A decision metric approach to PAPR performance analysis of an OM by gyvwpsjkko

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									  A decision metric approach to PAPR performance
      analysis of an OM-OFDM transmission
                                         K. Dhuness, P. Botha and B. T. J. Maharaj
                                Department of Electrical, Electronic and Computer Engineering
                                             University of Pretoria, South Africa
                                         Tel:+27 12 4204760, Fax: +27 12 3625000
                        Email: kdhuness@tuks.co.za, philip.botha@mweb.co.za, sunil.maharaj@up.ac.za

                                                                                                    TABLE I
   Abstract—In this paper, a novel method called offset modu-                         AN IDEAL PAPR REDUCTION METHOD
lation (OM-OFDM) is proposed, to control the peak-to-average
power ratio (PAPR) of an OFDM signal. The theoretical band-
width occupancy of the proposed offset modulated signal is                       Requirements                     Methods not Complying
derived. Using this bandwidth occupancy a closed form theo-                                                         to the requirements
                                                                                Low complexity                   Partial transmitted sequence
retical bit error rate (BER) expression for an offset modulated
                                                                                                                      Selective mapping
transmission is further derived, validated and compared to                                                               DAR clipping
OFDM. A BER comparison between OM-OFDM and OFDM                                Does not lead to an                 Non-linear companding
at a PAPR value of 13 dB, shows that both methods offer                     increase in average power
similar BER characteristics for additive white Gaussian noise            Does not affect the coding gain                     Coding
(AWGN) channel conditions. Furthermore, by using a newly                       Does not require any                        CE-OFDM
applied decision metric, the authors show that OM-OFDM offers             further bandwidth expansion            Partial transmitted sequence
between 64.6%-46.8% net performance gain (at a BER of 10−4 )         or the transmission of side information          Selective mapping
when compared to a clipped OFDM and OFDM transmission in                 Does not lead to a severe BER                      Clipping
an AWGN channel.                                                                degradation as the                       DAR clipping
                                                                           number of carriers increases                    CE-OFDM
   Index Terms—PAPR, OFDM, OM-OFDM, DVB-T

                      I. INTRODUCTION
                                                                    an OM-OFDM transmission is derived. Using these bandwidth
   Orthogonal frequency division multiplexing (OFDM), has
                                                                    occupancy results, in Section IV, a closed form bit error rate
found wide application in many wireless standards, such as
                                                                    expression for an OM-OFDM transmission is derived and
digital video broadcasting (DVB), worldwide inter-operability
                                                                    validated. In Section V, a newly applied decision metric (D)
for microwave access (WiMAX) IEEE 802.16d and recently
                                                                    is presented. Using this metric in Section VI, OM-OFDM,
in long term evolution (LTE). However, it is a well known
                                                                    OFDM, a classically clipped OFDM and a DAR clipped
fact that OFDM is plagued by a large peak-to-average power
                                                                    OFDM transmission are compared. To conclude this paper in
ratio (PAPR). This high PAPR necessitates the need for
                                                                    Section VII the benefits of OM-OFDM are discussed.
over designed power amplifiers, which ultimately reduces the
battery life of the mobile devices. Various methods [1], [2]                     II. PROPOSED OFFSET MODULATION
have been suggested to reduce the PAPR, these are: clip-               Consider the complex output of a N -point inverse Fourier
ping, decision aided reconstruction (DAR) clipping, coding,         transform, OFDM signal, given by
partial transmission sequence, selective mapping, non-linear
                                                                                                  N −1
companding transforms and constant envelope OFDM phase                                 1                         2πtk

modulation (CE-OFDM). These are by no means all the                            m(t) = √                  Xk ej    Ts    ,   0 ≤ t < Ts          (1)
                                                                                        N         k=0
methods, but rather the more popular ones. Ideally a method
is required which meets the requirements summarized in              where Ts is the symbol duration and Xk represents the
Table I. In this paper, the authors propose such a method           complex signal, which may also be written as ak + jbk . This
called offset modulation (OM-OFDM), which requires low              signal may be modulated using the method shown below.
implementation complexity, does not require any additional                              (m(t))                    (m(t))
bandwidth expansion or the transmission of side information to               Φ1 (t) =            and Φ2 (t) =             . (2)
                                                                                         ς                           ς
reconstruct the original message signal. It also does not lead to
                                                                    Here,   and , refer to the real and imaginary parts of the
an average power increase, nor does it lead to a severe bit error
                                                                    OFDM message signal, ς refers to a constant division term.
rate (BER) degradation as the number of carriers increases,
                                                                    Whereas, Φ1 (t) and Φ2 (t) represent the equivalent real and
thus meeting the highest number of requirements in Table I,
                                                                    imaginary OFDM mapping. These, Φ1 (t) and Φ2 (t) terms may
when compared to the other methods. The proposed offset
                                                                    now be combined into a unique co-sinusoid, given by
modulation method is developed in Section II. Thereafter, in
Section III, a closed form bandwidth occupancy expression of           cos(2πfc t + Φ1 (t) + Ψos ) − cos(2πfc t + Φ2 (t)).                      (3)
Alternatively, Eq (3) may also be written as                                                                                                        is a severe BER degradation and a spectrally untidy signal.
                                                                                                                                                    OM-OFDM, on the other hand, deals with constellations
                               Φ2 (t) − Φ1 (t) − Ψos
                            2 sin                     ·                                                                                             containing both real and imaginary components. The real and
                                         2                                                                                                          imaginary components are combined in a unique manner; the
                                Φ1 (t) + Ψos + Φ2 (t)                                                                                               Ψos and ς terms ensure that the receiver can successfully detect
                   sin 2πfc t +                                                                                                               (4)
                                           2                                                                                                        the originally transmitted signal. This process produces a
where, Ψos refers to an offset term. In this type of modu-                                                                                          spectrally efficient signal illustrated in Fig. 4, when compared
lation the parameters (Ψos , ς) are chosen such that Ψos >>                                                                                         to a classical OFDM transmission. Hence the only similarity
Φ2 (t)−Φ1 (t), when Ψos is sufficiently large and Φ2 (t), Φ1 (t)                                                                                     that OM-OFDM and CE-OFDM share, is that at one point they
are sufficiently small. This implies that the Ψos term will                                                                                          both employ a form of phase modulation. Other than that the
dominate the expression, hence the name offset modulation                                                                                           two methods are completely different, leading to a completely
(OM-OFDM) is proposed to describe this operation. A block                                                                                           novel method. The transmission may appear to be a phase
diagram, showing the possible processes involved during an                                                                                          modulated signal, therefore losing its attractive OFDM prop-
OM-OFDM transmission is shown in Fig. 1. Thus far the                                                                                               erties. However, the OM-OFDM systems transmitter receiver
                                                                                                                                                    structure (Fig. 1) maintains the fundamental OFDM building
                                                                                                                                                    blocks. Thus the OM-OFDM equalization process is identical
   Input                                                       Up                                               OM
   Message                                IFFT                Sample                                          Modulator                             to that employed in OFDM. Channel state information (CSI)
                                                                                                                                                    is extracted from the pilot symbols and used during the
                                                                                                                                                    equalization process to mitigate the effects of fading. Thus,
                                                                                                              Channel                               OM-OFDM still maintains the ease of equalization. However,
                                                                                                                                                    the OM-OFDM transmission contains a dominant component
                                                                                                                                                    (Fig. 4) given by 2J0 (β)2 sin(2πfc t − Ψ2 ) (discussed in Sec-
                                                                                                                                                                                               os
 Output                                                           Down                                    OM
 Message
                            Equalizer              FFT            Sample                               Demodulator                                  tion IV). By subtracting −γ2J0 (β) sin(2πfc t − Ψ2 ), 0 ≤
                                                                                                                                                                                          2                os


                                                                                                                                                    γ < 1 (where γ is the dominant frequency component
                                                                                                                                                    control factor) from the dominant frequency component at the
                            Fig. 1.           Transmitter Receiver Structure                                                                        transmitter (Fig. 2), and re-instating the subtracted term at the
                                                                                                                                                    receiver (Fig. 3), the PAPR may be controlled. This is not
 Input              Re(t)         +
             S/P                      S            cos[.]
                                      +                                   +
                                                                      S
                                                   cos[.]                 -
                            -1                                                     cos(2pft)              +
                                                                                                                  +
                                                                                                                                     Output                                    1.5
                            V         YOS                                                                     S            S                                                                                              13 dB OM−OFDM
                                                   sin[.]                              sin(2pft)          +            -                                                                                                  13 dB OFDM
                                                                          -
                                                                      S
                    Im(t)                          sin[.]                 +                   2
                                                                                          2 gJ0(b) sin(2pft-0.5Y OS)
                                                                                                                                                                                1
                                                                                                                                                                                                                      Dominant OM−OFDM
                                                                                                                                                               Amplitude (V)




                                                                                                                                                                                                                          Component
                                                                                                                                                                                            OFDM


                                  Fig. 2.          OM Modulator Structure
                                                                                                                                                                               0.5

 Input   +
             S          LPF        arccos[.]
         +
             x                              0.5             0.5   +                           +                   Re(t)
                                                                      S                               S
                                                                  +                               -                                  Output
                                                                                 0.5
                                                                                                      YOS         V            P/S                                              0
                                                                                                                                                                                8.2   8.4      8.6           8.8         9        9.2
                                              cos[2pft]           -                                                   Im(t)
                                                                      S                                                                                                                              Bandwidth (Hz)                        7
                                               cos[.]                                                                                                                                                                                   x 10
                                                                  +
                                                                  2                                       2


                                                          LPF                 arccos[.]                                                             Fig. 4. An averaged normalized bandwidth occupancy comparison between
         x=2 gJ2(b) sin(2pft-0.5YOS)
               0
                                                                                                                                                    OM-OFDM and OFDM with identical throughput when using a 64-QAM 8k
                                                                                                                                                    mode of the DVB - T standard [4].
                                 Fig. 3.          OM Demodulator Structure

                                                                                                                                                    the case in a classical OFDM and CE-OFDM transmission.
proposed method may appear to be similar, if not identical,
                                                                                                                                                    As the dominant component becomes prominent, the PAPR of
to constant envelope OFDM phase modulation (CE-OFDM),
                                                                                                                                                    the signal decreases. However, because in reality some energy
which has been well documented [3]. However, the resultant
                                                                                                                                                    restrictions are imposed on a transmitter, the other components
CE-OFDM signal is spectrally untidy and is ideally suited for
                                                                                                                                                    can contain less energy leading to a BER trade-off.
constellations without imaginary components (BPSK). In cases
where imaginary components exist (e.g. as in 64-QAM), this
constellation is uniquely mapped onto a different constellation                                                                                       III. BANDWIDTH OCCUPANCY OF OFFSET MODULATION
without imaginary components (e.g. 64-QAM to 64-PAM
mapping). Such a mapping process results in a severe BER                                                                                               In this section the bandwidth occupancy of an OM-OFDM
degradation. Hence CE-OFDM has the ideally required 3 dB                                                                                            transmission will be investigated by considering a discrete
PAPR (which is permanently fixed), but the price paid for this                                                                                       complex OFDM signal given by Eq (5). This is an extension
                         nTs
of Eq (1), (t =           N ),   giving                                                        components of interest. In most cases the adapted phase
                                               N −1
                                                                                               deviation (β1 and β2 ) of the signal is not known beforehand;
                                        1                     2πnk                             however, a reasonably good approximation can be made, based
                         mn      =     √              Xk ej    N
                                         N     k=0
                                                                                               on
                                               N −1
                                        1
                                 =     √              Xk ejwn k .                        (5)                              α1    ≈         E[max(| (m(t))|)]
                                         N     k=0
                                                                                                                          α2    ≈         E[max(| (m(t))|)]
In the above expression, wn , is an arbitrary chosen variable                                                                             α1
used to simplify the analysis, Eq (5) may also be written as                                                              β1    ≈
                                                                                                                                           ς
                         N −1                                                                                                             α2
                 1                                                                                                        β2    ≈            .                                                            (11)
mn      =       √               (ak + jbk )(cos(wn k) + j sin(wn k)) (6)                                                                   ς
                  N      k=0

it can then be shown that                                                                      Here, α1 and α2 , refer to the real and imaginary phase devi-
                                      N −1                                                     ations of the OFDM signal respectively, and E [ ] is the ex-
                         [mn ]
   Φ1n        =                ≈             β1 cos(wn k) − β2 sin(wn k)                       pected value. Typically, there is no interest in all the frequency
                          ς                                                                    components, but rather in the more dominant components.
                                      k=0
                                      N −1                                                     Hence, the bandwidth can be defined by considering only
                         [mn ]
   Φ2n        =                ≈             β2 cos(wn k) + β1 sin(wn k). (7)                  those sidebands which contain significant power. Suppose, for
                          ς
                                      k=0                                                      explanation purposes, the first two components (2x = 2) are
Here, Φ1n and Φ2n are the equivalent real and imaginary                                        of interest and β = β1 = β2 . Then by inspection of Eq (10),
discrete OFDM mapping, whereas β1 and β2 are constants                                         for this particular case, the frequency spectrum is shown in
defined as the adapted real and imaginary phase deviation of an                                 Fig. 5. This frequency spectrum is different from that of a
OM-OFDM signal respectively. After incorporating this into
the unique co-sinusoidal (Eq (3)), the following expression is
obtained
                                               N −1
  un    ≈            ej(2πfc n+Ψos +                  β1 cos(wn k)−β2 sin(wn k))
                                                                                                Amplitude (V)




                                                                                                                                      2
                                               k=0                                                                                 |2J0(b) sin(0.5(-Y os
                                                                                                                                                       ))|

                                                                                                                                             |-2J1 (b)J 0(b)sin(0.25( p-2Yos))-2J 0(b)J 1(b) sin(0.25(- p-2Yos))|
                                           N −1
                −        ej(2πfc n+        k=0    β2 cos(wn k)+β1 sin(wn k))
                                                                                     . (8)
                                                                                                                                                                           2
                                                                                                                                                                       |-2J1(b) sin(0.5(-Yos ))|
In the above expression, un is the discrete signal which is
to be transmitted. With the aid of Bessel functions [5], the
Fourier series can be written as
                                           ∞                                                                    fc-2f d    fc-fd           fc                fc +f d           fc +2f d
            j(β sin(wn k))                                  j(lwn k)
        e                         =               Jl (β)e                                                                      Frequency (Hz)
                                       l=−∞
                                         ∞                                                     Fig. 5. Theoretical derived (Eq (10)) frequency spectrum of an OM-OFDM
            j(β cos(wn k))                                    j(mwn k+ mπ )                    signal.
        e                         =                Jm (β)e              2        .       (9)
                                       m=−∞

Here, Jl (β) and Jm (β) are Bessel functions of the first kind of                               conventional phase modulated signal. The squaring of the
order l and m respectively with argument β. After substituting                                 Bessel functions limits the bandwidth occupancy of the signal.
Eq (9) into Eq (8), and if l = m then                                                          If β is sufficiently small (β = 0.02), it can be seen that a large
                                                                                               percentage of the power is constrained within these (2x = 2)
                    2x     2x−y
                                               π(2x − 2z − y) − 2Ψos                           frequency components. The dominant frequency component is
   un       ≈                      2 sin                                             ·
                                                         4                                     given by 2J0 (β)2 sin(2πfc t− Ψ2 ), provided Ψos >> Φ2 (t)−
                                                                                                                                 os
                  y=0       z=0
                                                                |−x+z|
                                                                                               Φ1 (t). By subtracting −γ2J0 (β)2 sin(2πfc t − Ψ2 ), 0 ≤
                                                                                                                                                    os

                                        |−x + z + 1 |
                                                  2                                            γ < 1 (where γ is the dominant frequency component
                  J|−x+z| (β1 )                                             ·
                                         −x + z + 1
                                                  2
                                                                                               control factor) from the dominant frequency component at
                                                        1              |x−y−z|                 the transmitter (Fig. 2) and re-instating the subtracted term
                                           |x − y − z + 2 |                                    at the receiver (Fig. 3), the PAPR may be controlled. The
                  J|x−y−z| (β2 )                                                 ·
                                            x−y−z+ 1    2                                      receiver has knowledge of the subtracted term by examining
                                                             Ψos                               the PAPR of the incoming signal, from which the Ψos , ς and
                  sin 2π(fc + yfd ) − yπ +                              .            (10)      γ terms can be extracted by using a simple look-up table
                                                              2
                                                                                               (similar to Table III). In the next section, the manner in which
In Eq (10), fd is an integer multiple of the modulation                                        the dominant frequency component is varied and the resultant
frequency and 2x refers to an even number of frequency                                         BER characteristics are presented.
                                                                                                                                       TABLE III
    IV. BIT ERROR RATE CHARACTERISTICS OF OFFSET                                                          PARAMETERS FOR A 64 - QAM OM - OFDM SYSTEM                   (α = 0.27)
                          MODULATION
                                                                                                                   PAPR     Ψos            ς                 γ           ϕ
  It can be shown by using [6], that the noise variance at the                                                      7 dB    1.596     44000/16384          0.86         0.2
output of the various branches of the demodulator (Fig. 3) can                                                      8 dB    1.596     44000/16384           0.9        0.251
be written as                                                                                                       9 dB    1.596     44000/16384          0.925       0.34
                                                                                                                   10 dB    1.596     44000/16384          0.943       0.44
            2            No                2    No                                                                 11 dB    1.596     44000/16384          0.962       0.53
           σx ≈                     and σy ≈              (12)                                                     12 dB    1.596     44000/16384          0.97        0.67
                                                 2
                    4 sin2 −ϕ2                                                                                     13 dB    1.596     44000/16384            1           1

where by inspection, ϕ is a constant term and may be
approximated by Table II.
                                                                                                          0
                                                                                                         10
                                                                                                                                                                  7 dB OM−OFDM
                                                                                                                                                                  7 dB Theoretical
                             TABLE II                                                                                                                             8 dB OM−OFDM
             SELECTION OF A ϕ TERM , BASED ON γ     AND   α                                                                                                       8 dB Theoretical
                                                                                                          −1                                                      9 dB OM−OFDM
                                                                                                         10




                                                                          Average Bit Error Rate (BER)
                                                                                                                                                                  9 dB Theoretical
                                                                                                                                                                  10 dB OM−OFDM
                                                                                                                                                                  10 dB Theoretical
                    0 < α < 0.1     0.1 ≤ α < 0.2     0.2 ≤ α < 0.3                                                                                               11 dB OM−OFDM
                                                                                                          −2                                                      11 dB Theoretical
                                                                                                         10
                                                                                                                                                                  12 dB OM−OFDM
                                                                                                                                                                  12 dB Theoretical
      β sin(Ψos )
 ϕ≈     4(1−γ)
                    0 ≤ γ < 0.99    0 ≤ γ < 0.97      0 ≤ γ < 0.96                                                                                                13 dB OM−OFDM
                                                                                                                                                                  13 dB Theoretical
                                                                                                          −3
      β sin(Ψos )                                                                                        10
 ϕ≈     5(1−γ)
                    0.99 ≤ γ < 1    0.97 ≤ γ < 1      0.96 ≤ γ < 1


                                                                                                          −4
                                                                                                         10
Here, γ is the dominant frequency component control factor                                                     0           10          20            30              40               50
                                                                                                                                Average SNR per bit (Eb/No)(dB)
and the, α and β terms originate from Eq (11). Based on this an
approximate theoretical BER for an OM-OFDM transmission
                                                                       Fig. 6.   Theoretically predicted (Eq (13)) and simulated bit error rate
through an AWGN channel, can be derived and written as                 comparison.
                                                √
                   k · (M − 2) + ℘ · k(M − 2 M + 2)
      BER ≈
                            √       M · k2
                     ℘ · (2 M − M − 1)                                   V. DETERMINING AN OPTIMUM SOLUTION FOR OFFSET
                   +                                       (13)                                                                     MODULATION
                             M · k2
where                                                                     Liang [7] et al. have proposed a decision metric (D),
                                                                       to deal with the relationship between amplifier efficiency,
                                    kξb
               ℘    = erfc                    and                      amplifier distortion, signal bandwidth occupation, throughput
                                   ξav No                              and power consumption. The authors have adapted this metric
                                                   
                                                                       to incorporate PAPR, to investigate whether the proposed OM-
                                   4k sin2 (− ϕ )ξb
                    = erfc                   2     .          (14)   OFDM transmission, has an optimum solution and whether a
                                       ξav No                          net gain exists for such a solution. The decision metric is given
                                                                       by
        ξb
Here, No refers to the signal-to-noise ratio (SNR) per bit,
                                                                                                                                                  Et
ξav is defined as the energy per symbol, M denotes the M-                                                                                          No
ary levels, M = 2k , when k is even and erfc denotes the                                                                            D      =      Rb
                                                                                                                                                       .                                   (15)
                                                                                                                                                  W
error function. It should be noted that the theoretically derived
expression does not accept a γ = 1; if such a term arises, then        Here, Rb is the data rate and W refers to the bandwidth occu-
ϕ = 1. This simplifies Eq (13) into a BER expression for an             pancy. Typically during fair comparisons, identical throughput
AWGN transmission. Also, Table II assists in the choice of             and bandwidth occupancies are used, thus Rb remains constant
                                                                                                                   W
Ψos and γ terms to minimize the BER degradation. In order                                                  Et
                                                                       and the metric simplifies to D ∝ No . In Eq (15), No is the
to validate the theoretically derived expressions, by means of         noise power spectral density for a specific BER and Et is
a simulation (the 8k mode of the DVB-T standard [4]), 64-              the total energy per bit. Unlike traditional approaches, which
QAM Gray-coded OM-OFDM data were transmitted through                   only take into account the received energy per bit (Eb ) and
an AWGN channel. The parameters used for the 64-QAM OM-                often ignore the total energy consumption (e.g. dc power
OFDM transmission are given in Table III. From Fig. 6, it              consumption of the amplifier). Here, Et incorporates the total
can be seen that the theoretically predicted results (Eq (13))         energy per bit and can be written as
and the simulated results correlate fairly well, thus validating
the theoretically derived expression.                                                                                           Et = Eb + Ew .                                             (16)
In Eq (16), Ew is the wasted energy per bit due to inefficient                                                     discussed in Section I. When using the same DVB-T standard,
power amplifier utilization. In the next section, this metric is                                                   OM-OFDM allows the PAPR of the signal to be varied,
applied and the benefits of using an OM-OFDM transmission                                                          while still maintaining identical throughput and bandwidth
are presented.                                                                                                    occupancy as an OFDM transmission. Hence a direct com-
                                                                                                                  parison between OFDM and OM-OFDM can be made when
                                            VI. R ESULTS AND D ISCUSSION                                          both methods offer the same PAPR (13 dB) as shown in
   In all the results which follow, a 64-QAM Gray-coded                                                           Fig. 7. From this OM-OFDM and OFDM comparison, it is
8k mode of the DVB-T standard was used to transmit OM-                                                            noted that both methods offered similar BER characteristics
OFDM, OFDM, clipped OFDM and DAR clipped OFDM                                                                     at a PAPR of 13 dB. Also a BER comparison between a
data through an AWGN channel. Identical throughput and                                                            clipped OFDM signal and a DAR clipped OFDM signal,
bandwidth occupancies were used to ensure a fair compari-                                                         indicates that for high PAPR (12 dB) values, both methods
son between the various methods. Perfect carrier and timing                                                       offer similar BER characteristics. However, for lower PAPR
synchronization is assumed. The parameters used for the OM-                                                       (8 dB) values the DAR clipped technique, performs better
OFDM transmission is given in Table III. When classically                                                         than the traditional clipping method. At these lower PAPR
clipping a signal, both in-band and out-of-band distortion is                                                     values both the clipped and DAR clipped transmissions, BER
introduced. In order to minimize the in-band distortion both                                                      plateaued. For clipping and DAR clipping these BER plateaus
the clipped OFDM signal and DAR clipped OFDM signal                                                               occur when PAPR ≤ 11dB and PAPR ≤ 10dB respectively
were over-sampled by a factor of 2, when compared to both                                                         for this particular case. OM-OFDM on the other hand does
OFDM and OM-OFDM. To limit the out-of-band distortion                                                             not suffer from this BER plateau effect.
both clipped OFDM signal and DAR clipped OFDM signal
                                                                                                                  B. A decision metric comparison between OM-OFDM,
were filtered before transmission with a 14th order Butterworth
                                                                                                                  OFDM, a clipped OFDM signal and a DAR clipped OFDM
bandpass filter, with a 9 dB ripple in the pass-band and a
                                                                                                                  transmission
42 dB stop attenuation. The DAR process also involved two
iterations, before obtaining a BER value.                                                                            In order to facilitate a direct comparison between OM-
                                                                                                                  OFDM, OFDM, clipped OFDM and DAR clipped OFDM,
A. A BER comparison between OM-OFDM, OFDM, a clipped                                                              the decision metric discussed in Section V was employed.
OFDM signal and a DAR clipped OFDM transmission                                                                   By using this metric and employing two standard off-the-
   Offset modulated, OFDM, clipped OFDM data and DAR                                                              shelf (OTS) RF power amplifiers, an FPD2000AS [9] and
clipped OFDM data were sent through an AWGN channel by                                                            a AN10858 [8] power amplifier, a 10th and 2nd degree
using the parameters previously mentioned. A BER compar-                                                          polynomial was used to describe the power added efficiency
ison, between the various methods is shown in Fig. 7. The                                                         for these particular amplifiers, respectively. The results, when
                                                                                                                  using the decision metric for these two amplifiers is shown in
                                   0
                                                                                                                  Fig. 8 and Fig. 9. In both these comparisons it should be noted
                                  10
                                                                                          8 dB Clipped
                                                                                          8 dB DAR Clipped
                                                                                          8 dB OM−OFDM                                     41
                                                                                          12 dB Clipped                                             Clipped OFDM
                                   −1                                                     12 dB DAR Clipped                                         DAR Clipped OFDM
                                  10
   Average Bit Error Rate (BER)




                                                                                          12 dB OM−OFDM                                                                    Optimum DAR Clipped and Clipped
                                                                                                                                           40       OM−OFDM                OFDM operating point
                                                                                          13 dB OM−OFDM
                                                                                                                                                    OFDM
                                                                                          13 dB OFDM

                                                                                                                                           39
                                                                                                                     (Et/No)/(Rb/W) (dB)




                                   −2
                                  10
                                                                                                                                                                                                    OFDM
                                                                                                                                           38


                                   −3
                                  10
                                                                                                                                           37



                                                                                                                                           36
                                   −4
                                  10                                                                                                                     Optimum OM−OFDM operating point
                                        0   5   10        15      20        25       30          35          40
                                                     Average SNR per bit (Eb/No)(dB)                                                       35
                                                                                                                                                7    8        9          10        11        12        13
                                                                                                                                                                       PAPR (dB)

Fig. 7. A bit error rate comparison between an OM-OFDM, OFDM, clipped
OFDM and DAR clipped OFDM signal.                                                                                 Fig. 8. System performance, at a BER of 10−4 for an FPD2000AS RF
                                                                                                                  power amplifier.
averaged PAPR of an OFDM transmission when using the
8k mode of the DVB-T standard according to simulations is                                                         that both the clipped OFDM and DAR clipped OFDM results
13 dB. This PAPR value has also independently been verified                                                        have been abridged due to the fact that the clipped OFDM
by [8]. This PAPR is fixed for an OFDM transmission and                                                            BER plateaued, thus it was unable to produce the specific
may only be changed by adopting one or all of the methods                                                         BER. When using these standard OTS power amplifiers, the
                         36
                                                                              conditions. The authors have further proposed a newly applied
                        35.5
                                       Clipped OFDM                           decision metric, to investigate whether the proposed OM-
                                       DAR Clipped OFDM                       OFDM transmission, has an optimum solution and whether
                         35            OM−OFDM
                                       OFDM                                   a net gain exists for such a solution. OM-OFDM has been
                        34.5
                                                                              shown by using this metric, to offer between 4.5 dB - 2.7
  (Et/No)/(Rb/W) (dB)




                         34
                                                                              dB (64.6%-46.8%) net performance gain (at a BER of 10−4 )
                        33.5                                                  when compared to a DAR clipped OFDM, a clipped OFDM
                         33                                                   and OFDM transmission. This performance gain, combined
                        32.5                                                  with the fact that OM-OFDM requires low implementation
                         32                                                   complexity and does not lead to an average power increase. It
                        31.5                                                  also does not require any additional bandwidth expansion or
                         31
                                                                              the transmission of any side information to reconstruct the
                                                                              original message signal. Furthermore it does not lead to a
                        30.5
                               7   8         9       10
                                                   PAPR (dB)
                                                               11   12   13   severe BER degradation as the number of carriers increase.
                                                                              These aspects make it a good alternative approach to current
                                                                              methods already in the field. Future work on OM-OFDM will
Fig. 9. System performance, at a BER of 10−4 for an AN10858 RF power
amplifier.                                                                     focus on other channel conditions.
                                                                                                           R EFERENCES
optimum operating point for an OM-OFDM transmission is                        [1] S. H. Han and J. H. Lee, “An overview of peak-to-average power
                                                                                  ratio reduction techniques for multicarrier transmission,” IEEE Wireless
at a PAPR of 10 dB (where a minimum decision metric                               Communications Magazine, vol. 12, no. 2, pp. 56–65, April 2005.
occurs) and for a DAR clipped and classically clipped OFDM                    [2] T. Jiang and Y. Wu, “An overview: Peak-to-average power ratio reduction
transmission is shown to be at a PAPR of 12 dB. At this                           techniques for OFDM signals,” IEEE Transactions on Broadcasting,
                                                                                  vol. 54, no. 2, pp. 257–268, June 2008.
optimum operating point, when using the FPD2000AS RF                          [3] S. C. Thompson, “Constant Envelope Phase Modulation,” PhD Thesis,
power amplifier, OM-OFDM offers a 2.88 dB (48%), 4.46 dB                           University of California, San Diego, 2005.
(64.2%) and 4.51 dB (64.6%) net performance gain (at a BER                    [4] ETS 300 744, “Digital Video Broadcasting (DVB); Framing structures,
                                                                                  channel coding and modulation for digital Terrestrial television (DVB-
of 10−4 ) when compared to OFDM, a DAR clipped OFDM                               T),” European Telecommunication Standard Doc. 300, March 1997.
signal and a clipped OFDM signal respectively. Similarly                      [5] R. E. Zeimer and W. H. Tranter, Principles of communications: systems,
when using the AN10858 RF power amplifier, OM-OFDM                                 modulation, and noise, 3rd ed. Washington D.C, 1990.
                                                                              [6] J. G. Proakis and M. Salehi, Communication systems engineering, 2nd ed.
is shown to offer a 2.74 dB (46.8%), 3.43 dB (54.6%) and                          Prentice-Hall, 2002.
3.48 dB (55.1%) net performance gain (at a BER of 10−4 )                      [7] C. Liang, J. Jong, W. E. Stark, and J. R. East, “Nonlinear Amplifier
when compared to OFDM, a DAR clipped OFDM signal                                  Effects in Communication Systems,” IEEE Transactions on Microwave
                                                                                  Theory and Techniques, vol. 47, no. 8, pp. 257–268, August 1999.
and a clipped OFDM signal respectively. At the optimum                        [8] N. Semiconductors. (2010) AN10858.pdf. [Online]. Available: http:
operating point of an OM-OFDM transmission (10 dB), the                           //www.nxp.com/documents/application note/
FPD2000AS and AN10858 RF power amplifier, produces a                           [9] R. M. Devices. (2009) FPD2000ASDS.pdf. [Online]. Available:
                                                                                  http://www.rfmd.com/CS/Documents/
decision metric result of 36.04 dB and 31.20 dB respectively.
This comparison indicates that the AN10858 amplifier offers
a 4.84 dB improvement over the FPD2000AS amplifier, thus
making it a better amplifier for this particular application.
This result was intuitively expected since the AN10858 RF                     Kahesh Dhuness received his B.Eng and M.Eng in Electrical and Elec-
                                                                              tronic Engineering from the University of Johannesburg in 2004 and 2006,
power amplifier has being specifically designed for this current                respectively. After which he was employed as a Systems Engineer at SAAB
application (8k mode of the DVB - T standard).                                Grintek. In 2008, he joined the Department of Electrical, Electronic and
                                                                              Computer Engineering at the University of Pretoria. Mr Dhuness is currently
                                            VII. CONCLUSION                   a PhD candidate, his research work is supported by the SENTECH Chair in
                                                                              Broadband Wireless Multimedia Communication, at the University of Pretoria.
   The authors have proposed a novel method called offset
modulation to control the PAPR of an OFDM transmission.
The theoretical bandwidth occupancy of the proposed offset
modulation signal was derived. This derivation proved that
                                                                              Sunil Maharaj received his BSc Eng and MSc Eng in Electronic Engineering
OM-OFDM is spectrally more efficient than CE-OFDM. Using                       from University of Natal (Durban). He received the MSc in Operational
this bandwidth occupancy results, a closed form theoretical bit               Telecommunications with merit from University of Coventry and a PhD in
error rate expression for an offset modulation transmission is                Wireless Communications from University of Pretoria. Professor Maharaj
                                                                              previously worked as a Microwave Design Engineer at EMLAB Pty Ltd
further derived. This mathematically derived BER expression                   and then at the Eastern Cape Technikon. He currently holds the position of
has been shown to agree with the simulated results, thus                      SENTECH Chair in Broadband Wireless Multimedia Communications in the
validating the derivation. A BER comparison between OM-                       Department of Electrical, Electronic and Computer Engineering at University
                                                                              of Pretoria. His research interests are in MIMO Channel Modeling, OFDM-
OFDM and OFDM at a PAPR value of 13 dB, shows that both                       MIMO Systems and Cognitive Radio.
methods offer similar BER characteristics for AWGN channel

								
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