10-06-2017, 07:09 AM
Introduction
Orthogonal Frequency Division Multiplexing (OFDM) is a multicarrier modulation system. The transmission channel is divided into a number of subchannel in which each subchannel is assigned a subcarrier. Conventional OFDM systems use IFFT and FFT algorithms at the transmitter and receiver respectively to multiplex the signals and transmit them simultaneously over a number of subcarriers. The system employs guard intervals or cyclic prefixes (CP) so that the delay spread of the channel becomes longer than the channel impulse response (Peled & Ruiz, 1980; Bahai & Saltzberg, 1999; Kalet, 1994; Beek et al.,1999; Bingham, 1990; Nee and Prasad, 2000). The system must make sure that the cyclic prefix is a small fraction of the per carrier symbol duration (Beek et al.,1999; Steendam & Moeneclaey, 1999). The purpose of employing the CP is to minimize inter-symbol interference (ISI). However a CP reduces the power efficiency and data throughput. The CP also has the disadvantage of reducing the spectral containment of the channels (Ahmed, 2000; Dilmirghani & Ghavami, 2007, 2008). Due to these issues, an alternative method is to use the wavelet transform to replace the IFFT and FFT blocks (Ahmed, 2000; Dilmirghani & Ghavami, 2007, 2008; Akansu & Xueming, 1998; Sandberg & Tzannes, 1995). The wavelet transform is referred as Discrete Wavelet Transform OFDM (DWT-OFDM). By using the transform, the spectral containment of the channels is better since they are not using CP (Ahmed, 2000; Dilmirghani & Ghavami, 2007, 2008). The illustration of the superior subchannel containment attributes in wavelet has been described in detailed by (Sandberg & Tzannes, 1995) as compared to Fourier. The wavelet transform also employs Low Pass Filter (LPF) and High Pass Filter (HPF) operating as Quadrature Mirror Filters satisfying perfect reconstruction and orthonormal bases properties. It uses filter coefficients as approximate and detail in LPF and HPF respectively. The approximated coefficients is sometimes referred to as scaling coefficients, whereas, the detailed is referred to wavelet coefficients (Abdullah et al., 2009; Weeks, 2007). In some literatures, these two filters are also called subband coding since the signals are divided into sub-signals of low and high frequencies respectively. The purpose of this chapter is to show the simulation study of using the Matrices Laboratory (MATLAB) on the wavelet based OFDM particularly DWT-OFDM as alternative substitutions for Fourier based OFDM. MATLAB is preferred for this approach because it offers very powerful matrices calculation with wide range of enriched toolboxes and simulation tools. To the best of the authors knowledge, there is no study on the descriptive procedures of simulations using MATLAB with regards of flexible transformed models in an OFDM system, especially when dealing with wavelet transform. Therefore, this chapter is divided into three main sections: section 2 will explain conventional FFT-OFDM, section 3 will describe in detail the models for DWT-OFDM, and section 4 will discuss the Bit Error rate (BER) result regarding those two transformed platforms, DWT-OFDM versus FFT-OFDM.
Introduction
Orthogonal Frequency Division Multiplexing (OFDM) is a multicarrier modulation system. The transmission channel is divided into a number of subchannel in which each subchannel is assigned a subcarrier. Conventional OFDM systems use IFFT and FFT algorithms at the transmitter and receiver respectively to multiplex the signals and transmit them simultaneously over a number of subcarriers. The system employs guard intervals or cyclic prefixes (CP) so that the delay spread of the channel becomes longer than the channel impulse response (Peled & Ruiz, 1980; Bahai & Saltzberg, 1999; Kalet, 1994; Beek et al.,1999; Bingham, 1990; Nee and Prasad, 2000). The system must make sure that the cyclic prefix is a small fraction of the per carrier symbol duration (Beek et al.,1999; Steendam & Moeneclaey, 1999). The purpose of employing the CP is to minimize inter-symbol interference (ISI). However a CP reduces the power efficiency and data throughput. The CP also has the disadvantage of reducing the spectral containment of the channels (Ahmed, 2000; Dilmirghani & Ghavami, 2007, 2008). Due to these issues, an alternative method is to use the wavelet transform to replace the IFFT and FFT blocks (Ahmed, 2000; Dilmirghani & Ghavami, 2007, 2008; Akansu & Xueming, 1998; Sandberg & Tzannes, 1995). The wavelet transform is referred as Discrete Wavelet Transform OFDM (DWT-OFDM). By using the transform, the spectral containment of the channels is better since they are not using CP (Ahmed, 2000; Dilmirghani & Ghavami, 2007, 2008). The illustration of the superior subchannel containment attributes in wavelet has been described in detailed by (Sandberg & Tzannes, 1995) as compared to Fourier. The wavelet transform also employs Low Pass Filter (LPF) and High Pass Filter (HPF) operating as Quadrature Mirror Filters satisfying perfect reconstruction and orthonormal bases properties. It uses filter coefficients as approximate and detail in LPF and HPF respectively. The approximated coefficients is sometimes referred to as scaling coefficients, whereas, the detailed is referred to wavelet coefficients (Abdullah et al., 2009; Weeks, 2007). In some literatures, these two filters are also called subband coding since the signals are divided into sub-signals of low and high frequencies respectively. The purpose of this chapter is to show the simulation study of using the Matrices Laboratory (MATLAB) on the wavelet based OFDM particularly DWT-OFDM as alternative substitutions for Fourier based OFDM. MATLAB is preferred for this approach because it offers very powerful matrices calculation with wide range of enriched toolboxes and simulation tools. To the best of the authors knowledge, there is no study on the descriptive procedures of simulations using MATLAB with regards of flexible transformed models in an OFDM system, especially when dealing with wavelet transform. Therefore, this chapter is divided into three main sections: section 2 will explain conventional FFT-OFDM, section 3 will describe in detail the models for DWT-OFDM, and section 4 will discuss the Bit Error rate (BER) result regarding those two transformed platforms, DWT-OFDM versus FFT-OFDM.