Impact of Guard Interval in Proposed MIMO-OFDM System for wireless communication

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					                                                                 (IJCSIS) International Journal of Computer Science and Information Security,
                                                                                                                    Vol. 8, No. 9, 2010

 Impact of Guard Interval in Proposed MIMO-OFDM
         System for wireless communication
                         M.P.Chitra                                                               Dr.S.K. Srivatsa
        Research Scholar, Sathyabama University,                                Senior Professor, St.Joseph College of Engineering,
                    Chennai, India.                                                               Chennai, India.

Abstract - Alamouti’s space-time coding scheme for Multi-Input               very simple decoding and has been adopted in third generation
Multi-Output (MIMO) system has drawn much attention in 4G                    (3G) cellular systems such as W-CDMA. Recently, many
wireless    technologies.   Orthogonal     frequency     division            literatures proposed space-time block coding schemes
multiplexing (OFDM) is a popular method for high data rate                   applicable to OFDM systems based on the Alamouti scheme
wireless transmission. OFDM may be combined with antenna                     [2]. When channel can be assumed to be approximately
arrays at the transmitter and receiver to increase the diversity             constant during two consecutive OFDM symbol durations, the
gain and enhance the system capacity on time variant and                     Alamouti scheme is applied across two consecutive OFDM
frequency selective channels, resulting in Multi-Input Multi-                symbols and is referred to as the Alamouti STBC-OFDM or
Output (MIMO) configuration. This paper explores varies
                                                                             simply A-STBC-OFDM.
physical layer research challenges in MIMO-OFDM system
design including channel modeling, space time block code                         The combination of the multiple –input multiple output
techniques, channel estimation and signal processing algorithms              (MIMO) signal processing with orthogonal frequency –division
used for performing time and frequency synchronization in                    multiplexing (OFDM) communication system is considered as
MIMO-OFDM system .The proposed system is simulated in mat                    a promising solution for enhancing the data rates of the next
lab and analyzed in terms of BER with signals to noise ratio                 generation wireless communication systems operating in
(SNR).The difference of BER for coded and uncoded MIMO                       frequency – selective fading environments. The High
system and also the impact of guard interval are simulated using             Throughput Task Group which establish IEEE 802.11n
different wireless channel.
                                                                             standard is going to draw up the next generation wireless local
    Keywords - Multi-Input Multi-Output (MIMO); orthogonal                   area network (WLAN) proposal based on the 802.11 a/g which
frequency division multiplexing (OFDM); Bit error rate (BER);                is the current OFDM- based WLAN standards . The
signals to noise ratio (SNR); Single input single output (SISO);             IEEE802.11n standard based on the MIMO OFDM system
space time block code (STBC)                                                 provides very high data throughput rate from the original data
                                                                             rate 54Mb/s to the rate in excess of 600 Mb/s because the
                                                                             technique of the MIMO can increase the data rate by extending
                       I. INTRODUCTION
                                                                             an OFDM –based system .However ,the IEEE 802.11n
    Orthogonal frequency division multiplexing (OFDM) and                    standard also increases the computational and hardware
space-time coding have been receiving increased attention due                complexities greatly ,compared with the current WLAN
to their potential to provide increased capacity for next                    standards .It is a challenge to realize the physical layer of the
generation wireless systems. OFDM supports high data rate                    MIMO OFDM system with minimal hardware complexity and
traffic by dividing the incoming serial data stream into parallel            power consumption
low-rate streams, which are simultaneously transmitted on
orthogonal sub-carriers[1]. For large enough and a sufficiently                  The FFT/IFFT processor is one of the highest
large guard interval, the channels as seen by each of the sub-               computational complexity modules in the physical layer of the
carriers become approximately frequency flat and allow for                   IEEE 802.11n standard. If employing the traditional approach
high order modulation. Due to this desirable feature, OFDM                   to solve the simultaneous multiple data sequences, several FFT
has been adopted in many commercial systems such as the                      processors are needed in the physical layer of a MIMO OFDM
IEEE 802.11a, ETSI HIPERLAN type2 wireless LAN systems                       system. Thus the hardware complexity of the physical layer in
and DAB, DVB-T broadcasting systems.                                         MIMO OFDM system will be very high .This paper proposes
                                                                             an FFT processor with a novel multipath pipelined architecture
         Space-time coding is a communication technique for                  to deal with the issue of the multiple data sequences for MIMO
wireless systems that realizes spatial diversity by introducing              OFDM applications. The 128/64 FFT with 1-4 simultaneous
temporal and spatial correlation into the signals transmitted                data sequences can be supported in our proposed processor
from different transmits antennas. Many space-time trellis and               with minimal hardware complexity. Furthermore, the power
block codes have been proposed for flat fading channels. Most                consumption can also be saved by using higher radix FFT
significantly, Alamouti discovered a very simple space-time                  algorithm.
block code (STBC) for transmission with two antennas
guaranteeing full spatial diversity and full rate. It lends itself to

                                                                                                       ISSN 1947-5500
                                                                        (IJCSIS) International Journal of Computer Science and Information Security,
                                                                                                                           Vol. 8, No. 9, 2010
                       II.         CHANNEL MODELS                                orthogonal. When p = n and {xi } are real, G is a linear
                                                                                 processing orthogonal design which satisfies the condition that
A. Additive White Gaussian Noise channel                                         GT G = D, where D is the diagonal matrix with the (i,i)th
   With the transmitted signal vector x, the received signal                     diagonal element of the form (l1i x12 +l2i x22+ … + lni xn2 ),
vector y is given by, y = x + n where ‘n’ represents additive                    with the coefficients l1i,l2i,…lni > 0. Without loss of
white Gaussian noise vector. It follows the normal distribution                  generality, the first row of G contains entries with positive
with mean µ and variance σ2.                                                     signs. If not, one can always negate certain columns of G to
                                                                                 arrive at a positive row.

         f ( n) = 1 / (2πσ 2 ) exp(−( n − µ ) 2 / 2σ 2 )          (1)                                                 x1     x2  x3  x4 
                                                                                                                                          
                                                                                                                      − x 2 x1 − x 4 x3 
                                                                                                                G4 = 
B. Flat Fading channel model                                                               x1 x 2                    − x3 x 4   x1 − x 2 
                                                                                     G2 =                                                
                                                                                           − x 2 x1 
                                                                                                                     − x 4 − x3 x 2 x1 
   It is modeled as, y= ax + n where a is the fading                                                                                                           (4)
coefficients with PDF and n is the additive white Gaussian
noise vector.                                                                        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
          f ( a ) = 2a exp(− a 2 )             fora > 0.         (2)             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
C. Frequency selective fading channel                                            contains specific c constellation symbols (or linear
    In this model the channel is considered as a multi-path                      combinations of them), which are transmitted from the n
fading channel. It consists of multiple independent Rayleigh                     antennas as follows: At time t, the entries of row t of C are
faders, which is modeled as complex-valued random processes.                     simultaneously transmitted from the n antennas, with the ith
By assuming uniform antenna pattern and uniform distributed                      antenna sending the ith entry of the row. So each row of C
incident power, the received signal at the receiver can be                       gives the symbols sent at a certain time, while each column of
expressed as                                                                     C gives the symbols sent by a certain antenna.

                                                                                 B. Receive Diversity.
                 y =   ∑       j
                                   a   j   *x+ n
                                                           (3)                       The base-band representation of the classical two-branch
                                                                                 Maximal Ratio Receive Combining (MRRC) scheme. At a
    where ‘n’ is the additive white Gaussian noise and ‘j’                       given time, a signal s0 is sent from the transmitter. The channel
represents multi-path from transmitter.                                          between the transmit antenna and the receive antenna zero is
                                                                                 denoted by h0 and between the transmit antenna and the
                                                                                 receive antenna one is denoted by h1 where h0 = α0 ejθ0 h1 =
                        III.           MIMO SYSTEM.
                                                                                 α1 ejθ1.
A. Space – Time Codes.                                                               Noise and interference are added at the two receivers. The
    Space-time codes (STC) provide transmits diversity for the                   resulting received base band signals are r0 = h0 s0 + n0, r1 =
Multi-Input Multi-Output fading channel. There are two main                      h1 s1 + n1.
types of STC’s namely space-time block codes (STBC) and                             Where n0 and n1 represent complex noise and interference.
space-time trellis codes (STTC). Space-time block codes
operate on a block of input symbols, producing a matrix output                       Assuming n0 and n1 are Gaussian distributed, the
whose columns represent time and rows represent antennas.                        maximum likelihood decision rule at the receiver for these
Their main feature is the provision of full diversity with a very                received signals is to choose signal si if and only if (iff).
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                            d 2 (r 0, h0 si ) + d 2 (r1, h1s i ) ≤ d 2 (r 0, h0 s k ) + d 2 (r1, h1s k )
traditional TCM (Trellis Coded Modulation) for a single-
antenna channel, Space-time trellis codes provide coding gain.                       where d2(x, y) is the squared Euclidean distance between
Since they also provide full diversity gain, their key advantage                 signals x and y calculated by the following expression:
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.                                      d 2 ( x, y ) = ( x − y )( x 2 − y 2 )            (6)
   An STBC is defined by a p x n transmission matrix G,
whose entries are linear combinations of x1,…xk and their                            The receiver combining scheme for two-branch MRRC is
conjugates x1*,…,xk*, and whose columns are pair wise –                          as follows:

                                                                                                                    ISSN 1947-5500
                                                                                   (IJCSIS) International Journal of Computer Science and Information Security,
                                                                                                                                      Vol. 8, No. 9, 2010
                     2                                             2                          D. Channel Estimation.
 (α 0 2 + α12 − 1) si + d 2 (s0 `, si ) ≤ (α 0 2 + α12 − 1) sk + d 2 (s0 `, sk )
                                                                                                1) Enhance Channel Estimation
                                                                                                 Frequency domain and is written in matrix notation
    The maximal-ratio combiner may then construct the signal
s0′, so that the maximum likelihood detector may produce s0″,
which is a maximum likelihood estimate of s0.                                                                           Y = SH + N             (9)

C. Alamouti’s Transmit Diversity Scheme.                                                          Where Y is the Fourier Transform of y, S is the Fourier
   1) Two-Branch Transmit Diversity with One Receiver                                         transforms of S, N is the Fourier Transform of n and H is the
    The base-band representation of the two-branch transmit                                   Fourier transform of h. H can also be represented as
diversity scheme. The Encoding and Transmission Sequence at
a given symbol period, two signals are simultaneously                                                                      H = F .h
transmitted from the two antennas. The signal transmitted from                                                                           (10)
antenna zero is denoted by s0 and from antenna one by s1.
During the next symbol period signal (-s1*) is transmitted from                                  Where F is N x N is the unitary FFT matrix. Therefore Y
antenna zero, and signal s0* is transmitted from antenna one                                  can be represented as,
where * is the complex conjugate operation. The encoding is
done in space and time (space-time coding) [4]. The encoding                                                          Y = SF .h + N
may also be done in space and frequency. Instead of two                                                                                        (11)
adjacent symbol periods, two adjacent carriers may be used
                                                                                                                       Y = Qh + N              (12)
                         TABLE I.            ENCODING TABLE
                                                                                                 Where Q = X F.The estimated channel response in time
                                    Antenna 0           Antenna 1                             domain can be obtained by the LS estimator as,
                   Time t           S0                  S1
                   Time t+T         -S1*                S0*
                                                                                                                    h = Q H Q ) −1 Q H Y        (12)
   2) Transmit diversity with receiver diversity
    It is possible to provide a diversity order of 2M with two                                    Where QH denotes the Hermitian transpose. The successful
transmit and M receive antennas. For illustration, we discuss                                 implementation of the estimator depends on the existence of
the special case of two transmit and two receive antennas in                                  the inverse matrix (Q H Q). If the matrix (Q H Q) is singular
detail. The generalization to M receive antennas is trivial.                                  (or close to singular), then the solution does not exist (or is not
                                                                                              reliable) [5]. But it is a rare case.
    The base band representations of the scheme with two
transmit and two receive antennas. The encoding and                                           E. Training Sequence used.
transmission sequence of the information symbols for this
configuration is identical to the case of a single receiver.                                     To increase the performance of the channel estimation for
                                                                                              OFDM systems in the presence of ISI, Kim and Stuber
     Similarly, for s1, using the decision rule is to choose signal                           proposed this training sequence given by
si iff

                                                                                                               A. exp( j 2π (n / 2) 2 / N )
                                                                                                      X (n) =                                       nεN
                                                   2                                                          0
                                                                                                                                                    n εM
          (α 0 + α 1 + α 2 + α 3 − 1) si
               2         2     2         2
                                                       + d ( s1 `, s i ) ≤
          (α 0 2 + α 1 2 + α 2 2 + α 3 2 − 1) sk       + d 2 ( s1 `, s k )                        where N is the set of sub-carrier odd indices, where M is
                                                                                              the set of sub-carrier odd indices.
   The combined signals are equivalent to that of four branch                                     Transmitted data with pilot. It has alternative zeros. By
MRRC,. Therefore, the resulting diversity order from the new                                  doing so, the transformation of the training sequence in the
two-branch transmit diversity scheme with two receivers is                                    time domain has the special property that its first half is
equal to that of the four-branch MRRC scheme.                                                 identical to its second half, while the desirable peak-to-average
                                                                                              power ratio of one is still retained. In our work, this training
         It is interesting to note that the combined signals from                             sequence is applied to the LS estimator for MIMO-OFDM
the two receive antennas are the simple addition of the                                       systems.
combined signals from each receive antenna. Hence conclude
that, using two transmit and M receive antennas, using the
                                                                                              F. Channel coefficients.
combiner for each receive antenna and then simply add the
combined signals from all the receive antennas to obtain the                                      The Actual, estimated coefficients through least square
same diversity order as 2M- branch MRRC.                                                      estimator and error between them. These Coefficients are

                                                                                                                             ISSN 1947-5500
                                                              (IJCSIS) International Journal of Computer Science and Information Security,
                                                                                                                 Vol. 8, No. 9, 2010
generated using Monte- carlo simulation. The error is in the           frequency-selective channels at a reduced Bit Error Rate (BER)
order of 10-3.                                                         with high quality signal. One of the most important properties
                                                                       of OFDM transmissions is the robustness against multi-path
                                                                       delay spread [6]. This is achieved by having a long symbol
               TABLE II.         CHANNEL COEFFICIENTS
                                                                       period, which minimizes the inter-symbol interference. Un-
            Estimated                 Actual          Error            fortunately, this condition is difficult to fulfill in MIMO-
        -0.7239 - 0.6893i       -0.7243 + 0.6895i   -0.0004            OFDM systems, since the GI length is a system parameter,
        -0.0626 - 0.6063i       -0.0627 + 0.6063i   -0.0000            which is assigned by the transmitter. But the maximum
        -0.1315 + 0.4757i       -0.1317 - 0.4766i   -0.0009
        -0.3951 - 0.0034i       -0.3940 + 0.0030i   0.0011
                                                                       propagation delay is a parameter of the channel, which depends
        0.0143 + 0.2363i        0.0138 - 0.2367i    -0.0004            on the transmission environment. MIMO can be used either for
        -0.1753 + 0.0735i       -0.1752 - 0.0735i   0.0001             improving the SNR or data rate. For improving the data rate,
        0.1065 + 0.0430i        0.1077 - 0.0429i    -0.0011            A-STBC-OFDM system is used.
        -0.0655 + 0.0239i       -0.0652 - 0.0252i   -0.0002
        0.0411 + 0.0211i        0.0412 - 0.0209i    0.0000             A. Proposed FFT Algorithm
                                                                           Given a sequences x(n) ,an N-points discrete Fourier
                                                                       transform (DFT) is defined as

                                                                                                         N −1
                                                                                                 X (k ) = ∑ x[n]      kn
                                                                                                         n =0        WN        (14)

                                                                           Where x[n] and X (k ) are complex numbers. The twiddle
                                                                       factor is

                                                                       WN = e − j ( 2πnk / N ) =
                                                                                                            2πnk            2πnk
                                                                                                     cos(        ) − j sin(      )
                                                                                                             N               N

                       Figure 1. Transmitter

                                                                           Because 128- point FFT is not a power of 8, the mixed –
                                                                       radix FFT algorithm, including the radix-2 and radix -8 FFT
                                                                       algorithms, is needed. Since the algorithm has been derived in
                                                                       detail previously [7], it wills de described briefly here
                                                                                 First let
                                                                                n=64n1+n2 , {n1=0,1 and n2=0,1……63.
                                                                                k=k1+2k2, {k1=0,1and k2 =0, 1……63.                           (16)
                                                                          Using (16),(14) can be rewritten as,

                                                                                                      63 1
                                                                            X (2k 2 + k1 ) =
                                                                                                     ∑∑x[64n + n ]W
                                                                                                     n2 =0n1=0
                                                                                                                     1    2   128
                                                                                                                                 (64n1+n2 )(2k2 +k1)

                                                                                 63       1

                                                                                ∑{∑ x(64n1 + n2 )W2 1 1 W128k1 }W642k2
                            Figure 2. Receiver                                                            n2      n nk

                                                                             = n2 = 0   n1 = 0
                IV.    MIMO – OFDM SYSTEM
   In the area of Wireless communications, MIMO-OFDM is
considered as a mature and well establishes technology. The
main advantage is that it allows transmission over highly

                                                                                                         ISSN 1947-5500
                                                                 (IJCSIS) International Journal of Computer Science and Information Security,
                                                                                                                    Vol. 8, No. 9, 2010
                   V.      SIMULATION RESULTS

              Parameter                  Specification
        Number of Sub-carrier       64
        FFT size                    64
        Modulation type             BPSK
        Channel model               AWGN, Fading Channel
        Doppler Frequency           50Hz
        Guard Interval              10
        Guard Interval              10

    The performance of SISO systems under AWGN and
Fading channel From the graph, the following observations are
made. In additive white Gaussian noise (AWGN), using typical
modulation and coding schemes, reducing the effective bit
error rate (BER) from 10-2 to 10-3 may require only 2 or 3 dB                Figure 5. Performance of A-STBC – OFDM with MIMO – OFDM.
higher signal to-noise ratio (SNR). Achieving the same in a
multi-path fading environment, however, may require up to 10
dB improvement in SNR.
    In fading channel, using typical modulation and coding
schemes, reducing the effective bit error rate (BER) in MIMO
systems from 10-2 to 10-3 may require only 1-4 dB SNR.
Achieving the same in SISO system required greater than 10

                                                                                   Figure 6. Performance Under various Guard Interval

                                                                              The performance of A-STBC OFDM with MIMO-OFDM,
                                                                          obviously space time coded system performs well in higher
                                                                          SNR region when the SNR is greater than 15 dB the BER is
                                                                          less than 10-3 in coded MIMO-OFDM system. But uncoded
              Figure 3. Performance of SISO Systems.                      MIMO system the bit error rate is greater than 10-2 when the
                                                                          SNR is greater than 15 dB.
                                                                              The performance of the MIMO-OFDM is increased when
                                                                          the guard interval is increased. When the guard interval is 10,
                                                                          the BER is decreased less than 10-2 in SNR 15dB.

                                                                              OFDM is an effective technique to combat multi-path delay
                                                                          spread for wideband wireless transmission. OFDM with
                                                                          multiple transmit and receive antennas form a MIMO system to
                                                                          increase system capacity. The system with STC (A-STBC-
                                                                          OFDM) and with high guard interval achieves the system
                                                                          requirements of high quality transmission and high data rate
                                                                          transmission. The performance of the MIMO – OFDM system
                                                                          is optimized with minimum bit error rate.
        Figure 4. Performance of Alamouti’s transmit diversity

                                                                                                     ISSN 1947-5500
                                                                       (IJCSIS) International Journal of Computer Science and Information Security,
                                                                                                                          Vol. 8, No. 9, 2010
[1]   I. Barhumi, G. Leus, and M. Moonen, “Optimal training design for
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[2]   Die Hu, Luxi Yang,Yuhui Shi, and Lianghua He, “Optimal Pilot
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[3]   Sarod Yatawatta and Athina P. Petropulu, “Blind Channel Estimation in
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[4]   Nadem H. Dawod,Ian D. Marsland,and Roshdy H. M. Hafez,” Improved
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[5]   Tsuyoshi Kashima, Kazuhiko Fukawa, and Hiroshi Suzuki,“Adaptive
      MAP Receiver via the EM Algorithm and Message Passings for MIMO-
      OFDM Mobile Communications” IEEE JOURNAL ON SELECTED
[6]   Heunchul Lee, Byeongsi Lee and Inkyu Lee. “Iterative Detection and
      Decoding With an Improved V-BLAST for MIMO-OFDM Systems”
      VOL. 24, NO. 3 MARCH 2006.

                                                                                                          ISSN 1947-5500

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