A systematic design of high-rate complex orthogonal space-time block codes

In this letter, a systematic design method to generate high-rate space-time block codes from complex orthogonal designs for any number of transmit antennas is proposed. The resulting designs have the best known rates. Two constructions with rates 2/3 and 5/8 are further illustrated for 6 and 7 transmit antennas, respectively.     

A high-rate orthogonal space-time block code

We present a space-time block code from complex orthogonal designs for 5 transmit antennas, which can send 10 information symbols in a block of 15 channel uses and hence have rate 2/3. Simulation results show that this orthogonal space-time block code with rate 2/3 for five transmit antennas can achieve diversity gain over those orthogonal space-time block codes with higher rates for less number of transmit antennas.     

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     

Full-diversity full-rate complex-field space-time coding

Exciting developments in wireless multiantenna communications have led to designs aiming mainly at one of two objectives: either high-performance by enabling the diversity provided by multi-input multi-output (MIMO) channels or high-rates by capitalizing on space-time multiplexing gains to realize the high capacity of MIMO fading channels. By concatenating a linear complex-field coder (a.k.a. linear precoder) with a layered space-time mapper, we design systems capable of achieving both goals: full-diversity and full-rate (FDFR), with any number of transmit- and receive-antennas. We develop FDFR designs not only for flat-fading but for frequency-selective, or, time-selective fading MIMO channels as well. Furthermore, we establish the flexibility of our FDFR designs in striking desirable performance-rate-complexity tradeoffs. Our theoretical claims are confirmed by simulations.     

A new high-rate differential space-time block coding scheme

A new high-rate differential space-time transmission scheme based on spatial multiplexing of Alamouti-encoded information streams is developed. At the receiver, joint space-time differential interference cancellation and decoding is performed, realizing diversity and rate gains, without requiring channel knowledge or bandwidth expansion. Our focus is on the case of two information streams with two transmit antennas per stream on flat-fading channels for simplicity. However, using previously published techniques, the development readily extends to more than two information streams, to more than two transmit antennas per stream, and to frequency-selective channels.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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     

Combining ideal beamforming and Alamouti space-time block codes

The simplest Alamouti space-time block code is coupled with a larger number of transmit antennas via ideal beamforming to achieve higher diversity gain. It is shown that the combined system can remain both full diversity and full code rate without orthogonality loss. Simulation results show a significant performance gain over the conventional space-time block codes.     

Nonlinear space-time block codes designed for iterative decoding

Iterative decoding of space-time block codes (STBCs) and channel codes have shown to achieve very good performance. Using tools such as EXIT charts, the performance can be predicted and also used for design. However almost all work so far has concentrated on linear STBCs. Therefore nonlinear STBCs that are designed to work well with iterative decoding are investigated. It is shown that they can outperform linear STBCs since their characteristics are quite different when supplying a priori information from a channel decoder. Analysis, design rules and simulation results for the nonlinear codes are presented.