Optimal training design for multiple-antenna communications

In this paper, we propose a systematic approach to the design of optimal training for multiple-antenna communications. We first derive two design criteria for general optimal training: one is in the time domain and the other is in the frequency domain. The frequency-domain design criterion leads to a systematic design procedure that can be used to construct any optimal training sequences. Combining the two design criteria, we further derive a design criterion for optimal training with the extra constraint on the constant modulus. Two classes of optimal constant-modulus designs are found. It is shown that the existing optimal constant-modulus training design is a special case of the second class of our designs