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Performance of symbol-sampled receivers over unknown continuous-time channels

Symbol-sampled receivers that estimate the channel blindly or semi-blindly have had their performance evaluated via Forney's FIR model for the equivalent channel, the discrete time transversal filter (DTTF). This model, which allows maximum likelihood sequence estimation, contains a matched filter, and thus requires a priori knowledge of the continuous-time channel impulse response. As a consequence, if the channel is continuous and unknown, and if we keep sampling at the symbol-rate, it is unrealistic to use the DTTF model, which becomes an upper bound on the system performance. Using an alternative model for the equivalent discrete-time channel, where the continuous-time channel is unknown and the matched filter is replaced by a receive filter matched to the symbol waveform, we investigate the performance loss considering both a theoretical and a practical point of view. First, we estimate the theoretical performance loss, in terms of the information rate, relative to the case when the continuous-time channel is known a priori (DTTF). Later, considering a practical system for semi-blind symbol-sampled equalization and turbo decoding, we perform computer simulations which agree with the theoretical results, and show that the loss in performance is negligible when the optimum sampling instant is available.