Characterization of $2\times 2$ full diversity space-time codes and inequivalent full rank spaces

Document Type: Research Paper

Authors

1 Department of Pure Mathematics‎, ‎Faculty of Mathematics and Computer‎, ‎Shahid Bahonar University of Kerman‎, ‎Kerman‎, ‎Iran.

2 Department of Pure Mathematics‎, ‎Faculty of Mathematics and Computer‎, ‎Shahid Bahonar University of Kerman‎, ‎Kerman‎, Iran

3 Young Researchers Society‎, ‎Shahid Bahonar University of Kerman‎, ‎Kerman‎, Iran.

Abstract

‎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 $2\times 2$ 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 $M_{2}(\mathbb{C})$ and $M_{2}(\mathbb{R})$ whose nonzero elements are invertible‎. ‎Finally‎, ‎for any natural number $n>1$‎, ‎we construct infinitely many inequivalent subspaces of $M_{n}(\mathbb{C})$ whose nonzero elements are invertible.

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Main Subjects

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History

• Receive Date: 28 January 2017
• Revise Date: 11 October 2017
• Accept Date: 13 October 2017