A Set of Space-Time Block Codes for the High-Rate Transmission Scheme with One Information Bit

In [1], the authors have proposed one high rate transmission scheme for Space-Time Block Codes (STBC) without additional system source such as power, bandwidth and time slot. To maintain the full rank property of the coding gain matrix, we propose a set of STBCs for 4 transmit antennas transmission to transmit one additional information bit achieving rate-9/8. Another orthogonal STBC code with rate-1 is proposed in this paper within the set. It shows by computer simulation results that by employing the set of STBCs, it achieves better bit error rate (BER) performance and throughput than that of [1] with a valid BER improvement at the high SNR region above 20dB.


Introduction
Since transmit diversity for wireless communication has been introduced in [2,3].Space-time block coding (STBC) is an efficient transmit diversity scheme to combat detrimental effects of wireless fading channels.STBC from orthogonal designs are attracting wider attention due to their amenability for fast maximum likelihood (ML) decoding algorithm and full diversity [3,4].STBCs are a set of practical signal design techniques aimed at approaching the information theoretic capacity for multiple-input and multiple-output (MIMO) channels.Alamouti code is an elegant and seminal STBC design for a two-transmit antenna system [4].It achieves full-rate, i.e.rate one, full diversity transmission using two time slots for signals with complex constellations, which are employed in most current commercial wireless systems.The orthogonal code design from Tarokh et al. is a generalization of Alamouti code for systems with an arbitrary number of transmit antennas [2,3].It has been proved however, the orthogonal design for complex signals with linear decoding complexity achieving full-rate full-diversity transmission is not available for the number of antennas more than two [3].The system with higher number of antennas has to either suffer from rate loss or put up with more decoding complexity.
The class of linear STBC is the major category of space-time codes and can be divided into subclasses like Linear Dispersion Codes [5], Orthogonal STBC (OSTBC) [2][3][4] and Quasi Orthogonal STBC (QOSTBC) [6] which is typical designed for more than two antenna systems with increased, but not exponentially, decoding complexity [4][5][6].
A class of STBCs [1,7] is proposed for a high rate>1 transmission scheme by exploiting the inherent algebraic structure for 2 and 4 transmit antennas.In order to maintain the full rank property of coding gain matrix for two STBC codewords selected from two STBCs, respectively, one of two STBCs should be scaled by weighted factor and rotated by an angle.To compare the high rate transmission scheme with the rate-1 case such as Alamouti and Jafarkhani schemes, the system performance is attenuated due to rotating or scaling one transmit matrix selected from the class.In order to compensate the loss of system performance, we propose another orthogonal STBC matrix with rate-1 as one candidate in the set to maintain the full rank property of coding gain matrix for 4 transmit antennas case while two codewords are selected from two candidate matrices, respectively.Simulation results show that the BER performance is similar with Jafarkhani code in the high SNR region (20-25dB) due to full rank property of coding gain matrix.

System Model
Consider a MIMO system with N transmitting and M receiving antennas with transmit vector

Original Works
The author proposed one transmission scheme to transmit one additional information bit without additional source.The transmission scheme employs two STBC matrices 1 and 2  to represent the information of bit b for 0 or 1, respectively ( , , , , 0) , where each row represents an antenna index and e ) ach column represents either a time instance for STBC, and , , , x x x x are selected from an alphabet (QPSK Superscript  denotes complex conjugate.The system performance is mainly dependent on the coding gain matrix between 1  and 2  .The coding gain defined in [2] Modulation).
must be a full rank matrix with the determinant as large as possible, where 1 C and 2 C are STBC codewords [1] corresponding to the TBC m rix.It is easy to check the coding gain matrix for 1  and 2 . ˆ S at where

Trans ission Scheme
To check previous works [1,7], the diversity gain of high rate transmission of STBCs is weak compared to Jafarkhani code with rate-1.The si that the BER gap between [1] an has an almost 3dB gap in the high We propose a new set of STBCs in this paper to transmit one additional information bit b with an improvement of BER performance compared to [1].

A Set of STBC Matrices
Similar to the method of [1], we consider a set of 4  ( , , , , 0) .
The is the Alamouti code [4] and shown as ( , ( , ) ( , ) where we denote y as 1 1 2 x e x   and denote z as where denotes absolute value and H denotes the  Hermitian of a matrix.

Angle
The set of these two ST is used to transm ne additional bit with optimization of coding ga in [1] achieving high f the additional bit b comes from these two can ion of the additional bit b is 0 the candidate ( 7) is lected the transmitted matrix.Otherwise, the c 8) is another transmitted matrix to transmit additional bit b = 1.To achieve good div rmance coding gain defined in [2]

( ) H C C
 mu g the STBC m of d st be a full rank matrix.The drawback in [1] is that while 1 C and 2 C are selected from 11  and 22 ,  respectively, the coding gain matrix CG is singular or null in submatrix to lose full rank property.To solve this problem in [1], the authors proposed a criterion to scale or rotate the transmitted symbols in 11  or 22 ,  by a weighted factor and an angle to guarantee full rank property [2].Due to the weighted factor and rotated angle the coding ain matrix also loses little divers ultiplied with a weighted factor individually transmits to the receiver.In rder to compensate the loss iversity gain we also propose another orthogonal STBC matrix 22  to make the coding gain matrix be full rank.If this coding gain matrix without a weighted factor or null submatrices is also full rank, the design does not lose diversity gain.

Analysis of Coding Gain Matrix
In order to select the optimum values of 1 ity ga ile in wh o  and 2  ， the determinate of the coding gain matrix should be as large as possible, where and are selected from and deriv fi 1 2 respectively.We will neglect the mathematical x is given by ( 13) To   The b information is dependent on minimum me between these two metrics substituting previous decoding results into first step.

Numerical Results
In this section, some simulation results demonstrate validity of the propose   , the BER performance of the proposed hi rate-9 8 transmission scheme is similar to the QOSTBC case, but there also exists a isible g p in the low SN / region ason is that the system performance depends on 11 , 

22
 and coding gain matrix between them, and the curve should deserve a similar form with 11  and 22  .Moreover, the BER performance of proposed design is almost 2dB away from the conventional high r -9/8 design with power scaling or angle rotation [1] at the BER of 5 10 .


In Figure 3, the effective throughput performance is shown to compare the proposed scheme and the original works [1].The effective throughput is defined as where R is the space-time code rate FER means the frame error rate, and each frame [2] and  contains 9 bits information.In the high SNR region a 0 FER  similar to Figure 2 that the $FER$ corresponds to BER and the BER performance of the proposed scheme is better than that of [1], the proposed transmission scheme achieves 2.25 bits per channel transmission whereas the effective throughput of the QOSTBC is 2 bits.A crossing point exits at a SNR level of 12dB.Similarly, the effective throughput performance of high rate-9/8 [1] is also simulated in this figure.From 10dB to 20dB of SNR, the effective throughput has been improved compared to [1] due to low FER in the proposed design.

Conclusions to transmit one additional information bit
A new set of STBCs including OSTBC and QOSTBC is proposed achieving high rate-9/8.The OSTBC is an candidate in the set to maintain the full rank property of the coding ix.From the simulation results, the system performance is improved with a similar BER performance to Jafarkhani scheme in the high SNR region.In the future works, we are interested in enlarging the set of STBC matrices and combining some error correcting codes to reduce the coding rate to achieve better system performance by exploiting the additional information bit.

1  and 2 
scheme.QPSK modulation and flat fading channel are consid lations.Two combinations of ered in all simuare shown to verify the BER performance depending on different values of 1  and 2  in Figure 1.

Figure 2
Figure2shows the BER performances versus SNR to compare the proposed design with the QOSTBC (7) nal high rate desi 1] and receiving an he

Figure 2 .
Figure 2. BER performance of high rate design for 4 antennas.

Figure 3 .
Figure 3. Effective throughputs of high rate design for 4 ntennas.

Figure 1 .
Figure 1.BER performance of high rate design with different angles.