Paz-Penagos / INGE CUC, vol. 14 no. 2, pp. 97-105, Julio - Diciembre, 2018 OFDM comparison with FFT and DWT processing for DVB-T2 wireless channels Comparación OFDM con procesado FFT y DWT para canales inalámbricos DVB-T2. DOI: https://doi.org/10.17981/ingecuc.14.2.2018.09 Artículo de Investigación. Fecha de Recepción:16/06/2018. Fecha de Aceptación: 17/12/2018. Hernán Paz-Penagos Escuela Colombiana de Ingeniería Julio Garavito. Bogotá, (Colombia) [email protected] To cite this paper: H. Paz Penagos, “OFDM comparison with FFT and DWT processing for DVB-T2 wireless channels” INGE CUC, vol. 14, no. 2, pp. 97-105, 2018. DOI: http://doi.org/10.17981/ingecuc.14.2.2018.09 Abstract Resumen Introduction− Recent studies on the FFT processing Introducción− Recientes estudios sobre el procesado (Fast Fourier Transform) or DWT (Discrete Wavelet FFT (Fast Fourier Transform) o DWT (Discrete Wavelet Transform) of the OFDM signal (Orthogonal Frequency Transform) de la señal OFDM (Orthogonal Frequency Di- Division Multiplexing) have shown pros and cons for vision Multiplexing) han demostrado pros y contras para DVB-T2 (Digital Video Broadcasting-Second Generation comunicaciones de radio DVB-T2 (Digital Video Broad- Terrestrial) radio communications; however, the benefits casting – Second Generation Terrestrial); sin embargo, aún falta comparar las prestaciones de ambos tipos de of both types of processing have yet to be compared for procesamiento para el mismo escenario. the same scenario. Objetivo− El objetivo de esta investigación es comparar Objective− The objective of this research is to compare la respuesta del canal inalámbrico con ruido AWGN (Ad- the response of the wireless channel with AWGN noise ditive White Gaussian Noise Channel) y desvanecimiento (Additive White Gaussian Noise Channel) and Rayleigh Rayleigh y Rician en la banda de UHF (Ultra High Fre- and Rician fading in the UHF (Ultra High Frequency) quency). band Metodología− Se simuló en Matlab®, específicamente Methodology− The transmission of DVB-T2 information en Simulink, la transmisión de información DVB-T2 con with OFDM modulation and FFT and DWT processing modulación OFDM y procesado FFT y DWT. was simulated in Matlab®, specifically in Simulink. Resultados− Los resultados del estudio demostraron ser Results− The results of the study proved to be more ef- más eficientes para el sistema DWT en comparación con ficient for DWT system than FFT system, due to the low el Sistema FFT, por la baja tasa de bits errados, eficiencia rate of erroneous bits, spectral efficiency and reduction espectral y reducción del cociente entre la potencia pico of the Peak-to-Average Power Ratio (PAPR), for Eb / No a promedio (PAPR: Peak-to-Average Power Ratio), para relations greater than 10dB. relaciones Eb/No mayores a 10dB. Conclusiones− En este artículo se presentan los diseños Conclusions− In this article, we present the designs of de ambos sistemas y los resultados de la experiencia both systems and the results of the research experience; de investigación; así mismo, se discute la aplicabilidad likewise, the practical applicability of these systems is práctica de estos sistemas y se sugieren mejoras para discussed, and improvements are suggested for future trabajos futuros. work. Palabras clave− Canal inalámbrico; ruido AWGN; des- Keywords− Wireless channel, AWGN noise, fading, vanecimientos; comunicaciones de banda ancha; proc- broadband communications, DWT and FFT esado FFT y DWT; desempeño. © The author; licensee Universidad de la Costa - CUC. INGE CUC vol. 14 no. 2, pp. 97-105. Julio - Diciembre, 2018 Barranquilla. ISSN 0122-6517 Impreso, ISSN 2382-4700 Online OFDM comparison with FFT and DWT processing for DVB-T2 wireless channels I. INTRODUCTION family of Wavelets from expansions and continues translations of itself. If g is a mother Wavelet func- Orthogonal Frequency Division Multiplexing (OFDM) tion, then the set {τt, Ds, g}, is the family generated has been widely adopted in wireless communication. by g for all expansions s and all displacements (t). The aim of this paper is to compare the performance Table 1 shows two features of the Haar Wavelet type. of an OFDM modulated signal with FFT and DWT This family was used in the simulation by H. Paz [5]. processing when it is transmitted through a wireless channel with AWGN noise and Rayleigh and Rician TABLE 1. DEfiNITION OF TIME AND FREQUENCY fading. The OFDM scheme usually uses Fast Fourier DOMAIN OF THE HAAR TYPE WAVELET. Transform (FFT) to produce orthogonal sub-carri- ers; however, these systems have drawbacks in their Time Domain Frequency Domain transmission by high PAPR, low spectral efficiency and the frequency and/or time synchronization dif- ficulty 1[ ]. An alternative platform beside IFFT and FFT is the discrete wavelet transforms (DWT) which has been considered in Abdullah and Hussain [2]. It Source: Ecitronica Research Group uses low pass filter (LPF) and high pass filter (HPF) operating as quadrature mirror filters satisfying per- The processing through the wavelet transform is fect reconstruction and orthonormal bases properties. implemented quickly and recursively through the This performance of OFDM modulated signal filter banks in quadrature. Detail coefficients dj cor- with FFT and DWT processing could be evaluated responding to the high-frequency bands at the de- considering parameters such as BER, eye diagram, composition level J, are calculated as the discrete spectral efficiency, PAPR, and the constellation di- circumvolution of the in signal x(k) with the high-pass agram; however, for this research, BER, spectral filter g(k); and with the approximation coefficients efficiency, and Peak-to-Average Power Ratio were (dk), that correspond to the low frequency bands, are considered. Applying wavelet packet transform with calculated as the discrete circumvolution in signal the OFDM improves the bit error rate, spectral effi- x(k) with the low-pass filterh(k) . These last ones, act ciency and reduces the Peak-to-Average Power ratio as mirror filters in quadrature that allows perfect performance over wireless communications. For this reconstruction of the processed signal orthonormal reason, OFDM-FFT tends to be replaced by OFDM– properties. DWT [3]. One advantage of FFT and DWT processing is to shape the power spectrum of the DVT-T2 signal to II. THEORETICAL FRAMEWORK make it robust in AWGN noise, Rayleigh and Rician fading at the radio channel. OFDM processed WDT or OFDM modulation is formed from the sum of N FFT is currently used in ADSL: Asymmetric Digital unique-carrier modulations typically QAM type us- Subscriber Line, PLC: Power Line Communications, ing N different carrier frequencies. By this type of digital TV under DRM standards: Digital Radio Mon- modulation, each symbol is transmitted occupying diale and DAB: Digital Audio Broadcasting; and has more time and less bandwidth regarding the unique been investigated by Schulze [6] and ETSI [7], [8] as carrier modulation, the transmission of each group the right modulation scheme for wireless noisy com- of n symbols is transmitted in parallel, occupying munication channels (Wi-Fi and WiMAX, fourth-gen- adjacent carrier frequency, orthogonal and spaced eration telephony LTE and UWB: Ultra-Wide Band). between each other by an integer number of cycles An OFDM variation is the introduction of a chan- (cyclic prefix). IFFT and FFT algorithms guarantee nel coding to multiplexing called COFDM (Coded the orthogonally of the carriers in the receptor and Orthogonal Frequency Division Multiplexing). This minimize operations to be performed on the data. The scheme is characterized by its resistance to multipath IFFT processing, realized in the transmitter, trans- effects, resistance to small changes in signal attenua- form the band base signal of the frequency domain tion and phase distortion, networks single frequency to the time and the FFT makes the inverse function use permission and ability to transmit a signal to in the receiver. mobile receivers [9]. Another processing that can be done through mod- The communication channel where an OFDM ulated signals OFDM is by Discrete Wavelet Trans- signal propagates is characterized by its impulse form (DWT), that is a projection of a signal over the response of a given duration and properties over vector space generated by the base functions (ortho- time changes. In this context, the knowledge of the normal or bi-orthogonal) that are obtained of the dila- propagation characteristics is a key for better use tation/contraction (according to an operator of scale from digital communications systems to new appli- change) and displacement of a passband function pro- cation scenarios. Respecting to the characteristics totype, well localized both in time and in frequency of fading in the channel, several types are identified called mother wavelet [4]. This function generates a in the Fig. 1. 98 Paz-Penagos / INGE CUC, vol. 14 no. 2, pp. 97-105, Julio - Diciembre, 2018 Average attenuation Large-scale fading of signal dueto movements over large areas Variations around the average s n o i t Frequency selective a t s fading e f Description in the i n domain of time delay a m Flat fading r e d Spreading on time of a f l the signal e Frequency selective n n fading a h Description in the C frequency domain Flat fading Short-scale fading dueto small changes in the position Fast fading Description in time domain Slow fading Channel time variation Fast fading Description in the Doppler shift domain Slow fading Fig. 1. Fading types in a wireless channel. Source: Authors. The simplest way to deal with fading is to use with the objective of improving the transmitted aver- during transmission a big enough power or a binary age power of the system parameters, reception error speed small enough, for the ratio between the symbol rate or spectral efficiency (transmission speed). energy and the noise power high enough to maintain The effect of fading is the decreasing of the re- an efficient error rate during a specified time frac- ceived power and a distortion of its waveform.