Perfect Space-Time Block Codes and Ultra-Wideband

In this report, we present the techniques for constructing Space-Time Block Codes based on division algebra. Even though commutative division algebra can be applied for the construction, we focus on noncommutative division algebra, especially in the construction of so-called perfect space-time (ST) block codes. These codes provide full rate, full diversity and non-vanishing constant minimum determinant for increasing spectral efficiency, uniform average transmitted energy per antenna and good shaping. Even though the perfect codes exist only for 2, 3, 4 and 6 antenna systems, these codes may potentially be used in many wireless applications because of space limitation of the devices, e.g. cell phones and laptops. The design of these codes is based on the assumptions of flat fading channels where the channel gains are complex Gaussian random variables. On the other hand, Ultra-Wideband (UWB) is a promising technology for indoor environment wireless applications and lately, research has focused on the possibility of using multiple antennas for these systems. Due its large bandwidth, UWB channels experience so-called frequency-selective phenomena and it violates the assumptions of flat fading for the design of the perfect codes. Because of different channel assumptions, it seems that the perfect codes cannot be used in UWB systems, however it was shown that ST codes designed for flat fading channels still provide at least the some advantage even in the presence of frequency-selective fading channels [4]. With the objective to give an answer or opinion whether the perfect codes can be used in UWB systems, we proceed as follow. We investigate the construction of ST block codes for frequency-selective channels and the validity of ST codes desinged for flat fading channels in frequency-selective channels. We also investigate the state of art of ST block codes in UWB systems. Based on this knowledge, we provide a short discussion and give some thought whether the perfect codes can be used in UWB systems.