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Performance evaluation of OFDM and single-carrier systems using frequency domain equalization and phase modulation

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In this paper, we study the performance of the continuous phase modulation (CPM)-based orthogonal frequency division multiplexing (CPM-OFDM) system. Also, we propose a CPM-based single-carrier frequency domain equalization (CPM-SC-FDE) structure for
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  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 single-carrier systems usingfrequency domain equalization and phase modulation Emad S. Hassan 1 , Xu Zhu 2 , Said E. El-Khamy 3 , Moawad I. Dessouky 1 ,Sami A. El-Dolil 1 and Fathi E. Abd El-Samie 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 (CPM-OFDM) system. Also, we propose a CPM-based single-carrierfrequency domain equalization (CPM-SC-FDE) structure for broadband wireless communication systems.The proposed structure combines the advantages of the low complexity of SC-FDE, in addition toexploiting the channel frequency diversity and the power efficiency of CPM. Both the CPM-OFDMsystem 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 CPM-based 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 CPM-OFDM system and the proposed CPM-SC-FDEsystem, respectively. The results also show that, when CPM is utilized in SC-FDE systems, they canoutperform CPM-OFDM systems by about 5dB. Copyright    2010 John Wiley & Sons, Ltd. Received 18 March 2009; Revised 6 October 2009; Accepted 15 January 2010KEY WORDS : SC-FDE; 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 peak-to-average 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 El-Samie, Department of Electronics and Electrical Communications, Faculty of Electronic Engineering, Menoufia University, 32952 Menouf, Egypt. † E-mail: 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 CPM-OFDM system, the OFDM signal is used to phase-modulate 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 CPM-OFDM mode, easily.SC-FDE has found a great popularity for application in wireless communication systems, espe-cially for severe frequency-selective environments due to its effectiveness and low complexity[15–17]. Compared with OFDM, SC-FDE 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 CPM-OFDM system with FDE.In addition, we propose a CPM-SC-FDE structure for broadband wireless communications.The proposed structure combines the key characteristics of CPM and SC-FDE systems to producea constant envelope SC-FDE waveform. The performance of the proposed system is comparedwith the CPM-OFDM system and the conventional OFDM system.The remainder of this paper is organized as follows. Section 2, presents the CPM-OFDM systemmodel. The FDE process and the design of the equalizers are explained in Section 3. Section 4presents the proposed CPM-SC-FDE 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 CPM-OFDM SYSTEM MODELThe block diagram of the CPM-OFDM system is shown in Figure 1. Let  X  ( k  ) denote the  M  -aryquadrature amplitude-modulated (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 inter-block interference (IBI), which is assumed to have a longer length than the channel impulse response.The continuous-time CPM-OFDM signal  s ( t  ) is then generated at the output of the digital-to-analog (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 De-mapping 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 CPM-OFDM system. Copyright    2010 John Wiley & Sons, Ltd.  Int. J. Commun. Syst.  2011;  24 :1–13DOI: 10.1002/dac  PERFORMANCE EVALUATION OF OFDM AND SINGLE-CARRIER 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 real-valued 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 real-valued 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 discrete-time 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 impulseresponseismodelledasawide-sensestationaryuncorrelatedscattering(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 continuous-timereceived 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 single-sided power spectral density  N  0 . The output of the analog-to-digital (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 equal-ized 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 domain-equalized 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 mean-squared 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 SINGLE-CARRIER 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 signal-to-noise ratio (SNR), making anoptimum trade-off 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 CPM-SC-FDE SYSTEM MODELIn this section, the system model of the proposed CPM-SC-FDE structure is presented. The block diagram of the CPM-SC-FDE 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 SC-FDE systems are of equal complexity [15,17]. Matters become different when using CPM, where as shown in Figures 1 and 4, the CPM-OFDM system needs two DFToperations and two IDFT operations. This makes the CPM-OFDM system more complex than theproposed CPM-SC-FDE 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 CPM-SC-FDE system over amultipath fading channel. Similar to the CPM-OFDM, 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 CPM-OFDM case, the data symbols have an additional transformation by using the IDFT,  x  ( n ) = IDFT[  X  ( k  )], but in the SC-FDE 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
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