Space-time Block Research Articles

A Novel Differential Chaos Shift Keying Scheme With Transmit Diversity

A novel differential chaos shift keying scheme with transmit diversity, referred to as <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">TD-DCSK scheme</i> , is proposed in this letter. The proposed TD-DCSK scheme can achieve full diversity and high data rate by advisably designing the space-time (ST) block of the transmitted signal. With the designed ST block, the transmitter with multiple transmit antennas in the TD-DCSK scheme requires only one radio frequency chain, which is particularly important for keeping low hardware complexity. We derive the theoretical expression of bit-error rate (BER) and diversity order of the TD-DCSK scheme over multipath Rayleigh fading channels, and analyze its hardware complexity. Simulation results illustrate the superiority of the proposed scheme and validate the accuracy of the theoretical derivation. The proposed TD-DCSK scheme stands out as a promising solution for low-power and low-cost short-range wireless communications.

Multiple-antenna techniques in nonorthogonal multiple access: a review

As a promising physical layer technique, nonorthogonal multiple access (NOMA) can admit multiple users over the same space-time resource block, and thus improve the spectral efficiency and increase the number of access users. Specifically, NOMA provides a feasible solution to massive Internet of Things (IoT) in 5G and beyond-5G wireless networks over a limited radio spectrum. However, severe co-channel interference and high implementation complexity hinder its application in practical systems. To solve these problems, multiple-antenna techniques have been widely used in NOMA systems by exploiting the benefits of spatial degrees of freedom. This study provides a comprehensive review of various multiple-antenna techniques in NOMA systems, with an emphasis on spatial interference cancellation and complexity reduction. In particular, we provide a detailed investigation on multiple-antenna techniques in two-user, multiuser, massive connectivity, and heterogeneous NOMA systems. Finally, future research directions and challenges are identified.

Full-Diversity Dispersion Matrices From Algebraic Field Extensions for Differential Spatial Modulation

We consider differential spatial modulation (DSM) operating in a block fading environment and propose sparse unitary dispersion matrices (DMs) using algebraic field extensions. The proposed DM sets are capable of exploiting full transmit diversity and, in contrast to the existing schemes, can be constructed for systems having an arbitrary number of transmit antennas. More specifically, two schemes are proposed: 1) field-extension-based DSM (FE-DSM), where only a single conventional symbol is transmitted per space–time block; and 2) FE-DSM striking a diversity–rate tradeoff (FE-DSM-DR), where multiple symbols are transmitted in each space–time block at the cost of a reduced transmit diversity gain. Furthermore, the FE-DSM scheme is analytically shown to achieve full transmit diversity, and both proposed schemes are shown to impose decoding complexity, which is independent of the size of the signal set. It is observed from our simulation results that the proposed FE-DSM scheme suffers no performance loss compared with the existing DM-based DSM (DM-DSM) scheme, whereas FE-DSM-DR is observed to give a better bit-error-ratio performance at higher data rates than its DM-DSM counterpart. Specifically, at data rates of 2.25 and 2.75 bits per channel use, FE-DSM-DR is observed to achieve about 1- and 2-dB signal-to-noise ratio (SNR) gain with respect to its DM-DSM counterpart.

Adaptive Space–Time Coding Using ARQ

We study the energy-limited outage probability of the block space-time coding (STC)-based systems utilizing automatic repeat request (ARQ) feedback and adaptive power allocation. Taking the ARQ feedback costs into account, we derive closed-form solutions for the energy-limited optimal power allocation and investigate the diversity gain of different STC-ARQ schemes. In addition, sufficient conditions are derived for the usefulness of ARQ in terms of energy-limited outage probability. The results show that, for a large range of feedback costs, the energy efficiency is substantially improved by the combination of ARQ and STC techniques if optimal power allocation is utilized.

Linear Precoder Design for Doubly Correlated Partially Coherent Fading MIMO Channels

We consider the single-user multiple-input multiple-output (MIMO) precoder design problem for the doubly spatially correlated partially coherent Rayleigh fading channels with discrete inputs. The objective is to design a linear precoder to adapt to the degradation caused by the imperfect channel estimation at the receiver and the transmit-receive antenna correlation. The system is partially coherent so that the MIMO channel coefficients are estimated at the receiver and its error covariance matrix is fed back to the transmitter. We utilized the cutoff rate (CR) expression, an alternative to the mutual information (MI), and propose to use it as a design criterion to design the linear precoders. A linear precoder is obtained by numerically maximizing the CR with respect to the precoder matrix with a given average power constraint. Furthermore, the precoder matrix is decomposed using singular value decomposition (SVD) into the input shaping matrix, power loading matrix, and beamforming matrix. The beamforming matrix is found to coincide with the eigenvectors of the transmit correlation matrix. The power loading and input shaping matrices are solved numerically using the difference of convex (d.c.) functions programming algorithm and optimization under the unitary constraint, respectively. A 2-block alternating optimization (AO) algorithm is proposed to solve the input shaping matrix and power loading matrix iteratively. Precoders are designed to be used in conjunction with two MIMO transmission schemes: the spatial multiplexing (SM) and space-time (ST) block transmission modes. The frame error rate (FER) and average MI are used as the performance metrics to validate the performance of the newly designed CR-precoders in comparison with the conventional no-precoding case and cutoff rate optimized partially coherent constellations (PCCs). Numerical examples show that the performance gains of the designed precoders are significant compared to the CR-PCCs and conventional codewords.

Robust differential modulations for asynchronous cooperative systems

Accurate channel state information and time/frequency synchronization are challenging to acquire in mobile ad hoc cooperative set-ups, where resource-constrained relaying terminals rapidly (dis)join cooperation. This paper derives low-complexity differential modulations and cooperative transmission schemes so that detection at the receiver is feasible without channel knowledge or synchronization information. A simple distributed doubly-differential (DD) time-division multiplexing (TDM) scheme using diagonal space–time (ST) unitary codes is derived to bypass multiple carrier frequency offsets (CFOs) and collect space diversity. Precoded differential orthogonal frequency division multiplexing (OFDM) transmissions are derived to additionally bypass timing offsets and collect multipath diversity using either DD diagonal or single-differential (SD) orthogonal ST block codes (OSTBCs). DD diagonal mappings suffer from considerable coding gain and signal-to-noise ratio (SNR) loss due to unitary constellation constraints and noise enhancement at the receiver. SD-OSTBCs achieve higher performance with reduced decoding complexity, at the cost of reduced CFO mitigation range. Simple and robust non-coherent selective and adaptive transmissions are also included, showing that full space and multipath diversity can still be achieved even with decoding errors at relays. Simulations corroborate theoretical claims.

An Improved Complex Decoding Scheme for Diagonal Algebraic STBC over Fading Channels

We present a new decoding scheme of complex lattice for diagonal algebraic Space-time (ST) block codes in multiple-antennas systems. With multidimensional complex constellation symbols rotation and Hadamard transform, the constructed code is capable of achieving full diversity over a fast fading channels. At the receiver the received signals have structure similar to diagonal matrix, which is easy to decode. The Maximum-likelihood (ML) decoding of the proposed codes can be implemented by the improved complex sphere decoder, without doubling the channel matrix. It is shown that the complex lattice decoding scheme for proposed codes in a multiple-antennas system yields excellent performance and low decoding complexity.

On the design of full-rate full-diversity space-time block codes for multiple-input–multiple-output systems with a turbo minimum mean square error equaliser at the receiver side

Non-orthogonal space-time block (STB) code structures used to be optimised considering a maximum-likelihood detection, but depending on the modulation order and/or the antenna number, the prohibitive complexity of such a receiver makes it infeasible in practice. Suboptimal low-complexity receiver structures like linear detectors can be applied instead, yielding degradation of performance compared with the predictions. When a forward error correction (FEC) code is used upstream of the STB code, an iterative receiver consisting of a FEC decoder and an interference canceller (IC) co-operating according to the turbo equalisation principle, can achieve near-optimal performance. This study aims to define the construction of full-rate full-diversity linear dispersion codes with reduced peak-to-average power ratio (PAPR), taking into account the serial concatenation with a FEC at the transmitter and a minimum mean square error (MMSE) turbo equaliser at the receiver. Optimisation criteria are mutual information maximisation, symbol error rate minimisation at the MMSE–IC output, full-diversity thanks to the threaded algebraic space time concept and PAPR minimisation. Explicit constructions are given and the resulting code efficiency is analysed through comparison with equivalent perfect STB codes.

Frequency-Domain Equalization for Orthogonal and Quasi-Orthogonal STBCs over Frequency-Selective Wireless and Power-Line Channels

In recent years, combination of single-carrier frequency-domain equalization (SC-FDE) and space-time block coding/code (STBC) techniques to exploit the advantages of both, has received a great attention. In this paper we propose new techniques for combining SC-FDE with orthogonal and Quasi-orthogonal STBCs applicable to any number of transmit antennas. For Quasi-orthogonal STBC we first propose a new structure for codes with four transmit antennas and then extend it to higher numbers. We convert Quasi-orthogonal system to two equivalent orthogonal subsystems and equalize and decode these subsystems based on our proposed procedure for orthogonal codes. Finally, we present our simulation results for different frequency-selective wireless and power-line channels and show that a significant SNR gain is achieved when SC-FDE is combined with diversity techniques.

Coherent Versus Noncoherent

In this article, we investigate the design philosophies of the existing space-time (ST) block codes (STBCs) in the open literature, namely the orthogonal approach and layered method, followed by the introduction of the generalized linear dispersion architecture. We will demonstrate that the powerful linear dispersion structure is capable of unifying the entire suite of existing schemes and, as a further benefit, it offers extra design flexibility so that diverse system requirements can be satisfied. Furthermore, after characterizing the fundamental relationship between STBCs and differential STBCs (DSTBCs), we highlight the benefits of noncoherently detected schemes, which are capable of exploiting the advantages of multiple antennas, while circumventing the potentially excessive burden of multiantenna channel estimation. Additionally, the linear dispersion structure can also be applied in systems, where the multiantenna array is formed in a distributed fashion by multiple single-antenna-aided cooperating mobile stations. Hence, the design of colocated and cooperative multiple-input-multiple-output (MIMO) systems aiming for achieving diversity is linked from a linear dispersion perspective.

Dispersion Matrix Optimization for Space-Time Shift Keying

In this Letter, we introduce an efficient dispersion matrix optimization technique for the recent concept of Space Time Shift Keying (STSK). By exploiting the STSK-specific signal structure relying on the dispersion-matrix activation, rather than the classic spatial multiplexing, computational complexity imposed by the system optimization is reduced by tens of times, in comparison to that of the conventional approach. Our simulation results reveal that the proposed technique substantially reduces computational cost and time required for the dispersion-matrix optimization, which is especially beneficial for large search-space scenarios, such as a high number of transmit antennas, symbols per space-time block and constellation points.

Zero-Forcing DFE Transceiver Design Over Slowly Time-Varying MIMO Channels Using ST-GTD

This paper considers the optimization of transceivers with decision feedback equalizers (DFE) for slowly time-varying memoryless multi-input multi-output (MIMO) channels. The data vectors are grouped into space-time blocks (ST-blocks) for the spatial and temporal precoding to take advantage of the diversity offered by time-varying channels. The space-time generalized triangular decomposition (ST-GTD) is proposed for application in time-varying channels. Under the assumption that the instantaneous channel state information at the transmitter (CSIT) and receiver (CSIR), and the channel prediction are available, we also propose the space-time geometric mean decomposition (ST-GMD) system based on ST-GTD. Under perfect channel prediction, the system minimizes both the arithmetic MSE at the feedback detector, and the average un-coded bit error rate (BER) in moderate high signal to noise ratio (SNR) region. For practical applications, a novel ST-GTD based system which does not require channel prediction but shares the same asymptotic BER performance with the ST-GMD system is also proposed. At the moderate high SNR region, our analysis and numerical results show that all the proposed systems have better BER performance than the conventional GMD-based systems over time-varying channels; the average BERs of the proposed systems are non-increasing functions of the ST-block size.

Fast Optimal Decoding of Multiplexed Orthogonal Designs by Conditional Optimization

This paper focuses on conditional optimization as a decoding primitive for high rate space-time codes that are obtained by multiplexing in the spatial and code domains. The approach is a crystallization of the work of Hottinen which applies to space-time codes that are assisted by quasi-orthogonality. It is independent of implementation and is more general in that it can be applied to space-time codes such as the Golden Code and perfect space-time block codes, that are not assisted by quasi-orthogonality, to derive fast decoders with essentially maximum likelihood (ML) performance. The conditions under which conditional optimization leads to reduced complexity ML decoding are captured in terms of the induced channel at the receiver. These conditions are then translated back to the transmission domain leading to codes that are constructed by multiplexing orthogonal designs. The methods are applied to several block space-time codes obtained by multiplexing Alamouti blocks where it leads to ML decoding with complexity O(N 2) where N is the size of the underlying QAM signal constellation. A new code is presented that tests commonly accepted design principles and for which decoding by conditional optimization is both fast and ML. The two design principles for perfect space-time codes are nonvanishing determinant of pairwise differences and cubic shaping, and it is cubic shaping that restricts the possible multiplexing structures. The new code shows that it is possible to give up on cubic shaping without compromising code performance or decoding complexity.

Spectral efficient transmit diversity techniques without cyclic prefix for fading relay channels

This paper proposes spectral efficient relay-assisted transmit diversity techniques, i.e., space-time and space-frequency block codes (STBC/SFBC), for single carrier frequency-domain equalization (SC-FDE). The proposed systems achieve spatial diversity over frequency selective channels in a distributed fashion without cyclic prefix (CP), which increases spectral efficiency of conventional relay-assisted systems. In practical mobile applications, the CP-less distributed STBC (D-STBC) SC-FDE suffers from the time selectivity of wireless fading channels, resulting in a deviation from the basic assumption of Alamouti codeword. In order to obtain a reliable performance over doubly selective channels, the CP-less D-SFBC SC-FDE and its efficient implementation are presented. Further, the performance of these two distributed SC transmissions is analytically compared over fast fading (i.e., time selective) environments. For evaluation of mean square error over fast fading channels, we present a channel model that captures the time-varying nature of wireless channels. It is shown through analysis that the CP-less DSFBC SC-FDE outperforms the CP-less D-STBC SC-FDE when there exists a severe Doppler spread. Timing synchronization and highly accurate channel estimation of the proposed systems are also addressed for practical implementations. Simulation results show that the proposed systems approach the lower bound of full-CP systems, thus increasing the spectral efficiency.

Multiple description quantizer design for multiple-antenna systems with MAP detection

We study the design of index assignment based multiple description quantizers for multiple-antenna systems with slow Rayleigh fading. A time-interleaver is employed at the transmitter to provide independent channel instances for the multiple descriptions, and a maximum a posteriori (MAP) detector is employed at the receiver to jointly decode the multiple descriptions. The concatenation of index assignment, binary phase-shift keying modulators, space-time orthogonal block coder, multiple-antenna channel, and MAP detector is modeled as a discrete memoryless channel. We optimize multiple description vector quantizers using an upper bound of the channel transition probability achieved by the MAP detector. The proposed scheme of combining multiple description coding and space-time orthogonal block coding is shown to be superior to each individual coding scheme.

Achieving full transmit diversity for PPM constellations with any number of antennas via double position and symbol permutations

We present a general technique for constructing minimal-delay rate-1 Space-Time (ST) block codes for Pulse Position Modulations (PPM) with an arbitrary number of transmit antennas. We show that the novel idea of time-domain constellation extension as well as introducing joint position and symbol permutations achieves a full transmit diversity order while maintaining unipolar transmissions. This renders the proposed scheme suitable for low-cost Time-Hopping Ultra- Wideband (TH-UWB) systems as well as Free-Space Optical (FSO) communications with direct detection.

New PAPR-preserving mapping methods for single-carrier FDMA with space-frequency block codes

Innovative mapping schemes for Space-Frequency Block Codes (SFBC) which are compatible with the structure of Single-Carrier Frequency Division Multiple Access (SC-FDMA) systems are introduced. We first show that existing space-time and space-frequency block codes lack flexibility in terms of framing or cause a degradation of the signal envelope properties when combined with SC-FDMA. Then, we present an Alamoutibased orthogonal code designed for 2 transmit antennas that makes use of an innovative mapping in the frequency domain to preserve the low envelope properties of SC-FDMA. Next, an extension of this concept to a quasi-orthogonal code for 4 transmit antennas is presented and analyzed. We prove the good performance of the proposed schemes over multiple-input multiple-output (MIMO) channels both in static and in highmobility scenarios.

Performance of Block Space-Time Code in Wireless Channel Dynamics

In this work, we observe the behavior of block space-time code in wireless channel dynamics. The block space-time code is optimally constructed in slow fading. The block code in quasistatic fading channels provides affordable complexity in design and construction. Our results show that the performance of the block space-time code may not be as good as conventionally convolutional coding with serial transmission for some channel features. As channel approaches fast fading, a coded single antenna scheme can collect as much diversity as desired by correctly choosing the free distance of code. The results also point to the need for robust space-time code in dynamic wireless fading channels. We expect that self-encoded spread spec-trum with block space-time code will provide a robust performance in dynamic wireless fading channels.

High-rate Complex Orthogonal Space-time Block Codes for 5 and 6 Transmit Antennas

Based on orthogonal designs, space-time (ST) block codes that enable full diversity as well as a simple maximum likelihood (ML) decoding algorithm at the decoder can be constructed for more than two transmit antennas. For real constellations (such as PAM), ST block codes with transmission rate 1 can be designed from the real Hurwitz-Radon families for any number of transmit antennas. However, for complex constellations (such as M-PSK or M-QAM), ST block codes for more than two transmit antennas can only be constructed with rates less than 1. Previous attempts have been concentrated on complex orthogonal designs that provide ST block codes with full diversity and high transmission rates. In this paper, we present two rate 2/3 complex ST block codes from orthogonal designs for five and six transmit antennas, respectively. Simulation results are provided to demonstrate the significant performance gains made by the proposed ST block codes.

Space-Time Codes for MIMO Ultra-Wideband Communications and MIMO Free-Space Optical Communications with PPM

In this paper, we consider the problem of space-time (ST) coding with pulse position modulation (PPM). While all the existing ST block codes necessitate rotating the phase or amplifying the amplitude of the transmitted symbols, the proposed scheme can be associated with unipolar PPM constellations without introducing any additional constellation extension. In other words, full transmit diversity can be achieved while conveying the information only through the time delays of the modulated signals transmitted from the different antennas. The absence of phase rotations renders the proposed scheme convenient for low- cost carrier-less multiple-input-multiple-output (MIMO) time- hopping ultra-wideband (TH-UWB) systems and for MIMO free-space optical (FSO) communications with direct detection. In particular, we propose two families of minimal-delay ST block codes that achieve a full transmit diversity order with PPM. Designate by n the number of transmit antennas and by M the number of modulation positions. For a given set of values of (n, m), the first family of codes achieves a rate of 1 symbol per channel use (PCU) which is the highest possible achievable rate when no constellation extensions are introduced. The second family of codes can be applied with a wider range of (n, m) at the expense of a reduced rate given by: R=1/n+n-1/n log <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> (M-1)/n log <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> (M).