Full-rate full-diversity STBCs for three and four transmit antennas

A novel technique is presented for the construction of full-rate, fulldiversity space?time block codes (STBCs) from orthogonal STBCs (OSTBCs), having empty slots left in their codeword matrices for orthogonality. Two new STBCs are obtained, which are both fullrate and full-diversity, for three and four transmit antennas. The higher decoding complexity of these structures is reduced owing to non-orthogonality by using a conditional maximum-likelihood decoder. The new optimised codes provide better error performance than their full-rate full-diversity counterparts given in the literature.     

Semiorthogonal Space–Time Block Codes

In this paper, a new class of full-diversity, rate-one space-time block codes (STBCs) called semiorthogonal algebraic space-time block codes (SAST codes) is proposed. SAST codes are delay optimal when the number of transmit antennas is even. The SAST codeword matrix has a generalized Alamouti structure where the transmitted symbols are replaced by circulant matrices and the commutativity of circulant matrices simplifies the detection of transmit symbols. SAST codes with maximal coding gain are constructed by using rate-one linear threaded algebraic space-time (LTAST) codes. Compared with LTSAT codes, SAST codes not only reduce the complexity of maximum-likelihood detection, but also provide remarkable performance gain. They also outperform other STBC with rate one or less. SAST codes also perform well with suboptimal detectors such as the vertical-Bell Laboratories layered space-time (V-BLAST) nulling and cancellation receiver. Finally, SAST codes attain nearly 100% of the Shannon capacity of open-loop multiple-input-single-output (MISO) channels.     

Single-symbol maximum likelihood decodable linear STBCs

Space-time block codes (STBCs) from orthogonal designs (ODs) and coordinate interleaved orthogonal designs (CIOD) have been attracting wider attention due to their amenability for fast (single-symbol) maximum-likelihood (ML) decoding, and full-rate with full-rank over quasi-static fading channels. However, these codes are instances of single-symbol decodable codes and it is natural to ask, if there exist codes other than STBCs form ODs and CIODs that allow single-symbol decoding? In this paper, the above question is answered in the affirmative by characterizing all linear STBCs, that allow single-symbol ML decoding (not necessarily full-diversity) over quasi-static fading channels-calling them single-symbol decodable designs (SDD). The class SDD includes ODs and CIODs as proper subclasses. Further, among the SDD, a class of those that offer full-diversity, called Full-rank SDD (FSDD) are characterized and classified. We then concentrate on square designs and derive the maximal rate for square FSDDs using a constructional proof. It follows that 1) except for N=2, square complex ODs are not maximal rate and 2) a rate one square FSDD exist only for two and four transmit antennas. For nonsquare designs, generalized coordinate-interleaved orthogonal designs (a superset of CIODs) are presented and analyzed. Finally, for rapid-fading channels an equivalent matrix channel representation is developed, which allows the results of quasi-static fading channels to be applied to rapid-fading channels. Using this representation we show that for rapid-fading channels the rate of single-symbol decodable STBCs are independent of the number of transmit antennas and inversely proportional to the block-length of the code. Significantly, the CIOD for two transmit antennas is the only STBC that is single-symbol decodable over both quasi-static and rapid-fading channels.     

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.     

Diversity performance of precoded orthogonal space-time block codes using limited feedback

Orthogonal space-time block codes (OSTBCs) are simple space-time codes that can be used for open-loop transmit diversity systems. OSTBCs, however, can only be designed for certain numbers of transmit antennas. Channel-dependent linear precoders have been proposed to overcome this deficiency, but it is not clear what conditions the precoder design must satisfy to guarantee full diversity order. In this letter, we show necessary and sufficient conditions for linear precoded OSTBCs to provide full diversity order. We show that limited feedback precoding can achieve full diversity order using fewer bits than limited feedback beamforming. We also present a simplified version of antenna subset selection for OSTBCs that can provide full diversity order with low complexity and only a small amount of feedback.     

On the nonexistence of rate-one generalized complex orthogonal designs

Orthogonal space-time block coding proposed recently by Alamouti (1998) and Tarokh et al. (1999) is a promising scheme for information transmission over Rayleigh-fading channels using multiple transmit antennas due to its favorable characteristics of having full transmit diversity and a decoupled maximum-likelihood (ML) decoding algorithm. Tarokh et al. extended the theory of classical orthogonal designs to the theory of generalized, real, or complex, linear processing orthogonal designs and then applied the theory of generalized orthogonal designs to construct space-time block codes (STBC) with the maximum possible diversity order while having a simple decoding algorithm for any given number of transmit and receive antennas. It has been known that the STBC constructed in this way can achieve the maximum possible rate of one for every number of transmit antennas using any arbitrary real constellation and for two transmit antennas using any arbitrary complex constellation. Contrary to this, in this correspondence we prove that there does not exist rate-one STBC from generalized complex linear processing orthogonal designs for more than two transmit antennas using any arbitrary complex constellation.     

Gaussian integers and interleaved rank codes for space–time block codes

This paper presents the design of space–time block codes (STBCs) over maximum rank distance (MRD) codes, energy‐efficient STBCs, STBCs using interleaved‐MRD codes, the use of Gaussian integers for STBCs modulation, and Gabidulin's decoding algorithm for decoding STBCs. The design fundamentals of STBCs using MRD codes are firstly put forward for different number of transmit antennas. Extension finite fields (Galois fields) are used to design these linear block codes. Afterward, a comparative study of MRD‐based STBCs with corresponding orthogonal and quasi‐orthogonal codes is also included in the paper. The simulation results show that rank codes, for any number of transmit antennas, exhibit diversity gain at full rate contrary to orthogonal codes, which give diversity gain at full rate only for two transmit antennas case. Secondly, an energy‐efficient MRD‐STBC is proposed, which outperforms orthogonal STBC at least for 2 × 1 antenna system. Thirdly, interleaved‐MRD codes are used to construct higher‐order transmit antenna systems. Using interleaved‐MRD codes further reduces the complexity (compared with normal MRD codes) of the decoding algorithm. Fourthly, the use of Gaussian integers is utilized in mapping MRD‐based STBCs to complex constellations. Furthermore, it is described how an efficient and computationally less complex Gabidulin's decoding algorithm can be exploited for decoding complex MRD‐STBCs. The decoding results have been compared against hard‐decision maximum likelihood decoding. Under this decoding scheme, MRD‐STBCs have been shown to be potential candidate for higher transmit antenna systems as the decoding complexity of Gabidulin's algorithm is far less, and its performance for decoding MRD‐STBCs is somewhat reasonable. Copyright © 2015 John Wiley & Sons, Ltd.     

Extending orthogonal block codes with partial feedback

During the last few years a number of space-time block codes have been proposed for use in multiple transmit antennas systems. We propose a method to extend any space-time code constructed for m transmit antennas to m p transmit antennas through group-coherent codes (GCCs). GCCs make use of very limited feedback from the receiver (as low as 1 bit). In particular the scheme can be used to extend any orthogonal code (e.g., Alamouti code) to more than two antennas while preserving low decoding complexity, full diversity benefits, and full data rate.     

Using Orthogonal and Quasi-Orthogonal Designs in Wireless Relay Networks

Distributed space-time coding was proposed to achieve cooperative diversity in wireless relay networks without channel information at the relays. Using this scheme, antennas of the distributive relays work as transmit antennas of the sender and generate a space-time code at the receiver. It achieves the maximal diversity when the transmit power is infinitely large. This paper is on the design of practical distributed space-time codes (DSTCs). We use orthogonal and quasi-orthogonal designs which are originally used in the design of space-time codes for multiple-antenna systems. It is well known that orthogonal space-time codes have full diversity and linear decoding complexity. They are particularly suitable for transmissions in the network setting using distributed space-time coding since their ldquoscale-freerdquo property leads to good performance. Our simulations show that they achieve lower error rates than the random code. We also compare distributed space-time coding to selection decode-and-forward using the same orthogonal designs. Simulations show that distributed space-time coding achieves higher diversity than selection decode-and-forward (DF) when there is more than one relay. We also generalize the distributed space-time coding scheme to wireless relay networks with channel information at the relays. Although our analysis and simulations show that there is no improvement in the diversity, in some networks, having channel information at the relays saves both the transmission power and the transmission time.     

Differential Coding for Non-Orthogonal Space-Time Block Codes with Non-Unitary Constellations over Arbitrarily Correlated Rayleigh Channels

In this paper, we propose a maximum likelihood (ML) decoder for differentially encoded full-rank square nonorthogonal space-time block codes (STBCs) using unitary or non-unitary signal constellations, which is also applicable to fullranked orthogonal STBC (OSTBC). As the receiver is jointly optimized with respect to the channel and the unknown data, it does not require any knowledge of channel power, signal power, or noise power to decode the signal, and the decision is purely based on two consecutively received data blocks. We analyze the effect of channel correlation on the performance of the proposed system in Rayleigh fading channels. Assuming a general correlation model, an upper bound of the pair-wise error probability (PEP) of the differential OSTBCs is derived. An approximate bound of the PEP for the differential nonorthogonal STBCs is also derived. We propose a precoder designing criterion for differential STBC over arbitrarily correlated Rayleigh channels. Precoding improves the system performance over the correlated Rayleigh MIMO channels. Our precoded differential codes differ from the previously proposed precoder designs for differential OSTBC in the following ways: 1) We propose a precoder design for arbitrarily correlated Rayleigh channels, whereas the previous work considers only for transmit correlation. 2) The previous work is only applicable to the OSTBCs with PSK constellations, whereas our precoder is applicable to any type of full-rank square STBCs with unitary and non-unitary signal constellations.     

Space-time block codes based on coordinate symmetric orthogonal designs

Space-time block codes based on coordinate symmetric orthogonal designs are proposed. Compared with space-time block codes from complex orthogonal design when the code rate is the same and the transmission rate is fixed, space-time block codes from coordinate symmetric orthogonal design with more transmit antennas can reduce the bit error rate and symbol error rate. Also these new codes have the same low decoding complexity as space-time block codes from complex orthogonal designs.     

Limited feedback unitary precoding for orthogonal space-time block codes

Orthogonal space-time block codes (OSTBCs) are a class of easily decoded space-time codes that achieve full diversity order in Rayleigh fading channels. OSTBCs exist only for certain numbers of transmit antennas and do not provide array gain like diversity techniques that exploit transmit channel information. When channel state information is available at the transmitter, though, precoding the space-time codeword can be used to support different numbers of transmit antennas and to improve array gain. Unfortunately, transmitters in many wireless systems have no knowledge about current channel conditions. This motivates limited feedback precoding methods such as channel quantization or antenna subset selection. This paper investigates a limited feedback approach that uses a codebook of precoding matrices known a priori to both the transmitter and receiver. The receiver chooses a matrix from the codebook based on current channel conditions and conveys the optimal codebook matrix to the transmitter over an error-free, zero-delay feedback channel. A criterion for choosing the optimal precoding matrix in the codebook is proposed that relates directly to minimizing the probability of symbol error of the precoded system. Low average distortion codebooks are derived based on the optimal codeword selection criterion. The resulting design is found to relate to the famous applied mathematics problem of subspace packing in the Grassmann manifold. Codebooks designed by this method are proven to provide full diversity order in Rayleigh fading channels. Monte Carlo simulations show that limited feedback precoding performs better than antenna subset selection.     

Real-Domain Decoder for Full-Rate Full-Diversity STBC with Multidimensional Constellations

In this letter, we present a new maximum likelihood (ML) decoding algorithm for space time block codes (STBCs) that employ multidimensional constellations. We start with a lattice representation for STBCs which transforms complex channel models into real matrix equations. Based on the lattice representation, we propose a new decoding algorithm for quasiorthogonal STBCs (QO-STBC) which allows simpleML decoding with performance identical to the conventional ML decoder. Multidimensional rotated constellations are constructed for the QO-STBCs to achieve full diversity. As a consequence, for quasi-orthogonal designs with an arbitrary number of transmit antennas N (N ? 4), the proposed decoding scheme achieves full rate and full diversity while reducing the decoding complexity from ∂(M_c^N/2) to ∂(M_c^N/4) in a M_c-QAM constellation.     

一族满分集度酉空时分组码

对于接收端和发送端均不具备信道状态信息的MIMO系统,本文将Cayley变换与对角块正交空时分组码结合,提出了一种新的酉空时分组码构造方法。新构造的空时分组码适用于任意发送天线数为偶数的MIMO系统,能提供满发送分集度和1.5符号/信道利用的信息传输率,并可采用球检测法等低计算复杂度检测算法得到准最优的检测结果。     

No-Zero-Entry Space-Time Block Codes Over Time-Selective Fading Channels for MIMO Systems

In MIMO systems, space-time block code (STBC) is good solution for improving system performance. Among the STBCs, coordinate interleaved orthogonal designs (CIODs) combined with QR-decomposition-based decision-feedback decoding (QR-DDF) allow achieving good performance for time-selective fading channels. However, half of entries in codeword matrix of CIODs are zeros. These zero entries result in high peak-to-average power ratio (PAPR) and also impose a severe constraint on hardware implementation of the code when turning off some of the transmitting antennas whenever a zero is transmitted. In this paper, we propose a new design of space-time block codes without zero entry in codeword matrix (NZE-STBCs) for time-selective fading channels. The main advantage of the proposed NZE-STBCs is that its peak-to-average ratio (PAPR) is 3 dB lower than that of CIODs, and its hardware implementation is also easier due to eliminating on-off switchers without sacrificing performance. Moreover, similar as CIODs, the proposed NZE-STBCs can use low complexity QR-DDF decoder over time-selective fading channels to enhance performance and reduce decoding complexity. Simulation results show that the proposed NZE-STBCs outperform CIODs for three transmit antennas while performing the same for two and four transmit antennas.     

Fast differential unitary space-time demodulation via square orthogonal designs

This paper presents a natural concatenation between the real or complex square orthogonal designs and the differential unitary space-time modulation scheme for multiple transmit antennas. This concatenation renders the differential unitary space-time demodulator to detect in a decoupled way the information symbols and hence to have a very low decoding complexity. This fast differential demodulation method for multiple transmit antennas can be regarded as a generalization of the existing differential detection method proposed by Tarokh and Jafarkhani for two and four transmit antennas based on orthogonal designs. By using a systematic matrix-vector representation, a unified and simplified form of differential unitary demodulation via square orthogonal designs for any number of transmit antennas and any transmission rate in bits per channel use is provided.     

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.     

Capacity Analysis for Transmit Antenna Selection Using Orthogonal Space-Time Block Codes

Antenna selection for multiple-input multiple-output (MIMO) where only a subset of antennas at the transmitter and/or receiver are activated for signal transmission is a practical technique for the realization of full diversity. Despite extensive research, closed-form capacity expressions for MIMO systems employing transmit antenna selection (TAS) and orthogonal space-time block codes (OSTBCs) are not available. We thus derive the exact closed-form capacity expressions when an OSTBC is employed and N transmit antennas out of total L_t antennas are selected for transmission. The expressions are valid for a frequency-flat Rayleigh fading MIMO channel and avoid numerical integration methods     

Universal space-time coding

A universal framework is developed for constructing full-rate and full-diversity coherent space-time codes for systems with arbitrary numbers of transmit and receive antennas. The proposed framework combines space-time layering concepts with algebraic component codes optimized for single-input-single-output (SISO) channels. Each component code is assigned to a "thread" in the space-time matrix, allowing it thus full access to the channel spatial diversity in the absence of the other threads. Diophantine approximation theory is then used in order to make the different threads "transparent" to each other. Within this framework, a special class of signals which uses algebraic number-theoretic constellations as component codes is thoroughly investigated. The lattice structure of the proposed number-theoretic codes along with their minimal delay allow for polynomial complexity maximum-likelihood (ML) decoding using algorithms from lattice theory. Combining the design framework with the Cayley transform allows to construct full diversity differential and noncoherent space-time codes. The proposed framework subsumes many of the existing codes in the literature, extends naturally to time-selective and frequency-selective channels, and allows for more flexibility in the tradeoff between power efficiency, bandwidth efficiency, and receiver complexity. Simulation results that demonstrate the significant gains offered by the proposed codes are presented in certain representative scenarios.     

Closed-form blind MIMO channel estimation for orthogonal space-time block codes

In this paper, a new computationally simple approach to blind decoding of orthogonal space-time block codes (OSTBCs) is proposed. Using specific properties of OSTBCs, the authors' approach estimates the channel matrix in a closed form and in a fully blind fashion. This channel estimate is then used in the maximum-likelihood (ML) receiver to decode the information symbols. The proposed estimation technique provides consistent channel estimates, and, as a result, the performance of the authors' blind ML receiver approaches that of the coherent ML receiver, which exploits the exact channel state information (CSI). Simulation results demonstrate the performance improvements achieved by the proposed blind decoding algorithm relative to the popular differential space-time modulation scheme.