Full-rate Space-time Block Code Research Articles

Multiple Complex Symbol Golden Space-Time Labeling Diversity

The Golden code is a full-rate space-time block code (STBC), which achieves a diversity order of $2N_{r}$ , where $N_{r}$ is the number of receive antennas. The multiple complex symbol Golden code (MCS-Golden code) is a generalized Golden code. The MCS-Golden code not only achieves full-rate but also achieves a diversity order of $2^{n}{N_{r}}$ , $n$ , $n\ge {1}$ , is an integer, and $2^{n}$ is the number of multiple complex symbols in the MCS-Golden code system. In this paper, we apply the labelling diversity technique to the MCS-Golden code to form a new type of STBC, named as multiple complex symbol Golden space-time labelling diversity (MCS-GSTLD). The proposed MCS-GSTLD achieves a diversity order of $2\times {2^{n}}{N_{r}}$ , and further improves error performance compared to the MCS-Golden code. We also formulate the theoretical average bit error probability (ABEP) for the proposed MCS-GSTLD system. Furthermore, we apply sphere decoding with sorted detection subset (SD-SDS) to detect the transmitted symbols in the MCS-GSTLD system. Simulation results show that the SD-SDS scheme achieves the theoretical ABEP for $N_{r}>2$ . Both theoretical and simulation results demonstrate that with the same spectral efficiency and four receive antennas, the 2CS-GSTLD achieves at least 1.3 dB signal-to-noise ratio (SNR) gain compared to the 2CS-Golden code at a BER of $3\times {10^{-6}}$ , while the 4CS-GSTLD achieves at least 0.7 dB SNR gain compared to the 4CS-Golden code.

Golden Coded GFDM for 5G Communication

The 5th Generation (5G) of wireless communication will be heterogeneous to support various traffic types and applications. Generalized Frequency Division Multiplexing (GFDM) is a 5G non-orthogonal waveform contender that offers scalable and spectrally compliant air interface which addresses the needs of 5G requirements. To aid the demand of high-capacity and reliable transmission, multiple antenna techniques are relied upon. In this work, the 5G modulation scheme GFDM is combined with a full rate Space–Time Block Code (STBC) with nonvanishing determinant called Golden Codes to exploit the diversity to the fullest. The proposed work is implemented in a real-time SDR test-bed called Wireless Open Access Research Platform (WARP). The proposed work is compared with 4G OFDM modulation in both Golden Coded and Uncoded case. The performance is assessed in terms of BER and Capacity/Bandwidth resolution. From the investigations, it is seen that the BER performance of Golden Coded GFDM outperforms the Uncoded GFDM by 3 dB SNR gain and attains a near-equal performance as OFDM. Also, it is evident from the analysis that, there is a 3.5 bps/Hz gain in capacity when compared to OFDM.

Performance of Full Rate Non-Orthogonal STBC in Spatially Correlated MIMO Systems

Spatial correlation is a crucial impairment for practical Multiple Input Multiple Output (MIMO) wireless communication systems. It is important to consider spatial correlation between antennas in actual communication scenario at both sides, i.e. transmit and receive side. Furthermore, we have considered nonorthogonal full rate STBC in MIMO systems equipped with four transmit antennas and four receive antennas in a quasi-static Rayleigh fading channel. In this paper, Bit Error Rate (BER) performance of full rate non-orthogonal Space Time Block code (STBC) is obtained using simulations in MIMO wireless communication systems. Spatial correlation is assumed between antennas at both the transmitter and the receiver sides. For this analysis, we have considered various transmit antenna spacing values of d t = 0.1π, 0.2π, and 0.4π keeping fixed d r = 0.1π and various receive antenna spacing values of d r = 0.1π, 0.2π, and 0.4π keeping fixed d t = 0.1π. The obtained results show that the transmitting diversity is more serious than the receiving diversity in the spatially correlated antenna environment for the specified signal-to-noise ratio. This study will be useful for actual wireless communication implementation where spatial correlation antennas are present in the practical environment of the MIMO wireless communication system.

Full-rate Space-time Block Code for Four Transmit Antennas with Linear Decoding

Full-rate Space-time Block Code for Four Transmit Antennas with Linear Decoding

Efficient detection methods for amplify-and-forward relay-aided device-to-device systems with full-rate space-time block code

Relay-aided device-to-device (D2D) communication is a promising technology for the next-generation cellular network. We study the transmission schemes for an amplify-and-forward relay-aided D2D system which has multiple antennas. To circumvent the prohibitive complexity problem of traditional maximum likelihood (ML) detection for full-rate space-time block code (FSTBC) transmission, two low-complexity detection methods are proposed, i.e., the detection methods with the ML-combining (MLC) algorithm and the joint conditional ML (JCML) detector. Particularly, the method with the JCML detector reduces detection delay at the cost of more storage and performs well with parallel implementation. Simulation results indicate that the proposed detection methods achieve a symbol error probability similar to that of the traditional ML detector for FSTBC transmission but with less complexity, and the performance of FSTBC transmission is significantly better than that of spatial multiplexing transmission. Diversity analysis for the proposed detection methods is also demonstrated by simulations.

Simply decoded efficient full‐rate space–time block codes over correlated Rician fading channels

A novel technique is presented to design efficient full-rate space–time block codes (STBCs) over correlated Rician fading channels. The authors first derive a formula for the achievable information rate of a linear dispersion coded multi-input single-output system as a function of correlation at the transmitter in a Rician fading channel. In addition, the authors obtain the bit-error-rate (BER) equations for this system, when multiple phase shift keying and multiple quadrature amplitude modulation schemes are used at the transmitter. Therefore with regard to derived formulae and using a genetic algorithm, a method is presented to construct STBCs over correlated Rician fading channels. The efficient designed STBCs for two and four transmit antennas enjoy full-rate, simple structure, simple processing at the receiver, better BER performance than associated orthogonal STBCs at practical signal-to-noise ratios (SNRs) and higher achievable information rate than them at all SNRs.

Integer Space-Time Block Codes for Practical MIMO Systems

Full-rate space-time block codes (STBCs) achieve high spectral-efficiency by transmitting linear combinations of information symbols through every transmit antenna. However, the coefficients used for the linear combinations, if not chosen carefully, result in (i) large number of processor bits for the encoder and (ii) high peak-to-average power ratio (PAPR) values. In this letter, we propose a new class of full-rate STBCs called Integer STBCs (ICs) for multiple-input multiple-output (MIMO) fading channels. A unique property of ICs is the presence of integer coefficients in the code structure which enables reduced numbers of processor bits for the encoder and lower PAPR values. We show that the reduction in the number of processor bits is significant for small MIMO channels, while the reduction in the PAPR is significant for large MIMO channels. We also highlight the advantages of the proposed codes in comparison with the well known full-rate algebraic STBCs.

Optimal space-time coding under iterative processing

In this paper, we deal with the design of a full-rate space-time block coding (STBC) scheme optimized for linear iterative decoding over fast fading multiple-input multiple-output (MIMO) channel. A general and simple coding scheme called diagonal threaded space-time (DTST) code is presented for an arbitrary number of transmit and receive antennas. Theoretical analysis shows that DTST code associated with linear iterative decoding tends towards full diversity performance while providing maximum MIMO multiplexing gain. Simulation results confirm the ability of DTST to outperform the state-of-the-art STBC and conventional spatial data multiplexing schemes under iterative processing.

Generalized Silver Codes

For an <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">nt</i> transmit, <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">nr</i> receive antenna system ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">nt</i> × <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">nr</i> system), a full-rate space time block code (STBC) transmits at least <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">nmin</i> = <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">min</i> ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">nt</i> , <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">nr</i> ) complex symbols per channel use. The well-known Golden code is an example of a full-rate, full-diversity STBC for two transmit antennas. Its ML-decoding complexity is of the order of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2.5</sup> for square <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> -QAM. The Silver code for two transmit antennas has all the desirable properties of the Golden code except its coding gain, but offers lower ML-decoding complexity of the order of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> . Importantly, the slight loss in coding gain is negligible compared to the advantage it offers in terms of lowering the ML-decoding complexity. For higher number of transmit antennas, the best known codes are the Perfect codes, which are full-rate, full-diversity, information lossless codes (for <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">nr</i> ≥ <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">nt</i> ) but have a high ML-decoding complexity of the order of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sup> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">min</sup> (for n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> <; nt, the punctured Perfect codes are considered). In this paper, a scheme to obtain full-rate STBCs for 2a transmit antennas and any n <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> with reduced ML-decoding complexity of the order of M <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sup> ( <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> min-3/4)-0.5 is presented. The codes constructed are also information lossless for <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">nr</i> ≥ <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">nt</i> , like the Perfect codes, and allow higher mutual information than the comparable punctured Perfect codes for <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">nr</i> <; <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">nt</i> . These codes are referred to as the generalized Silver codes, since they enjoy the same desirable properties as the comparable Perfect codes (except possibly the coding gain) with lower ML-decoding complexity, analogous to the Silver code and the Golden code for two transmit antennas. Simulation results of the symbol error rates for four and eight transmit antennas show that the generalized Silver codes match the punctured Perfect codes in error performance while offering lower ML- decoding complexity.

A Full-Rate Full-Diversity 2x2 Space-Time Block Code with Linear Complexity for the Maximum Likelihood Receiver

From engineering point of view, the simplicity of the decoder is a very important factor in designing different space-time block codes (STBCs) in wireless communications systems. On the other hand, full-diversity is an important factor which causes STBCs to have valid performance in terms of bit error rate (BER). High symbol transmission rate is also a significant factor in designing STBCs. Regarding these three characters, this paper proposes a full-rate STBC which benefits from a linear complexity for the optimum receiver and full-diversity properties. This code is designed for two transmit antennas and the complexity of its optimum receiver is linear for any arbitrary number of receive antennas. Simulation results also show that the performance of the proposed code is close to the performance of the Golden code when 4-QAM constellation is considered, and it effectively outperforms the Golden code when BPSK constellation is employed.

Blind Multiuser Detection for Synchronous High Rate Space-Time Block Coded Transmission

We propose a new joint receiver for the blind detection of synchronous co-channel multiuser signals modulated with orthogonal space-time block codes (OSTBC). We exploit the algebraic structure of the orthogonal space-time block codes and the constellation feature of Quadrature Amplitude Modulation (QAM) signals to develop a blind zero-forcing (ZF) detector based on quadratic programming (QP) with desirable convergence properties. Focusing on high rate space-time block codes in synchronous co-channel multiuser systems, we propose a successive processing joint receiver based on the proposed blind detector with low computational complexity and fast convergence. For signal detection in single user MIMO systems, the proposed QP algorithm has performance similar to that of maximum-likelihood receiver with wireless channel information. Unlike many existing techniques, our new receiver is applicable to full-rate orthogonal space-time block codes such as the practically popular Alamouti code. Furthermore, our QP receiver for multiuser detection relaxes stringent conditions on the number of receive antennas of the multi-input-multi-output (MIMO) transceiver systems.

Optimization of Fast-Decodable Full-Rate STBC with Non-Vanishing Determinants

Full-rate STBC (space-time block codes) with non-vanishing determinants achieve the optimal diversity-multiplexing tradeoff but incur high decoding complexity. To permit fast decoding, Sezginer, Sari and Biglieri proposed an STBC structure with special QR decomposition characteristics. In this paper, we adopt a simplified form of this fast-decodable code structure and present a new way to optimize the code analytically. We show that the signal constellation topology (such as QAM, APSK, or PSK) has a critical impact on the existence of non-vanishing determinants of the full-rate STBC. In particular, we show for the first time that, in order for APSK-STBC to achieve non-vanishing determinant, an APSK constellation topology with constellation points lying on square grid and ring radius √m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> +n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> (m,n integers) needs to be used. For signal constellations with vanishing determinants, we present a methodology to analytically optimize the full-rate STBC at specific constellation dimension.

Optimal Power Scaling for Quasi-Orthogonal Space-Time Block Codes with Power Scaling and Square Lattice Constellations

Recently proposed full-rate quasi-orthogonal space-time block codes (QSTBCs) with power scaling is able to achieve full-diversity through linearly combining two adequately power scaled orthogonal space-time block codes (OSTBCs). While in our initial work we numerically derived the optimal value of the power scaling factor to achieve full-diversity, our goal in this letter is to analytically derive the optimal power scaling, especially for square lattice constellations (e.g., 4-QAM, 16-QAM, etc.) by maximizing the coding gain.

A Linear Programming Receiver for Blind Detection of Full Rate Space-Time Block Codes

We present a new approach to the blind detection of full rate space-time block coded transmissions. Our method is based on linear programming and is globally convergent. We exploit the implicit structure of space-time block codes to cast the problem as linear programming to be solved efficiently. Unlike several known methods, the proposed technique is applicable to full-rate space-time block codes such as the popular Alamouti orthogonal code and the quasi-orthogonal space time code. Moreover, we utilize the code structure of these full rate codes to achieve simultaneous detection of all coded data streams without relying on successive schemes that are prone to error propagation. For orthogonal space-time codes, our algorithm allows near maximum likelihood detection of orthogonal codes without channel knowledge. We also can generalize the application of the proposed receiver to be used with nonorthogonal codes. Our proposed algorithm can provide performance competitive with existing techniques without imposing any conditions on the number of receive antennas.

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.

Low ML-Decoding Complexity, Large Coding Gain, Full-Rate, Full-Diversity STBCs for 2 $\times$ 2 and 4 $\times$ 2 MIMO Systems

This paper deals with low maximum-likelihood (ML)-decoding complexity, full-rate and full-diversity space-time block codes (STBCs), which also offer large coding gain, for the 2 transmit antenna, 2 receive antenna (2 × 2) and the 4 transmit antenna, 2 receive antenna (4 × 2) MIMO systems. Presently, the best known STBC for the 2 × 2 system is the Golden code and that for the 4 × 2 system is the DjABBA code. Following the approach by Biglieri, Hong, and Viterbo, a new STBC is presented in this paper for the 2 × 2 system. This code matches the Golden code in performance and ML-decoding complexity for square QAM constellations while it has lower ML-decoding complexity with the same performance for non-rectangular QAM constellations. This code is also shown to be information-lossless and diversity-multiplexing gain (DMG) tradeoff optimal. This design procedure is then extended to the 4 × 2 system and a code, which outperforms the DjABBA code for QAM constellations with lower ML-decoding complexity, is presented. So far, the Golden code has been reported to have an ML-decoding complexity of the order of M 4 for square QAM of size M. In this paper, a scheme that reduces its ML-decoding complexity to M 2?(M) is presented.

New rate-2 STBC design for 2 TX with reduced-complexity maximum likelihood decoding

We propose a new full-rate space-time block code (STBC) for two transmit antennas which can be designed to achieve maximum diversity or maximum capacity while enjoying optimized coding gain and reduced-complexity maximum-likelihood (ML) decoding. The maximum transmit diversity (MTD) construction provides a diversity order of 2Nr for any number of receive antennas Nr at the cost of channel capacity loss. The maximum channel capacity (MCC) construction preserves the mutual information between the transmit and the received vectors while sacrificing diversity. The system designer can switch between the two constructions through a simple parameter change based on the operating signal-to-noise ratio (SNR), signal constellation size and number of receive antennas. Thanks to their special algebraic structure, both constructions enjoy low-complexity ML decoding proportional to the square of the signal constellation size making them attractive alternatives to existing full-diversity full-rate STBCs in [6], [3] which have high ML decoding complexity proportional to the fourth order of the signal constellation size. Furthermore, we design a differential transmission scheme for our proposed STBC, derive the exact ML differential decoding rule, and compare its performance with competitive schemes. Finally, we investigate transceiver design and performance of our proposed STBC in spatial multiple-access scenarios and over frequency-selective channels.

Some Designs and Normalized Diversity Product Upper Bounds for Lattice-Based Diagonal and Full-Rate Space–Time Block Codes

In this paper, we first present two tight upper bounds for the normalized diversity products (or product distances) of 2ntn2 diagonal space-time block codes from quadratic extensions on \BBQ (i) and \BBQ ( \mmbzeta6), where i =radic{-1} and \mmbzeta6=exp( i 2pi/6). Two such codes are shown to reach the tight upper bounds and therefore have the maximal normalized diversity products. We present two new diagonal space-time block codes from higher order algebraic extensions on \BBQ (i) and \BBQ ( \mmbzeta6) for three and four transmit antennas. We also present a nontight upper bound for normalized diversity products of 2ntn2 diagonal space-time block codes with QAM information symbols, i.e., in \BBZ [i ], from general 2ntn2 complex-valued generating matrices. We then present an nntnn-diagonal space-time code design method directly from 2n real integers based on extended complex lattices (of generating matrix size nntn2n) that are shown to have better normalized diversity products than the optimal diagonal cyclotomic codes do. We finally use the optimal 2ntn2 diagonal space-time codes from the optimal quadratic extensions to construct two 2ntn2 full-rate space-time block codes and find that both of them have better normalized diversity products than the Golden code does.

New Minimum Decoding Complexity Quasi-Orthogonal Space-Time Block Code for 8 Transmit Antennas

In this paper, a new full-rate space-time block code (STBC) possessing a quasi-orthogonal (QO) property is proposed for QAM and 8 transmit antennas. This code is designed by serially concatenating a real constellation-rotating precoder with the Alamouti scheme. The QO property enables ML decoding to be done with joint detection of only four real symbols like the conventional minimum decoding complexity QO-STBC (MDC-QO-STBC). However, the proposed code is guaranteed to achieve full spatial diversity for general QAM unlike the MDC-QO-STBC which is specifically presented for only 4-QAM. By computer simulation results, we show that the proposed code exhibits the identical and slightly degraded error performance with the MDC-QO-STBC for 4-QAM and the Sharma's QO-STBC for 4 and 16-QAM, respectively. Finally, we present a new modified scheme of the original code so that there is no any discontinuity of transmission at each transmit antenna, without any loss of error performance.

A New Full-Rate Full-Diversity Space-Time Block Code With Nonvanishing Determinants and Simplified Maximum-Likelihood Decoding

A new 2times2 full-rate full-diversity linear dispersion space-time block code (STBC) is designed by augmenting the generator of the lattice of the Alamouti's orthogonal STBC and optimizing it according to the criterion of the maximal worst codeword difference determinant. The proposed STBC is proved to satisfy the nonvanishing determinant property and, therefore, to achieve the optimal diversity-multiplexing gain (DMG) tradeoff, while offering a reduced computational complexity of maximum- likelihood (ML) decoding as compared to other existing full-rate STBCs. The performance of our new code is shown to be comparable to that of the best full-rate STBCs known so far.