Full-Diversity Codes for MISO Systems Equipped With Linear or ML Detectors

Abstract

Abstract-In this paper, a general criterion for space time block codes (STBC) to achieve full-diversity with a linear receiver is proposed for a wireless communication system having multiple transmitter and single receiver antennas (MISO). Particularly, the STBC with Toeplitz structure satisfies this criterion and therefore, enables full-diversity. Further examination of this Toeplitz STBC reveals the following important properties: a) The symbol transmission rate can be made to approach unity. b) Applying the Toeplitz code to any signalling scheme having nonzero distance between the nearest constellation points results in a non-vanishing determinant. In addition, if QAM is used as the signalling scheme, then for independent MISO flat fading channels, the Toeplitz codes is proved to approach the optimal diversity-vs-multiplexing tradeoff with a ZF receiver when the number of channel uses is large. This is, so far, the first nonorthogonal STBC shown to achieve the optimal tradeoff for such a receiver. On the other hand, when ML detection is employed in a MISO system, the Toeplitz STBC achieves the maximum coding gain for independent channels. When the channel fading coefficients are correlated, the inherent transmission matrix in the Toeplitz STBC can be designed to minimize the average worst case pair-wise error probability.

On Improving the Tradeoff between Symbol Rate and Diversity Gain Using Quasi-Orthogonal Space-Time Block Codes with Linear Receivers

“…This means the decoding delay is small and it has tolerance to channel conditions. A comparison of the symbol rate for O 3,4 , Q 4,4 , Toeplitz Codes [11], and Overlapped Alamouti Codes (OAC) [12] are described in Table 1. Table 1 shows that a higher symbol rate can be achieved if we use Q-OSTBC as the base code.…”

“…So, STBCs which have a good tradeoff between symbol rate and diversity gain with linear receivers have received much attention [11]- [13]. Liu et al [11] proposed Toeplitz Codes which improve the symbol rate of STBC with linear receivers.…”

“…Liu et al [11] proposed Toeplitz Codes which improve the symbol rate of STBC with linear receivers. Shang and Xia [12] improved the symbol rate and diversity gain by combining Toeplitz Codes and Alamouti's OSTBC.…”

“…Also, Wang et al [13] extended their approach and proposed a construction method of STBCs combining Toeplitz Codes and general OSTBCs to improve the tradeoff. The codes proposed in [13] are called Group Orthgonal-Toeplitz Codes (GOTCs) including OSTBC [2]- [5], Toeplitz Codes [11], and Overlapped Alamouti Codes (OACs) [12] as special cases. However, the symbol rate of GOTCs is limited to that of the base OSTBCs which is used when it is generated.…”

Asynchronous cooperative communication systems: A survey on signal designs

“…A simple space-time coding scheme with the OFDM approach 2) Most space-time code designs achieving full diversity are based on ML receiver. STCs achieving full spatial diversity with linear receivers have been studied recently, in [51][52][53][54] is used, and ZF (ML) receiver is adopted. …”