Noise Reduction in Fast Fading Channel Using OFDM/TDM by ijcsiseditor


									                                                             (IJCSIS) International Journal of Computer Science and Information Security,
                                                             Vol. 9, No. 8, August 2011


       Mr.A.Sagaya Selvaraj, Asst.Professor & Head                           Dr.R.S.D.Wahidabanu, Professor &Head
       Department of Electronics and Communication Engg .                    Department of Electronics and Communication Engg
       IFET College of Engineering, Villupuram -108                          Govt.College of Engg. Salem-11
       Research Scholar, Anna University, Chennai, India                     Anna University, Coimbatore, India
       E-mail:                                         E-mail:

ABSTRACT                                                                      objectives of my paper is to design and evaluate Orthogonal
        Orthogonal Frequency Division Multiplex (OFDM)                        Frequency Division Multiplexing (OFDM) in a Multipath
modulation is being used more and more in telecommunication,                  Fading Channel using computer simulation (MATLAB).To
wired and wireless.. OFDM can be implemented easily, it is                    obtain and compare between the theoretical and simulation
spectrally efficient and can provide high data rates with
                                                                              result for Orthogonal Division Multiplexing (OFDM) in
sufficient robustness to channel imperfections. MMSE-FDE can
                                                                              Raleigh channel. To obtain and compare the Bit Error Rate
improve the transmission performance of OFDM combination
                                                                              (BER) Performance of OFDM.
with time division multiplexing (OFDM/TDM).
       To improve the tracking ability against fast fading robust
pilot-assisted channel estimation is done that uses time-domain               2. OFDM/TDM TRANSMITTER RECEIVER MODEL
filtering   on   a    slot-by-slot   basis   and   frequency-domain
interpolation. The mean square error (MSE) of the channel                      2.1 FDM TRANSMITTER CONFIGURATION
estimator is obtained and then a tradeoff between improving the                         The following figure shows the configuration of an
tracking ability against fading and the noise reduction is done.              OFDM transmitter[1][2]. In the transmitter, the transmitted
BER is calculated by mat lab simulator and compared with
                                                                              high speed data is first converted into parallel data of N sub
conventional OFDM. It is proved that the OFDM/TDM using
                                                                              channels. Then, the transmitted data of each parallel sub
MMSE-FDE achieves a lower BER and provides better tracking
                                                                              channel is modulated by BPSK based modulation.
ability against fast fading.
Keywords:                  Orthoganal        Frequency     Division

Multiplexing(OFDM), BER (Bit Error Rate), MMSE (Minimum

Mean Square Error), Feedback Decision Equalization, …


            In this paper, we focused on designing the mat lab
code for particular channel conditions that affects the BER
performance          for    Orthogonal       Frequency     Division
Multiplexing (OFDM) [1]. The channel used is Raleigh
Channel BPSK modulation has been used in this paper. We                                          fig 2.1. OFDM Transmitter
derive the mean square error and using MMSE-FDE, we
again prove that the BER is reduced [4] [8] [9]. The main

                                                                                                        ISSN 1947-5500
                                                        (IJCSIS) International Journal of Computer Science and Information Security,
                                                        Vol. 9, No. 8, August 2011

2.1.1OFDM TRANSMITTER STRUCTURE                                                             S(t)=sk (t-kNm)for t=0~Nc-1,

                                                                         where k=[t/Nm] with [x] representing the largest integer
                                                                         smaller than or equal to x and s k(t) is the k-th OFDM signal
                                                                         with Nm subcarriers, is given by

                                                                         for t=0~Nm-1, where Es and Tc represent the symbol energy
       fig 2.2 OFDM Frame Structure
                                                                         and the sampling period, respectively. Before transmission,
                                                                         the last Ng samples in the OFDM/TDM frame are inserted as
         The OFDM/TDM transmission system model is
                                                                         the GI at the beginning of the frame.
shown in the above Fig.2.1 Tc-spaced discrete time
representation is used, where Tc represents the fast Fourier
                                                                         3.2 GUARD INTERVAL
transform (FFT) sampling period. To reduce the PAPR, the
                                                                                   One key principle of OFDM is that since low rate
inverse FFT (IFFT) time window for the conventional
                                                                         modulation scheme, where the symbols are relatively long
OFDM is divided into K slots (which constitute the
                                                                         compared to the channel time characteristics suffer less from
OFDM/TDM frame) shown in Fig 2.1. An OFDM signal
                                                                         inter symbol interference caused by multi path. It is the
with   reduced   number    of   sub   carriers   (Nm=Nc/K)is
                                                                         advantageous to transmit a number of low rate streams in
transmitted during each time slot without inserting guard
                                                                         parallel instead of a single high rate stream. Since the
interval (GI) between consecutive OFDM signals, where Nc
                                                                         duration of each symbol is long, it can be affordable to insert
is the number of sub carriers in the conventional OFDM[1].
                                                                         a guard interval between the OFDM symbols and thus the
Hence, the transmission data rate is kept the same as
                                                                         inter symbol interference can be eliminated. The transmitter
conventional OFDM, while the number of sub carriers is
                                                                         sends s cyclic prefix during the guard interval. The guard
reduced by a factor of K, thus reducing the PAPR[6].
                                                                         interval also reduces the sensitivity to time synchronization
3.1 TRANSMIT SIGNAL                                                      problems[8].
       A sequence of Nc            data-modulated      symbols
                                                                                  The orthogonality of sub channels in OFDM can be
{d(i);i=0~Nc-1} is transmitted during one OFDM/TDM
                                                                         maintained and individual sub channels can be completely
frame(equal to the IFFT block size of the conventional
                                                                         separated by using an FFT circuit at the receiver when there
OFDM). The data-modulated symbol sequence {d(i)} of Nc
                                                                         are no ISI and inter carrier interference (ICI) introduced by
symbols is divided into K blocks of Nm=Nc/K symbols each.
                                                                         transmission channel distortion. The spectra of OFDM signal
The k-th block symbol sequence is denoted by {dk(i);
                                                                         are not strictly band limited, the distortion due to multi path
i=0~Nm-1},where dk(i)=d(kNm+i) for k=0~K-1. Nm-point
                                                                         fading causes each sub channel to spread the power into the
IFFT is applied to generate a sequence of K OFDM signals
                                                                         adjacent channel. Moreover, the delayed wave with the delay
with Nm subcarriers. The OFDM/TDM signal can be
                                                                         time larger than 11 symbol time contaminates the next
expressed using the equivalent low pass representation as
                                                                         symbol. In order to reduce this distortion, a simple solution is

                                                                                                   ISSN 1947-5500
                                                         (IJCSIS) International Journal of Computer Science and Information Security,
                                                         Vol. 9, No. 8, August 2011

to increase the symbol duration or the number of carriers.                          r(t)=h(τ,t)s(t-τ)dτ+n(t)
However, this method may be difficult to implement in terms
                                                                              Where h(τ,t) is the impulse response of the radio channel
of carrier stability against Doppler frequency and FFT size.
                                                                          at time t, and n(t) is the complex AWGN.
Another way to eliminate ISI is to create a cyclically
extended guard interval, where each OFDM symbol is
                                                                          3.3 FREQUENCY DOMAIN EQUALISATION
preceded by a periodic extension of the signal itself.
                                                                           The GI inserted OFDM/TDM signal is transmitted over a
The total symbol duration:
                                                                          wireless channel. We assume a Tc-spaced time-delay discrete
                     Ttotal = Tg + Tn
                                                                          channel having L propagation paths with distinct time delays
                                                                          {τl; l=0~L-1}.
                 Tg = guard time interval
          Each symbol is made of two parts. The whole signal
                                                                                   The discrete-time impulse response h(t) of the
is contained in the active symbol, the last part of which is
                                                                          channel can be expressed as
also repeated at the start of the symbol and is called a guard
interval. When the guard interval is longer than the channel
impulse response or the multi path delay, the effect of ISI can
be eliminated.
          However, the ICI or in band fading still exists. The
                                                                          3.4 OFDM RECEIVER CONFIGURATION
ratio of the guard interval to the useful symbol duration is
                                                                                    At the receiver, received signal r(t) is filtered by a
application dependent[9][11]. The insertion of guard interval
                                                                          band pass filter, which is assumed to have sufficiently wide
will reduce the data throughput; Tg is usually smaller than
                                                                          pass band to introduce only negligible distortion in the signal.
                                                                          An orthogonal detector is then applied to the signal where the
After the insertion of a guard interval, the OFDM signal is
                                                                          signal is down converted to IF band. Then, an FFT circuit is
given by
                                                                          applied to the signal to obtain Fourier coefficients of the
 s’(t)=∑∑di (k)exp(j2πfi(t-kTtotal))f’(t-kTtotal)
                                                                          signal in observation periods [iTTotal , iTTotal + Ts].
where f’(t) is the modified pulse waveform of each symbol
defined as

        The OFDM signal is transmitted to the receiver;
however, the transmitted data, s’(t) is contaminated by multi
path fading and AWGN. At the receiver, the received signal                              FIG 3.4. OFDM Receiver
is given by

                                                                                                    ISSN 1947-5500
                                                                   (IJCSIS) International Journal of Computer Science and Information Security,
                                                                   Vol. 9, No. 8, August 2011

The output, di’(k), of the FFT circuit of the ith OFDM                              decomposed into Nc frequency components {R(n); n=0~Nc-
subchannel is given by                                                              1}by applying Nc-point FFT as
            di’(k) = 1/Ts r(t) exp (-j2ðfi(t-kTtotal))dt                                        R(n)=S(n)H(n)+∏(n)
      If the characteristics of delayed wave, hi’(k) in a
                                                                                        where S(n), H(n) and Π(n) are the signal component, the
multipath fading environment can be estimated, therefore the
                                                                                    channel gain and the noise component at the nth frequency,
received data also can be equalized as
                                                                                    respectively, given by
           di’’ (k) = (hi’ * (k)) / (hi’(k)hi’ * (k) )) (di’(k))
where * indicates the complex conjugate.
By comparing dk and di’’ (k), the BER performance can be
calculated. The BER depends on the level of the receiver’s
noise. In OFDM transmission, the orthogonal is preserved
and the BER performance depends on the modulation scheme
in each sub channel.                                                                One-tap FDE is applied as

                                                                                    Here w(n) is the equalization weight for the nth frequency
                                                                                    and Πˆ (n) is the noise component after equalization. We
                                                                                    consider MMSE-FDE.

                                                                                    4. DIGITAL MODULATION SCHEMES
                                                                                    4.1 DIGITAL MODULATION
           FIG 3.4.1. OFDM Receiver Structure
                                                                                              Nowadays, digital modulation is much popular

The received signal can be expressed as                                             compared to analog modulation. The move to digital
                                                                                    modulation       provides      more       information            capacity,
                                                                                    compatibility with digital data services, higher data security,
                                                                                    better   quality     communications,       and     quicker         system
                                                                                    availability. Developers of communications systems face
                                                                                    these constraints:
for t=-Ng~Nc-1, where η(t) is the additive white Gaussian
                                                                                              Available bandwidth
noise (AWGN) process with zero mean and variance 2N0/Tc
                                                                                              Permissible power
with N0 being the single-sided power spectrum density. After
                                                                                              Inherent noise level of the system
removing the GI, the received signal {r(t); t=0~Nc-1} is

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     The RF spectrum must be shared, yet every day there                  modulate a cosine (or sine) wave and the amplitude along the
are more users        for that   spectrum as demand         for           quadrature axis to modulate a sine (or cosine) wave.
communications services increases. Digital modulation
schemes have greater capacity to convey large amounts of
information than analog modulation schemes.

         PSK is a modulation scheme that conveys data by
changing, or modulating, the phase of a reference signal (i.e.
                                                                                              fig 4.2. Constellation Diagram
the phase of the carrier wave is changed to represent the data
                                                                                    In PSK, the constellation points chosen are usually
signal). A finite number of phases are used to represent
                                                                          positioned with uniform angular spacing around a circle. This
digital data. Each of these phases is assigned a unique pattern
                                                                          gives maximum phase-separation between adjacent points
of binary bits; usually each phase encodes an equal number
                                                                          and thus the best immunity to corruption. They are positioned
of bits. Each pattern of bits forms the symbol that is
                                                                          on a circle so that they can all be transmitted with the same
represented by the particular phase.
                                                                          energy. In this way, the moduli of the complex numbers they
                                                                          represent will be the same and thus so will the amplitudes
There are two fundamental ways of utilizing the phase of a
                                                                          needed for the cosine and sine waves. Two common
signal in this way:
                                                                          examples are binary phase-shift keying (BPSK) which uses
                                                                          two phases, and quadrature phase shift keying (QPSK) which
(i) By viewing the phase itself as conveying the information,
                                                                          uses four phases, although any number of phases may be
in which case the demodulator must have a reference signal
                                                                          used. Since the data to be conveyed are usually binary, the
to compare the received signal's phase against; (PSK) or
                                                                          PSK scheme is usually designed with the number of
                                                                          constellation points being a power of 2.
(ii) By viewing the change in the phase as conveying
information – differential schemes, some of which do not
                                                                          4.3 BIT RATE AND SYMBOL RATE
need a reference carrier (to a certain extent) (DPSK).

                                                                                    To    understand     and     compare       different   PSK
A convenient way to represent PSK schemes is on a
                                                                          modulation format efficiencies, it is important to first
constellation diagram. This shows the points in the Argand
                                                                          understand the difference between bit rate and symbol rate.
plane where, in this context, the real and imaginary axes are
                                                                          The signal bandwidth for the communications channel
termed the in-phase and quadrature axes respectively due to
                                                                          needed depends on the symbol rate, not on the bit rate.
their 90° separation. Such a representation on perpendicular
                                                                          Symbol rate=bit rate \ the number of bits transmitted
axes lends itself to straightforward implementation. The
                                                                          with each symbol
amplitude of each point along the in-phase axis is used to
                                                                                  Bit rate is the frequency of a system bit stream. Take,
                                                                          for example, a radio with an 8 bit sampler, sampling at 10

                                                                                                    ISSN 1947-5500
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                                                          Vol. 9, No. 8, August 2011

kHz for voice. The bit rate, the basic bit stream rate in the
radio, would be eight bits multiplied by 10K samples per
second, or 80 Kbits per second. (For the moment we will
ignore the extra bits required for synchronization, error
correction, etc.).                                                                                                             .


           We will derive the theoretical equation for bit error
rate (BER) with Binary Phase Shift Keying (BPSK)
modulation scheme in Additive White Gaussian Noise
(AWGN) channel. With Binary Phase Shift Keying (BPSK),
the binary digits 1 and 0 maybe represented by the analog

levels           and           respectively. The system model
is as shown in the Figure below.

                                                                           fig 4.4.1. conditional probability density function with bpsk

                                                                           .If the received signal is greater than zero(y>0), then the
                                                                           receiver assumes that binary “1” was transmitted. If the
                                                                           received signal is less than zero(y<0),then the receiver
                                                                           assumes that binary “0” was transmitted.

                                                                           i.e., y>0, s1 is transmitted and

fig 4.4. Simplified Block Diagram with BPSK Transmitter-                       y<=0, s0 is transmitted
                                                                                 Probability of error given S1 was transmitted With this

4.4.1 COMPUTING THE PROBABILITY OF ERROR                                   threshold, the probability of error given S1 is transmitted is
                                                                           p(e\s1)(the area in the blue region) Probability of error given
The received signal is,                                                    S0 was transmitted Similarly the probability of error given S0

                         when bit 1 is transmitted and                    is transmitted is p(e\s2)(the area in the green region) Total
                                                                           probability of bit error:
                         when bit 0 is transmitted.
The conditional probability distribution function (PDF) of
for the two cases are:                                                                                                             .

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Given that we assumed that s1and s0are equally                             ionospheric layers, reflection from the earth’s surface or from
probable i.e. p (s1)=p(s0)=1/2, the bit error probability is,              more than one ionospheric layer, and so on. Multipath fading
                                                                           occurs when a transmitted signal divides and takes more than
                              .                                            one path to a receiver and some of the signals arrive out of
                                                                           phase, resulting in a weak or fading signal. Some
                                                                           transmission losses that effect radio wave propagation are
                                                                           ionospheric absorption, ground reflection and free space
                                                                           losses. Electromagnetic interference (EMI) both natural and
                                                                           man made, interfere with radio communications.
                                                                                     The maximum useable frequency (MUF) is the
The given function is the complementary error function
                                                                           highest frequency that can be used for communications

5.1 MULTIPATH                                                              between two locations at a given angle of incidence and time
          In wireless communications, multipath is the                     of day. The lowest usable frequency (LUF) is the lowest

propagation phenomenon        that   results on radio signals              frequency that can be used for communications between two

reaching the receiving antenna by two or more paths. Causes                locations.

of multipath include atmospheric ducting, ionospheric
reflection and refraction and reflection from terrestrial object           5.3MULTIPATH CHANNEL CHARACTERISTICS

such as mountains and buildings. The effects of multipath                            Because there are obstacles and reflectors in the

include constructive and destructive interference and phase                wireless propagation channel, the transmitted signal arrivals

shifting of the signal. This causes Rayleigh Fading named                  at the receiver from various directions over a multiplicity of
after Lord Rayleigh. Rayleigh fading with a strong line of                 paths. Such a phenomenon is called multipath. It is an

sight is said to have a Rician distribution or tobe Rician                 unpredictable set of reflections and/or direct waves each with

fading.                                                                    its own degree of attenuation and delay. Multipath is usually

          In digital radio communications such as GSM                      described by: Line-of-sight (LOS): the direct connection
Multipath can cause errors and affect the quality of                       between the transmitter (TX) and the receiver (RX).

communications. The errors are due to Inter symbol                           Non-line-of-sight (NLOS): the path arriving after reflection

interference (ISI). Equalizers are often used to correct the ISI.          from reflectors. The illustration of LOS and NLOS is shown

Alternatively, techniques such as orthogonal frequency                     below.
division modulation and Rake receivers may be used.

          Multipath Fading is simply a term used to describe
the multiple paths a radio wave may follow between
transmitter and receiver. Such propagation paths include the
ground wave, ionospheric refraction, re radiation by the
                                                                                    fig 5.4. Effect Of Multipath On Mobile Station

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  Characteristics of a Multipath Channel are                                    As shown in the model above, the path between base
– this is the interval for which a symbol remains inside a               station     and   mobile      stations     of     terrestrial     mobile
multipath channel                                                        communications is characterized by various obstacles and
with one line of sight (LOS) path & several multipath, the               reflections. The radio wave transmitted from the base station
signals from the multipath being delayed and attenuated                  radiates in all directions.
version of the signal from the LOS path Multipath will cause                    These radio waves, including reflected waves that are
amplitude and phase fluctuations, and time delay in the                  reflected off of various objects, diffracted waves, scattering
received signal.                                                         waves, and the direct wave from the base station to the
                                                                         mobile station.
6 COMMUNICATION CHANNEL                                                         Therefore the path lengths of the direct, reflected,
6.1 RAYLEIGH FADING CHANNEL                                              diffracted, and scattering waves are different, the time each
         Rayleigh fading is a statistical model for the effect           takes to reach the mobile station is different. The phase of the
of a propagation environment on a radio signal such as that              incoming wave also varies because of the reflection.
used by wireless devices. It assumes that the power of a                         As a result, the receiver receives a superposition
signal that has passed through such a transmission medium                consisting of several waves having different phase and time
(also called a communications channels will vary randomly                of arrival. The generic name of a radio wave in which the
or fade according to a Rayleigh distribution – the radial                time of arrival is retarded in comparison with this direct wave
component of the sum of two uncorrelated Gaussian random                 is called a delayed wave.
variables. It is reasonable model for tropospheric and                             Then, the reception environment characterized by a
ionospheric signal propagation as well as the effect of heavily          superposition of delayed waves                  is called       multipath
built up urban environment on radio signals. Rayleigh fading             propagation environment.
is most applicable when there is no line of sight between the
transmitter and receiver.                                                7. CHANNEL ESTIMATION TECHNIQUES FOR
                                                                         7.1 VARIOUS CHANNEL ESTIMATION TECHNIQUES
                                                                         Channel estimation can be done in 3 ways. They are:
                                                                           1.        Channel estimation with TDM pilot.
                                                                           2.       Channel estimation with FDM pilot.
                                                                           3.       Channel estimation TDM pilot with first order

           Fig 6.2. Principle Of Multipath Channel

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                                                                        7.1.2 CHANNEL ESTIMATION WITH TDM-PILOT
                                                                        AND TDFF

                                                                        Fig 7.1.2. Channel Estimation With TDFF

                                                                        The pilot signal {p(i); i = 0 ∼ Nm−1} is inserted into(K −
                                                                        1)th slot (i.e., dK−1(i) = p(i) for i = 0 ∼ Nm −1)and into the
        Fig 7.1. General Pilot Symbol Assisted OFDM                     GI as a cyclic prefix .Since the same pilot is used for all
                                                                        frames, the (g − 1)th frame’s pilot slot acts as a cyclic prefix
7.1.1 CHANNEL ESTIMATION WITH TDM-PILOT                                 for the gth frame’s GI. Thus, the channel estimation can be
        For   OFDM/TDM        with   pilot-assisted   channel           performed using the gth frame’s Nm-sample GI. Similar
estimation using TDM-pilot ,a pilot signal is transmitted               frame structure was presented for SC transmission. The
followed by Nd OFDM/TDM data frames is given below. Nc                  channel gain estimate and noise variance estimate to be used
subcarriers are used as pilots. First, by reverse modulation,           for FDE are denoted by          He,g(n)and 2σ2e,g respectively.
the instantaneous channel gain estimate Hg(n) at the nth                Hg(n) and σ2g are replaced by He,g(n) and σ2e,grespectively.
subcarrier is obtained .Then, Nc-point IFFT is applied to {             The received pilot {rg(t); t = −Nm ∼ −1} in the GI is filtered
Hg(n); n=0∼ Nc−1} to obtain the instantaneous channel                   on a slot-by-slot basis by the time-domain first-order filtering
impulse response {h(τ); τ =0∼ Nc−1}. Assuming that the                  to increase the signal-to-noise power ratio (SNR) of the pilot
actual channel impulse response is present only within the              signal. The filtered pilot signal is obtained as
GI, the estimated channel impulse response beyond the GI is
replaced with zeros to reduce the noise Finally, Nc-point FFT
is applied to obtain the improved channel gain estimates
{He,g(n); n=0∼ Nc−1}.                                                   for t=−Nm∼ −1, where γ is the forgetting factor with the
                                                                        initial condition r0(t) = r0(t). Then, Nm-point FFT is applied
                                                                        to decompose {rg(t); t = −Nm ∼ −1} into Nm sub carrier
                                                                        components {Rg(q); q=−Nm∼ −1} as

Fig 7.1.1. OFDM Pilot Block Insertion

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                                                       Vol. 9, No. 8, August 2011

With q=n\k for n=0                and the initial condition             domain interpolation is used to obtain the channel gains for
R0(q)=R0(q). The instantaneous channel gain estimate at the             all frequencies (i.e., n=0∼ Nc−1). Nm-point IFFT is
qth subcarrier is obtained by removing the pilot modulation             performed on      { Hg(q); q = 0 ∼ Nm −1} to obtain the
                                                                        instantaneous channel impulse response {h(τ); τ =0∼ Nm−1}
                                                                        and then, Nc-point FFT is applied to obtain the interpolated
                                                                        channel gain estimates {He,g(n); n=0∼ Nc−1}.

                                                                        7.2 PILOT SEQUENCE SELECTION
  where                       ,P(q) and P(q) denotes the qth
frequency     component      of   {p(t);   t=0∼ Nm−1}.Since

               the channel estimates are obtained only at the
frequencies n=0, Nm, 2Nm,. . ., (Nc-1) . Hence, an
interpolation is necessary to obtain the channel gains for all
frequencies (i.e., n = 0 ∼ Nc −1). Frequency-domain
interpolation is applied. First, Nm-point IFFT is performed on
{ Hg(q); q = 0 ∼ Nm−1} to obtain the instantaneous channel
impulse response {h(τ); τ = 0 ∼ Nm−1} as

          Then, Nc-point FFT is applied to obtain the
interpolated channel gain estimates {He,g(n); n = 0 ∼ Nc −1}
for all Nc frequencies as

                                                                                        Fig 7.2. Pilot Amplitude
                                                                       (a) constant amplitude in frequency-domain (FD),
7.1.3 CHANNEL ESTIMATION WITH FDM-PILOT                                (b) constant amplitude in time-domain (TD) and
          For pilot-aided channel estimation with FDM-pilot            (c) constant amplitude in both time- and frequency domains
using frequency-domain interpolation an Nm equally-spaced              (Chu).
pilot subcarriers among     Nc subcarriers are used. First, by                  A selection of pilot sequence is an important design
reverse modulation, the instantaneous channel gain estimate {          issue. If the amplitude of P(n) drops at some frequencies, the
Hg(q); q = nNm for n =0 ∼ Nc−1} at the pilot subcarriers is            noise component in the channel estimate will be enhanced and
obtained. where Nm is the number of pilot subcarriers. Since           thereby, the estimation accuracy will degrade leading to poor
q = nNm , the channel estimates are obtained only at the               performance. To avoid the noise enhancement, it is desirable
frequencies n=0, Nm, 2Nm,. . ., (Nc-1)Hence, the frequency-            that P(n) has constant amplitude irrespective of n. On the

                                                                                                  ISSN 1947-5500
                                                         (IJCSIS) International Journal of Computer Science and Information Security,
                                                         Vol. 9, No. 8, August 2011

contrary, if P(n) is constant for all n, a large     amplitude            8. SIMULATION RESULTS AND ANALYSIS
variation may appear in p(t) and consequently, the pilot signal                     We assume BPSK data-modulation with Nc=256
may be distorted due to nonlinear power amplification. So chu             and Nm=16. Chu sequence is used as the pilot given by
sequence is used as the pilot which makes amplitude constant
                                                                                                                     for t=0∼ Nm−1 .
in both time and frequency domain.
                                                                          (R2-1)The propagation channel is an L=16-path block
                                                                          Rayleigh fading channel having exponential power delay
                                                                          profile with decay factor α as shown below. The zero-mean
          The noise component at the qth pilot subcarrier can
                                                                          independent complex path gains {hl; l=0∼ L−1} remain
 be estimated by subtracting the received pilot component
                                                                          constant over one OFDM/TDM frame length and vary frame-
 He,g(q) P(q) from Rg(q) as
                                                                          by-frame. Without loss of generality, we assume τ0 = 0 < τ1
                                                                          < · · · < τL−1 and that the lth path time delay is τl = lΔ,
                                                                          where Δ (≥ 1) denotes the time delay separation between
 for q=0 ∼ Nm−1.
                                                                          adjacent paths. The maximum time delay of the channel is
                                                                          equal to the GI length (i.e., L=Ng).
 The noise variance estimate can be obtained as


          By applying Nc-point IFFT after FDE, we obtain the
 time-domain OFDM/TDM signal rˆ(t) , which can be
 expressed as

   for t=0~Nc-1.

 Then, the decision variable for the ith data symbol in the k th
                                                                          Fig 8.1. Average BER Performance
 slot    can be obtained using Nm-point FFT as

                                                                          We plot the average BER performance using the proposed
                                                                          channel estimation as a function of Eb/N0 for fDTs=0.0001
                                                                          and α=0 dB. The optimum γ is used for each Eb/N0 value. It
 for i=0~Nm-1 and k=0~K-1.
                                                                          can be seen from the above figure that the OFDM/TDM with

                                                                                                    ISSN 1947-5500
                                                        (IJCSIS) International Journal of Computer Science and Information Security,
                                                        Vol. 9, No. 8, August 2011

the proposed channel estimation achieves a much better BER               8.1 TRADE OFF BETWEEN THE NOISE REDUCTION
performance than OFDM; the required Eb/N0 for BER=10−3                   AND ROBUSTNESS AGAINST THE CHANNEL TIME
reduces by about 6.5 dB in comparison
with OFDM using TDM-pilot when fDTs=0.0001. The                          The MSE equation is given by,
Eb/N0 degradation of OFDM/TDM in comparison to ideal
channel estimation is only about 0.6 dB.
Since γ is one of the key parameters in the estimator, the
robustness of the algorithm is discussed when γ is fixed.
                                                                                                      The MSE of channel estimator with time-domain
                                                                         first-order filtering and frequency-domain interpolation is not
                                                                         a function of the channel frequency-selectivity and it is only
                                                                         a function of Es/N0 and the channel time selectivity.
                                                                         The first term of the above equation represents the influence
                                                                         of AWGN, while the second term represents the influence of
                                                                         the channel time-selectivity. Thus, a trade-off is present; as
                                                                         the                    filter    coefficient       γ     increases       (decreases),       the
                                                                         channelestimator becomes more (less) robust against the
                                                                         channel time selectivity while on the other hand, the
                                                                         estimator ability to reduce the noise decreases (improves).
                                                                         (R2-1) This trade-off property computed using the above
                                                                         equation and is plotted as a graph .

            Fig 8.1.1. BER In Raleigh Channel                                                   BER for BPSK modulation with 2x2 MIMO and MMSE equalizer (Rayleigh channel)

                                                                                                                                            theory (nTx=2,nRx=2, ZF)
         The above figure illustrates the average bit error                                      -1                                         theory (nTx=1,nRx=2, MRC)
                                                                                                10                                          sim (nTx=2, nRx=2, MMSE)
rate (BER) performance with: (i) ideal CE, (ii) optimum γ
(i.e., γopt) and (iii) fixed γ. BER performance is plotted as a
function of Eb/N0 at fDTs=10−2. The figure shows that, for a
                                                                               Bit Error Rate

lower Eb/N0 (i.e., Eb/N0<15 dB), the BER with fixed γ=0.5
is almost the same as with γopt. As expected, γopt and fixed                                     -3

γ=0.5 give the same BER atEb/N0=15 dB because γ=0.5 is
optimum value at Eb/N0=15 dB and fDTs=10−2. However,                                             -4
as Eb/N0 increases (i.e., Eb/N0>15 dB) the BER with fixed
γ=0.5 approaches a floor value of about BER=10−3, while                                          -5
the performance with γopt consistently improves.                                                      0         5            10            15            20             25
                                                                                                                             Average Eb/No,dB

                                                                                                          Fig 8.1.2 . MMSE Equalization

                                                                                                                       ISSN 1947-5500
                                                        (IJCSIS) International Journal of Computer Science and Information Security,
                                                        Vol. 9, No. 8, August 2011

9 CONCLUSION                                                             [5] M. Hsieh and C. Wei, ”Channel estimation for OFDM
           Thus the performance evaluation of OFDM/TDM                   systems based on comb-type pilot arrangement in frequency
using MMSE-FDE with practical channel estimation in a fast               selective fading channels,” IEEE Trans. Consumer Electron.,
fading channel was presented. A tracking against fast fading             Vol. 44, No. 1, Feb. 1998.
is improved by robust pilot-assisted channel estimation that
uses time-domain first-order filtering on a slot-by-slot basis           [6] (R1) W. Zeng, X. Xia and P. C. Ching, ”Optimal training
and frequency-domain interpolation. The MSE of the channel               and pilot pattern design for OFDM systems in Rayleigh
estimator     using time-domain    first-order   filtering and           fading,” IEEE Trans. Comm., Vol. 52, No. 4, Dec. 2006.
frequency-domain interpolation was derived and then, a
tradeoff between      improving the tracking ability against             [7] Y.-C. Choi, P. J. Voltz and F. A. Cassara, ”On channel
fading and the noise reduction was discussed. It was shown               estimation and detection for multicarrier signals in fast and
that the OFDM/TDM using MMSE-FDE provides a lower                        selective rayleigh fading channels,” IEEE Trans. Comm.,
BER and a very good tracking ability against fading in                   Vol. 49, No. 8, pp. 1375-1387, Aug. 2001.
comparison with conventional OFDM while keeping the
same data-rate transmission.                                             [8] D. Falconer, S.L. Ariyavisitakul, A. Benyamin-Seeyar,
                                                                         and B. Eidson, ”Frequency-domain equalization for single-
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