Characterization of 2×2 full diversity space-time codes and inequivalent full rank spaces

‎In wireless communication systems‎, ‎space-time codes are applied to encode data when multiple antennas are used in the receiver and transmitter‎. ‎The concept of diversity is very crucial in designing space-time codes‎. ‎In this paper‎, ‎using the equivalent definition of full diversity space-time codes‎, ‎we first characterize all real and complex 2×2 rate one linear dispersion space-time block codes that are full diversity‎. ‎This characterization is used to construct full diversity codes which are not derived from Alamouti scheme‎. ‎Then‎, ‎we apply our results to characterize all real subspaces of M2(C) and M2(R) whose nonzero elements are invertible‎. ‎Finally‎, ‎for any natural number n 1‎, ‎we construct infinitely many inequivalent subspaces of Mn(C) whose nonzero elements are invertible.