Finite-Alphabet Constant-Amplitude Training Sequences for Multiple-Antennas

We propose a method to identify training sequences for multiple-antenna transmissions over quasi-static frequency-selective channels. These sequences are constructed to belong to a standard constant-amplitude 2m-PSK constellation (such as BPSK, QPSK etc) to simplify the transmitter/receiver implementation. Many practical systems use training of predetermined length. Optimal sequences do not exist for all training sequence lengths and constellation alphabets. The proposed method allows us to identify training sequences that belong to a standard constellation for an arbitrary training sequence length and an arbitrary number of unknown channel taps. Performance bounds derived indicate that these sequences achieve near-optimum performance.