New Space–Time Code Constructions for Two-User Multiple Access Channels

Abstract

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> This paper addresses the problem of constructing multiuser multiple-input multiple-output (MU-MIMO) codes for two users. The users are assumed to be equipped with <formula formulatype="inline"><tex Notation="TeX">$n_{t}$</tex> </formula> transmit antennas, and there are <formula formulatype="inline"> <tex Notation="TeX">$n_{r}$</tex></formula> antennas available at the receiving end. A general scheme is proposed and shown to achieve the optimal diversity-multiplexing gain tradeoff (DMT). Moreover, an explicit construction for the special case of <formula formulatype="inline"><tex Notation="TeX">$n_{t}=2$</tex></formula> and <formula formulatype="inline"><tex Notation="TeX">$n_{r}=2$</tex></formula> is given, based on the optimization of the code shape and density. All the proposed constructions are based on cyclic division algebras and their orders and take advantage of the multi-block structure. Computer simulations show that both the proposed schemes yield codes with excellent performance improving upon the best previously known codes. Finally, it is shown that the previously proposed design criteria for DMT optimal MU-MIMO codes are sufficient but in general too strict and impossible to fulfill. Relaxed alternative design criteria are then proposed and shown to be still sufficient for achieving the multiple-access channel diversity-multiplexing tradeoff. </para>