A fundamental problem in training-based channel estimation for various communication systems is the preamble design. Two crucial aspects in such a design are the achievable mean square error (MSE) and the corresponding peak-to-average power ratio (PAPR). In this letter, preamble-based least squares (LS) channel estimation in CP-OFDM systems is considered. Ignoring the PAPR aspect, several MSE-optimal preambles and a necessary condition for their existence are presented. To this end, a training energy constraint, containing also the energy spent to the cyclic prefix (CP), is imposed. This constraint differs from the usual training energy constraints in the existing literature, which ignore the CP energy during training. These preambles contribute in the completion of existing results concerning MSE-optimal preambles in CP-OFDM systems. However, since high PAPR is an issue concerning these optimal designs, we show how these MSE-optimal preambles can be combined with the usual Zadoff-Chu (ZC) sequences to enlarge the class of PAPR-optimal preambles that achieve good MSE performance at the same time.
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