Full Diversity Non-Coherent Alamouti-Based Toeplitz Space-Time Block Codes

Recently, the Liu-Zhang-Wong's Toeplitz space-time block code and the Shang-Xia's Alamouti code-based overlapped space-time block code have been developed to enable coherent full diversity with the linear receivers for a wireless communication system having multiple transmitter antennas and a single receiver antenna. In this paper, such a noncoherent system is considered, in which channel state information is unavailable at both the transmitter and receiver. Using the Alamouti coding scheme and the Toeplitz matrix structure, a novel noncoherent nonunitary space-time block code, which is called an Alamouti-based Toeplitz space-time block code, is proposed. By the fundamentals of Galois theory and algebraic number theory, two important properties on the two Alamouti codes generated from a pair of coprime phase shift keying (PSK) constellations, i.e., the uniqueness of factorization itself and the shift-invariant uniqueness of factorization, are first revealed and rigorously proved. Then, it is further shown that it is these two kinds of unique factorizations that enable the unique blind identification of both the channel coefficients and the transmitted signals by only processing two block received signals, as well as noncoherent full diversity with a generalized likelihood ratio test (GLRT) receiver. In addition, a full diversity unitary code design is also proposed by simply applying the QR decomposition to the full diversity nonunitary Alamouti-based Toeplitz space-time block code. Computer simulations demonstrate that the nonunitary and unitary codes presented in this paper outperform the differential codes and the signal-to-noise-ratio (SNR)-efficient training scheme based on the coherent orthogonal space-time block codes in the current literature.