Otto L . van Linden An Analytical Performance Evaluation of a Coded OFDM - Based Transmission Scheme , using a Markov model for a Frequency Selective Channel

In this report the performance of an error-correcting code on a wide-band frequency selective Rayleigh fading channel with an OFDM-based transmission scheme is estimated by means of an analytical model. In the European dTTb project', a transmission scheme for a new digital terrestrial TV system is under development. This scheme uses OFDM to divide the wide-band channel into a large number of narrow-band subchannels to tackle the frequency selectivity and to combat the Inter-Symbol Interference. The transmission scheme must allow portable (indoor) reception which implies that the transmission channel is a multipath channel. This multipath channel suffers from frequency selective fading. The individual subchannels will have different but mutually dependent signal powers at the receiver. The dependency degrades the performance of an error-correcting code, designed to correct random errors, with respect to an infinitely interleaved fading channel. O n an infinitely interleaved fading channel it is assumed that the individual subchannels have mutually independent signal powers, i.e., where random errors occur. In this report estimations of the performances of binary [n,k,d] BCH codes on this particular channel are made by using an analytical model. This model is an extended GilbertElliott model which uses a Markov chain. The Markov chain performs a kind of quantization of the received signal-to-noise ratio within one subchannel. Further, it models the dependency between the signal powers of the subchannels. The results obtained from the analytical model are compared with the results of a simulation. It is found that the model gives a good estimation of the performance for small signal-to-noise ratios. The range over which the model corresponds with the simulation results depends on the number states used in the Markov chain. For instance, for an extended binary [256,224,9] BCH code we have obtained good estimations up to a signal-to-noise ratio of 25 dB with a 4-state model. A performance improvement of the error-correcting code can be obtained by interleaving of the consecutive information symbols over a number of subchannels. A few results obtained from the analytical model are shown. From these results, it is observed that one needs an interleaving distance of approximately twice the coherence bandwidth of the ' Digital Terrestrial Television Broadcasting. 'Orthogonal Frequency Division Multiplex @ Philips Electronics N.V. I UR 005/93 Unclassified channel, in order to obtain performances approximately similar to the infinitely interleaved channel.