35.8 Performance of OFDM Systems by fjhuangjun


									                              Performance of OFDM Systems with
                                 Adaptive Nonlinear Ampli ers
               Je-hong Jong, Kyounghoon Yang , Wayne E. Stark, and George I. Haddad

                           Department of Electrical Engineering and Computer Science
                            The University of Michigan, Ann Arbor, Michigan, U.S.A.
                                       Department of Electrical Engineering
                    Korea Advanced Institute of Science and Technology KAIST, Taejon, Korea

   Abstract | Orthogonal frequency division multiplexing
OFDM is known for its high peak-to-mean-envelope-                                                 ej 2fc t
power ratio. This requires a large ampli er power output         dt          bt          At                  si t so t
backo , when linear ampli cation is needed, resulting in
low dc to RF power conversion e ciency of the ampli er.                 IFFT          ht                     Ref g AMP
Recently, adaptive dc bias controlled ampli ers were pro-
posed, which achieve both high power e ciency and linear-
ity. In this paper, we quantify and optimize the power con-                             Fig. 1. Transmitter
sumption of OFDM systems when the proposed ampli ers
are used. The bit error rate BER and adjacent channel
power ratio ACPR are obtained through computer sim-          achieves both high e ciency and linearity. In this pa-
ulation to help quantifying the ampli er nonlinear e ects.     per, we quantify and optimize the power consumption
It is found that power consumption can be greatly mini-
mized by using adaptive ampli ers, especially with highly      of OFDM systems when the proposed ampli ers are
nonconstant envelope modulated signals such as OFDM.           used. Pulse shaped QPSK modulation scheme, which has
                                                               smaller envelope variations, is also considered as a special
                    I. Introduction                            case of OFDM when the number of subcarrier is one.
   The need for low power and high speed transmission            The paper is organized as follows. In Section II, the
is well recognized in current and future mobile personal       communication system and channel model considered are
communications. Battery life now becomes one of the            given. In addition, three di erent types of dc bias con-
most important factors determining the size and weight         trolled ampli er are described: 1 xed, 2 single, and
of portable terminals, such as mobile phones and note-         3 dual dc bias controlled ampli ers. In Section III, a
books 1 , 2 . Besides voice communication, high speed          performance measure to optimize power consumption is
data transmission e.g. images and videos is also required    de ned. Also a simpli ed asymptotic analysis of the per-
to meet expected future needs.                                 formance measure with OFDM is performed to help gain
   Orthogonal frequency division multiplexing OFDM is        some insight into the performance measure and dc bias
an e ective multicarrier modulation technique for such         schemes. In Section IV, the bit error rate BER and ad-
high speed data applications, especially in an interfer-       jacent channel power ratio ACPR are obtained through
ence limited environment such as a multipath fading            computer simulation. Moreover, optimum ampli er out-
channel 3 . However, because of its high peak-to-mean-         put backo s are obtained. Section V nally concludes the
envelope-power ratio PMEPR 4 when linear ampli ca-           paper.
tion is required, the ampli er average output power has
to be backed o . This results in low dc to RF power                       II. System and Channel Model
conversion e ciency for conventional xed dc bias power         A. Modulation
ampli ers. Even for single carrier systems, this low con-
version e ciency usually happens when bandwidth e -                   A block diagram of the transmitter is shown in Fig. 1.
cient modulation schemes are used, such as pulse shaped            The basic principle behind OFDM is to split a data stream
quadrature phase shift keying QPSK and quadrature                dt into M streams serial to parallel process, each of
amplitude modulation QAM, because of their envelope              which is transmitted on a separate carrier. In our OFDM
variations.                                                        system, the number of carriers, M , is 64 and each car-
   Recently, a technique for adaptively controlling the            rier is modulated with QPSK. This modulation scheme is
dc bias of a power ampli er was proposed in 5 , which              implemented by the inverse fast Fourier transform tech-
                                                                   nique IFFT which eliminates the complexity involved
  This research is supported by the Department of Defense Research in using a large number of oscillators. This scheme oper-
& Engineering Multidisciplinary University Research Initiative on ates block-wise every MT seconds. That is M symbols
 Low Power Low Noise Devices" and managed by the Army Re-                                    s
search O ce ARO under grant ARO DAAH04-96-1-0001.                are transmitted every MTs and each symbol constitutes

                                          0-7803-5538-5/99/$10.00 (c) 1999 IEEE
2 information bits. The modulated signal                                                 TABLE I
                                                                        Parameters for different dc bias schemes
             si t = RefAtej 2fc tg
                     = Vi t cos2fc t + t         1           Bias scheme     CV;0    CI;0   CV;1    CI;1
                                                                       Fixed bias      1       1      0       0
where Vi t = jAtj is the voltage envelope of the signal,           Single bias     1       0      0       1
t = 6 At is the phase, and fc is the carrier frequency.           Dual bias       0       0      1       1
The complex signal At bt  ht is the output signal
of the square root raised cosine transmitter lter ht with    which is denoted by Vo t, is obtained by the Fourier series
roll-o factor , and bt is the parallel to serial processed   expansion or so called Chebyshev transform 6 , 9  of
output of the IFFT, given by                                   the instantaneous voltage characteristics which are those
                   M ,1
                   X                                           of ideal soft-limiter in 5 at the fundamental carrier fre-
        bt =          bc;l t , lTs  for t 2 0; MTs 2     quency fc . This is
                                                                          et;                             for et  1
where t is the Dirac delta function and                       Vo t = 2 et asin 1  + 1 , 21  1 ; for et  1 5
                                                                                      et        e t 2

                            M ,1
          bc;l = p1             fdi k + jdq kge j2M
                                                             3 where et is the normalized input voltage envelope, de-
                       M k=0                                       ned as
                                                                                      et = Vi t=Vi;m :               6
where dik 2 f,1; 1g and dq k 2 f,1; 1g are informa-
tion bits. In a QPSK transmitter, M is simply set to The value Vi;m is the maximum sinusoid input envelope
1 in 2 and 3. As can be seen in 3, the amplitude voltage that can be ampli ed linearly.
distribution becomes complex Gaussian from the central             The signal power is related to the envelope voltage by
limit theorem as M increases, resulting in higher enve-
lope variations.                                                    Pi t = Vi2t=2      and       Po t = Vo2 t=2 7
B. Ampli er and channel model                                    and the power output backo OBO of the ampli er is
   The modulated signal, si t, is rst ampli ed and then de ned as
corrupted by additive white Gaussian noise AWGN with                          OBO = Psat=Po = Vsat=Vo2
two sided power spectral density N0 =2.                          which is the ratio of saturation power Psat to average out-
B.1 Ampli er input and output characteristics                    put power Po . Note that the averagings over-bars are
                                                                 done over the input envelope variations, i.e., over et.
   The ampli er model considered in this paper is a band- The saturation voltage V  is set to be the asymptotic
pass memoryless nonlinear model. In this model, the re- output voltage, i.e., maxsat t = limet!1 Vo t = 4 .
lationship between the input and output signal of the For a given saturation power, smaller OBO gives larger              
ampli er is described by the two memoryless functions, average output power resulting in more power e ciency;
namely amplitude AM AM and phase AM PM non- however, it gives more signal distortion resulting in more
linearities 6 . In this model, when the input to the am- required received power for a given BER for nonconstant
pli er is the modulated signal in 1, the output of the envelope signals. The goal of this paper is to nd an op-
ampli er is expressed as                                         timum OBO which minimizes the average power required
     so t = F Vi t cosf2fc t + t + Vi tg: 4 for reliable communications.
The functions F Vi t and Vi t denote AM AM and B.2 Ampli er dc bias schemes
AM PM, respectively. In a bandpass model, it is assumed             Based on the model presented in 5 , three di erent dc
that the harmonics spectral component centered around bias controlled schemes are considered: 1 xed, 2 sin-
nfc ; n = 0; 2; 3; 4; :: : generated by nonlinearities are re- gle, and 3 dual. The xed bias scheme is used in con-
jected by an ideal zonal lter around the carrier frequency ventional class A ampli ers, where dc power is constant
fc . In this paper, we assume no AM PM e ects. This regardless of the magnitude of the input power. In the dc
is because a solid state power ampli er SSPA usually bias controlled schemes, when the dc power dotted line
has negligible AM PM Vi t  0, and it is found, in Fig. 2 changes according to the input signal power
by computer simulation, that the e ects of AM AM are level as opposed to a xed dc power dashed line. This
much more signi cant than AM PM 7 , 8 .                          reduces dc power consumption especially in the low input
   The relationship AM AM between the input voltage power levels which are more predominant than high input
envelope Vi t and the output voltage envelope F Vi t, power levels. A detailed description of these schemes can

                                          0-7803-5538-5/99/$10.00 (c) 1999 IEEE
be found in 5 . The mathematical relationship between                                                              Pdc( t ) for a fixed dc bias
dc power, Pdc t and normalized input voltage envelope,                                                   Pdc,m

et, is as follows:                                                    dc power     Pdc( t )
                                                                                                                         Pdc( t )
                                                                                                                                        Po ( t )

Pdc t= CV;0 + CV;1etCI;0 + CI;1et; for et  1
          Pdc;m ;                            for et  1    Pi ( t )              AMP          Po ( t )

Pdc;m = 1
                                                                                                                                       Pi ( t )
The parameters CV;0, CV;1, CI;0, and CI;1 depend on the
con guration of dc bias controlled schemes, and are listed
in Table 1. Notice that the dc power is a linear function                  Fig. 2. Ampli er characteristics
of normalized input et for the single bias scheme and a
quadratic function for the dual bias scheme.               We note that the input signal power is neglected in this
                                                           TDD, assuming the ampli er gain output power input
             III. Performance Measures                     power is high. The detailed explanation is given in 10 .
   In this section, we rst brie y describe the objective
function, total dc power degradation TDD, which will B. Implications of TDD
be used to optimize system power consumption. Then we         In this subsection, we discuss the asymptotic behavior
discuss some insight we have gained from the simpli ed of OBO dB , SOBO dB when OBO is large, with
asymptotic analysis of TDD with OFDM. Finally, we close the three ampli er models given in Section II. B. From the
this section with a discussion of the performance measure simpli ed asymptotic analysis, we will gain some insight
for out-of-band interference, ACPR.                        into TDD and show the potential power saving that can
                                                           be realized with dc bias controlled ampli ers.
A. Objective function, TDD                                    Since the output power increases monotonically with
   To optimize power consumption of the systems, we        the input power in our ampli er model, large OBO means
adopt TDD which is proposed in 10 . The de nition of small normalized input power, i.e., e2 1. In this case,
TDD is as follows:                                         the probability that et is greater than one is small, and
                                                           let's assume
       TDD dB = OBO dB , S OBO dB                          Z1                              Z1
                    + Eb =N0 OBO dB               9     e  efe e de and e2  e2 fe e de 11
                                                                           0                                       0

where E b =N0 OBO is called E b =N0 degradation given    where fe e is the probability density function of et.
by                                                          From this, when OBO is large
      E b =N0OBO dB , E b =N0linear dB         10                       4=2 Vo;m
                                                                                                              4= 12
                                                                                           2                        2
                                                            OBO = 2 R 1 2                 R1 2
and E b =N0OBO is the required average received signal             Vo;m 0 e fe e de + 1 Vo efe e de      e2
energy per bit to noise density ratio to meet a target BER and, similarly,
e.g. 10,4 at a given OBO, which is greater than or equal
to that with a linear ampli er E b=N0 Linear. The                               8
                                                                                       1;     for xed bias
increase, Eb =N0 OBO, results from the signal wave-               SOBO  : 1=e; for single bias              13
form distortion of the nonlinear ampli cationlow OBOs.                               1=e2 ; for dual bias:
The second term in 9, S OBO = Pdc;m =P dc , denot-
ing a dc power saving or a correction term that can be Hence, when OBO is large, the power ampli er ine -
achieved by using a dc bias controlled ampli er or that is ciency term OBO dB , SOBO dB
needed for any ampli er which has a non- xed dc power;          8
S OBO  1, and equality holds for the xed bias scheme             OBO dB;                    for xed bias
for all OBOs                                                    : 20 log4= + 10 loge=e2 ; for single bias 14
   In summary, the rst two terms in 9 represent the am-           20 log4=  2:1 dB;      for dual bias:
pli er ine ciency and the last term denotes the receiver
performance degradation from the nonlinear signal distor- If we assume that Eb =N0 OBO  0 dB for large OBO,
tion. We want to minimize degradations from both ampli- the above result implies that the TDD can be nite even
  er ine ciency and the signal distortion. It can be shown for in nite OBO in the dual bias scheme, whereas it can
that an optimum OBO to minimize the required P dc to be in nite for the xed bias ampli er. For dual bias, when
meet target BER also gives the minimum value of TDD. OBO is large, OBO dB , SOBO dB has a constant

                                         0-7803-5538-5/99/$10.00 (c) 1999 IEEE
value of 2.1 dB, regardless of the statistics of the modu-
lated signal envelope. Since the envelope of the OFDM                        12

signal assuming the number of subcarriers is larger than                                                                                             Fixed Bias
                                                                                                                                                      Single Bias
10 can be wellp  approximated by the Rayleigh random                        10                                                                       Dual Bias

variable, e = e2 =2 in this case. Thus, from 12
and 14, for single bias in OFDM,                                              8

OBO dB , SOBO dB  5 log   + 1 OBO dB:

                                                                  TDD (dB)

The single bias scheme reduces the slope of OBO dB                            4

by a factor of half. These observations can help de-
signing power e cient ampli ers jointly with modulation
schemes, since di erent modulation schemes have di er-

ent envelope statistics                                                         0
                                                                                    1       2         3       4         5       6         7       8         9       10

C. Out-of-band interference                                                                                       OBO (dB)

   The out-of-band interference power is usually quanti ed
by the ACPR, which is de ned as a ratio of the out-of-                                                              a
band signal power in the adjacent channel to the in-band
signal power, given as

                                                                                            Fixed Bias
               R fc ,B              R fc +3B                                                Single Bias

                 fc ,3B So f  df + fc +B So f  df ; 15
                                                                            5               Dual Bias

  ACPRB  =               R fc +B
                            fc ,B So f  df                                4

where ,B; B is the desired in-band, and So f  is the
                                                                 TDD (dB)

power spectral density of the ampli ed signal so t.                       3

     IV. Simulation Results and Discussions                                 2

   A Monte Carlo method is used in the simulation. The
signals are oversampled with a rate of 16 16 samples are
taken in each Ts seconds for the BER calculation and

with a rate of 32 for the ACPR calculation. For accurate
results, a higher sampling rate is needed for the ACPR cal-                 0
                                                                            0.5         1       1.5       2       2.5       3       3.5       4            4.5      5

culation than for the BER. The square root raised cosine                                                          OBO (dB)
  lter with roll-o factor of 0.35 is used for the transmit-
ter and receiver lters with a nite impulse length of 96Ts,                                                         b
which is enough for ACPR calculation down to ,50 dB
at BTs = 2:0.                                                  Fig. 3. TDD dB for three di erent ideal dc bias schemes: a
                                                                   OFDM b QPSK
   Fig. 3 shows the TDD for the three di erent adaptive
dc bias ampli ers, when the target BER is 10,4. The
solid lines in the plots are the power ampli er ine ciency     TDD for OBO 8 dB is too small to be seen in the plot.
terms OBO dB , SOBO dB for each scheme, and              Optimum OBOs for QPSK in Fig. 3b are all no larger
the di erence between the solid line and curve for a given     than 0.5 dB for all three bias schemes. Hence, in terms
scheme is the E b=N0 degradation. As expected, E b =N0         of reducing dc power consumption, it is desirable to drive
increases as the OBO becomes smaller, and for OFDM,            the ampli er hard for QPSK modulation. However, these
the E b =N0 degradation is about 6.2 dB when OBO = 2           low output backo s increase spectral regrowth, and when
dB. However, E b=N0 degradation is very small for QPSK         out-of-band interference is a major concern, OBO must
due to its small envelope variations. Note that E b =N0        be larger. This issue will be discussed again when we
degradation is same for all the bias schemes, since the        examine ACPR.
bias schemes do not change the signal waveform.                   Fig. 4a shows ACPR dB at BTs = 1:35=2 of OFDM
   Optimum OBOs of OFDM in Fig. 3a, which give the           and QPSK. The ACPR of OFDM decays slowly approxi-
minimum values of the TDDs, are found to be 4, 5, and          mately piece-wise inverse linear with OBO, and is about
8 dB for the xed, single, and dual dc bias schemes, re-        -15 dB when OBO = 1 dB. The ACPR of QPSK is smaller
spectively. For the dual bias scheme, the increase in the      than that of OFDM, and the slope is sharper than that

                                          0-7803-5538-5/99/$10.00 (c) 1999 IEEE
             −10                                                            −10                                                                       −15

                                                OFDM                                                                  OBO=1 dB                                                                  OBO=1 dB
                                                QPSK                                                                  OBO=2 dB                                                                  OBO=2 dB
             −15                                                                                                                                      −20
                                                                                                                      OBO=3 dB                                                                  OBO=3 dB
                                                                                                                      OBO=4 dB                                                                  OBO=4 dB
                                                                            −20                                       OBO=5 dB                                                                  OBO=5 dB
             −20                                                                                                      OBO=7 dB                                                                  OBO=7 dB

                                                             ACPR(B) (dB)

                                                                                                                                       ACPR(B) (dB)
 ACPR (dB)


             −30                                                            −35

             −35                                                            −40


                                                                            −50                                                                       −50
               1   2   3     4      5   6   7          8                      0.6   0.8   1      1.2    1.4     1.6     1.8      2                      0.6   0.8   1      1.2    1.4     1.6     1.8      2

                             OBO (dB)                                                     Normalized frequency BT                                                   Normalized frequency BT
                                                                                                                s                                                                         s

                             a                                                                b                                                                        c
                           Fig. 4. a ACPR at     B Ts    =1 35 2; ACPR vs. normalized frequency
                                                             :                =                                                  BTs : b OFDM and c QPSK

of OFDM. Above OBO = 5 dB, QPSK is almost linearly                                                     the dual bias scheme is used. This is especially desirable
ampli ed, resulting in constant residual ACPR in theory                                               when the adjacent channel interference ACPR from the
it should be zero, which is from the truncation of lter                                               nonlinear ampli cation is a major concern, requiring a
time response in the simulation. Figs. 4b and c show                                               large ampli er backo .
ACPR versus B in OFDM and QPSK, respectively. The
ACPR still decays slowly with B .                                                                                                References
   We note that E b=N0 degradation decays relatively fast                                              1 L. E. Larson, Radio frequency integrated circuit technology
                                                                                                          for low-power wireless communications," IEEE Personal Com-
with OBOs, as seen in Fig 3. This degradation can be                                                      mun., vol. 5, pp. 11 19, June 1998.
further reduced by channel coding and spread spectrum                                                  2 E. Biglieri, G. Caire, and G. Taricco, Coding and modulation
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                                                                                                       4 Simon Shepherd, John Orriss, and Stephen Barton, Asymp-
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operating saturation region low OBOs, is minimal when

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