increase in bandwidth
efficient equalization techniques are required for reducing the
echoes in the channel. This can be achieved by implementing
orthogonal frequency division multiplexing (OFDM) at the
transmitter and the receiver ends of the antenna. OFDM can
also reduce the effects of multipath.
Spatially multiplexed MIMO is considered to boost the
throughput and due to this high throughput, the multi path
character of the environment causes the channel to be
frequency selective [2]. Now, OFDM transforms these
frequency selective MIMO channels into a collective set of
Parallel frequency flat MIMO channels, thus increasing the
frequency efficiency.
An important concept in smart antenna or MIMO technology
is beam forming; it is through which one increases the average
signal to noise ratio (SNR) through by focusing energy in
desired directions. If one estimates the response of
each antenna element to a desired transmitted signal, one
can optimally combine the elements with weights selected
as a function of each element response. One then can maximize the
average desired signal level and minimize the level
of other components (noise and/or interference).
MIMO systems which employ diversity techniques can be
basically grouped into two categories. Group one requires the
channel state information at the receiver but not at the
transmitter. These systems involve space time codes. The second
group requires the CSI at the transmitter end also, this approach
is called as beam forming. This technique seperates the MIMO
channel into parallel independent subchannels. If we only use the
best sub channel it is called as single beamforming. If we use all
the subchannels it is called as multiple beamforming.
An essential feature of MIMO systems is the ability to turn
multi-path propagation, which is traditionally a pitfall in wireless
transmission, into a benefit for the user. MIMO effectively
takes advantage of random fading and when available,
multipath delay spread [3], [4], for multiplying transfer rates.
Another important advantage of an OFDM system is that it is
capable of extensively reducing the equalization complexity by
equalization in the frequency domain. Hence, we can
implement the MIMO-OFDM with an IFFT at the transmitting
end and a FFT at the receiver side.
OFDM is a multi carrier modulation technique which converts a
frequency selective channel into a parallel set of frequency flat
sub channels with a separation of „f1‟ within each of the sub
carrier. The spectra of subcarriers are overlapping but they are
mutually orthogonal which enables effective utilization of the
bandwidth. The separation of „f1‟ is maintained to prevent inter
carrier-interference [5]. Thus, by selecting the appropriate sub-
carrier spacing in relation to the channel coherence bandwidth,
OFDM can be used to convert a frequency selective channel into
a parallel spectra of frequency flat sub-channels.
A technique called spatial multiplexing seeks to enhance the
spectrum eﬃciency by simultaneous transmission of
independent data streams. This is done by turning multipath
propagation, normally a handicap of mobile communication into
a beneﬁt for the system as mentioned earlier. A method knows as
space time coding allows us to improve the link reliability [6].
The data stream is encoded and is transmitted through multiple
antenna elements with high correlation, this redundancy in time
and space allows the receiver to combine optimally the signal
components at the respective receiver end.
This improves the data rate of the system. In a multipath fading
situation the additional diversity leads to even more improved
received signal quality as the additional diversity increases the
average quality of the received signal.
In this paper we attempt to address recent advances and an
MIMO-OFDM in Wireless Communication
Mithul Thanu Muthukumar
T

overview of the MIMO OFDM transmission system.
In part two we talk about MIMO and in part three we discuss
the modulation techniques used in OFDM. Part four we
discuss upon the Space time coding techniques and part five
gives an overview of MIMO OFDM system model. Part six
talks about STC in MIMO OFDM and part seven we discus on
space time frequency codes (STF) in MIMO systems. Part
eight is a small discussion on MIMO in 3GPP and part nine is
the conclusion.
Figure 1: MIMO-OFDM system with input and output
stages.[7]
2. MULTIPLE INPUT MULTIPLE OUTPUT SYSTEM
Multi antenna antennae can be operated in three modes.
They are the multiple antenna at the transmitter end is used for
beam forming. Transmitter or the receiver antenna is used for
diversity purposes or both the transmitter and receiver
antennas are used for spatial multiplexing purpose which is
generally referred to MIMO.
In Spatial multiplexing the data symbols are transmitted on
the channel at the same frequency by different antenna within
the same time interval. In this case multipath propagation is
assumed for operation of the system. The channel capacity of a
MIMO system is better in case of multipath than in LOS [8].
The above matrix is the time variant characteristic of a
MIMO channel. Where represents the time
variant channel transfer function between the Nth transmitter
antenna and the Nth receiver antenna [2].
From Shannon law the capacity of a MIMO channel was
derived as follows [8] [9]:
(1)
Where H is the channel matrix, Hh- transpose conjugate and I
the Identity matrix.
Figure 2:MIMO system with M transmitters and N receivers
3. MODULATION TECHNIQUE IN OFDM SYSTEMS
Modulation is the process through which digital information
is mapped into analog so that it can be transmitted over a given
channel. When a signal is modulated the binary bit sequence is
converted to an analog waveform. There can be either coherent
or non-coherent modulation techniques. Coherence modulation
uses a reference phase between the transmitter and the receiver
which brings accurate demodulation with receiver complexity
[10].
By allowing the amplitude to vary with the phase QAM can be
achieved. It is represented in the figure below. The transmitted
M-ary QAM symbol I s expressed as
(2)
Where an and bn are the amplitudes and M gives the measured
power of the modulation.
The average signal energy Es is obtained as
Figure 3: QAM constellation

4. SPACE TIME CODING
The wireless channel introduces various losses to the
transmitted signal in the form of large and small scale fading.
The remedy for these impairments it to apply diversity to the
system. Time diversity scheme is relatively new to spatial
diversity which is used in 2G systems.
The issue with time diversity is that the channel state
information (CSI) is not instantaneously available at the
transmitter side. Hence, we employ channel codes which will
provide optimum performance. Space time code combines the
channel code design and the uses of multiple transmit antennas
[11]. The encoded data is basically spilt into n number of
streams which is transmitted by the n number of antennas. At
the receiver side the received signal is a superimposition of
these simultaneously transmitted symbols impaired by noise
and ISI. We employ channel estimation techniques and
decoding algorithms to our advantage and obtain gain in
coding and diversity.
Figure 4: Space time coder
Various techniques for STC have been proposed the most
important are
 BLAST-Bell Labs Layered Space architecture by
Foschini[12]
 Space time Trellis Codes (STTC) by Tarokh [13]
 Space time Block Codes (STBC) by Alamouti [14]
From the investigations of Foschini and Gans who compares
the Shannon capacity of Single input single output (SISO) and
MIMO systems Reveal that the capacity of the system grows
linearly with the number of transmit antennas ,as long as the
number of receiver antennas is greater than or equal to the
number of transmit antennas [12].
The development in BLAST (8 element arrays in both ends
of wireless link) has proved to increase the capacity of wireless
systems in indoor environments significantly. It is able to
achieve a throughput of nearly 1Mbps over a narrowband
channel and because of this spectral efficiency is greatly
increased. The scattering plays a major role in the performance
of a BLAST system as this system exploits multipath rather
than mitigate it, hence the more the multi path the better the
performance of a blast system. In this system in order to
decouple the successive sub-channels arriving from the
transmit antennas the receiver uses a multi user detection
technique preceded by a sorting algorithm.
Space time Trellis Codes (STTC), was proposed by Tarokh.
The STTC is a technique which employs interrelations
between signals in the space domain and signals in the time
domain. The encoder is composed of a n number of
polynomials which are different and generated to determine
the simultaneously transmitted symbols. The receiver is based
upon channel estimation of these fade coefficients and
Maximum Likelihood Sequence Estimation (MLSE) decoder,
which computers the lowest accumulated Euclidean distance
metric to extract the most likely transmitted sequence [11].In
the STTC the multiple symbols associated with the trellis
branch are transmitted over the space domain rather than the
time domain and the multiple symbols are also uncorrelated
due to the physical separation between antenna elements which
leads to improved spectral efficiency. In case of STTC the
diversity advantage is proportional to the number of antenna
elements [13].
The decoder complexity is very high in case of STTC. I order
to overcome this problem a simpler transmit diversity scheme
was proposed by Alamouti called as Space-time Block codes
(STBC). STBC maps a block of input sequence of symbols
into both space and time domains there by creating orthogonal
sequences that will be transmitted by different transmit
antennas. The STBC decoder has a very simple architecture
and yet manages to obtain the same diversity advantage.
Figure 5a: Transmitter diversity with space-time block coding
[5]
The above figures represent the basic architecture for a 2
antenna element transmit and receive section for Space-time
block coding. The input signal or the information is fed into
the encoder which maps it into symbol constellations. At a
given time the Symbols c1 and c2 are transmitted
simultaneously from both the transmit antennas.
Figure 5b: Receiver for space-time block coding [5].

The received signal can be represented as
R1 = h1c1 + h2 c2 + n1 (3)
R2= -h1c*
2 + h2c*
1 + n2 [5]
Where h1 and h2 represents the channel from transmitter 1 and
transmitter 2 to their respective receivers.
The above equation can be rewritten in the matrix form as
This provides us with the ST block codes at the transmitter
end. The matrix H is orthogonal and hence the noise vector
will have zero mean and covariance [5]. With a help of a
simple linear combiner at the receiver end we apply the below
decoding rule for c1 and c2 [14].
(4)
Hence, we require only two complex multiplications and one
complex addition for decoding one symbol. Thus the receiver
complexity is greatly reduced and the same diversity gain is
achieved for the Space-time block coding. The SNR for c1 and
c2 is given as
SNR= α x Es / Nq
Hence a diversity of order two is obtained at the receiver [5].
5 .MIMO OFDM SYSTEM
We consider a MIMO-OFDM system that has both transmit
and receive antennas, in such a system the MIMO-OFDM
system model and be implemented by using IFFT at the
modulation side and using a FFT at the demodulation side.
Let X={X0,X1,…..Xn-1} represent the length of a data symbol.
The IDFT of the symbol block X will provide us the time
domain sequence [15] .
xn = IFFTN{{Xk}(n)
A guard interval is introduced in the sequence X in order to
mitigate the effect of channel delayspread.
Figure 6: Frame structure of OFDM system.
The G denotes the guard interval length. The sequence X is
passed through a pair of ADC to generate the real and
imaginary part with sample rate = 1/Ts and the analog I and Q
signals are unconverted to the RF channel. The guard interval
length must be equal to or exceed the channel impulse
response in order to prevent ISI [15]. Due to the guard interval
the discrete linear convolution of the transmitted sequence
with the channel impulse response becomes a circular
convolution. The OFDM symbol time can be represented as
T = NT + GT it is the time taken to transmit one full OFDM
symbol. On the receiver side the G is removed from the
receiver block and DFT is performed on the resulting sequence
and the sequence is obtained.
Pilot insertion: Constant tracking is required for the channel
coefficients, which is aided by pilot symbols or variable
subcarrier position [16].
Figure 7: Pilot tone generation
For different standards the insertion of pilot tones at the
respective subcarrier will vary. For a MIMO system the Pilot
sequence Pn is coded over space and time to form orthogonal
matrices.

Figure8: MIMO OFDM Using 2 individual space-time
encoders, each using 2 transmit antennas.
6. MIMO-OFDM AND SPACE-TIME CODING
From the above figure (8) we have Nt number of
transmitters and Nr number of receivers. The above system
is realized using a space time encoder block which concerts
the single stream of binary data into Nt parallel streams of
constellation symbols. All these streams are fed into a IFFT
block and transmitted by their respective antennas.
After the FTT processing at the receiver side as
mentioned earlier MLSE algorithm is use to decode the
stream. A interference cancellation scheme is employed at
the receiver end which attempts to separate the received
signal due to other space time encoders [17].Again MLSE is
employed in decoding followed by interference cancelation.
With proper cyclic extension and sample timing we have,
(5)
Hij[n,k] represents the normalized channel frequency
response of block n of the OFDM system for its kth
tone. In
the above case after normalization and assuming the same
signal strength for each of the transmitter antennas the space
time code can be approximated to a Gaussian interference
characterized by instantaneous channel frequency response
[17].
Space time processing for a MIMO-OFDM system can be
approached by two methods. First, multicarrier delay-
diversity modulation and a closed loop system which has
the channel knowledge at the transmitting end.
Multicarrier delay diversity modulation
With the help of multiple transmitting antennas delayed
copies of the same signal is transmitted and through
maximum likelihood sequence estimation the receiver
obtains the transmitted sequence [18][19]. Delay diversity is
the natural option for OFDM systems as OFDM systems
can mitigate frequency-selective fading. OFDM in
combination with multi carrier delay diversity modulation
(MDDM) can achieve full spatial diversity on flat fading
channels [20]. One of the main advantages of using MDDM
is that it is a highly flexible approach which allows the
number of transmitter antenna to be changed without
affecting the employed codes.
Closed loop MIMO-OFDM
I case of the closed loop MIMO-OFDM system the channel
knowledge is already available to the transmitter. Since
OFDM is capable of reducing a frequency selective to a
spectra of flat fading MIMO channels, this closed loop
system is capable of eigendbeamforming [21] on a tone by
tone basis to convert the frequency selective channel into a
collection of M and N parallel subchannels.
Figure 9:Eigendbeamforming and OFDM in a closed loop
system.
7.SPACE-TIME-FREQUENCY (STF) CODING FOR MIMO-OFDM
SYSTEMS
The Space time codes were basically designed to extract the
special diversity from a flat fading MIMO channel but they
are ineffective at extracting the multipath diversity of a
frequency selective fading channel [18]. Hence to achieve
full diversity requires the information to be spread over both
the tones and over the transmitting antennas. To achieve this
we employ a new technique called as Space-time-frequency
code which maps information symbol over the tones as well
as the antennas. Thus, it enables to extract both the
frequency and the spatial diversity.
In a general OFDM system which does not exploit the
frequency diversity, the data streams meant for the OFDM
tones enter the ST coders which is then transmitted through
different antennas and transmitted across the frequency
channel as shown in the figure below.

Figure 10(a) separate coding for each tone (b) Joint
space/time/frequency coding [22]
As mentioned earlier coding through the tones is
necessary to exploit the frequency diversity of the system.
Hence as shown in the figure 10 (b) a coder must be able to
perform in such a way that it uses all the symbols from the
every tone as input and must be able to distribute the output
to all the tones of all the antennas simultaneously.
Considering Nt transmit antennas and Nf tones the size of
the coder can be determines as NtNf. The transmit antennas
sends the signal over the channel and the channel matrix can
be represented as
[22]
h(i,j) represents the transfer function.
We are almost able to achieve capacities close to mean
capacity using this system as coding across all the channels
enables us to exploit inherent diversity among antennas and
the tones and the capacity fluctuations due to fading is
almost completely eliminated. If the tones are widely
separated generally there is no crosstalk but even if the
tones overlap and create crosstalk it is eliminated by the
carrier orthogonality. Since this system allows coding in
time possible it exploits all forms of diversity namely space,
time and frequency.This system is most effective in cases
where there is very less time diversity and in most practical
conditions if either the transmitter or the receiver is
stationary not too much time diversity is available and this
system will be most effective in such cases.
8.MIMO IN 3GPP LTE AND BEYOND
The key components of MIMO in 3GPP are spatial
multiplexing, beamforming and transmit diversity which has
enabled MIMO systems to prove very high data rates with
spectral efficiency. To support 3GPP downlink data rates of
upto 300 Mbps and 75mbps in the uplink needs to be
achieved [23]. In the 3GPP LTE standard MIMO systems
have effectively been able to improve the cell coverage,
data rates and the average cell thoughput. The 3GPP system
adopted various number of MIMO technologies comprising
of single-user MIMO, Multi-user MIMO, dedicated
beamforming and rank-1 loop pre coding.
The MU-MIMO technology enables the application of
different spatial layers to various users with the same time
and frequency resource. The closed loop precoding allows
improved data coverage utilizing the SU-MIMO system.
Data coverage extension is also achieved through the
dedicated beamforming technique of MIMO systems.
The SU-MIMO is applied to the Physical download
shared channel (PDSCH) which represents the physical
layer which is responsible for the transmission of data from
the network to the UE. It can be operated in two different
modes namely, Closed-loop spatial multiplexing mode and
the open loop spatial multiplexing mode.
To achieve the requirements of 3GPP and beyond MIMO
systems have to achieve a downlink spectrum efficiency of
30bps/Hz and uplink peak spectrum efficiency of 15bps/Hz
[23]. Which are the specifications for LTE advanced
system. These are the challenges faced by the current
MIMO systems.
9.CONCLUSION
In this paper we have seen how a MIMO-OFDM system
operates and uses diversity coding techniques in wireless
systems to improve spectral efficiency and reduce
interference. MIMO-OFDM system has clearly been a
success in 3G systems and WLANS and is definitely a
promising breakthrough in the area of wireless and cellular
communications. With developments in diversity coding
techniques MIMO has managed to reduce complexity and
overcome a few drawbacks. With ongoing research and its
backward compatibility it holds lot of potential to achieve
high data rates in the future of wireless communication
systems.
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University press,2005
Mithul Thanu Muthukumar received the
B.Sc degree in Electronics and communications Engineering from Anna
University, Tamilnadu, India. Currently pursuing his Masters Degree in
Electrical and Electronics Engineering at the University of Colorado at
Boulder. His areas of interests are Wireless and Cellular communications,
Remote sensing and Satellite Communications.

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