Optimal design of constant-modulus training sequences with constrained length

In this letter, we consider optimal training designs for multiple-antenna cyclic-prefix-based single-carrier transmissions over frequency-selective channels. Our objective is to find optimal training sequences such that the mean-squared error of least-squares channel estimates is minimized, under constraints on the power, length, and modulus of training sequences. A sufficient design criterion is proposed, based on which two classes of optimal designs are identified. It is shown that the second class includes the existing optimal Chu sequence designs as special cases