ERROR PERFORMANCE FOR ORTHOGONAL FREQUENCY DIVISION MULTIPLEXING IN ASYMMETRIC DIGITAL SUBSCRIBER LOOPS

Abstract

The Orthogonal Frequency Division Multiplexing (OFDM), commonly referred to by a generic name: Multi-Carrier Modulation (MCM), is a multi-carrier modulation technique that has proved its potential in digital broadcasting and in wired system. One recent successful implementation of OFDM technique is in Asymmetric Digital Subscriber Loops (ADSL) technology that has been selected by ANSI for transmission of digitally compressed video signals over telephone lines. The high performance/cost tradeoff makes OFDM an attractive transmission scheme for ADSL. In this thesis, the OFDM-ADSL system has been thoroughly analyzed in terms of symbol error rate (SER). A novel methodology called Fourier series expansion is adopted in analysis of error performance of the system. A motivation for using the Fourier Series is to obtain the spectrum of a given signal, which describes the frequency content of the signal. As the OFDM technique mainly involved two processes: IFFT and FFT, we can see the advantage and simplicity by using the frequency components of the signal in analysis. In ADSL environment, channel distortion, thermal noise, impulse noise and far-end cross talk (FEXT) are the minor impairments to the OFDM-ADSL system. We focus on the first two impairments in analysis. The power spectrum density of the thermal noise can be modeled as Additive White Gaussian Noise (A WGN). The main feature of OFDM system is the avoidance of intersymbol interference (ISI) and interchannel interference (ICI), which are introduced by the severe amplitude and phase distortion of the subscriber loops. To derive a closed-form expression for evaluating the error performance of the OFDM-ADSL system, we model a periodic 3-symbol pattern by using Fourier series expansion. The primary effect of attenuation and delay distortion in the channel is that each subchannel is received with a different amplitude and phase, so that the channel can be grossly characterized by a single complex number for each subband. This does great help to find the closed-form expression of the error rate as a function of signal-to-noise ratio (SNR). ISI and ICI cause the loss of orthogonality of the subchannels. The addition of the cyclic prefix or guard interval is to combat the linear channel distortion. When the extended guard interval is longer than the channel impulse response, ISI can be eliminated. However, the ICI still exists since the channel distortion ruined the orthogonality condition. The ratio of guard interval to useful symbol duration is application-dependent. An optimal guard interval ratio is found in computation.