Combining beamforming and orthogonal space-time block coding

Multiple transmit and receive antennas can be used in wireless systems to achieve high data rate communication. Efficient space-time codes have been developed that utilize a large portion of the available capacity. These codes are designed under the assumption that the transmitter has no knowledge about the channel. In this work, on the other hand, we consider the case when the transmitter has partial, but not perfect, knowledge about the channel and how to improve a predetermined code so that this fact is taken into account. A performance criterion is derived for a frequency-nonselective fading channel and then utilized to optimize a linear transformation of the predetermined code. The resulting optimization problem turns out to be convex and can thus be efficiently solved using standard methods. In addition, a particularly efficient solution method is developed for the special case of independently fading channel coefficients. The proposed transmission scheme combines the benefits of conventional beamforming with those given by orthogonal space-time block coding. Simulation results for a narrow-band system with multiple transmit antennas and one or more receive antennas demonstrate significant gains over conventional methods in a scenario with nonperfect channel knowledge     

Application of quasi-orthogonal space-time block codes in beamforming

It is well known that when channel information is available at the transmitter, transmit beamforming scheme can be employed to enhance the performance of a multiple-antenna system. Recently, Jongren et al. and Zhou-Giannakis proposed a new performance criterion based on partial channel side information at the transmitter. With this criterion, an optimal beamforming matrix was constructed for the orthogonal space-time block codes. However, the same method has not been applied to the recently proposed quasi-orthogonal space-time block codes (QSTBCs) due to the nonorthogonal nature of the quasi-orthogonal designs. In this paper, the issue of combining beamforming with QSTBCs is addressed. Based on our asymptotic analysis, we extend the beamforming scheme from Jongren et al. and construct the beamforming matrices for the quasi-orthogonal designs. The proposed beamforming scheme accomplishes high transmission rate as well as high-order spatial diversity. The new QSTBC beamformer can be presented as a novel four-directional or eight-directional eigen-beamformer that works for systems with four or more transmit antennas. Simulations for systems with multiple transmit antennas demonstrate significant performance improvement over several other widely used beamforming methods at various SNRs and for channels with different quality of feedback.     

Design of concatenated space-time block codes using signal space diversity and the Alamouti scheme

New full-rate space-time block codes achieving full diversity for quadrature amplitude modulation (QAM) using an even number of transmit antennas over quasi-static Rayleigh fading channels are proposed. The proposed codes are constructed by serially concatenating unitary rotating precoders with the Alamouti code. The coding advantage of the proposed code for a codeword pair corresponding to any distinct input pair is shown to be greater than or equal to that of the ST-CR code.     

Diagonal algebraic space-time block codes

We construct a new family of linear space-time (ST) block codes by the combination of rotated constellations and the Hadamard transform, and we prove them to achieve the full transmit diversity over a quasi-static or fast fading channels. The proposed codes transmit at a normalized rate of 1 symbol/s. When the number of transmit antennas n=1, 2, or n is a multiple of four, we spread a rotated version of the information symbol vector by the Hadamard transform and send it over n transmit antennas and n time periods; for other values of n, we construct the codes by sending the components of a rotated version of the information symbol vector over the diagonal of an n × n ST code matrix. The codes maintain their rate, diversity, and coding gains for all real and complex constellations carved from the complex integers ring Z [i], and they outperform the codes from orthogonal design when using complex constellations for n > 2. The maximum-likelihood (ML) decoding of the proposed codes can be implemented by the sphere decoder at a moderate complexity. It is shown that using the proposed codes in a multiantenna system yields good performances with high spectral efficiency and moderate decoding complexity     

Efficiently decoded full-rate space-time block codes

Space-time block codes with orthogonal structures typically provide full-diversity reception and simple receiver processing. However, rate-1 orthogonal codes for complex constellations have not been found for more than two transmit antennas. By using a genetic algorithm, rate-1 space-time block codes that accommodate very simple receiver processing at the cost of reduced diversity are designed in this paper for more than two transmit antennas. Simulation results show that evolved codes combined with efficient outer codes provide better performance over fading channels than minimum-decoding-complexity quasiorthogonal codes at typical operating signal-to-noise ratios. When the fading is more severe than Rayleigh fading, the spectral efficiency is specified, and an efficient outer code is used, evolved codes outperform orthogonal space-time block codes.     

High-throughput error correcting space-time block codes

This letter investigates using an error correction code (ECC) to construct the space-time block code (STBC). Block ECCs over several Galois fields are considered. The resulting STBCs have significantly higher throughput and better performance than orthogonal STBCs, at the cost of increased decoding complexity.     

On diagonal algebraic space-time block codes

Theoretical and practical aspects of diagonal algebraic space-time block codes over n transmit and m receive antennae are examined. These codes are obtained by sending a rotated version of the information symbols over the principal diagonal of the n /spl times/ n space-time matrix over n transmit antennae and n symbol periods. The output signal-to-noise ratios of two predecoding filters and two decoding algorithms are derived. Analysis of the information loss incurred by using the codes considered is used to clarify their structures, and the expected performances. Different algebraic real and complex rotations presented in the literature are analyzed and compared as regards the achieved coding gains, the complexities, performances, and peak-to-mean envelope power ratios.     

Design of channel-estimate-dependent space-time block codes

So far, the assumption of no channel knowledge at the transmitter has generally been inherent in the design of space-time codes. This paper, on the other hand, assumes that quantized channel information obtained from a feedback link is available at the transmitter and investigates how such channel information can be incorporated into the design of unstructured space-time block codes. Efficient codes are found by means of a gradient search over a continuous alphabet. Simulation results for an uncorrelated Rayleigh fading scenario using two and four transmit antennas and one receive antenna show the benefits of the code designs.     

Performance analysis of distributed Alamouti space-time codes in full-duplex cooperative communication system

The error performance of distributed Alamouti space-time code (DASTC) was investigated in a 3-node full-duplex (FD) cooperative communication system with the presence of residual self-interference (RSI).Based on the asymptotic expression of the pairwise error probability in the high transmit power region,the diversity and coding gain were derived.The impact of residual self-interference on the construction of space-time code was analyzed and the achievable condition of diversity gain was obtained.Analytical results show that DASTC achieves full rate and full diversity in the FD cooperative communication system with high transmit power and low RSI.The error performance of the FD system is superior to which of the half-duplex system under the same spectral efficiency constraint.The diversity and coding gain can be increased by sufficiently suppressing the self-interference,and the spectral efficiency and power efficiency can be improved as well.     

Performance of concatenated channel codes and orthogonal space-time block codes

In this paper we analyze the performance of an important class of MIMO systems that of orthogonal space-time block codes concatenated with channel coding. This system configuration has an attractive combination of simplicity and performance. We study this system under spatially independent fading as well as correlated fading that may arise from the proximity of transmit or receive antennas or unfavorable scattering conditions. We consider the effects of time correlation and present a general analysis for the case where both spatial and temporal correlations exist in the system. We present simulation results for a variety of channel codes, including convolutional codes, turbo codes, trellis coded modulation (TCM), and multiple trellis coded modulation (MTCM), under quasi-static and block-fading Rayleigh as well as Rician fading. Simulations verify the validity of our analysis.     

Capacity achieving high rate space-time block codes

It is well known, that the Alamouti scheme is the only space-time code from orthogonal design achieving the capacity of multiple-input multiple-output (MIMO) wireless communication system with n/sub T/=2 transmit antennas and n/sub R/=1 receive antenna. In this work, we propose the n-times stacked Alamouti scheme for n/sub T/=2n transmit antennas and show that this scheme achieves the capacity in the case of n/sub R/=1 receive antenna. For the more general case of more than one receive antenna, we show that if the number of transmit antennas is higher than the number of receive antennas we achieve a high portion of the capacity with this scheme.     

Rate-one space-time block codes with full diversity

Orthogonal space-time block codes provide full diversity, and maximum-likelihood (ML) decoding for orthogonal codes can be realized on a symbol-by-symbol basis. It has been shown that rate-one complex orthogonal codes do not exist for systems with more than two transmit antennas. For a general system with N transmit and M receive antennas, it is very desirable to design rate-one complex codes with full diversity. In this letter, we provide a systematic method of designing rate-one codes (real or complex) for a general multiple-input multiple-output system. Full diversity of these codes is then achieved by constellation rotation. A generalized, reduced-complexity decoding method for rate-one codes is also provided.     

Channel estimation for space-time orthogonal block codes

Channel estimation is one of the key components of space-time systems design. The transmission of pilot symbols, referred to as training, is often used to aid channel acquisition. In this paper, a class of generalized training schemes that allow the superposition of training and data symbols is considered. First, the Cramer-Rao lower bound (CRLB) is derived as a function of the power allocation matrices that characterize different training schemes. Then, equivalent training schemes are obtained, and the behavior of the CRLB is analyzed under different power constraints. It is shown that for certain training schemes, superimposing data with training symbols increases CRLB, and concentrating training power reduces CRLB. On the other hand, once the channel is acquired, uniformly superimposed power allocation maximizes the mutual information and, hence, the capacity.     

Matrices analysis of quasi-orthogonal space-time block codes

In this paper, according to the analysis of existing transmission matrices of quasi-orthogonal space-time block codes (STBC), we generalize some of their characters and derive several new patterns to enrich the family of quasi-orthogonal STBC.     

On decoding algorithm and performance of space-time block codes

In this letter, we present a unified mathematical expression for the decoding algorithm of space-time block codes (STBC). Based on the unified expression, we make a comparison of the STBC transmit diversity and the maximal-ratio combining MRC receive diversity, and analyze the symbol error probability for the STBC transmissions. The effects of the channel correlation and the number of transmit and receive antennas on the performance of the STBC are discussed.     

Variable-rate space-time block codes in M-ary PSK systems

We consider a multiple antenna system when combined array processing with space-time coding is used. We present variable rate space-time block codes for two, three, and four transmit antennas and optimize the transmit power so that the average bit-error rate (BER) is minimized. Numerical results show that this optimum power allocation scheme provides significant gain over the equal power allocation scheme. We then classify all the variable rate space-time block codes having the same code rates and identify the unique code that achieves the lowest BER. We explicitly compute the performance of the variable rate codes over a Rayleigh-fading channel. The proposed variable rate space-time block codes are useful for unequal error protection in multiple transmit antenna systems.     

Square-matrix embeddable space-time block codes for complex signalconstellations

Space-time block codes for providing transmit diversity in wireless communication systems are considered. Based on the principles of linearity and unitarity, a complete classification of linear codes is given in the case when the symbol constellations are complex, and the code is based on a square matrix or restriction of such by deleting columns (antennas). Maximal rate delay optimal codes are constructed within this category. The maximal rates allowed by linearity and unitarity fall off exponentially with the number of transmit antennas     

On orthogonal space-time block codes and transceiver signal linearization

We present a necessary and sufficient condition for any orthogonal space-time block code (STBC) to allow transceiver signal linearization (as in the well-known case of the Alamouti scheme). Then, we show that all square orthogonal STBC's that satisfy the condition have rate that goes to zero linearly with the number of transmit antennas. Hence, multiple-antenna systems with orthogonal STBC's and satisfactory rate are possible only If we abandon the linearization property or utilize non-square codes (except for the 2 /spl times/ 2 Alamouti code).     

完美空时分组码及其高性能解码算法

根据完美空时分组码（STBC）的结构特点提出了等效的垂直-贝尔实验室空时（V-BLAST）模型，在对该模型进行最小均方误差-判决反馈均衡（MMS-DFE）预处理之后，提出一种有边界约束的Fano解码器。该解码器可达到几乎最大似然（ML）性能，在很大的信噪比区域范围内其复杂度比目前典型的解码器低，而且该解码器可用于发射天线数大于接收天线数的系统。直接在复数域计算和处理，该解码器适用于任何星座形式。该解码器可用于任何能等效成V-BLAST模型的空时系统。仿真结果表明了该解码器的有效性。