Space Time Block Codes In MIMO Wireless Communication System

The non-vanishing deteminant(NVD) is a fuandamental and important performance index for Space Time Block Codes(STBC). It has been shown that the NVD property is a necessary and sufficient condition for the STBC scheme to achieve the diversity-multiplexing gain trade-off(DMGT). Hence how to construct a STBC scheme with the NVD property becomes a very significant problem.Extensive work has been done on STBC, aiming at finding the codes with the NVD property. Field extension and cyclic division algebras have been proposed as the canonical tools to construct the codes with NVD over a variety of the signal sets, since they naturally yield the full-rank codes. And their algebraic properties can be further exploited to design the better performance codes.In this paper, based on Sethuraman, Rajan and Shashidhar’s result, we present a method to construct the full-rank codes with NVD from field extension and the minimal determinant at least one over a wide range signal sets. We also utilize cyclic division algebras(CDA) ( K / F ,σ,γ) to give another construction method for the number of the transmit antennas n =φ( p1 u p 2v) /d2, gcd(φ( p1 u ),φ( p2 v))= d, where p1 , p 2are distinct odd primes andφ( ) is the Euler totient function. As an application, we describe all cyclic division algebras ( K / F ,σ,γ) such that F = (i ), [ K : F ] = n =φ( p1 u p2 v) /d2 andγ= 1 + i, where gcd(φ( p1 u ),φ( p2v)) = 2 or 4 and p1 , p2≤100. Moreover, we prove that the both codes have the NVD property.