A New Design Criterion for Linear Receiver STBCs Based on Full-Rank Spaces

In this paper, we study linear receiver space-time block codes (L-STBCs). These codes are very important and applicable because the simplest decoders, namely, ZF and MMSE, can be implemented at the receiver to decode these codes. Design criterion of L-STBCs is the primary basis needed for research in this field. The only criterion put forth to date is based on two conditions on the equivalent channel matrix. In this paper, first, we propose a systematic guideline for determining the equivalent channel matrix of a wide range of L-STBCs, including all the existing L-STBCs, and then, we derive a new design criterion for these L-STBCs with only one condition on the code structure. In addition, we show that there is a strong connection between full-diversity L-STBCs and full-rank subspaces of matrices. Finally, L-STBCs with orthogonal equivalent channels are characterized.