Full Diversity Blind Alamouti Space–Time Block Codes for Unique Identification of Flat-Fading Channels

In this paper, we consider a systematic design of a full diversity blind Alamouti space-time block code for a wireless communication system having two transmitter antennas and a single receiver antenna, in which the channel is completely unknown at both the transmitter and the receiver. The key idea is to alternatively transmit Alamouti codes with different phase shift keying (PSK) constellations, say, withp-PSK andq-PSK. To provide the theoretical analysis of its unique identification and full diversity conditions, we first establish a general theorem for factorizing apq-PSK constellation into a product of ap-PSK constellation and aq-PSK constellation. Then, we prove that a necessary and sufficient condition for both the factorization and a set of solutions of the resulting Alamouti Diophantine equation from our code design to be unique is thatpandqare coprime. The same condition assures that the channel and the transmitted signal can be blindly and uniquely identified. Furthermore, a closed-form solution to determine the channel coefficients and the transmitted symbols are obtained. Also, we prove that our code enables full diversity for the generalized-likelihood ratio test (GLRT) receiver ifpandqare coprime. When finite length of the received data is available, the unitarity and linearity of our code design allow us to utilize the semi-definite relaxation (SDR) decoder or the sphere decoder so that the joint estimation of the channel and symbols can be efficiently implemented.