Ofdm mimo and v-blast algorithm-key to high speed wireless communication

International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN
0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 2, March – April (2013), © IAEME
426
OFDM-MIMO AND V-BLAST ALGORITHM-KEY TO HIGH SPEED
WIRELESS COMMUNICATION
Sanjay D Deshmukh1
, Rishi Bagadia2
, Prachi Kapoor3
, Dharmesh Gohil4
1
Asst.Professor, Department of Electronics and Telecommunication, Rajiv Gandhi Institute of
Technology, India.
2,3,4
Department of Electronics and Telecommunication, Rajiv Gandhi Institute of Technology,
India.
ABSTRACT
Orthogonal frequency division multiplexing( OFDM ) is a multi-carrier modulation
scheme, which may be combined with antenna arrays at the transmitter and receiver to
increase the diversity gain and/or to enhance the system capacity on time-variant and
frequency-selective channels, resulting in a multiple-input multiple-output (MIMO)
configuration .This paper presents an overview of the OFDM-MIMO wireless technology
covering channel models, performance limits and trans-receiver system .The significance of
OFDM lies in its inherent capability to reduce inter-symbol interference(ISI) using cyclic
prefix. Using simulations, the OFDM signal has been generated with the help of
mathematical transforms namely the Fourier transform. The comparison of bit error rate
(BER) and signal to noise ratio (SNR) for various modulation schemes has been performed
and the best one is selected for transmission. Also the comparison of BER and SNR for
Single Input Single Output (SISO), Single Input Multiple Output (SIMO) and Multiple Input
Multiple Output (MIMO) is graphically observed. And with MIMO proving to be the best,
the effect on capacity is observed for increased number of antennas.For MIMO systems,
Vertical Bell Labs Space Time Algorithm (V-BLAST) is an ordered successive cancellation
method applied to receiver and at every stage the stream with the highest SNR is
decoded.This paper also presents an overview of the V-BLAST architechture.
Keywords: Bit error rate(BER) ,Cyclic prefix , Inter-symbol interference(ISI) , Multiple-
input multiple-output (MIMO), Orthogonal frequency division multiplexing(OFDM) , Signal
to noise ratio (SNR) ,Vertical Bell Labs Space Time Algorithm(V-BLAST).
INTERNATIONAL JOURNAL OF ELECTRONICS AND
COMMUNICATION ENGINEERING & TECHNOLOGY (IJECET)
ISSN 0976 – 6464(Print)
ISSN 0976 – 6472(Online)
Volume 4, Issue 2, March – April, 2013, pp. 426-440
© IAEME: www.iaeme.com/ijecet.asp
Journal Impact Factor (2013): 5.8896 (Calculated by GISI)
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IJECET
© I A E M E

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1. INTRODUCTION
The growing demand of multimedia services and the growth of Internet related
contents lead to increasing interest to high speed communications. The requirement for wide
bandwidth and flexibility imposes the use of efficient transmission methods that would fit to
the characteristics of wideband channels especially in wireless environment where the
channel is very challenging. In wireless environment the signal is propagating from the
transmitter to the receiver along number of different paths, collectively referred as multipath.
While propagating the signal power drops of due to three effects: path loss, macroscopic
fading and microscopic fading. Fading of the signal can be mitigated by different diversity
techniques. To obtain diversity, the signal is transmitted through multiple (ideally)
independent fading paths e.g. in time, frequency or space and combined constructively at the
receiver. A promising solution for significant increase of the bandwidth efficiency and
performance under noise is the exploitation of the spatial dimension. Multiple input-multiple-
output (MIMO) exploits spatial diversity by having several transmit and receive antennas [1].
OFDM is modulation method known for its capability to mitigate multipath. In OFDM the
high speed data stream is divided into narrowband data streams, corresponding to the
subcarriers or sub channels. As a result the symbol duration is several times longer than in a
single carrier system with the same symbol rate. The symbol duration is made even longer by
adding a cyclic prefix to each symbol. As long as the cyclic prefix is longer than the channel
delay spread OFDM offers inter-symbol interference (ISI) free transmission. The paper
explains these concepts in detail with the help of equations providing a better understanding
[2].Another key advantage of OFDM is that it dramatically reduces equalization complexity
by enabling equalization in the frequency domain. OFDM, implemented with IFFT at the
transmitter and FFT at the receiver, converts the wideband signal, affected by frequency
selective fading, into narrowband flat fading signals thus the equalization can be performed in
the frequency domain [3].
The combination MIMO-OFDM is very natural and beneficial since OFDM enables
support of more antennas and larger bandwidths since it simplifies equalization dramatically
in MIMO systems. The combination of MIMO and OFDM has been designed to improve the
data rate and the Quality of Service of the wireless system by exploiting the multiplexing
gain and/or the diversity gain which is a major problem in communication. This paper
provides a general overview of this promising transmission technique. [4]
In order to separate the N simultaneously transmitted signals at the receiver, several
space time coding (STC) and space division multiplexing (SDM) techniques are developed.
STC introduces a spatiotemporal correlation among all the transmitted signals for the
improvement of information protection, while the aim of SDM is to enhance the data rate.
The diagonally-layered space-timearchitecture proposed by Foschini , now known
asdiagonal Bell Laboratories Layered Space-Time or D-BLAST, is one such approach. D-
BLAST utilizes multi-element antenna arrays at both transmitter and receiver and an elegant
diagonally layered coding structure in which code blocks aredispersed across diagonals in
space-time. However, the diagonal approach suffers from certain implementation
complexities which make it inappropriate for initial implementation. D-BLAST faced certain
implementation complexities and was replaced by a simplified version of BLAST, known as
vertical BLAST or V-BLAST and is found exceptional in its spectral efficiency which ranges
from 20-40 bps/Hz for a reasonable range of SNR 24-34 dB. V-BLAST seems to provide the
best trade-off between the system performance and implementation complexity. A general
overview of the V-BLAST architecture has also been discussed in the paper.

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2. ORTHOGONAL FREQUENCY DIVISION MULTIPLEXING
Orthogonal Frequency Division Multiplexing (OFDM) is simply defined as a form of
multi-carrier modulation The original bandwidth is split into smaller and narrower sub-bands,
known as “sub-band” carriers where the carrier spacing is carefully selected so that each sub-
carrier is orthogonal to the other sub-carriers. Nulls in each sub-carrier's spectrum land at the
centre of all other sub-carriers.
2.1 Principle of OFDM transmission technology
The "orthogonal" part of the OFDM name indicates that there is a precise mathematical
relationship between the frequencies of the carriers in the system. It is possible to arrange the
carriers in an OFDM signal so that the sidebands of the individual carriers overlap and the signals
can still be received without adjacent carrier’s interference. Two signals are orthogonal if their
dot product is zero. That is, if we take two signals multiply them together and if their integral
over an interval is zero, then two signals are orthogonal in that interval. If a sine wave of
frequency m is multiplied by a sinusoid (sine or cosine) of a frequency n, then the product is
given by :
(1)
where both m and n are integers. By simple trigonometric relationship, this is equal
to a sum of two sinusoids of frequencies (n-m) and (n+m). Since these two components are each a
sinusoid, the integral is equal to zero over one period. So when a sinusoid of frequency n
multiplied by a sinusoid of frequency m, the area under the product is zero. In general for all
integers n and m, sin mx cos mx, cos nx, sin nx are all orthogonal to each other. These frequencies
are called harmonics. The orthogonality allows simultaneous transmission on a lot of sub-carriers
in a tight frequency space without interference from each other.
2.2 OFDM Transmission and Reception
Single high-rate bit stream is converted to low-rate N parallel bit streams. Each parallel bit stream
is modulated on one of N sub-carriers [5]. Each sub-carrier can be modulated differently, e.g.
BPSK, QPSK or QAM. To achieve high bandwidth efficiency, the spectrum of the sub-carriers is
closely spaced and overlapped. This overlapping property makes OFDM more spectral efficient
than the conventional multicarrier communication schemes.The block diagrams of OFDM
transmitter and receiver are as represented below:
Fig.1 OFDM-MIMO Transmitter block diagram

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Fig.2 OFDM-MIMO Receiver block diagram
A guard interval is inserted between symbols to avoid inter symbol interference (ISI) caused
by multipath distortion
2.2.1 Serial to Parallel Conversion
Data to be transmitted is typically in the form of a serial data stream. In OFDM, each
symbol typically transmits 40- 4000 bits, and so a serial to parallel conversion stage is needed
to convert the input serial bit stream to the data to be transmitted in each OFDM symbol. The
data allocated to each symbol depends on the modulation scheme used and the number of
subcarriers. At the receiver the reverse process takes place, with the data from the subcarriers
being converted back to the original serial data stream.
2.2.2 Interleaver
OFDM is invariably used in conjunction with channel coding(forward error
correction), and almost always uses frequency and/or time interleaving.
Frequency(subcarrier) interleaving increases resistance to frequency-selective channel
conditions such as fading. For example, when a part of the channel bandwidth fades,
frequency interleaving ensures that the bit errors that would result from those subcarriers in
the faded part of the bandwidth are spread out in the bit-stream rather than being
concentrated. Similarly, time interleaving ensures that bits that are originally close together in
the bit-stream are transmitted far apart in time, thus mitigating against severe fading as would
happen when travelling at high speed.
The reason why interleaving is used on OFDM is to attempt to spread the errors out in
the bit-stream that is presented to the error correction decoder, because when such decoders
are presented with a high concentration of errors the decoder is unable to correct all the bit
errors, and a burst of uncorrected errors occurs.
2.2.3 Signal Mapping
A large number of modulation schemes are available allowing the number of bits
transmitted per carrier per symbol to be varied. Digital data is transferred in an OFDM link
by using a modulation scheme on each subcarrier. A modulation scheme is a mapping of data
words to a real (In phase) and imaginary (Quadrature) constellation, also known as an I-Q
constellation. The number of bits that can be transferred using a single symbol corresponds to
log2(M), where M is the number of points in the constellation, thus 256-QAM transfers 8 bits
per symbol. Increasing the number of points in the constellation does not change the
bandwidth of the transmission, thus using a modulation scheme with a large number of
constellation points, allows for improved spectral efficiency. For example 256-QAM has a

430
spectral efficiency of 8 b/s/ Hz, compared with only 1 b/s/Hz for BPSK. However, the greater
the number of points in the modulation constellation, the harder they are to resolve at the
receiver.
2.2.4 Frequency to Time Domain Conversion
The OFDM message is generated in the complex baseband. Each symbol is
modulated onto the corresponding subcarrier using variants of phase shift keying (PSK) or
different forms of quadrature amplitude modulation (QAM). The data symbols are converted
from serial to parallel before data transmission. The frequency spacing between adjacent
subcarriers is Nπ/2, where N is the number of subcarriers. This can be achieved by using the
inverse discrete Fourier transform (IDFT), easily implemented as the inverse fast Fourier
transform (IFFT) operation.
As a result, the OFDM symbol generated for an N-subcarrier system translates into N
samples, with the ith
sample being at the receiver, the OFDM message goes through the exact
opposite operation in the discrete Fourier transform (DFT) to take the corrupted symbols
from a time domain form into the frequency domain. In practice, the baseband OFDM
receiver performs the fast Fourier transform (FFT) of the received message to recover the
information that was originally sent.
2.2.5 Inter symbol interference
In OFDM, ISI usually refers to interference of an OFDM symbol by previous OFDM
symbols .For OFDM the system bandwidth is broken up into N subcarriers, resulting in a
symbol rate that is N times lower than the single carrier transmission. This low symbol rate
makes OFDM naturally resistant to effects of Inter-Symbol Interference (ISI) caused by
multipath propagation. In multipath propagation, multiple signals arrive at the receiver at
different times due to the transmission distances being different. This spreads the symbol
boundaries causing energy leakage between them.
2.2.6 Guard period
Fig.3 Cyclic Prefix in OFDM
The effect of ISI on an OFDM signal can be further improved by the addition of a
guard period to the start of each symbol. This guard period is a cyclic copy that extends the
length of the symbol waveform. Each subcarrier, in the data section of the symbol has an
integer number of cycles. Because ofthis, placing copies of the symbol end-to-end results in a
continuous signal ,with no discontinuities at the joints. Thus by copying the end of a symbol
and appending this to the start results in a longer symbol time. Figure 3 shows the insertion of
a guard period, also known as cyclic prefix. The transmitted signal consists of a sequence of
these OFDM symbols. To denote different OFDM symbols when a sequence of symbols

431
rather than a single symbol is being considered we need to extend the notation to include a
time index.
Let xሺ݅ሻ ൌ ሾ‫ݔ‬଴ሺ݅ሻ‫ݔ‬ଵሺ݅ሻ‫ݔ‬ଶሺ݅ሻ … … ‫ݔ‬ேିଵሺ݅ሻሿ்
(2)
be the output of the IFFT in the ith symbol period. In most OFDM systems, a CP is added to
the start of each time domain OFDM symbol before transmission. In other words a number of
samples from the end of the symbol is appended to the start of the symbol [6]. So instead of
transmitting:
xሺ݅ሻ ൌ ሾ‫ݔ‬଴ሺ݅ሻ‫ݔ‬ଵሺ݅ሻ‫ݔ‬ଶሺ݅ሻ … … ‫ݔ‬ேିଵሺ݅ሻሿ்
(3)
the sequence,
‫ݔ‬஼௉ሺ݅ሻ ൌ ሾ‫ݔ‬ேିீሺ݅ሻ … . . ‫ݔ‬ேିଵሺ݅ሻ, ‫ݔ‬଴ሺ݅ሻ … . . ‫ݔ‬ேିଵሺ݅ሻሿ ்
(4)
is transmitted, where G is the length of the cyclic prefix.
The total length of the symbol is T=Tg+Ts, where Tsis the total length of the symbol in
samples, Tgis the length of the guard period in samples. In addition to protecting the OFDM
from ISI, the guard period also provides protection against time-offset.
3 .OFDM EQUATIONS
Let ሼ‫ݏ‬௡,௞ሽ௞ୀ଴
ேିଵ
be the complex symbols transmitted at the nth OFDM block, then the
OFDM modulated signal can be represented by:
‫ݏ‬௡ሺ‫ݐ‬ሻ ൌ ෌ ‫ݏ‬௡,௞݁௝ଶగ௞∆௙௧ேିଵ
௞ୀ଴
(5)
where Ts, ∆f and N are the symbol duration, the sub channel space and the number of sub
channels of OFDM signals, respectively. For the receiver to demodulate the OFDM signal the
symbol duration should be long enough such that Ts∆f = 1 which is also called the orthogonal
condition since it makes ݁ି௝ଶగ௞∆௙௧
orthogonal to each other for different k. With the
orthogonal condition, the transmitted symbols sn,kcan be detected at the receiver by:
s n,k=
ଵ
்௦
‫׬‬ ‫ݏ‬௡ሺ‫ݐ‬ሻ ݁ି௝ଶగ௞∆௙௧்௦
଴
݀‫ݐ‬ ሺ6ሻ
The sampled version of the baseband OFDM signal s(t) in (2) can be expressed as:
‫ݏ‬௡ ൬݉
ܶ௦
ܰ
൰ ൌ ෍ ‫ݏ‬௡,௞݁௝ଶగ௞∆௙௠
೅ೞ
ಿ ൌ
ேିଵ
௞ୀ଴
෍ ‫ݏ‬௡,௞݁௝
మ೘ഏೖ
ಿ
ேିଵ
௞ୀ଴
ሺ7ሻ
which is actually the inverse discrete Fourier transform (IDFT) of the transmitted symbols
ሼ‫ݏ‬௡,௞ሽ௞ୀ଴
ேିଵ
and can efficiently be calculated by fast Fourier transform (FFT). It can easily be
seen that demodulation at the receiver can be performed using DFT instead of the integral in
(6).

432
A cyclic prefix is critical for OFDM to avoid inter symbol interference caused by the
delay spread of wireless channels. Without the CP, the length of the OFDM symbol is Ts.
With the CP, the transmitted signal is extended to T = Tg + Ts and can be expressed as:
(t) = −Tg ≤ t ≤ Ts(8)
It is obvious that :
(t) = sn(t + Ts) for –Tg≤ t ≤ 0, (9)
which is why it is called the Cyclic prefix.
4. MULTIPLE INPUT MULTIPLE OUTPUT (MIMO) TECHNIQUE
Multiple-Input-Multiple-Output (MIMO) is a cutting edge antenna technology
transmitting multiple data streams on multiple transmitters to multiple receivers. Multiple
antennas are used especially when the link has Non-Line-of-Sight. MIMO increases the range
and data rates both.
Fig.4 SISO,SIMO AND MISO representation
Now the capacity of different antenna systems will be studied in order to see the
dramatic increases in capacity obtained by using MIMO systems. The expressions are
approximate, but they give an intuition for the derived benefits in terms of channel capacity
when using multiple antennas.
4.1 Types of smart antenna technology
4.1.1 Single-Input, Single-Output (SISO)
Assume that for a given channel, whose bandwidth is B, and a given transmitter
power of P the signal at the receiver has an average signal-to-noise ratio of SN . Then, an
estimate for the Shannon limit on channel capacity, C, is
C B. log2 (1 + SNR0) (10)
4.1.2 Single-Input, Multiple-Output (SIMO)
For the SIMO system, we have N antennas at the receiver. If the signals received on
these antennas have on average the same amplitude, then they can be added coherently to
produce an N2
increase in the signal power. Hence, there is an overall increase in the SNR,
SNR = N.SNR0
(11)

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Thus, the channel capacity for this channel is approximately equal to
C B. log2 (1 + N.SNR0) (12)
4.1.3 Multiple-Input, Single-Output (MISO)
In the MISO system, we have M transmitting antennas. The total transmitted power is
divided up into the M transmitter branches. If the signals add coherently at the receiving
antenna we get approximately an M-fold increase in the SNR as compared to the SISO case.
Thus, the overall increase in SNR is approximately,
SNR؆
ெమሺௌூீே஺௅௉ைௐாோ/ெሻ
ேைூௌா
=M.SNR0(13)
Channel capacity for this channel is approximately equal to:
C B. log2 (1 + M.SNR0) (14)
4.1.4 Multiple-Input, Multiple-Output (MIMO)
Different signal transmitted by each antenna, in MIMO using the same bandwidth and
still be able to decode correctly at the receiver. The capacity of each one of these channels is
roughly equal to:
C B. log2 (1 +
ே
ெ
.SNR0) (15)
But, since we have M of these channels (M transmitting antennas), the total capacity of the
system is,
C M.B. log2 (1 +
ே
ெ
.SNR0) (16)
Thus, as we can see from (16), we get a linear increase in capacity with respect to the
number of transmitting antennas. So, the key principle at work here, is that it is more
beneficial to transmit data using many different low-powered channels than using one single,
high-powered channel.
4.2 MIMO System Model
Fig.5 2×2 MIMO System Model

434
Let us consider single user MIMO communication system with 2 antennas at the
transmitter and 2 antennas at the receiver. Consider that we have a transmission sequence is
{x1, x2,...........,xn}. In normal transmission, we send x1 in the first time slot, x2 in the second
time slot and xn in the nth time slot. Now we have two transmit antennas, we may groups the
symbols into groups of two. In the first time slot, send x1 and x2 from the first and second
antenna. In the second time slot, send x3 and x4 from the first and second antenna and in next
time slot x5 and x6 and so on. Let us consider for 2 x 2 MIMO. The signal received on the
first antenna is given by:
r1 = h11s1 + h12s2 + n1 (17)
The signal received on the second antenna is given by:
r2= h21s1 + h22s2 + n2 (18)
where, ‫ݕ‬1ܽ݊݀‫ݕ‬2 are the received symbol on the first and second antenna respectively,ℎ11 is
the channel from 1‫ݐݏ‬ transmit antenna to 1‫ݐݏ‬ receive antenna,ℎ12 is the channel from 2݊݀
transmit antenna to 2݊݀ receive antenna,ℎ21 is the channel from 1‫ݐݏ‬ transmit antenna to 2݊݀
receive antenna, ℎ22 is the channel from 2݊݀ transmit antenna to 2݊݀ receive antenna, ‫ݏ‬1ܽ݊݀‫ݏ‬2
are the transmitted symbols and ݊1ܽ݊݀݊2 is the noise on 1‫ݐݏ‬ܽ݊݀ 2݊݀ receive antennas
respectively.
‫݊ݍܧ‬ (1) and ‫݊ݍܧ‬ (2) can be represented in matrix form:
൤
‫1ݕ‬
‫2ݕ‬
൨=ቂ
ℎ11 ℎ12
ℎ21 ℎ22
ቃ ቂ
‫1ݏ‬
‫2ݏ‬
ቃ+ ቂ
݊1
݊2
ቃ (19)
The sampled baseband representation of signal is given by:
y = H x + n (20)
For a system with ‫ܯ‬ܶ transmit antennas and ‫ܯ‬ܴ receive antennas, the MIMO channel at a
given time instant may be represented as a ‫ܯ‬ܴ × ‫ܯ‬ܶ matrix:
቎
‫ܪ‬ଵ,ଵ ‫ڮ‬ ‫ܪ‬ଵ,ெ೅
‫ڭ‬ ‫ڰ‬ ‫ڭ‬
‫ܪ‬ெೃ,ଵ ‫ڮ‬ ‫ܪ‬ெೃெ೅
቏ (21)
5. MIMO OFDM CONJUNCTION
All Wireless links are affected by three common problems of speed, range and
reliability. These parameters are interlinked to each other by strict rules. Speed could be
increased only by sacrificing range and reliability. Range could be extended at the expense of
speed and reliability .And reliability could be improved by reducing speed and range. MIMO-
OFDM provides the 'all in one package' by providing the speed, range and reliability
simultaneously.
With OFDM, a single channel within a spectrum band can be divided into multiple,
smaller sub-signals that transmit information simultaneously without interference. Because
MIMO technology is able to link together many smaller antennas to work as one, it can
receive and send these OFDM's multiple sub-signals in a way that allows the bandwidth to be
substantially increased to each user as required.

435
OFDM is the technique used to mitigate the multipath propagation problem and
MIMO is used for the efficient usage of spectral bandwidth thus combining these techniques
results in wireless system that has best spectral coverage, reliable transmission in highly
obstructive environment, and data rates in 100's of megabits.
MIMO caters the spatial diversity whereas OFDM can use either FDD or TDD
multiplex technique. In the spatial domain, MIMO provide greater capacity. In the time
domain, the modulation method OFDM simplifies the equalization process by eliminating the
inter symbol interference (ISI). With the combination of MIMO and OFDM, greater channel
capacities could be realized with robustness to channel impairments like ISI through cyclic
prefix (CP) and multipath fading through adaptive bit loading.
OFDM creates the slow time varying channel streams and MIMO has capacity of
transmitting the signals over multiple channels by use of an array of antennas thus the
combination of OFDM and MIMO can generate extremely beneficial results. OFDM signals
are greatly affected by the presence of objects, while on the other hand the MIMO takes its
advantage from multipath propagation. So the concept is to generate the OFDM signals and
subject to MIMO antennas.
5.1 MIMO OFDM System Model
The general transceiver structure of MIMO-OFDM is presented above. The system
consists of N transmit antennas and M receive antennas The OFDM signal for each antenna is
obtained by using inverse fast Fourier transform (IFFT)[7] and can be detected by fast
Fourier transform (FFT).The received MIMO-OFDM symbol of the n:th subcarrier and the
m:th OFDM symbol of the i:th receive antenna after FFT can be written as:
ܴ௜ሾ݊, ݉ሿ ൌ ∑ ‫ܪ‬௜,௝ሾ݊, ݉ሿ‫ܣ‬௝ሾ݊, ݉ሿ ൅ ܹ௜
ே
௝ୀଵ ሾ݊, ݉ሿ(22)
where Aj[n,m] is the transmitted data symbol on n:th carrier and m:th OFDM symbol,
Wi[n,m] is the additive noise contribution at i:th receive antenna for the corresponding
symbol in frequency domain and Hi,j[n,m] is the channel coefficient in the frequency domain
between the j:th transmit antenna and the i:th receive antenna:
‫ܪ‬ሾ݊, ݉ሿ ൌ ∑ ℎ௜
ூିଵ
௜ୀ଴ ሾ݉ሿ݁ି௝ଶП௥೔௡/்
(23)
where n takes values between 0 to N-1 I is the number of channel taps in time domain and
h[m] is modelled as an independent zero-mean random Gaussian process. The impulse
response of the Rayleigh fading channel can be expressed as:
hሺt, τሻ ൌ ∑ h୧
୍ିଵ
୧ୀ଴ ሺtሻδሺτ െ τ୧ሺtሻሻ (24)
where hiis the tap gain and τiis the delay associated to the i:th tap. This delay can be
considered to be time invariant. The channel impulse response is assumed to be static over
one OFDM channel symbol duration Tchannel=T+T’, where T is the OFDM symbol duration
and T’ is the cyclic prefix duration. This corresponds to a slowly varying channel where the
coherence time is longer than the channel symbol duration. This assumption prevents from
experiencing inter-carrier interference (ICI). The channel matrix H is an N x M matrix
corresponding to the n:th subcarrier and m:th OFDM symbol:

436
‫ܪ‬ഥሾ݊, ݉ሿ ൌ ቎
‫ܪ‬ଵ,ଵሾ݊, ݉ሿ ‫ܪ‬ଵ,ଶሾ݊, ݉ሿ ‫ڮ‬ ‫ܪ‬ଵ,ேሾ݊, ݉ሿ
‫ڭ‬ ‫ڰ‬ ‫ڭ‬
‫ܪ‬ெ,ଵሾ݊, ݉ሿ ‫ܪ‬ெ,ଶሾ݊, ݉ሿ … ‫ܪ‬ெ,ேሾ݊, ݉ሿ
቏ ሺ25)
Taking the received data symbols of all antennas into account, the expression of the received
data symbol can be presented in the matrix form as follows:
ܴሬԦሾ݊, ݉ሿ ൌ ‫ܪ‬ഥሾ݊, ݉ሿ‫ܣ‬Ԧሾ݊, ݉ሿ ൅ ܹሬሬሬԦሾ݊, ݉ሿ(26)
where
‫ܣ‬Ԧሾ݊, ݉ሿ ൌ ሾ‫ܣ‬ଵ ሾ݊, ݉ሿ‫ܣ‬ଶሾ݊, ݉ሿ … … . ‫ܣ‬ேሾ݊, ݉ሿሿ்
(27)
ܴሬԦሾ݊, ݉ሿ ൌ ሾܴଵ ሾ݊, ݉ሿሾ݊, ݉ሿ … … . ܴேሾ݊, ݉ሿሿ்
(28)
are the Nx1 and Mx1 vectors of the transmitted and received data symbols. To obtain the
transmitted data symbols equation (25) should be solved which is called MIMO-OFDM
equalization.
The useful power ܲ௎ ൌ ‫ܥ|ہܧ‬ሺ݇ሻଶ|‫ۂ‬interference power can be expressed as,
ܲூ ൌ ‫ܫ|ہܧ‬ሺ݇ሻଶ|‫ۂ‬ (29)
The carrier to interference ratio (CIR) is given by:
CIR =
୔౑
୔౅
(30)
The bit error rate (BER) of MIMO-OFDM system employing QAM can be derived from CIR
as
Pୠ ൌ 3
8ൗ උ1 െ ሺ1 ඥ1 ൅ 5 ሺCIR 2⁄ ሻ⁄⁄ ሻඏ (31)
6. V-BLAST OVERVIEW
V-BLAST (Vertical-Bell Laboratories Layered Space-Time) is a detection algorithm
to the reception of multi antenna MIMO systems. Its principle is quite simple, first it detects
the most powerful signal with the highest SNR, and then it regenerates the received signal
from this user from available decision. Then, the signal regenerated is subtracted from the
received signal and with this new sign; it proceeds to the detection of the second user's most
powerful signal, since it has already cleared the first signal and so forth. This gives less
interference to a vector received.
6.1 V-BLAST System
In V-BLAST, the vector encoding process is simply a de-multiplex operation
followed by independent bit-to-symbol mapping of each sub stream. V-BLAST utilizes a
combination of old and new detection techniques to separate the signals in an efficient
manner, permitting operation at significant fractions of the Shannon capacity and achieving
large spectral efficiencies in the process. In procedure of V-BLAST detection, it is generally
assumed that the channel matrix estimate has no estimation error. In the real system, however
there exist the channel estimation errors, thereby causing degradation of system
performance.

437
Fig.6 V-BLAST System
A single data stream is de-multiplexed into M sub streams, and each sub stream is then
encoded into symbols and fed to its respective transmitter. Transmitters 1-M operate cochannel at
symbol rate 1/ T symbols/sec, with synchronized symbol timing. Each transmitter is itself an
ordinary QAM transmitter. The collection of transmitters in effect, comprises, a vector-valued
transmitter,where components of each transmitted M-vector are symbols drawn from a QAM
constellation. We assume that the same constellation is used for each sub-streams, and that
transmissions are organized into bursts of K symbols. The power launched by each transmitter is
proportional to 1/ M so that the total radiated power is constant and independent of M.
At the receiver, an array of antennas is again used to pick up the multiple transmitted sub
streams and their scattered images. Receivers 1-N are, individually, conventional QAM receivers.
These receivers also operate co-channel, each receiving the signals radiated from all M transmit
antennas. Each receiver antenna sees all of the transmittedsub-streams but superimposed and not
separately. However, if the multipath scattering is sufficient, then the multiple sub-streams are all
scattered slightly differently, because they originate from different transmit antennas that are
located at different points in space. By using sophisticated signal processing, these slight
differences in scattering allow the sub-streams to be identified and recovered. In effect, the
unavoidable multipath is exploited to provide a very useful spatial parallelism that is used to
greatly improve data transmission.
6.2 Decoding Algorithm of V-BLAST
V-BLAST detection uses of linear combinatorial nulling techniques such as ZF or MMSE
or non-linear methods like symbol cancellation. Each sub stream turn by turn is considered to be
the desired signal and all the others are interferers. Nulling is obtained by linear weighting of the
received signals [8].For V-BLAST, no channel knowledge required at transmitter.
6.2.1 Main Steps for V-BLAST detection
1. Ordering: choosing the best channel.
2. Nulling: using ZF, MMSE, ML.
3. Slicing: making a symbol decision
4. Canceling: subtracting the detected symbol
5. Iteration: going to the first step to detect the next
symbol.
The detection process consists of two main operations:
1.Interference suppression (nulling): The suppression operation nulls out interference by
projecting the received vector onto the null subspace (perpendicular subspace) of the subspace
spanned by the interfering signals. After that, normal detection of the first symbol is performed.
2. Interference cancellation (subtraction): The contribution of the detected symbol is subtracted
from the received vector.

438
7. RESULTS AND SIMULATIONS
Fig.7 OFDM Transmitted Spectrum Fig.8 Performance comparison for all
modulation techniques
Fig.9 Effect of number of antennas on Fig.10 Effect of Doppler shift on
MIMO MIMO systems
Fig.11 Performance comparison of SISO and MIMO
2 4 6 8 10 12 14 16 18 20
0
5
10
15
20
25
Signal to Noise Ratio(dB)
Capacity(bit/s/Hz)
MIMO Capacity
Shannon Capacity
MIMO, NT=NR=2
MIMO, NT=NR=3
MIMO, NT=NR=4
2 4 6 8 10 12 14 16
10
-2
10
-1
10
0
Signal to Noise Ratio
BitErrorRate
BER VS SNR for all modulation techniques
QAM-4
QAM-16
QAM-32
BPSK
QPSK
FSK
-10 -8 -6 -4 -2 0 2 4 6 8 10
-55
-50
-45
-40
-35
-30
-25
frequency, MHz
powerspectraldensity
OFDM transmitted spectrum
2 4 6 8 10 12 14 16
10
-3
10
-2
10
-1
10
0
BitErrorRate
BER Vs SNR for MIMO-OFDM
ep=0
ep=0.2
ep=0.4
2 4 6 8 10 12 14 16
10
-3
10
-2
10
-1
10
0
BitErrorRate
BER Vs SNR for SISO-OFDM,MIMO-OFDM
SISO-OFDM
MIMO-OFDM

439
The signal represented in the Figure 7 represents the OFDM transmitted spectrum. The
signal to noise ratio (E b/No) and the bit error rate (BER) for various modulation techniques was
compared and it was proved that QAM-32 is the most efficient modulation technique as seen in
Figure 8 . The effect of Doppler shift was studied on the MIMO-OFDM system as seen in Figure
10 .The value ep in figure gives the various values of normalized Doppler shift. With increase in
the Doppler Shift the BER increases thereby decreasing the signal quality [6].Now, the number of
receive and transmit antennas is increased progressively .i.e. 2, 3 ,4 antennas are used .In the
Figure 9, NT and NR denote the number of antennas used at transmitter and receiver respectively
.As the number of antennas is increased, the throughput increases and also the signal to noise
ratio increases. Thus, system performance improves with increased antennas.
The signal to noise ratio (E b/No) and the bit error rate(BER) for single input single output (SISO)
and multiple input multiple output(MIMO) antenna systems was compared. It is observed that the
bit error rate progressively decreases with a simultaneous increase in the Signal to Noise ratio as
observed form Figure 11. The increase in signal to noise ratio is indication of good quality signal
and low bit error rate indicates lesser erroneous transmissions. Overall, MIMO shows better
performance on both fronts. As seen above, MIMO system shows better performance than SISO.
AREAS FOR FUTURE RESEARCH
OFDM-MIMO has been adopted in several wireless standards such as digital audio
broadcasting (DAB), digital video broadcasting (DVB-T), the IEEE 802.11 and the IEEE 802.16a
standards.OFDM is also being pursued for dedicated short-range communications (DSRC) and as
a potential candidate for fourth-generation (4G) mobile wireless systems. However, the various
problems in the area of OFDM-MIMO need to be addressed so that the gains promised by the
technology can be fully leveraged in practical systems .Another critical area for research is
MIMO OFDM channel estimation
This paper provides the basis for system implementation characterized by a complete
design flow, starting from the initial idea and the algorithm definition, through the software and
finally to the hardware implementation using FPGA platform. Also, the V-BLAST approach that
significantly improves spectral efficiencies, and robustness as well as acceptable BER, while
offering simple VLSI could be explored as a next-generation solution.
CONCLUSION
OFDM is a modulation technique which is now used in most new and emerging
broadband wired and wireless communication systems because it is an effective solution to inter-
symbol interferencecaused by a dispersive channel
In this paper, we have briefly described OFDM for wireless communications. A typical OFDM
transmitter and receiver are described and the roles of the main signal processing blocks
explained. The time and frequency domain signals at various points in the system are described. It
is shown that if a cyclic prefix is added to each OFDM symbol, any linear distortion introduced
by the channel can be equalized.In this paper, we provide an overview of general multiple
antenna system and the general V- BLAST systemIt is observed that with increase in the Doppler
Shift the BER increases thereby decreasing the signal quality. The capacity of MIMO systems
increases with increase in number of transmitting and receiving antennas. OFDM and MIMO
together can generate extremely beneficial results. OFDM signals are greatly affected by the
presence of objects, while on the other hand the MIMO takes its advantage from multipath
propagation. V-BLAST is a detection algorithm to the reception of multi antenna MIMO systems
and shall form the backbone of next generation MIMO systems.
In conclusion, OFDM-MIMO is a very promising technology for wireless communications.

440
REFERENCES
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OFDM and Its Wireless Applications: A Survey”, IEEE Transactions On Vehicular
Technology, Vol. 58, May 2009.
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