INTERNATIONAL JOURNAL OF COMMUNICATION SYSTEMS
Int. J. Commun. Syst.
2011;
24
:1–13Published online 10 March 2010 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/dac.1125
Performance evaluation of OFDM and singlecarrier systems usingfrequency domain equalization and phase modulation
Emad S. Hassan
1
, Xu Zhu
2
, Said E. ElKhamy
3
, Moawad I. Dessouky
1
,Sami A. ElDolil
1
and Fathi E. Abd ElSamie
1
,
∗
,
†
1
Department of Electronics and Electrical Communications
,
Faculty of Electronic Engineering
,
Menouﬁa University
,
32952
,
Menouf
,
Egypt
2
Department of Electrical Engineering and Electronics
,
The University of Liverpool
,
L69 3GJ
,
U.K.
3
Department of Electrical Engineering
,
Faculty of Engineering
,
Alexandria University
,
Alexandria 21544
,
Egypt
SUMMARYIn this paper, we study the performance of the continuous phase modulation (CPM)based orthogonalfrequency division multiplexing (CPMOFDM) system. Also, we propose a CPMbased singlecarrierfrequency domain equalization (CPMSCFDE) structure for broadband wireless communication systems.The proposed structure combines the advantages of the low complexity of SCFDE, in addition toexploiting the channel frequency diversity and the power efﬁciency of CPM. Both the CPMOFDMsystem and the proposed system are implemented with FDE to avoid the complexity of the equalization.Two types of frequency domain equalizers are considered and compared for performance evaluation of both systems; the zero forcing (ZF) equalizer and the minimum mean square error (MMSE) equalizer.Simulation experiments are performed for a variety of multipath fading channels. Simulation results showthat the performance of the CPMbased systems with multipath fading is better than their performancewith single path fading. The performance over a multipath channel is at least 5 and 12dB better thanthe performance over a single path channel, for the CPMOFDM system and the proposed CPMSCFDEsystem, respectively. The results also show that, when CPM is utilized in SCFDE systems, they canoutperform CPMOFDM systems by about 5dB. Copyright
2010 John Wiley & Sons, Ltd.
Received 18 March 2009; Revised 6 October 2009; Accepted 15 January 2010KEY WORDS
: SCFDE; OFDM; CPM; ZF equalizer; MMSE equalizer; constant phase; power reduction;equalization
1. INTRODUCTIONOFDM is an effective multicarrier transmission technique for wireless communications because itprovides a high degree of immunity to multipath fading and impulsive noise, and it eliminates theneed for complicated equalizers [1,2]. One of the major drawbacks of multicarrier transmissionis the high peaktoaverage power ratio (PAPR) of the transmitted signals. This problem makesOFDM sensitive to nonlinear distortions caused by the transmitter power ampliﬁer (PA) [3]. Withoutsufﬁcient power backoff, the system suffers from spectral broadening, intermodulation distortion,and consequently, performance degradations. These problems can be solved by increasing the inputpower backoff (IBO), but this leads to a reduction in the efﬁciency of the PA [4,5].
∗
Correspondence to: Fathi E. Abd ElSamie, Department of Electronics and Electrical Communications, Faculty of Electronic Engineering, Menouﬁa University, 32952 Menouf, Egypt.
†
Email: fathi_sayed@yahoo.comCopyright
2010 John Wiley & Sons, Ltd.
2
E. S. HASSAN
ET AL.
Several techniques have been proposed to solve the PAPR problem such as clipping and ﬁltering,coding, tone reservation (TR), tone injection (TI), and multiple signal representation techniques,such as the partial transmit sequence (PTS) technique, the selective mapping (SLM) technique, andthe interleaving technique, [6–10]. These techniques achieve a PAPR reduction at the expense of an
increase in the transmitted signal power, the bit error rate (BER), and the computational complexity.An alternative approach to mitigating the PAPR problem is based on signal transformations. Thistechnique involves a signal transformation prior to ampliﬁcation, then an inverse transformation atthe receiver prior to demodulation. In [11–14], a phase modulator (PM) transform was considered
to generate signals with CPM. This scheme is attractive for wireless communications because of the constant envelope of the generated signals, which is needed for power efﬁcient transmitters, andits ability to exploit the diversity of the multipath channel, which is needed to improve the BERperformance. In the CPMOFDM system, the OFDM signal is used to phasemodulate the carrier.This system shares many of the same functional blocks with the conventional OFDM system. Thismakes the existing OFDM systems capable of providing an additional CPMOFDM mode, easily.SCFDE has found a great popularity for application in wireless communication systems, especially for severe frequencyselective environments due to its effectiveness and low complexity[15–17]. Compared with OFDM, SCFDE has a lower PAPR, less sensitivity to frequency synchro
nization errors, and a higher frequency diversity gain when a relatively high rate channel codingscheme is applied.The aim of this paper is to study the performance of the CPMOFDM system with FDE.In addition, we propose a CPMSCFDE structure for broadband wireless communications.The proposed structure combines the key characteristics of CPM and SCFDE systems to producea constant envelope SCFDE waveform. The performance of the proposed system is comparedwith the CPMOFDM system and the conventional OFDM system.The remainder of this paper is organized as follows. Section 2, presents the CPMOFDM systemmodel. The FDE process and the design of the equalizers are explained in Section 3. Section 4presents the proposed CPMSCFDE system model. Section 5 presents the phase demodulator.Section 6 provides the numerical results and the discussion. Finally, Section 7 provides someconcluding remarks.2. THE CPMOFDM SYSTEM MODELThe block diagram of the CPMOFDM system is shown in Figure 1. Let
X
(
k
) denote the
M
aryquadrature amplitudemodulated (QAM) data symbols. During each
T
second block interval, an
N
DFT
points inverse discrete Fourier transform (IDFT) is used to give the block of time samples
x
(
n
)corresponding to
X
(
k
). After that, the generated OFDM sequence,
x
(
n
), passes through a PM to givethe constant envelope sequence
s
(
n
)
=
exp(j
Cx
(
n
)), where
C
is a scaling constant. After the CPM,a cyclic preﬁx (CP) is added at the beginning of each data block to help mitigating the interblock interference (IBI), which is assumed to have a longer length than the channel impulse response.The continuoustime CPMOFDM signal
s
(
t
) is then generated at the output of the digitaltoanalog (D
/
A) converter. This CPM signal can be expressed as follows [14]:
s
(
t
)
=
A
e
j
(
t
)
=
A
e
j[2
hm
(
t
)
+
]
,
T
g
t
<
T
(1)
I/P Data QAMMapping IDFT Phase Modulation CP Insertion
MultipathChannel
D/AFDE A/D CP RemovalPhase Demodulation DFT
s(t)
QAM Demapping O/P Data
X(k) x(n) s(n)
r(t)
r(n)
s
~
(
n
)
x
~
(n) X
~
(
k
)
Figure 1. Block diagram of the CPMOFDM system.
Copyright
2010 John Wiley & Sons, Ltd.
Int. J. Commun. Syst.
2011;
24
:1–13DOI: 10.1002/dac
PERFORMANCE EVALUATION OF OFDM AND SINGLECARRIER SYSTEMS
3where
A
is the signal amplitude,
h
is the modulation index,
is an arbitrary phase offset used toachieve CPM [11],
T
g
is the guard period,
T
is the block period, and
m
(
t
) is a realvalued OFDMmessage signal comprised of
N
subcarriers and given as
m
(
t
)
=
C
N
N
k
=
1
I
k
q
k
(
t
) (2)where
I
k
are the realvalued data symbols:
I
k
=
ℜ{
X
(
k
)
}
,
k
N
/
2
−ℑ{
X
(
k
−
N
/
2)
}
,
k
>
N
/
2(3)
ℜ{
X
(
k
)
}
,
ℑ{
X
(
k
)
}
are the real and the imaginary parts of
{
X
(
k
)
}
, respectively, and
q
k
(
t
) is afunction used to represent the orthogonal subcarriers and is expressed as follows:
q
k
(
t
)
=
cos
2
kt T
,
k
N
2sin
2
(
k
−
N
/
2)
t T
,
k
>
N
2(4)Using Equations (3) and (4), Equation (2) can be rewritten as
m
(
t
)
=
C
N
N
/
2
k
=
1
ℜ{
X
(
k
)
}
cos
2
kt T
−
N
k
=
N
/
2
+
1
ℑ{
X
(
k
)
}
sin
2
(
k
−
N
/
2)
t T
(5)where
C
N
is a normalization constant used to normalize the variance of the message signal (i.e.
2
m
=
1), and consequently the variance of the phase signal,
2
=
(2
h
)
2
. This requirement isachieved by setting
C
N
as follows [14]:
C
N
=
2
N
2
I
(6)where
2
I
is the variance of the data symbols. The assumption that the data are independent andidentically distributed leads to
2
I
=
E
{
X
(
k
)

2
}=
1
M
M
l
=
1
(2
l
−
1
−
M
)
2
=
M
2
−
13(7)where
M
is the number of constellation points.If
J
denotes the oversampling factor, there will be
N
DFT
=
JN
samples per block. Then withthe help of Equations (1) and (5), the discretetime version of
s
(
t
) at the output of the PM can beexpressed as
s
(
n
)
=
A
exp
j
2
hC
N
N
/
2
k
=
1
I
k
cos
2
kn N
DFT
+
N
k
=
N
/
2
+
1
I
k
sin
2
(
k
−
N
/
2)
n N
DFT
+
(8)with
n
=
0
,
1
,
...
,
JN
−
1.Then, the transmitted signal
s
(
t
) passes through the multipath channel. The channel impulseresponseismodelledasawidesensestationaryuncorrelatedscattering(WSSUS)processconsistingof
L
discrete paths:
h
(
t
)
=
L
−
1
l
=
0
h
(
l
)
(
t
−
l
) (9)
Copyright
2010 John Wiley & Sons, Ltd.
Int. J. Commun. Syst.
2011;
24
:1–13DOI: 10.1002/dac
4
E. S. HASSAN
ET AL.
CP
N
g
N
DFT
N
g
N
F
=
N
DFT
+
N
g
N
F
: Number of samples per frame.
Figure 2. Transmitted data block.
where
h
(
l
) and
l
are the channel gain and delay of the
l
th path, respectively. The continuoustimereceived signal
r
(
t
) is expressed as
r
(
t
)
=
L
−
1
l
=
0
h
(
l
)
s
(
t
−
l
)
+
w
(
t
) (10)where
w
(
t
) is an additive white Gaussian noise (AWGN) with singlesided power spectral density
N
0
. The output of the analogtodigital (A
/
D) converter is sampled at
t
=
nT
=
JN
. The
n
th(
n
=−
N
g
,
...
,
0
,
...
,
N
DFT
−
1) sample of the received signal
r
(
t
) is given by
r
(
n
)
=
LJ
−
1
i
=
0
h
(
i
)
s
(
n
−
i
)
+
w
(
n
) (11)where
N
g
is the number of samples in the guard interval, and
N
DFT
is the number of samples perblock as shown in Figure 2.After the A
/
D, the CP samples are discarded and the remaining samples are equalized withan FDE process. Deﬁning
N
DFT
=
JN
, the received signal
r
(
n
) is transformed into the frequencydomain using an
N
DFT
points discrete Fourier transform (DFT). The received signal on the
m
th(
m
=
0
,
1
,
...
,
N
DFT
−
1) subcarrier is given by
R
(
m
)
=
H
(
m
)
S
(
m
)
+
W
(
m
) (12)where
R
(
m
),
H
(
m
),
S
(
m
), and
W
(
m
) are the
N
DFT
points DFT of
r
(
n
),
h
(
n
),
s
(
n
), and
w
(
n
),respectively.3. EQUALIZER DESIGNIn this section, the FDE and the design of the frequency domain equalizers are discussed. As shownin Figure 3, the received signal is equalized in the frequency domain after the DFT block. The equalized signal is then transformed back into the time domain by using the IDFT.Let
C
(
m
), (
m
=
0
,
1
,
...
,
N
DFT
−
1), denote the equalizer coefﬁcients for the
m
th subcarrier.The time domainequalized signal
˜
s
(
n
), which is the soft estimate of
s
(
n
), can be expressed asfollows:
˜
s
(
n
)
=
1
N
DFT
N
DFT
−
1
m
=
0
C
(
m
)
R
(
m
)e
j2
mn
/
N
DFT
,
n
=
0
,
1
,
...
,
N
DFT
−
1 (13)The equalizer coefﬁcients
C
(
m
) are determined to minimize the meansquared error between theequalized signal
˜
s
(
n
) and the srcinal signal
s
(
n
). The equalizer coefﬁcients are computed accordingto the type of the FDE as follows [18]:
•
The ZF equalizer:
C
(
m
)
=
1
H
(
m
)
,
m
=
0
,
1
,
...
,
N
DFT
−
1 (14)
Copyright
2010 John Wiley & Sons, Ltd.
Int. J. Commun. Syst.
2011;
24
:1–13DOI: 10.1002/dac
PERFORMANCE EVALUATION OF OFDM AND SINGLECARRIER SYSTEMS
5
DFT IDFT
r(n) R
[
m
]
C
(
m
)
s
~
(
n
) = IDFT{
C
(
m
)
R
(
m
)}
Figure 3. Frequency domain equalizer.
•
The MMSE equalizer:
C
(
m
)
=
H
∗
(
m
)

H
(
m
)

2
+
(
E
b
/
N
0
)
−
1
(15)where (
.
)
∗
denotes the complex conjugate. The ZF equalizer given in Equation (14) perfectlyeliminates the effect of the channel in the absence of noise, but when noise cannot be ignored,the ZF equalizer suffers from the noise enhancement phenomenon. On the other hand, the MMSEequalizer given in Equation (15) takes into account the signaltonoise ratio (SNR), making anoptimum tradeoff between channel inversion and the noise enhancement.Considering the MMSE equalizer described in Equation (15) and using Equation (12),Equation (13) can be rewritten as
˜
s
(
n
)
=
1
N
DFT
N
DFT
−
1
m
=
0

H
(
m
)

2
S
(
m
)

H
(
m
)

2
+
(
E
b
/
N
0
)
−
1
e
j2
mn
/
N
DFT
signal
+
1
N
DFT
N
DFT
−
1
m
=
0

H
(
m
)

∗
N
(
m
)

H
(
m
)

2
+
(
E
b
/
N
0
)
−
1
e
j2
mn
/
N
DFT
noise
(16)Notice that the MMSE equalizer and the ZF equalizer are equivalent at high SNRs. Consideringthe ZF equalizer, Equation (16) can be rewritten as
˜
s
(
n
)
=
1
N
DFT
N
DFT
−
1
m
=
0
S
(
m
)e
j2
mn
/
N
DFT
signal
+
1
N
DFT
N
DFT
−
1
m
=
0
N
(
m
)

H
(
m
)

e
j2
mn
/
N
DFT
noise
(17)4. THE PROPOSED CPMSCFDE SYSTEM MODELIn this section, the system model of the proposed CPMSCFDE structure is presented. The block diagram of the CPMSCFDE system is shown in Figure 4.It is known that the main difference between the conventional OFDM system and SC systems isin the utilization of the DFT and IDFT operations. In OFDM systems, an IDFT block is placed atthe transmitter to multiplex data into parallel subcarriers and a DFT block is placed at the receiverfor FDE, whereas in SC systems, both the DFT and the IDFT blocks are placed at the receiverfor FDE. When combined with DFT processing and the use of a CP, conventional OFDM systemsand conventional SCFDE systems are of equal complexity [15,17]. Matters become different
when using CPM, where as shown in Figures 1 and 4, the CPMOFDM system needs two DFToperations and two IDFT operations. This makes the CPMOFDM system more complex than theproposed CPMSCFDE system, which requires only a single DFT operation and a single IDFToperation for FDE.Consider the transmission of a block of data in the proposed CPMSCFDE system over amultipath fading channel. Similar to the CPMOFDM, the sequence
x
(
n
) passes through a PMto obtain a constant envelope sequence. Then CP is inserted between blocks to mitigate the IBI.In the CPMOFDM case, the data symbols have an additional transformation by using the IDFT,
x
(
n
)
=
IDFT[
X
(
k
)], but in the SCFDE case, no transformation is applied. At the receiver, the CP
Copyright
2010 John Wiley & Sons, Ltd.
Int. J. Commun. Syst.
2011;
24
:1–13DOI: 10.1002/dac