An algebraic space-time coding theory and its applications

The explosive demand of wireless communication requires better usage of limited spectrum. Employing uncorrelated multiple antennas in the system has been proven to dramatically increase the capacity. To realize a significant portion of the capacity, space-time coding is employed to take advantage of the space diversity introduced by multiple antennas in addition to the time diversity.; One of the challenges in space-time code design is to guarantee certain levels of space diversity. We developed an algebraic design theory to ensure Quadrature amplitude modulated (QAM) space-time codes achieve full space diversity in quasi-static fading channels based on binary rank theory by Hammons and El Gamal. It simplifies the check of space diversity of a code by transferring a nonlinear problem into a linear problem. Consequently, it offers a low complexity solution to an otherwise prohibitively complex problem. Although it is a sufficient condition of full space diversity, we found the theory is general enough to cover many computer searched “optimal” codes.; With the algebraic design theory, we can take advantage of the vast knowledge base of traditional error correction codes designed for single antenna systems by transforming some of them to space-time codes. With good Euclidean distances and guaranteed space diversity, these codes often provide good performance.; The theory enables us to propose a class of full diversity full rate space-time turbo codes. Both parallel concatenated and serially concatenated codes are designed. Additionally, we study the robustness of performance of both turbo codes and trellis codes in space-time correlated fading channels. The simulations demonstrate that the space-time turbo codes can take full advantage of space diversity and time diversity.; For multiple antenna systems in a symbol-spaced tap-delay-line channel, which is a special case of frequency selective fading channels, a method suitable for numerical calculation is developed to evaluate the outage probability. By introducing the concepts of virtual antenna, we transform the frequency diversity into virtual transmit diversity to derive the design criteria of space-time codes in such channels. Some full space diversity and full frequency diversity example codes are designed according to the performance criteria using the algebraic design theory for systems with and without channel interleavers.