PAPR Reduction Technique for LTE SC-FDMA Systems Using Root-Raised Cosine Filter

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					                                                      (IJCSIS) International Journal of Computer Science and Information Security,
                                                      Vol. 8, No. 6, September 2010




     PAPR Reduction Technique for LTE SC-FDMA
       Systems Using Root-Raised Cosine Filter
                                  Md. Masud Rana, Jinsang Kim and Won-Kyung Cho


                      Deptartment of Electronics and Radio Engineering, Kyung Hee University
                        1 Seocheon, Kihung, Yongin, Gyeonggi, 449-701, Republic of Korea
                                         Email: mamaraece28@yahoo.com


   Abstract—Recently, mobile radio communications have de-             rate transmission over mobile wireless channels. In OFDMA
veloped rapidly due to the endless demand for broadband                system, the entire channel is divided into many narrow sub-
multimedia access and wireless connection anywhere, and any            channels, which are transmitted in parallel, thereby increasing
time. With the emergence of diverse fourth generation (4G)
enabling technologies, signal processing has become ever in-           the symbol duration and reducing the intersymbol-interference
creasingly important for small power, small chip resources,            (ISI) [4], [8]. Despite many benefits of OFDMA for high speed
and efficient physical implementations of potential multimedia          data rate services, it suffer from high envelope fluctuation
wireless communication systems. In this paper, we analytically         in the time domain, leading to large PAPR. Because the
derive the time and frequency domain single carrier-frequency          high PAPR is detrimental to user mobile equipment (UE)
division multiplexing (SC-FDMA) signals. Simulation results
show that the SC-FDMA sub-carrier mapping scheme has a                 terminals, SC-FDMA has drawn great attention as an attractive
significantly lower peak-to average power ratio (PAPR) compared         alternative to OFDMA for uplink data transmission. It can be
to orthogonal frequency division multiplexing (OFDMA). In              regarded as DFT-spread OFDMA (DFTS-OFDM), where time
addition, the interleave FDMA (IFDMA) sub-carrier mapping              domain data signals are transformed to frequency domain by
scheme with root raised cosine filter reduced PAPR significantly         a DFT before going through OFDMA modulation. The main
than localized FDMA (LFDMA) and distributed (DFDMA) sub-
carrier mapping scheme. As a results, improves the mean power          benefit of DFTS-OFDM compared to OFDM scheme, is re-
output from a battery driven terminal equipment and power              duced variations in the instantaneous transmit power, implying
amplifier efficiency.                                                    the possibility for increased power-amplifier efficiency, low-
   Index Terms—CCDF, IFDMA, OFDMA, PAPR, root-raised                   complexity high-quality equalization in the frequency domain,
cosine, SC-FDMA.                                                       and flexible bandwidth assignment [12].
                                                                          In order to solve the high PAPR problem seen in the
                     I. I NTRODUCTION                                  uplink of OFDMA, research is now addressing techniques such
   The further increasing demand on high data rates in wireless        as a SC-FDMA. The most of the previous work related to
communication systems has arisen in order to support broad-            3GPP LTE uplink has been mainly focused on implementation
band services. The third generation partnership project (3GPP)         problems in the physical layer [2], [5], [9], [13]. In [10], [12]
members started feasibility study on the enhancement of the            proposed raised-cosine pulse shaping method that compare
universal terrestrial radio access (UTRA) in December 2004,            PAPR characteristics using the complementary cumulative
to improve the mobile phone standard to cope with future               distribution function (CCDF) for different subcarrier mapping.
requirements. This project was called long term evolution                 PAPR reduction is of the most importance performance
(LTE) [1].                                                             parameter in case of high amplitude signals subject to non
   LTE uses single carrier frequency division multiple access          linear power amplification. This situation more and more occur
(SC-FDMA) for uplink transmission and orthogonal frequency             due to the ever-growing demand in high spectral efficiency
division multiple access (OFDMA) for downlink transmission             advanced mobile telecommunications systems implying multi
[6]. SC-FDMA is a promising technique for high data rate               dimensional waveforms considerations for which the PAPR
transmission that utilizes single carrier modulation and fre-          is high. Pulse shaping is required for a single carrier sys-
quency domain equalization. Single carrier transmitter struc-          tem to bandlimit the transmit signal. This paper addresses
ture leads to keep the peak-to average power ratio (PAPR)              a theoretical analysis of the PAPR reduction of LTE SC-
as low as possible that is reduced the energy consumption.             FDMA systems when root-raised cosine (RRC) filter is used.
SC-FDMA has similar throughput performance and essentially             RRC is used as the transmit and receive filter in a digital
the same overall complexity as OFDMA [3], [10], [12]. A                communication system to perform matched filtering. The
highly efficient way to cope with the frequency selectivity             combined response of two such filters is that of the raised-
of wideband channel is OFDMA. OFDMA is an effective                    cosine filter. In this paper, we analytically derive the time and
technique for combating multipath fading and for high bit              frequency domain SC-FDMA signals. Simulation results show


                                                                  66                               http://sites.google.com/site/ijcsis/
                                                                                                   ISSN 1947-5500
                                                                                                       (IJCSIS) International Journal of Computer Science and Information Security,
                                                                                                       Vol. 8, No. 6, September 2010



                                                                                                                                            One radio frame = 20 Slots = 10 Sub-frames = 10 ms
that the SC-FDMA has a significantly lower PAPR compared
                                                                                                                            1 Slot = 7 OFDM symbols = 0.5 ms                                  2 Slots = 1 Sub-frame = 10 ms
to OFDMA system. In addition, we comparing the three forms
of SC-FDMA sub-carrier mapping scheme and find that the
interleave FDMA (IFDMA) sub-carrier mapping with root                                                                           1       2       3             4              ….……            15    16     17       19       20

raised cosine based pulse shapping method reduced PAPR
                                                                                                                                                                                                             Resource block:
significantly than localized FDMA (LFDMA) and DFDMA




                                                                                                                                                                          12 sub-carriers
                                                                                                                            1       2   3   4       5     6       7                                               Short CP:




                                                                                                                                                                            =180 kHz
                                                                                                                                                                                                          7 symbols x 12 sub-carriers
sub-carrier mapping scheme. As a results, improves the mean                                                                                                                                                       Long CP:
power output from a battery driven terminal equipment and                                                                                   Cyclic prefix                                                 6 symbols x 12 sub-carriers

power amplifier efficiency.                                                                                                           7 OFDM symbols                                                           1 resource element
   The rest of the paper is organized as follows. We describes                                                                                                                                               Pilot

the 3GPP LTE and LTE SC-FDMA system model in sec-
tion II and III, respectively. In section IV, we describes the                                                                                          Fig. 2.       LTE generic frame structure.
different SC-FDMA sub-carrier mapping scheme. In section
V, we describes the PAPR reduction technique for LTE SC-
FDMA systems. In section VI, we simulated and compare                                                                     blocks fit in a carrier of 1.4 MHz and 100 resource blocks
the proposed method with OFDMA for different sub-carrier                                                                  fit in a carrier of 20 MHz. Slots consist of either 6 or 7
mapping scheme. Finally, conclusions are made in section VII.                                                             OFDM symbols, depending on whether the normal or extended
                                                                                                                          cyclic prefix (CP) is employed. The CP is added in front of
                      II. 3GPP LTE
                                                                                                                          each block. The details transmission scheme parameters of
  The main purposes of the 3GPP LTE are substantially                                                                     the 3GPP LTE system are shown in Table I [7]. LTE uses SC-
improved end-user throughputs, low latency, reduced user                                                                  FDMA scheme for the uplink transmissions and OFDMA in
equipment (UE) complexity, high data rate, and significantly                                                               downlink transmission.
improved user experience with full mobility. First 3GPP LTE
                                                                                                                                                                           TABLE I
and LTE-advanced (LTE-A) specification is being finalized                                                                                                       LTE      SYSTEM PARAMETERS
within 3GPP release 9 and release 10, respectively [1].
 Year      2005            2006       2007        2008             2009           2010          2011       2012              Trans. bandwidth (MHz)                          1.25            2.5     5  10      15        20
                                               Release 7 study phase (HSPA+)                                                         FFT size                                128            256    512 1024    1536     2048
                                                                                                                               Occupied sub-carrier                           76            151    301  601     901     1200
                                                                Release 8 work phase (LTE)
                                                                                                                           Sampling frequency (MHz)                          1.92           3.84   7.6815.36  23.04     30.72
 Release
                                                                                Release 9 test specs                          No. of available PRBs                           6              12     25  50      75       100
                                                                                                  Release 10 (LTE            User plane latency (ms)                                                 <5
                                                                                                     advanced)                PRB bandwidth (kHz)                                                    180
                                                                                                                               Frame duration (ms)                                                    0.5
              Release 6                        Core     First     First UE        Initially                 Mass           Sub-carrier bandwidth (kHz)                                                15
                                                                                                            market
             HSPA uplink                       specs
                                              drafted
                                                         test
                                                        specs
                                                                certification   development                                       Coverage (km)                                                      5-30
                                                                                                                                 Mobility (km/hr)                                                   15-350
                                                                                                                             Peak data rates (Mbits/s)                                     DL: 100, and UL: 50
                                  Fig. 1.    LTE release timeline.                                                            Antenna configuration                              DL: 4x2, 2x2, 1x2, 1x1, and UL: 1x2, 1x1
                                                                                                                               Spectrum efficiency                            DL: 3-4 x HSDPA, and UL: 2-3 x HSUPA Rel.6
                                                                                                                            Control plane latency (ms)                        100 (idle to active), and 50 (dormant to active)
Specifically, the physical layer has become quite stable re-                                                                       Radio resource                                      DL: 3-4 fold higher than Rel.6
cently for a first implementation. LTE supports multipule input
multiput output (MIMO) with one, two, four, and eight antenna
elements at base station (BS) and mobile terminal. Both closed                                                                       III. LTE SC-FDAMA SYSTEM MODEL
and open loop MIMO operation is possible. The target of LTE-
                                                                                                                            The basic principle of a LTE SC-FDMA transmission sys-
A is to reach and surpass the international telecommunication
                                                                                                                          tem is shown in Fig. 3.
union (ITU) requirements. One of the important LTE-A ben-
                                                                                                                            At the transmitter side, a baseband modulator transmits the
efits is the ability to leverage advanced topology networks;
                                                                                                                          binary input to a multilevel sequences of complex number
optimized heterogeneous networks with a mix of macros with
                                                                                                                          m1 (q) in one of several possible modulation formats including,
low power nodes such as picocells, femtocells, ensures user
                                                                                                                          quandary phase shift keying (QPSK), and 16 level-QAM.
fairness, worldwide roaming, and new relay nodes [1].
                                                                                                                          These modulated symbols are perform a N-point discrete
   In 3GPP LTE, the basic unit of a transmission scheme is a
                                                                                                                          Fourier transform (DFT) to produce a frequency domain
radio frame which is ten msec long. They are divided into ten
                                                                                                                          representation [3]:
sub-frames, each sub-frame one msec long. Each sub-frame is
                                                                                                                                                             N −1
further divided into two slots, each of half msec duration. Fig.                                                                                          1 ∑            −j2πqn

2, shows the basic LTE generic frame structure [11]. The sub-                                                                                   s1 (n) = √        m1 (q)e N ,                                                    (1)
                                                                                                                                                           N q=0
carrier spacing in the frequency domain is 15 kHz. Twelve
of these sub-carriers together (per slot) is called a resource                                                            where m1 is the discrete symbols, q is the sample index, j is
block therefore one resource block is 180 kHz. Six resource                                                               the imaginary unit, and m1 (q) is the data symbol. The output


                                                                                                                     67                                                     http://sites.google.com/site/ijcsis/
                                                                                                                                                                            ISSN 1947-5500
                                                                 (IJCSIS) International Journal of Computer Science and Information Security,
                                                                 Vol. 8, No. 6, September 2010




       Input data
                                                                                 tones. Assume that the channel length of CP is larger than the
                                                   Output data
                                                                                 channel delay spread [8].
                                                                                    The transmitted symbols propagating through the radio
                                                  Demodulation                   channel can be modeled as a circular convolution between the
       Modulation
                                                                                 channel impulse response (CIR) and transmitted data blocks.
                                                           R(k)
               m1(q)                                                             At the receiver, the opposite set of the operation is performed.
                                                   Size-N IDFT                   The CP samples are discarded and the remaining N samples
       Size-N DFT
                                                           s3(m)                 are processed by the DFT to retrieve the complex constellation
                   s1(n)                                                         symbols transmitted over the orthogonal sub-channels. The
                                                    Equalization
                                                                                 received signals are de-mapped and equalizer is used to
        Subcarrier
         mapping                                                                 compensate for the radio channel frequency selectivity. After
                                                    Subcarrier
                                                    demapping
                                                                                 IDFT operation, the corresponding output is demodulated and
               s2(q)
                                                           r(m)                  soft or hard values of the corresponding bits are passed to the
     Size-M IDFT                                      Size-M
                                                                                 decoder.
                           Channel     Noise
                                                       DFT
               s(m)                                                                   IV. SC-FDMA SUB - CARRIER MAPPING SCHEME
           Cyclic
                                          +
                                                                                    There are two principal sub-carrier mapping modes-
        prefix(CP)             X                    Remove CP
         insertion                                                               localized mode, and distribution mode. An example of SC-
                                                                                 FDMA transmit symbols in the frequency domain for two
         Fig. 3.     LTE SC-FDMA transceiver system model [6].                   user, three sub-carrier per user and six sub-carriers in total
                                                                                 is illustrated in Fig. 4 [6].

of the DFT is then applied to consecutive inputs of a size-M                                             s1(1) s1(2) s1(3)
inverse DFT (M >N) and where the unused inputs of the IDFT
are set to zero. If they are equal (M=N), they simply cancel
out and it becomes a conventional single user single carrier
system with frequency domain equalization. However, if N is
smaller than M and the remaining inputs to the IDFT are set
to zero, the output of the IDFT will be a signal with ’single-                                                   (x)
carrier’ properties, i.e. a signal with low power variations, and
with a bandwidth that depends on N. The SC-FDMA is single-                                                       (y)
carrier, not single frequency. The data signal of each user
consists of a lot of frequency. DFT of SC-FDMA is used to
filter the frequency items and maps them into IDFT to reform                                                      (z)
single user waveform. This may justify the reduced peak-to-                                 Zeros                                   User 1
average power ratio (PAPR) experienced in the IDFT output.                                 Complex weight                           User 3
The details description of the sub-carrier mapping mode are in                                                                      User 2
section IV . PAPR is a comparison of the peak power detected                         Time domain                           Frequency domain
over a period of sample occurs over the same time period. The
PAPR of the transmit signal is defined as [14]:                                   Fig. 4. Multiple access scheme of SC-FDMA: (x) IFDMA mode, (y)
                        max0<m<T |s(m)|2                                         DFDMA mode, and (z) LFDMA.
               P AP R =    ∫ TN           ,                           (2)
                         1
                                |s(m)| dm
                                      2                                          In distributed sub-carrier mode, the outputs are allocated
                        TN 0                                                     equally spaced sub-carrier, with zeros occupying the unused
where T is the symbol period of the transmitted signal s(m).                     sub-carrier in between. While in localized sub-carrier mode,
PAPR is best described by its statistical parameter, com-                        the outputs are confined to a continuous spectrum of sub-
plementary cumulative distribution function (CCDF). CCDF                         carrier [10], [12]. Except the above two modes, interleaved
measures the probability of signal PAPR exceeding certain                        sub-carrier mapping mode of SC-FDMA (IFDMA) is another
threshold [12], [14]. To further reduce the power variations                     special sub-carrier mapping mode. The difference between
of the DFTS-OFDM signal, explicit spectrum shaping can be                        DFDMA and IFDMA is that the outputs of IFDMA are
applied. Spectrum shaping is applied by multiplying the fre-                     allocated over the entire bandwidth, whereas the DFDMA’s
quency samples with some spectrum-shaping function, e.g. a                       outputs are allocated every several sub-carriers. If there are
root-raised-cosine function (raised-cosine-shaped power spec-                    more than one user in the system, different sub-carrier map-
trum). The IDFT module output is followed by a CP insertion                      ping modes give different sub-carrier allocation [10], [12].
that completes the digital stage of the signal flow. A CP is                      In order to accommodate multiple access to the system and
used to eliminate ISI and preserve the orthogonality of the                      to preserve the constant envelope property of the signal, the


                                                                            68                               http://sites.google.com/site/ijcsis/
                                                                                                             ISSN 1947-5500
                                                           (IJCSIS) International Journal of Computer Science and Information Security,
                                                           Vol. 8, No. 6, September 2010




elements of transmitted signal s(m) are mapped, by using the               After IDFT operation, time domain signal can be described
LFDMA or IFDMA sub-carrier mapping rule.                                   as follows. Let m = Cq + c, where 0 ≤ c ≤ N − 1 and
   Here is output symbol calculation in IFDMA in time                      0 ≤ c ≤ C − 1. Then time domain transmitted signal can be
domain. The frequency samples after IFDMA sub-carrier                      represent as [12], [16]:
mapping is [12], [16]:
                {                                                                                          M −1
                                                                                                         1 ∑
                                    0≤n≤N −1
                                                                                                                       j2πml
                   s1 (q/C) = 1                                                             s(m) =              s2 (q)e M
       s2 (q) =                                                                                          M
                   0                else                                                                     l=0
                                                                                                         N −1
                                                                                                         ∑
where q = Cn, and C = M/N and it is the bandwidth                                                1 1                     j2π(Cq+c)l

expansion factor of the symbol sequence. If N = M/C                                          =                 s1 (l)e       CN                     (6)
                                                                                                 CN
                                                                                                         l=0
and all terminals transmit N symbols per block, the system
can handle C simultaneous transmissions without co-channel                 if c = 0, then
interference. After M-point IDFT operation (M > N ), time                                                  N −1
domain signal can be described as follows. Let m = N c + q,                                            1 1 ∑           j2πql
                                                                                            s(m) =      [       s1 (l)e N ]
where 0 ≤ c ≤ C − 1 and 0 ≤ q ≤ N − 1. The time domain                                                 C N
                                                                                                                l=0
IFDMA transmitted signal can be express as [12], [16]:                                                                     1
                                M −1                                                                                  =      m1 (q)                 (7)
                      1         ∑                j2πmq                                                                     C
               s(m) =                  s2 (q)e     M
                                                                                             ∑N −1                −j2πlp
                      M         q=0                                        Since m1 (q) =              m1 (p)e      N      , and if c ̸= 0, then
                                                                                                 p=0
                              N −1
                              ∑
                          1                                                                     N −1 N −1
                                                                                              1 ∑ ∑
                                                 j2πmn
                    =                 s1 (n)e      N                                                             −j2πlp j2π(Cq+c)l
                         NC                                                        s(m) =           [     m1 (p)e N ]e CN
                                n=0                                                          NC       p=0
                         N −1                                                                      l=0
                   1 1   ∑                                                                       N −1 N −1
                                                                                                 ∑ ∑
                                          j2π(N c+q)n
               =                s1 (n)e       N
                                                                                             1
                   CN    n=0
                                                                                       =                       m1 (p)e(j2π(q−p)/N +c/CN )l
                                                                                            NC
                           N −1                                                                   l=0 p=0
                    1 1     ∑                 j2πqn
                                                                                                  N −1
                                                                                                  ∑
                   = [
                    C N
                                    s1 (n)e     N     ].        (3)                          1                     1 − ej2π(q−p) ej2πc/C)
                                                                                        =                m1 (p)
                              n=0
                                                                                            NC    p=0
                                                                                                                  1 − e(j2π(q−p)/N +c/CN )
The square backed [.] of the above equation represent the N-
                                                                                                  N −1
                                                                                                  ∑
point IDFT operation. The above equation can be rewritten                                    1                             1 − ej2πc/C
                                                                                        =                m1 (p)
as                                                                                          NC    p=0
                                                                                                                  1 − e(j2π(q−p)/N +c/CN )
                               1
                                                                                                      N −1
                      s(m) = m1 (q),
                               C
                                                            (4)                    1                1 ∑            m1 (p)
                     ∑N −1                                                     =     (1 − ej2πc/C )                                                 (8)
                   1               j2πqn
where m1 (q) = N n=0 s1 (n)e N is the N-point IDFT                                 C                N n=0 1 − e(j2π(q−p)/N +c/CN )

operation. Therefore in case of IFDMA, every output symbol is
                                                                           So, the time domain LFDMA sub-carrier mapping signal has
simple a repeat of input symbol with a scaling factor of 1/C in
                                                                           exact copies of input time signals with a scaling factor of 1/C
time domain. When the sub-carrier frequency allocation starts
                                                                           in the N-multiple sample positions and in between values are
from f th sub-carrier i.e. q = Cn + f then the frequency
                                                                           sum of all the time input symbols in the input block with
samples after IFDMA sub-carrier mapping is
              {                                                            different complex-weighting (CW) [12].
                 s1 (q/C − f ) = 1      0≤n≤N −1                              Here is output symbol calculation in DFDMA in time
     s2 (q) =
                 0                      else                               domain. The frequency samples after DFDMA sub-carrier
and the time domain transmitted signal can be express as                   mapping is [12], [16]:
                       N −1                                                                   {
                   1 1 ∑           j2πqn j2πmf                                                  s1 (q/C) = 1 0 ≤ n ≤ N − 1
                                                                                                      ˜
          s(m) =    [       s1 (n)e N ]e M                                           s2 (q) =
                   C N n=0                                                                      0               else
                                   1 j2πmf                                 where 0 ≤ c ≤ C − 1, q = Cn, and 0 ≤ C ≤ C. Let
                                                                                                                     ˜
                                  =  e M m1 (q).            (5)
                                  C                                        m = N q + c where 0 ≤ c ≤ C − 1 and 0 ≤ q ≤ N − 1and
Thus, when the sub-carrier frequency allocation starts from                0 ≤ q ≤ N − 1. The time domain DFDMA transmitted signal
f th instead of zero then there is an additional phase rotation            can be express as [12], [16]:
of ej2πmf /M .
                                                                                                      M −1
   Here is output symbol calculation in LFDMA sub-carrier                                           1 ∑           j2πml

mapping in time domain. After DFT operation the frequency                                    s(m) =        s2 (q)e M
                                                                                                    M
                                                                                                               l=0
domain sub-carrier mapping signal can be written as
                  {                                                                               N −1
                                                                                              1 1 ∑
                                    0≤l ≤N −1
                                                                                                              j2π(Cq+c)l
                     s1 (l) = 1                                                             =          s1 (l)e CN Cl     ˜                          (9)
         s2 (q) =
                     0              N ≤l ≤M −1                                                CN
                                                                                                       l=0




                                                                      69                                     http://sites.google.com/site/ijcsis/
                                                                                                             ISSN 1947-5500
                                                        (IJCSIS) International Journal of Computer Science and Information Security,
                                                        Vol. 8, No. 6, September 2010



                                                                                                                 TABLE II
if c = 0 and according to the previous procedure, we obtain                                       THE SYSTEM PARAMETERS FOR SIMULATIONS
                              1     ˜
                     s(m) =     m1 (Cq)                     (10)                                      System parameters                            Assumptions
                              C
                ∑N −1         −j2πlp                                                             System bandwidth                                5M Hz
Since m1 (q) = p=0 m1 (p)e N , if c ̸= 0 and according                                         Number of sub-carriers                              512
to the previous procedure, we obtain                                                               Data block size                                  16
                                                                                                    Roll of factor                            0.0999999999
                             N −1
                           1 ∑
                                                                                                Oversampling factor                                  4
         1          ˜                      m1 (p)                                                                                                  104
s(m) =     (1 − ej2πCc/C )                 ˜        ˜
                                                         (11)                                   Number of iteration
         C                 N n=0 1 − e(j2π(Cq−p)/N +Cc/CN )                                 Sub-carrier mapping schemes                  DFDMA, IFDMA, LFDMA
                                                                                                Modulation data type                       Q-PSK and 16-QAM
So, the time domain symbols of DFDMA sub-carrier mapping                                    Spreading factor for IFDMA                              32
                                                                                            Spreading factor for DFDMA                              31
have the same structure as those of LFDMA sub-carrier
mapping.
 V. PAPR    REDUCTION TECHNIQUE FOR          LTE SC-FDMA                exceeded with probability less than 0.1 percentile PAPR. The
                       SYSTEMS
                                                                        PAPR calculation using various sub-carrier mapping schemes
   In case of high amplitude signals subject to non linear              for SC-FDMA and OFDMA system is shown in Fig. 5. The
power amplification, PAPR reduction is one of the most                   modulation scheme used for the calculation of PAPR is QPSK.
importance performance parameter. This situation more and               It can be seen that SC-FDMA sub-carrier mapping schemes
more occur due to the ever-growing demand in high spectral
efficiency telecommunications systems implying multi dimen-
                                                                                             0
sional waveforms considerations for which the PAPR is high.                                 10

In a single-carrier communication system, pulse shaping is
required to bandlimit the signal and ensures it meets the
spectrum mask. In this paper, a root raised cosine (RRC) filter
                                                                                             −1
is used to pulse shape the SC-FDMA signals. RRC is used                                     10

as the transmit and receive filter in a digital communication
system to perform matched filtering. The combined response
                                                                           Pr(PAPR>PAPRo)




of two such filters is that of the raised-cosine filter. The raised-
                                                                                             −2
cosine filter is used for pulse-shaping in digital modulation                                10              Proposed DFDMA
                                                                                                            Existing DFDMA
due to its ability to minimize intersymbol interference (ISI).                                              Proposed LFDMA
                                                                                                            Existing LFDMA
Its name stems from the fact that the non-zero portion of the                                               Proposed IFDMA
frequency spectrum of its simplest form β = 1 (called the                                                   Existing IFDMA
                                                                                                            OFDMA
                                                                                             −3
roll-off factor) is a cosine function, ’raised’ up to sit above                             10

the f (horizontal) axis. The RRC filter is characterized by
two values; β, and Ts (the reciprocal of the symbol-rate). The
impulse response of such a filter can be given as:
                                                                                            −4
                                                                                            10

         1 − β + 4β/π, t = 0
                                                                                                  1     2     3     4        5       6         7     8    9      10   11
         √
         β/ 2[(1 + 2/π) sin(π/β4) + (1 − 2/π) cos(π/β4)],
                                                                                                                                 PAPRo    dB


h(t) = t = ±T /β4
        
         sin[πt/Ts (1−β)]+4βt/Ts cos[πt/Ts (1+β)]
                   s
                                                                       Fig. 5. Comparison of CCDF of PAPR for SC-FDMA with OFDMA using
                     πt/Ts [1−(4βt/Ts )2 ])        , else
                                                                        QPSK.
It should be noted that unlike the raised-cosine filter, the
impulse response is not zero at the intervals of ±Ts . However,         gives lower PAPR values as compared to OFDMA scheme.
the combined transmit and receive filters form a raised-cosine           In addition, the root raised cosine pulse shaping method has
filter which does have zero at the intervals of ±Ts . Only in            lower PAPR than the case of existing pulse shapping method
the case of β = 0, does the root raised-cosine have zeros at            by more than 3dB. Due to the complex-weighting of LFDMA
±Ts .                                                                   and DFDMA equation would increase the PAPR. Due to the
                                                                        phase rotation it is unlikely that the LFDMA samples will
               VI.   PERFORMANCE ANALYSIS                               all add up constructively to produce a high output peak after
   The performance of the aforementioned PAPR reduction                 pulse shaping. But it is shown that LFDMA has a lower PAPR
technique is explored by performing extensive computer sim-             than DFDMA when pulse shaping is applied. Another PAPR
ulations. All simulation parameters of the LTE SC-FDMA                  simulation using various sub-carrier mapping schemes for LTE
systems are summarized in Table II [6].                                 SC-FDMA systems is shown in Fig. 6. The modulation scheme
   The CCDF)of PAPR, which is the probability that PAPR                 used for the calculation of PAPR is 16-QAM. It show that
is higher than a certain PAPR value PAPR0, is calculated by             IFDMA has lowest value of PAPR at 7.8dB which is 6.7dB in
Monte Carlo simulation. We compare the PAPR value that is               case of QPSK as modulation technique. Finally, we conclude


                                                                   70                                                        http://sites.google.com/site/ijcsis/
                                                                                                                             ISSN 1947-5500
                                                                               (IJCSIS) International Journal of Computer Science and Information Security,
                                                                               Vol. 8, No. 6, September 2010




                                                                                             [3] B. Karakaya, H.Arslan, and H. A. Cirpan, ”Channel estimation for LTE
                      0
                     10                                                                          uplink in high doppler spread,” Proc. WCNC, pp. 1126-1130, April 2008.
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                                                                                                 Computing, pp. 970-975, August 2008.
                      −1
                                                                                             [5] A. Ancora, C. Bona, and D.T.M. Slock, ”Down-sampled impulse response
                     10
                                                                                                 least-squares channel estimation for LTE OFDMA,” Proc. Int. Con. on
                                                                                                 Acoustics, Speech and Signal Processing, Vol. 3, pp. 293-296, April 2007.
                                                                                             [6] M. M. Rana, M. S.Islam, and A. Z. Kouzani, ”Peak to average power ratio
                                                                                                 analysis for LTE aystems,” Proc. Int. Con. on Communication Software
    Pr(PAPR>PAPRo)




                                                                                                 and Networks, pp. 516-520, February 2010.
                                   Proposed DFDMA
                      −2
                     10
                                                                                             [7] A. Ancora, C. B. Meili, and D. T. Slock, ”Down-sampled impulse
                                   Existing DFDMA                                                response least- squares channel estimation for LTE OFDMA,” Proc. Int.
                                   Proposed LFDMA                                                Con. on Acoustics, Speech, and Signal Processing, April 2007.
                                   Existing LFDMA                                            [8] L. A. M. R. D. Temino, C. N. I Manchon, C. Rom, T. B. Sorensen, and
                                   Proposed IFDMA                                                P. Mogensen, ”Iterative channel estimation with robust wiener filtering in
                                   Existing IFDMA
                                                                                                 LTE downlink,” Proc. Int. Con. on Vehicular Technology Conference, pp.
                      −3
                     10                                                                          1-5, September 2008.
                                   OFDMA
                                                                                             [9] J. Zyren, ”Overview of the 3GPP long term evolution physical layer,” Dr.
                                                                                                 Wes McCoy, Technical Editor, 2007.
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                                                                                                 uplink wireless transmission,” IEEE Vehicular Technology Magazine, vol.
                                                                                                 1, no. 3, pp. 30-38, September 2006.
                      −4
                     10
                           2   3       4        5      6      7   8   9   10     11          [11] M. Noune and A. Nix, ”Frequency-domain precoding for single carrier
                                                       PAPRo dB                                  frequency- division multiple access,” IEEE Commun. Magazine, vol. 48,
                                                                                                 no. 5, pp. 86-92, May 2010.
                                                                                             [12] H.G. Myung, J. Lim, and D. J. Goodman, ”Peak to average power ratio
                                                                                                 for single carrier FDMA signals,” Proc. PIMRC, 2006.
Fig. 6. Comparison of CCDF of PAPR for SC-FDMA with OFDMA using                              [13] S. Maruyama, S. Ogawa, and K.Chiba, ”Mobile terminals toward LTE
16-QAM.                                                                                          and requirements on device technologies,” Proc. Int. Con. on VLSI
                                                                                                 Circuits, pp. 2-5, June 2007.
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undesirable because they cause non linear distortions at the                                 [15] H. G. Myung, ”Introduction to single carrier FDMA,” Proc. Int. Con.
transmitter.                                                                                     on European Signal Processing (EUSIPCO), Poznan, Poland, September
                                                                                                 2007.
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                                           VII. C ONCLUSIONS                                     interleaved FDMA in terms of pilot multiplexing and channel estimation,”
   The efficiency of a power amplifier is determined by the                                        Proc. Int. Con. on PIMRC, 2007.
PAPR of the modulated signal. In this paper, we analysis
different sub-carrier mapping scheme for LTE SC-FDMA
systems. We derive the time and frequency domain signals
of different sub-carrier mapping scheme, and numerically
compare PAPR characteristics using CCDF of PAPR. We come
to the conclusion that the IFDMA sub-carrier mapping with
RRC pulse shaping method has lowest PAPR values compare
to the other sub-carrier mapping methods. As a results, im-
proves the mean power output from a battery driven terminal
equipment and power amplifier efficiency. Therefore, SC-
FDMA is attractive for uplink transmissions since it reduces
the high PAPR seen with OFDMA.

                                           ACKNOWLEDGMENT
  This research was supported by the Basic Science Research
Program through the National Research Foundation of Korea
(NRF) funded by the Ministry of Education, Science and
Technology (20100017118).

                                                    R EFERENCES
[1] Q. Li, G. li, W. Lee, M. Il. Lee, D. Clerckx, and Z. li, ”MIMO techniques
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[2] E. Dahlman, S. Parkvall, J. Skold, and P. Beming, ”3G evolution HSPA
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                                                                                        71                                     http://sites.google.com/site/ijcsis/
                                                                                                                               ISSN 1947-5500

				
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