Full Diversity Blind Space-Time Block Codes

Abstract

In this paper, the systematic design of a space-time block code is considered for a wireless communication system with multiple transmitter-receiver antennas and flat fading, in which channel state information is completely unknown. From the viewpoint of blind signal processing, a necessary and sufficient condition is given for the unique identification of the multi-input multi-output flat fading channel and transmitted signal. Then, some novel unique factorizations for a pair of coprime <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</i> -ary and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> -ary phase shift keying (PSK) constellations are established. With this and currently available coherent space-time block code designs, a method is developed to systematically construct full diversity blind nonunitary space-time block codes as well as unitary codes by just performing the QR decomposition of the nonunitary codes. It is proved that under a noise-free environment, the code design proposed in this paper can guarantee that the transmitted signals and the channel coefficients are uniquely identified, and that under a complex Gaussian noise environment in which <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</i> th-order and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> th-order statistics ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</i> and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> are co-prime) of the received signals are available, the channel coefficients can be still uniquely identified. In addition, a closed-form solution to determine the channel coefficients is obtained.