Space–Time Coding for Frequency Selective Fading Channel

Introduction: In this paper, we study the design of space–time codes for frequency selective quasi-static fading channels with nonnegligible ISI. It has been shown by Tarokh et al. [1] that the achievable diversity of a space– time code designed for flat fading channel is not reduced if it is used in a frequency selective fading channel. However, a full diversity space-time code designed for flat Rayleigh fading channel may not be able to exploit all the available diversities. We propose a design methodology for codes to achieve full diversity LtLrL , where Lt is the number of transmit antennas, Lr is the number of receive antennas, and L is the number of independent ISI taps. First we introduce the concept of the virtual antenna. This idea permits a formalization of the performance criteria. We also propose to use algebraic design theory [2] to find STC that provide full diversity in an ISI channel. Performance Criteria: Throughout the paper, we assume the number of receive antenna Lr be 1 because it does not affect performance criteria. Let N be frame size in terms of symbol time. A space-time code word J is an N Lt matrix with elements drawn from a finite alphabet. The code symbol matrix D is defined as D = f(J), where f( ) is an element-wise constellation mapping from the finite alphabet to points of a constellation on the complex plane. The element at ith column and jth row of D, Di(j), is transmitted from ith antenna at time j. In the scenario of quasi-static and time independent fading, if the fading coefficients are spatial independent with iid ISI taps, the performance criteria based on minimizing pairwise error probability can be proved to be maximizing diversity gain H and coding