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Performance Analysis Of Nonlinear Distortions For Downlink MC-CDMA Systems

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Performance Analysis Of Nonlinear Distortions For Downlink  MC-CDMA Systems Powered By Docstoc
					                                           (IJCSIS) International Journal of Computer Science and Information Security,
                                           Vol. 8, No. 8, November 2010




       PERFORMANCE ANALYSIS OF NONLINEAR
           DISTORTIONS FOR DOWNLINK
                MC-CDMA SYSTEMS
                                        Labib Francis Gergis
                               Misr Academy for Engineering andTechnology
                                            Mansoura, Egypt
                                          drlabeeb@yahoo.com



Abstract-Multi-carrier (MC) scheme became a                advantages of spectrum efficiency, interference
promising technique for its spectral efficiency            immunity, high data rate, and sensitivity to
and robustness against frequency-selective                 selective fading channels. Multi-carrier Coded-
fading. Multi-carrier code division multiple               division multiple-access (MC-CDMA) appears to
access (MC-CDMA) is a powerful modulation                  be a recommended candidate for future radio
technique that is being considered in many                 communication systems. It exploits the
emerging broadband communication systems.                  advantages of spread spectrum and the
MC-CDMA combines the advantages of multi-                  advantages of multi-carrier systems [1].
carrier modulation with that of code-division                 MC-CDMA signals are considered as
multiple access (CDMA) to offer reliable high-             superposition of many narrow-band signals, and
data-rate downlink cellular communication                  as a result suffer from strong envelope
services. The MC-CDMA signals are a                        fluctuations which make them very prone to
superposition of many narrow-band signals and,             nonlinear effects introduced by high power
as a result suffer from strong envelope                    amplifiers (HPA's) [2].
fluctuations which make them very prone to                     Power      amplifiers   (PA's)    are  vital
nonlinear effects introduced by high power                 components in many communication system. The
amplifier (HPA). HPA introduces conversion in              linearity of a PA response constitutes an
both amplitude and phase. In this paper we have            important factor that ensures signal integrity
focused on the signals at the output of the                and reliable performance of the communication
nonlinear distorting device. A practical                   system. High power amplifiers in microwave
technique for determining the bit error rate               range suffer from the effects of amplitude
(BER) of downlink MC-CDMA systems using                    modulation to amplitude modulation distortion
binary phase- shift keying (BPSK) modulation               (AM/AM), and amplitude modulation to phase
scheme. The results are applicable to systems              modulation distortion (AM/PM) [3], during
employing a coherent demodulation with                     conversions caused by the HPA amplifiers. These
maximal ratio combining (MRC) and equal gain               distortions can cause intermodulation (IM)
combining (EGC).                                           distortion, which is undesirable to system
                                                           designs. The effects of AM/AM and AM/PM
Keywords- MC-CDMA systems, high power                      distortions degrade the bit error rate
amplifiers, nonlinear distortions, maximal ratio           performance of a communication channel.
combining (MRC), equal gain combining (EGC).                   The amplitude and phase modulation
                                                           distortions are minimized using linearization
                                                           method. The linearization method requires
          1. INTRODUCTION                                  modeling the characteristics of the amplitude
                                                           distortion and phase distortion of the HPA.
    Future wireless radio networks need to                 A Saleh model [4] for traveling wave tube
make efficient use of the frequency spectrum by            (TWT) amplifiers, has been used to provide
providing high capacity in terms of number of              the linearization method and applied to
users allowed in the system. Due to the                    measured data from HPA that characterize




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                                            (IJCSIS) International Journal of Computer Science and Information Security,
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the distortion caused by the HPA. The                              2. MC-CDMA TRANSMITTER
measured data provides a performance                                        MODEL
curve indicating nonlinear distortion. The
forward Saleh model is a mathematical                            The input data symbols, am [k], are assumed
equation that describes the amplitude and                   to be binary antipodal where k denotes the kth
phase modulation distortions of the HPA.                    bit interval and m denotes the mth user. It is
     The BER analysis of MC-CDMA based on                   assumed that am [k] takes on values of -1 and +1
considering different kinds of assumptions, so              with equal probability.
far, have been dedicated in numerous researches                  As shown in Figure. 1, a single data symbol is
in advance .                                                replicated into N parallel copies. Each branch of
    Performance enhancement of MC-CDMA                      the parallel stream is multiplied by a chip from a
system through, space time trellis code (STTC)              spreading code of length N. Each copy is then
site diversity with multiple input multiple output          binary phase-shift keying (BPSK) modulated to a
(MIMO) technique was introduced in [5].                     subcarrier spaced apart from its neighboring
    A method efficiently suppressing multiple               subcarriers by F/Tb Hz where F is an integer
access interferences (MAI) in MC-CDMA to                    number. An MC-CDMA signal consists of the
improve the system capacity was proposed in [6].            sum of the outputs of these branches.
    The performance of fully loaded downlink                   As illustrated in Figure. 1, the transmitted
MC-CDMA systems in the presence of residual                 signal for MC-CDMA system corresponding to
frequency offset (RFO) in multipath Rayleigh                the kth data bit of the mth user is [10]
fading channels with minimum mean square                               N-1
error (MMSE) equalizers was presented in [7].               Sm(t) = ∑ Cm[i] am [k] ·
    The performance analysis of MC-CDMA                               i=0
communication systems over Nakagami-m fading                                cos ( 2π fct + 2πi (F/Tb)t        ·
channels was considered in [8].
    A downlink MC-CDMA system using binary                                  PTb (t-kTb)                                   (1)
phase-shift keying (BPSK) modulation scheme                                         Cm[i] Є { -1 , 1 }
and maximal ratio combining (MRC) in
frequency-selective Rician fading channels was              where Cm[0], Cm[1], ……, Cm[N-1] represent the
illustrated in [9].                                         spreading code of the mth user and PTb (t) is an
    The aim of this paper is to analyze the                 unit amplitude pulse that is non-zero in the
influences of the effects of the nonlinear                  interval [0,Tb].
distortions introduced by HPA in downlink MC-
CDMA over Rayleigh fading channel for mobile
satellite communication systems. The structure
of this paper is as follows. The basic principles
model of transmitter system is presented and
described in more details in section 2. Section 3
summarizes the HPA baseband models, which is
most commonly used in mobile satellite
communication systems. Subsequently in section
4, the channel model is described. The receiver
model will be described in section              5.
Performance analysis of linearized downlink
MC-CDMA based signal is carried out for both
EGC and MRC.

                                                               Fig. 1 Transmitter Model of MC-CDMA
                                                                               System




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 3. NONLINEARITY EFFECTS ON                                       subsequently results in increasing the bit error
                                                                  rate (BER), and the out-of-band energy
       MC-CDMA SIGNAL                                             radiation ( spectral spreading ).
       The response of broadband power
    amplifiers can have precarious memory
    effect. The influence of a memory-less
    nonlinearity U(.) can be decomposed into an
    amplitude distortion (AM/AM) and a phase
    distortion (AM/PM), which are both
    functions of the amplitude of the input signal
    to HPA. The complex signal So(t) at the
    output of HPA, can be defined as [11]

So(t) = U{Sm(t)} =   A (│Sm(t)│)    .
                exp ( j Φ(│Sm(t)│)) Sm(t)            (2)

A[Sm(t)] and Φ[Sm(t)] are the corresponding
AM/AM         and    AM/PM       characteristics
respectively, both dependent exclusively on Ux,
which is the input modulus to HPA, they are                      Fig. 2. AM/AM and AM/PM characteristics of
defined as Saleh Model for HPA [12]:                                      the Saleh model For TWTA HPA' s

    A[Ux] = αa Ux     /   1 + βa U2x
                                                                     The operating point of HPA is defined by
    Φ[Ux] = αΦ Ux     /    1 + βΦ U2x                (3)          input back-off (IBO) parameter which
                                                                  corresponds to the ratio of saturated output
   The values of αa, βa , αΦ and βΦ are defined in                power (Po), and the average input power ( Pav)
[3].                                                              [13] :
   The corresponding AM/AM and AM/PM                                IBOdB= 10 log10 ( Po / Pav)             (6)
curves so scaled are depicted in Fig. 2.
                                                                     The measure of effects due to the nonlinear
   While for solid state power amplifier types                    HPA could be decreased by the selection of
(SSPA's) AM/AM and AM/PM can be defined as                        relatively high values of IBO
                                                                     The output of HPA defined in Fig. 3, is
       A[Ux] = Ux     /   [1 + (Ux / Amax )2p]1/2p                expressed as
       Φ[Ux] = 0                                      (4)
                                                                      by =     A [ Ux ] ej(αx+ Φ[Ux])                              (7)
  Amax is the maximum output amplitude, and p
is a constant controls the smoothness of the                      where the input-output functional relation of the
   transition.                                                    HPA has been defined as a transfer function.
                                                                  Hence in order to obtain linearization, it may be
      Amax = max ( A[Ux] ) = αa As / 2               (5)          necessary to estimate a discrete inverse
                                                                  multiplicative function HPA-1 [.] such that
where As is the input saturation amplitude
equals 1 / √ βa
                                                                     bx = by . HPA-1 [Uy]                                          (8)

    The HPA operation in the region of its                           An alternative expression for the AM/AM
nonlinear characteristic causes a nonlinear                       distortion in (7), convenient for the theoretical
distortion of a transmitted signal, that                          formulation of the linearizer, is obtained by




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                                                                                            ISSN 1947-5500
                                                     (IJCSIS) International Journal of Computer Science and Information Security,
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multiplying the saturation input amplitude As                        bandwidth. This is achieved by pre-distortion of
in the expression (3). This gives                                    the signal prior to amplification with the inverse
                                                                     characteristics of the distortion that will be
  A[Ux] = (A2s αa Ux) / (A2s + A2s βa U2x)                           imposed by the power amplifier. Thus the output
                                                                     of the HPA is a linear function of the input to the
   A[Ux] = (A2s αa Ux) / (A2s + U2x)                   (9)           predistorter .

   The theoretical AM/AM inverse transfer                                      PD                              HPA
function A-1[.]could be determined by solving (9)
for Ux = A { A-1 [Ux] }                                                bx                       bpout                     by

   [u] =      ( A2s αa / 2U )       ·
                                                                     Fig. 4. Basic System Functional Diagram of Pre-
             1 -      1 – ( 2U / As αa )         2
                                                     (10)                         distortion Linearization

    Considering the alternative configurations
shown in Fig. 3, where the same input-output                            A description of the ideal theoretic AM/AM
function is applied as a pre-distorter [PD] for the                  and AM/PM inverse characteristics, valid for the
linearization of the same HPA. Letting ψ[.]                          normalized Saleh's HPA model is shown in Fig. 5
denote the AM/PM characteristic of the PD
block.
   For the case of a Pre-distortion, we have [12] :

                             j(αx+ ψ[Ux])
   bpout = A-1 [ Ux ] e                               (11)

     by =     A A-1 [ Ux ]              ·

            ej(αx+ ψ[Ux] +Φ[A-1[Ux] )                 (12)



   bx      PD        bpout     HPA          by

        ( A-1, ψ )            ( A, Φ )

  Fig. 3. Pre-distortion for HPA Linearization
                                                                       Fig. 5. AM/AM and AM/PM pre-distortion for
The ideal AM/PM correction requires that                                            the Saleh model

   ψ[Ux] = - Φ { A-1[Ux] }                            (13)

                         j(αx+ Φ[Ux])
                                                                                  4. CHANNEL MODEL
   bpin = A [ Ux ] e                                  (14)
                                                                         A frequency-selective fading channel with
   by = A-1 {         A [ Ux ] } ·                                   1/Tb << BWc << F/Tb is considered, where BWc is
                                                                     the coherence bandwidth. Each modulated
             ej(αx+ Φ[Ux] +ψ[A-1[Ux] )               (15)            subcarrier with transmission bandwidth of 1/Tb
                                                                     does not experience significant dispersion (Tb >>
                                                                     Td). Doppler shifts are very small, it is also
   Pre-distortion linearization idea, as depicted
                                                                     assumed that the amplitude and phase remain
in Fig. 4, can be used to linearize over a wide
                                                                     constant over the symbol duration, Tb.




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    For downlink transmissions, a terminal
receives interfering signal designated for other
users (m = 1, 2, …., M-1) through the same
channel as the wanted signal (m=0), the transfer
function of the continuous-time fading channel
for all transmissions from the base station to user
m = 0 can be represented as

    H (fc + i F/Tb) = ρm,i e jθm,i                  (16)

where ρm,i , and θm,i, are the random amplitude
and phase of the channel of the mth user at
frequency fc + i (F/Tb ). ρm,,i are assumed to be
independent and identically distributed (IID)                                          Fig. 6 Receiver Model
Rayleigh random variables. The random phases ,
θm,i are assumed to be IID random variables                            After adding the subcarrier signals together,
uniform on the interval of {0 , 2π} for all users                  the combined signal is then integrated and
and subcarriers.                                                   sampled to yield decision, Vo. For the kth bit, the
                                                                   decision variable is

         5. RECEIVER MODEL                                                      M-1     N-1
                                                                       Vo = ∑           ∑     ρm,i Cm[i] di am [k]         ·
                                                                             m=0       i=0
    For M active transmitters, the received signal                         (k+1)Tb
is [10]
                                                                           ∫ cos (2π fct +        2πF [i/Tb]t + θm,i )         ·
                                                                          kTb
           M-1 N-1
    r(t) = ∑ ∑ ρm,i Cm[i] am [k] ·                                        cos ( 2π fct + 2πF [i/Tb]t + θm,i )dt + η
        m=0   i=0
                                                                                                                                      (18)
    cos ( 2π fct + 2πi [F/Tb]t + θm,i ) + n (t)
                                                  (17)             where the corresponding AWGN term, η, is
                                                                   given as
where n(t) is additive white Gaussian noise                                      N-1    (k+1)Tb
(AWGN). The local-mean power at the ith
subcarrier of the mth user is defined to be ρm,i =
                                                                       η =      ∑        ∫        n(t) (2/Tb) di     ·
                                                                                i=0     kTb
Eρ2m,i / 2. Assuming the local-mean powers of the
subcarriers are equal, the total local-mean power                            cos (2π fct + 2πF [i/Tb]t + θm,i )dt                    (19)
of the mth user is equal to pm, = N pm,i .
     As shown in Figure. 6, the first step in                         Considering the two standard diversity
obtaining the decision variable involves                           reception techniques: Equal Gain Combining
demodulating each of subcarriers of the received                   (EGC) and Maximum Ratio Combining (MRC)
signal, which includes applying a phase
correction, θi , and multiplying the ith subcarrier                With EGC, the gain correction factor at the ith
signal by a gain correction, di.                                   subcarrier is given as

                                                                                         d0,i = c0 [i]                             (20)




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This scheme yields the decision variable                                             2- with MRC

                          N-1
  Vo = ao [k]          ∑        ρ,i0 + βint + η                     (21)             BER =
                      i=0
           N-1
                                                                                                                        P 0 Tb
ao [k]     ∑     ρ,i0 represents the desired signal, and                                  1/2 erfc                                              (27)
         i=0
                                                                                                       2( M -1)
the interference term,                βint,   is defined by                                                            (1-π/4)P0Tb+N0
                                                                                                         N
         M-1 N-1
βint = ∑ ∑            Cm[i] am [k] C0[i] ρm,i cos θ m,i
                                                            -

     m=0       i=0
                                                                    (22)                      7. NUMERICAL RESULTS

    For MRC scheme, the gain correction factor                                          A fair measure is given by using the
at the ith subcarrier is given as                                                    normalized minimal signal-to-noise ratio

                     d0,i = ρ0,i c0 [i]                             (23)                     SNRo = 10 log (PoTb / No) (dB)                         (28)

The decision variable for MRC scheme is                                              which is needed to achieve the wanted BER. Tb
expressed as                                                                         is the equivalent duration for one information
                                                                                     bit, No is the two sided spectral noise density,
                          N-1                                                        and Po is the given reference power of HPA. The
  Vo = ao [k]          ∑        ρ2,i0 + βint + η                    (24)             SNRo can be minimized by optimization of the
                      i=0                                                            HPA backoff. This becomes more clear, when eq.
                                                                                     (6) is used in eq. (28) :
where, the interference term,                     βint,   is defined in
this case by                                                                                 SNRo = 10 log (PoTb Pav / No Pav )

      M-1 N-1                                                                                         = 10 log (Eb / No) + OBO                    (29)
βint = ∑ ∑ Cm[i] am [k]C0[i]ρm,i ρo,i cos θ m,i                 -

     m=0       i=0                                                                      The average downlink bit error rate (BER)
                                                                     (25)            versus the number of interferes are examined.
                                                                                     For the sake of comparison, the BER for both
                                                                                     types of diversity, EGC and MRC are illustrated
   6. PERFORMANCE ANALYSIS                                                           under interferers numbers, N = 32, 64, and 128 ,
                                                                                     with SNR = 10 dB in Figures 7, and 8.
                                                                                        It can be seen that for a small numbers of
     The downlink BER had been calculated
                                                                                     users, MRC outperforms EGC. It was also
as [10]                                                                              demonstrated the PD effect to mitigate the
1-with EGC
                                                                                     nonlinearity distortions introduced from HPA in
                                                                                     Fig. 9, and Fig. 10.
BER =

                                        P 0 Tb
   1/2 erfc           π                                         (26)

                      4 2( M -1)
                                         (1-π/4)P0Tb+N0
                                N




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       1.e+0                                                                   1.e+0
                                                                                                                                           EGC case
               SNR = 10 dB                                                     1.e-1                                                        N = 128
                                                                                                                                             N = 128
                                                                               1.e-2
       1.e-1
                                                                               1.e-3
                                                                               1.e-4

       1.e-2                                                                   1.e-5
                                                                               1.e-6




                                                                         BER
 BER




                                                                               1.e-7
       1.e-3                                                                   1.e-8
                                                                               1.e-9
                                                                                             with PD (m=0 interferers)
                                                                               1.e-10          with PD ( m = 0)
       1.e-4                                                                                 without PD (oBo=5 dB) (m=0 interferers)
                                                     N = 128                   1.e-11
                                                     N = 64                                  with PD (m =70 interferers)
                                                                               1.e-12
                                                     N = 32                                  without PD (oBo = 5 dB) (m = 70 interferers)
       1.e-5                                                                   1.e-13
                    0        50     100      150   200        250                       0     5        10        15         20     25          30      35
                              No of Interferers                                                                  SNR dB

Fig. 7. BER versus the No. of Interferers for                                     Fig. 9. BER versus the SNR using PD
                EGC case                                                                      for EGC case



       1.e+0                                                                   1.e+0
                                                                               1.e-1                                                    MRC case
               SNR = 10 dB                                                                                                               N = 128
                                                                               1.e-2
       1.e-1                                                                   1.e-3
                                                                               1.e-4
                                                                               1.e-5
       1.e-2
                                                                               1.e-6
                                                                               1.e-7
                                                                         BER
 BER




       1.e-3                                                                   1.e-8
                                                                               1.e-9
                                                                               1.e-10
       1.e-4                                                                   1.e-11
                                                                               1.e-12
                                                                                            with PD (m = 0 interferers)
                                                     N = 128                   1.e-13
                                                                                            without PD (oBo = 5 dB) (m = 0 interferers)
       1.e-5                                                                   1.e-14
                                                      N = 64                                with PD (m = 70 interferers)
                                                                               1.e-15
                                                      N = 32                                without PD (oBo = 5 dB) (m = 70 interferers)
                                                                               1.e-16
       1.e-6
                                                                                        0     5       10       15          20    25        30       35
                    0        50     100      150   200     250
                                                                                                               SNR         dB
                              No of Interferers

Fig. 8. BER versus the No. of Interferers for                                    Fig. 10. BER versus the SNR using PD
                MRC case                                                                     for MRC case




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            8. CONCLUSIONS                                 [5] N. Kumaratharan, S. Jayapriya, and P.
                                                                Dananjayan, " Performance Enhancement of
    In this paper, the downlink transmission in                 MC-CDMA System through STBC based
MC-CDMA systems with nonlinear HPA of                           STTC Site Diversity", International Journal
transmitter over frequency-selective fading                     of Computer and Electrical Engineering,
channels was considered. This paper presented                   Vol. 2, No. 1, February, 2010.
results on a novel modulation, diversity, and              [6] B. Ness, "EQUAL BER POWER
multiple access technique.                                      CONTROL FOR UPLINK MC-CDMA
    For two diversity techniques considered,                    WITH MMSE SUCCESSIVE
MRC performed better than EGC.                                  INTERFERENCE CANCELLATION,"
    The performance of MC-CDMA would be                         Patent No. US 7,620,096 B2, Nov. 2009.
affected by nonlinearities introduced from                 [7] P. Reddy, and V. Reddy," BER Degradation
HPA's in the transmitter.                                       of MC-CDMA at high SNR with MMSE
   From previous discussions and plotted results,               Equalization and Residual Frequency
it can be concluded that in order to reduce the                 Offset," EURASIP Journal on Wireless
sensitivity of a MC-CDMA system to the                          Communications and Networking, Volume
nonlinear amplification, it is recommended to                   2009, Article ID 293264, 2009.
choose a special technique to mitigate these               [8] J. Iong, and Z. Chen, " PERFORMANCE
distortions. PD schemes had been selected to do                  ANALYSIS OF MC-CDMA
this mission, they attended to achieve a                         COMMUNICATION SYSTEMS OVER
significantly     improve     overall    system                  NAKAGAMI-M ENVIRONMENTS",
performance.                                                     Journal of Marine Science and Technology,
                                                                 Vol. 14, No. 1, pp. 58-63, 2006.
                                                             [9] Z. Hou, and V. dubey, " BER Performance
                                                                  for Downlink MC-CDMA Systems over
              REFERENCES                                          Rician Fading Channels", EURASIP
                                                                 Journal on Applier Signal Processing, pp.
[1] J. Iong, and Z. Chen, " Theoretical Analysis
                                                                 709-717, 2005.
    of an MC-CDMA System in Cellular
                                                            [10] N. Yee, J. Linnartz, and G. Fettweis,"
    Environments" Journal of Science and
                                                                  MULTICARRER CDMA IN INDOOR
    Engineering Technology, Vol. 6, No. 1, pp.
                                                                 WIRELESS RADIO NETWORKS", The
    37-50, 2010.
                                                                  Fourth International Symposium on
[2] M. Frikel, S. Safi, B. Targui, and M. Saad,"
                                                                  Personal Indoor and Mobile Radio
    Channel Identification Using Chaos for an
                                                                  Communications, PACIFICO
    Uplink/Downlink Multicarrier Code Division
                                                                   YOKOHAMA, JAPAN, September. 1993.
    Multiple Access System", JOURNAL OF
                                                           [11] A. Perotti, P. Rrmlein, and S. Benedetto, "
    TELECOMMUNICATIONS AND
                                                                 Adaptive Coded Continuous-Phase
    INFORMATION TECHNOLOGY, Vol. 1,
                                                                 Modulations for Frequency-Division
    pp. 48-54, 2010.
                                                                 Multiuser Systems", ADVANCES IN
[3] M. Chen, and O. Collins, " Multilevel Coding
                                                                 ELECTRONICS AND
    for Nonlinear ISI Channels", IEEE
                                                                 TELECOMMUNICATIONS, VOL. 1, NO.
    TRANSACTIONS ON INFORMATION
                                                                 1, APRIL 2010
    THEORY. VOL. 55, NO. 5, MAY 2009.
                                                           [12] S. Chang, "An efficient compensation of
[4] J. Gazda, P. Drotar, D. Kocur, and P.
                                                                 TWTA's nonlinear distortion in wideband
    Galajda," Performance Improvements of
                                                                 OFDM systems", IEICE Electronics
    MC-CDMA Microstatistic Multi-User
                                                                 Express, Vol. 6, No. 2, pp. 111-116, 2009.
    Detection in Nonlinear Fading Channels
                                                           [13] T.Tan," POWER AMPLIFIER
    Using Spreading Code Selection," TUBITAK.
                                                                 MODELING AND POWER AMPLIFIER
    Turk J Elec Engin. VOL. 8, NO. 1, April
                                                                 PREDISTORTION IN OFDM SYSTEM",
    2009.
                                                                 Journal of Science & Technology
                                                                 Development, Vol 11, No.02 - 2008




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