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We consider signal and receiver design for space-time Viterbi equalization for wireless transmission. We propose a search method to find good training sequences, termed min-norm training sequences, for least-square channel estimation. Compared to either a maximum-length sequence or a randomly generated training sequence, the training sequence obtained can drastically reduce the channel estimation error. We also derive a simple lower bound on the achievable channel estimation error of any training sequence. Knowledge of this lower bound helps the search for min-norm training sequences in that it facilitates a measure of the goodness of the best sequence examined so far. For operation under the situation with unknown channel response lengths, we propose a simple method to select the memory length (tap number) in the Viterbi equalizer based on the SNR of the received signal. The resulting equalization performance is found to be comparable with the case where a preset, fixed memory length is used. However, the proposed method often results in use of a smaller tap number, which translates into a reduction in the computational complexity. Simulation results show that at symbol error rate below 10 (SNR > 5 dB) the amount of complexity reduction is of the order of 5% to 25% on the average, for typical wireless channels.