Quasi-orthogonal Space-time Block Codes Research Articles

Optimal diversity product rotations for quasiorthogonal STBC with MPSK symbols

The optimal rotations for quasiorthogonal space-time block codes (STBC) with MPSK symbols are presented, where the optimality means that the optimal diversity product is achieved. The optimal diversity products of quasiorthogonal STBC with rotated MPSK constellations are given. The sensitivity of the diversity product to the rotation angle offset is studied.

A full-rate, full-diversity four-antenna quasi-orthogonal space-time block code

We present a complex, full-rate quasi-orthogonal space-time block code for four transmit antennas. Using carefully tailored constellation phase rotations, we show that this code achieves full diversity for specialized PSK-based constellations. The optimal receiver for the new code decouples the symbol detection problem into pairs of symbols, thus greatly reducing complexity. Finally, we present and compare performance of the new code with several other codes in the literature. The new code is shown to perform as well as the best known code of its class.

Closed-loop transmit diversity schemes for five and six transmit antennas

Closed-loop, rate-one, channel orthogonalized space-time block codes (CO-STBCs) for three and four transmit antennas using a single (real) phase feedback term have been proposed . These codes achieve full diversity and result in maximum likelihood (ML) decoding with only linear processing at the receiver similar to OSTBCs. In this paper, we propose a closed-loop STBC for five and six transmit antennas with rate 3/4, where the one parameter feedback angle can be evaluated in closed form. These codes achieve full diversity and are delay optimal. Simulation results comparing the error-rate performance of the CO-STBC with open-loop OSTBC as well as some quasiorthogonal space-time block codes are also provided. While the 1- to 5-dB gain accrued by the closed-loop scheme (over the open-loop methods) is not surprising, the novel contribution of this work is in the approach taken to derive the feedback parameter as a single phase term, which is purely a function of the channel gains.

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.

Closed-Loop Quasi-Orthogonal STBCs and Their Performance in Multipath Fading Environments and When Combined With Turbo Codes

Quasi-orthogonal space-time block codes (QO-STBCs) achieve full code rate at the expense of loss in diversity gain. We propose two feedback methods for QO-STBCs to achieve full diversity and full code rate. In the first method, signals radiated from various antennas are rotated by phasors according to feedback from the receiver, whereas the second method is based upon antenna weighting/selection. For high to moderate feedback error rates, it is demonstrated that the proposed methods outperform the quantized transmit beamformer. The performance improvement is also investigated for these closed-loop methods when the transmitted signal is error control coded.

Adaptive Channel-Matched Extended Alamouti Space-Time Code Exploiting Partial Feedback

Since the publication of Alamouti's famous space-time block code, various quasi-orthogonal space-time block codes (QSTBC) for multi-input multi-output (MIMO) fading channels for more than two transmit antennas have been proposed. It has been shown that these codes cannot achieve full diversity at full rate. In this paper, we present a simple feedback scheme for rich scattering (flat Rayleigh fading) MIMO channels that improves the coding gain and diversity of a QSTBC for 2n (n = 3, 4,…) transmit antennas. The relevant channel state information is sent back from the receiver to the transmitter quantized to one or two bits per code block. In this way, signal transmission with an improved coding gain and diversity near to the maximum diversity order is achieved. Such high diversity can be exploited with either a maximum-likelihood receiver or low-complexity zero-forcing receiver.

Signal constellations for quasi-orthogonal space-time block codes with full diversity

Space-time block codes (STBCs) from orthogonal designs proposed by Alamouti, and Tarokh-Jafarkhani-Calderbank have attracted considerable attention lately due to their fast maximum-likelihood (ML) decoding and full diversity. However, the maximum symbol transmission rate of an STBC from complex orthogonal designs for complex signals is only 3/4 for three and four transmit antennas, and it is difficult to construct complex orthogonal designs with rate higher than 1/2 for more than four transmit antennas. Recently, Jafarkhani, Tirkkonen-Boariu-Hottinen, and Papadias-Foschini proposed STBCs from quasi-orthogonal designs, where the orthogonality is relaxed to provide higher symbol transmission rates. With the quasi-orthogonal structure, the quasi-orthogonal STBCs still have a fast ML decoding, but do not have the full diversity. The performance of these codes is better than that of the codes from orthogonal designs at low signal-to-noise ratio (SNR), but worse at high SNR. This is due to the fact that the slope of the performance curve depends on the diversity. It is desired to have the quasi-orthogonal STBCs with full diversity to ensure good performance at high SNR. In this paper, we achieve this goal by properly choosing the signal constellations. Specifically, we propose that half of the symbols in a quasi-orthogonal design are chosen from a signal constellation set A and the other half of them are chosen from a rotated constellation e/sup j/spl phi// A. The resulting STBCs can guarantee both full diversity and fast ML decoding. Moreover, we obtain the optimum selections of the rotation angles /spl phi/ for some commonly used signal constellations. Simulation results show that the proposed codes outperform the codes from orthogonal designs at both low and high SNRs.

Performance of quasi-orthogonal space-time code with antenna selection

The performance of a quasi-orthogonal space-time block code with antenna selection is considered. Transmit antenna selection as well as receive antenna selection is studied. A new selection rule is proposed that minimises the average bit error ratio and achieves full diversity even if only a simple zero-forcing receiver is used.

Full-Rate Full-Diversity Linear Quasi-Orthogonal Space-Time Codes for Any Number of Transmit Antennas

We construct a class of linear quasi-orthogonal space-time block codes that achieve full diversity over quasistatic fading channels for any transmit antennas. These codes achieve a normalized rate of one symbol per channel use. Constellation rotation is shown to be necessary for the full-diversity feature of these codes. When the number of transmit antennas is a power of 2, these codes are also delay optimal. The quasi-orthogonal property of the code makes one half of the symbols orthogonal to the other half, and we show that this allows each half to be decoded separately without any loss of performance. We give an iterative construction of these codes with a practical decoding algorithm. Numerical simulations are presented to evaluate the performance of these codes in terms of capacity as well as probability of error versus SNR curves. For some special cases, we compute the pairwise probability of error averaged over all the channel states as a single integral that shows the diversity and coding gain more clearly.

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.

A quasi-orthogonal space-time block code

It has been shown that a complex orthogonal design that provides full diversity and full transmission rate for a space-time block code is not possible for more than two antennas. Previous attempts have been concentrated in generalizing orthogonal designs which provide space-time block codes with full diversity and a high transmission rate. We design rate one codes which are quasi-orthogonal and provide partial diversity. The decoder of the proposed codes works with pairs of transmitted symbols instead of single symbols.