Space-time Codes Research Articles

Space–Time Line Code

This paper characterizes rate-one (i.e., full rate) full-spatial-diversity-achieving communication schemes based on the channel state information (CSI) availability and antenna configurations, i.e., CSI at a transmitter (CSIT) or CSI at a receiver (CSIR) and the numbers of transmit and receive antennas M and N (denoted by M × N), respectively. The maximum ratio combining (MRC), maximum ratio transmission (MRT), and space-time block code (STBC) schemes are rate-one full-spatial-diversity-achieving method facilitated for communication systems with: 1) 1 × N and CSIR; 2) M × 1 and CSIT; and 3) M × 1 and CSIR, respectively. A novel space-time line code (STLC) is then introduced for a 1 × 2 system with CSIT, and it is extended to an M × 2 STLC. The proposed STLC uses CSI for encoding at the transmitter and enables the receiver to decode the STLC symbols without CSI. Also, the STLC encoding matrices with various code rates and decoding (combining) schemes are designed for the M × 3 and M × 4 STLC systems: A code rate of 3/4, 1/2, and 3/7 for the M × 3 systems and a code rate of 3/4, 4/7, and 1/2 for the M × 4 systems. For each STLC scheme, a full-diversity achieving STLC decoding method is designed. Based on analyses and numerical results, we verify that the proposed STLC scheme achieves a full diversity order, i.e., MN, and is robust against CSI uncertainty. It is also shown that the array processing gain is inversely proportional to the code rate. To verify the merit of STLC, we introduce a joint operation with STBC and STLC schemes, called an STBLC system. The STBLC system achieves full-spatial-diversity gain in both uplink and downlink communications. The new STLC achieving full-spatial diversity is scalable for various code rates and expected to be applied to various wireless communication systems along with MRC, MRT, and STBC.

Topology-Aware Space-Time Network Coding in Cellular Networks

Space-time network coding (STNC) is a time-division multiple access (TDMA)-based scheme that combines network coding and space-time coding by allowing relay nodes to combine the information received from different source nodes during the transmission phase and to forward the combined signal to a destination node in the relaying phase. However, STNC schemes require all the relay nodes to overhear the signals transmitted from all the source nodes in the network. They also require a large number of time-slots to achieve full diversity in a multipoint-to-multipoint transmission. Both conditions are particularly challenging for large cellular networks where, assuming a downlink transmission, base stations (BSs) and users only overhear a subset of all the BSs. In this paper, we exploit basic knowledge of the network topology in order to reduce the number of time-slots by allowing simultaneous transmissions from those BSs that do not overhear each other. Our results show that these topology-aware schemes are able to increase the spectral efficiency per time-slot and bit error rate with unequal transmit power and channel conditions.

Hierarchical Multi-Functional Layered Spatial Modulation

In pursuit of optimal index modulation -aided multiple-input multiple-output (MIMO) systems, where information is implicitly conveyed by relying on the on/off mechanism of the system’s components in addition to the classical amplitude, phase, or frequency components, we present in a tutorial style our novel multi-functional (MF) architecture of layered multi-set (LMS) modulation. This generalized framework subsumes various MIMO techniques exhibiting different multiplexing and diversity functionalities. Our LMS design relies on three constituents, namely the space-time (ST) unit, the layered unit and the spatial switching unit. More specifically, the ST unit relies on the generalized space-time shift keying (GSTSK) scheme, where $P$ – rather than one – out of $Q$ ST dispersion matrices are selected for dispersing an equivalent number of phase-shift keying/quadrature amplitude modulation symbols across the antennas and time-slots. In the layered unit, multiple GSTSK codewords are stacked within the layers of codewords spread over time and space. The spatial switching unit activates $N_{c}^{t}$ out of $N_{t}$ transmit antennas. Owing to its hierarchical MF architecture, our LMS system strikes a flexible design trade-off between the achievable throughput as well as the attainable diversity gain and it can potentially subsume various conventional MIMO schemes, such as Bell Lab’s Layered Space-Time, space-time block codes, layered steered space-time codes, spatial modulation (SM), space-shift keying, linear dispersion codes, generalized SM, STSK, GSTSK, quadrature SM and multi-set STSK. Additionally, we derive the LMS system’s discrete-input continuous-output memoryless channel capacity, which encompasses the capacity limit of all the LMS subsidiaries. We also propose a two-stage serially concatenated soft-decision (SD) based LMS detector by relying on an inner and an outer decoder that iteratively exchange their extrinsic information in order to achieve a near-capacity performance. Last but not least, we utilize the extrinsic information transfer charts for analyzing the convergence behavior of our SD-aided coded LMS scheme.

Chaotic Phase-Coded Waveforms With Space-Time Complementary Coding for MIMO Radar Applications

A framework for designing orthogonal chaotic phase-coded waveforms with space-time complementary coding is proposed for multiple-input multiple-output (MIMO) radar applications. The phase-coded waveform set to be transmitted is generated with an arbitrary family size and an arbitrary code length by using chaotic sequences. Due to the properties of chaos, this chaotic waveform set has many advantages in performance, such as anti-interference and low probability of intercept. However, it cannot be directly exploited due to the high range sidelobes, mutual interferences, and Doppler intolerance. In order to widely implement it in practice, we optimize the chaotic phase-coded waveform set from two aspects. First, the autocorrelation property of the waveform is improved by transmitting complementary chaotic phase-coded waveforms, and an adaptive clonal selection algorithm is utilized to optimize a pair of complementary chaotic phase-coded pulses. Second, the crosscorrelation among different waveforms is eliminated by implementing space-time coding into the complementary pulses. Moreover, to enhance the detection ability for moving targets in MIMO radars, a method of weighting different pulses by a null space vector is utilized at the receiver to compensate the interpulse Doppler phase shift and accumulate different pulses coherently. Simulation results demonstrate the efficiency of our proposed method.

An Expurgated Union Bound of Punctured Space-Time Turbo Codes

This paper presents a new technique to obtain an expurgated union bound on the frame error rate of punctured space-time turbo codes (STTuC) in quasi-static Rayleigh fading channels. The STTuC scheme is composed of two component space-time trellis encoders connected in parallel via an interleaver. An adjacent matrix of an augmented state diagram is defined which allows the enumeration of each punctured component encoder. The distance spectrum of the STTuC is then obtained using the concept of uniform interleaver. A method to identify the dominant error events is proposed and an expurgated union bound on the frame error rate of STTuC schemes is computed using these dominant error events. Comparisons with simulated results reveal that the expurgated union bound is tight for codes with different construction criteria for a wide range of signal to noise ratio.

Uneven Power Amplifier Shuffling for Space-Time Line Code Systems

In this paper, a novel power amplifier (PA) shuffling method is proposed for a space-time line code (STLC) system with uneven PA gains. The proposed method is composed of pre-shuffling and post-shuffling, which represent the assignment of STLC symbols to PAs and the allocation of PAs to transmit antennas, respectively. Through these shuffling procedures, the proposed scheme matches the larger gain PA to the larger effective channel gain with STLC in order to maximize the STLC decoding signal-to-noise ratio (SNR). A theoretical analysis provides a formula to compute the decoding SNR, and it is shown through numerical simulations that the proposed PA shuffling method can significantly improve the performance of conventional STLC systems, regardless of the channel state information uncertainty, especially when the number of transmit antennas is large.

Space–Time Line Code for Massive MIMO and Multiuser Systems With Antenna Allocation

This paper first investigates an M-by-2 massive multiple-input multiple-output (MIMO) system that transmits a single stream is investigated. For this system, we propose a space-time line code (STLC), which is a transmitting and combining (at a receiver) scheme that achieves full spatial diversity. For the STLC, two consecutive (time) information symbols are weighted as per channel gains (space), combined at each transmit antenna, and transmitted through the M transmit antennas for two consecutive symbol times. With two receive antennas, the STLC receiver simply combines the signals received in the two symbol times and achieves a diversity order of 2M (full diversity). We show that the proposed STLC asymptotically achieves the maximum (optimal) received signal-to-noise ratio as M increases with significantly reduced computational complexity compared with the optimal scheme. Because the proposed STLC receiver requires no or partial channel state information, it avoids the issue of massive MIMO channel estimation. Furthermore, the rigorous performance evaluation under spatially correlated and uncertain channel conditions reveals that the proposed STLC achieves comparable or better performance than the existing schemes, and the results verify that the proposed STLC scheme is a potential candidate for M-by-2 massive MIMO systems. Next, the transmit antenna allocation algorithms are devised for a multiuser STLC system. Each user achieves full diversity order from the corresponding MIMO channels after the antenna allocation. The signal-tointerference-plus-noise ratio (SINR) of each user is analyzed considering the multiuser interference and channel uncertainty, and its lower bound is derived. Using the SINR lower bound, greedy algorithms that allocate the transmit antennas are devised. Rigorous simulation demonstrates that multiuser STLC with the proposed antenna allocation is robust against channel uncertainty and can improve the average SINR, improving the quality of experience. Furthermore, it is observed that the proposed STLC with antenna allocation method achieves the best performance if M is sufficiently large. The results in this paper show that the STLC can be a potential candidate for an M-by-2 (multiuser) massive MIMO systems.

Dual Relay Selection for Cooperative NOMA With Distributed Space Time Coding

We consider a two-user multi-relay cooperative non-orthogonal multiple access (NOMA) network with distributed space–time coding. Two dual-relay selection strategies are proposed for cooperative NOMA, namely, two-stage dual relay selection with fixed power allocation (DRS-FPA) and two-stage dual relay selection with dynamic power allocation (DRS-DPA). Furthermore, lower and upper bounds on the outage probability for the DRS-FPA scheme and the exact outage probability for the DRS-DPA scheme are obtained in closed-form, respectively. Numerical results show that the proposed two-stage DRS schemes not only yield better outage performance than the existing single relay selection schemes without sacrificing spectral efficiency, but can also achieve full diversity gain.

Survey on different low complexity decoding algorithms for different orthogonal STBC MIMO wireless communication system under Rayleigh fading channel

In this paper, we have presented a survey based on the combination of spatial multiplexing and space time coding techniques under Rayleigh fading channel constraint in MIMO wireless communication systems. The decoding algorithms like Maximum Likelihood, V-BLAST and Sphere Decoder are analysed and their performance is evaluated using different orthogonal space-time block coding techniques, like quasi and rotated quasi-orthogonal space-time block codes. It has been observed that noise and interference get reduced by our proposed encoders with lower complexity at the receiver end. This improves the noise and interference performance by offering low complexity at the receiver. The paper also focuses on the performance of the combining effect of the demodulation algorithms with several other STBCs in the outcome.

Improved Super-Orthogonal Trellis-Coded Spatial Modulation Using STBC-CSM

Trellis coded modulation (TCM) is a scheme that enhances the error performance without extra power not bandwidth. This paper presents a modified Super-Orthogonal Trellis-Coded Spatial Modulation (SOTC-SM) based on a cyclic structure of the Space Time Coding. The developed code benefits from expanded codebook of the Space Time Block Coded Spatial Modulation (STBC-SM) to enhance the coding gain. The set-partitioning and the code design based on the expanded codebook was given for codes with rate of 2 and 3 bps and can be easily extended to higher rates. The Bit-Error Rate (BER) performance of the proposed scheme was evaluated via computer simulation. It was shown that the proposed scheme outperforms the SOTC-SM performance for the same number of transmit antennas.

Enhancement of Twice Quasi Orthogonal Space Time Block Coded (QOSTBC) Performance System with Zero Forcing EVCM Decoder

In today’s modern telecommunications systems, makes the number of studies and development of multiple antennas and multiple-input multiple-output (MIMO) systems to achieve high reliability and low complexity. One attractive approach to improve that performance is using technique transmit diversity which is spacetime block coding and receiver diversity i.e. zero forcing EVCM (ZF EVCM). Although some earlier MIMO standards were develop some space-time codes like (O-STBC)and (Q-OSTBC) to provide high reliability but they are limited able to achieve orthogonality. In this research will be proposed a MIMO system scheme which is an improvement of QOSTBC that used a transmission diversity technique. This improvement from QOSTBC is Twice QOSTBC uses a provision in two codeword matrices to be sent are arranged diagonally so as to have higher levels of orthogonality. In this case Twice QOSTBC highly structured (4x1) can be replaced as an equivalent EVCM channel H. The proposed Twice-QOSTBC’s results outperform other QOSTBC techniques with a difference around 3 dB for single-input multi-input (MISO) input configuration at 10-6 BER and receiver ZF EVCM has a very similar structure as the code matrix S of the underlying Twice QSTBC which can eliminates the system complexity.

Atmospheric channel model of maritime visible light communication based on repeated coding

Visible light communication (VLC) is a new type of wireless communication technology, and its applications in offshore ships and ship-shore lamp signal systems are drawing increasing attention as a supplement of communication net. In maritime environment, VLC system is affected by many factors, of which the wave fluctuation and atmospheric turbulence are the most noticeable. The turbulence will make signal intensity fluctuate randomly, and thus reducing the performance of VLC system operating in the atmosphere. To establish an effective VLC network in the actual marine environment, an effective channel transmission model needs to be established and used to study the performance of the maritime VLC link. Considering large aperture diameter receiver with the aperture averaging effect, log-normal distribution model is employed to deduce the mathematical expression of average bit error rate of maritime VLC system in atmospheric turbulence. By using time-diversity to transmit interleaved symbols with repeated coding in a maritime VLC system, it is possible to ensure that the code-word passes through multiple channels to resist the deep fade performance, and to reduce the bit error rate due to the occurrence of deep fading in a single channel. In the actual application process, in order to improve the system performance, the average signal-to-noise ratio usually increases with the transmission power increasing, but for a VLC system, there are some difficulties in making the high-power high-rate visible light transmitters. And the power will produce light pollution and even damage the naked eye. The implementation of the repetitive coding principle is simple, and in some special cases it is even better than the complex orthogonal space-time coding and other schemes, so studying the system performance of the repetitive coding scheme is of considerable value for practical application. Based on the modified Pierson-Moskowitz spectrum, the effect of wave height, transmission distance, atmospheric turbulence intensity, receiver aperture size and visibility on the average bit error rate of VLC system are analyzed. The performance of the VLC system between lighthouse and ship is affected by the fluctuations of the sea waves, and the average bit error rate changes with randomness and complexity like the sea waves in a short distance. As the wind speed increases, the marine environment becomes worse and the average bit error rate is undulate. The average bit error rate of maritime VLC increases with the increasing of transmission distance and atmospheric turbulence intensity, and with the decreasing of receiver aperture size, wavelength and average signal-to-noise ratio. Atmospheric turbulence intensity and visibility have a significant effect on the system performance, and it should be emphatically considered to take measures to reduce the influence. Increasing receiver aperture and repetitive coding are effective to a certain extent. In the present work a new model is proposed for evaluating the performance of a maritime VLC system and providing reference for practical application.

Natural orders for asymmetric space–time coding: minimizing the discriminant

Algebraic space–time coding—a powerful technique developed in the context of multiple-input multiple-output (MIMO) wireless communications—has profited tremendously from tools from Class Field Theory and, more concretely, the theory of central simple algebras and their orders. During the last decade, the study of space–time codes for practical applications, and more recently for future generation (5G $$+$$ ) wireless systems, has provided a practical motivation for the consideration of many interesting mathematical problems. One such problem is the explicit computation of orders of central simple algebras with small discriminants. In this article, we consider the most interesting asymmetric MIMO channel setups and, for each treated case, we provide explicit pairs of fields and a corresponding non-norm element giving rise to a cyclic division algebra whose natural order has the minimum possible discriminant.

MIMO-OFDM Based Energy Harvesting Cooperative Communications Using Coalitional Game Algorithm

In this paper, we consider the problem of cooperative communication between relays and base station in an advanced Multiple-Input Multiple-Output Orthogonal Frequency Division Multiplexing (MIMO-OFDM) framework, under the assumption that the relays are supplied by electric power drawn from energy harvesting (EH) sources. In particular, we focus on the relay selection, with the goal to guarantee the required performance in terms of capacity. In order to maximize the data throughput under the EH constraint, we model the transmission scheme as a nontransferable coalition formation game, with characteristic function based on an approximated capacity expression. Then, we introduce a powerful mathematical tool inherent to coalitional game theory, namely: The Shapley value to provide a reliable solution concept to the game. The selected relays will form a virtual dynamically-configured MIMO network that is able to transmit data to destination using efficient space-time coding techniques. Numerical results, obtained by simulating the EH-powered cooperative MIMO-OFDM transmission with algebraic space-time coding, prove that the proposed coalitional game-based relay selection allows us to achieve performance very close to that obtained by the same system operated by guaranteed power supply. The proposed methodology is finally compared with some recent related state-of-the-art techniques showing clear advantages in terms of link performance and goodput.

Sequential Closed-Form Semiblind Receiver for Space-Time Coded Multihop Relaying Systems

In this letter, we present a sequential closed-form semi-blind receiver for a one-way multi-hop amplify-and-forward (AF) relaying system. Assuming Khatri-Rao space-time (KRST) coding at each relay, it is shown that the system with K relays can be modeled by means of a generalized nested PARAFAC model. Decomposing this model into K +1 third-order PARAFAC models, we develop a closed-form semi-blind receiver for jointly estimating the information symbols and the individual channels, at the destination node. Each step consists of a Khatri-Rao factorization. Parameter identifiability conditions are given, and simulation results are provided to illustrate the effectiveness of the proposed semi-blind receiver. Index Terms—Multi-hop relaying, sequential closed-form semi-blind receiver, space time (ST) coding, amplify-and-forward, generalized nested PARAFAC model. I. INTRODUCTION Relay nodes will play an important role in 5G communication systems. In such systems, the high-capacity wireless backhaul offers operators an alternative solution to conventional backhauling using multi-hop short-distance communications [1]–[4]. Tensor decompositions have been widely exploited for point-to-point wireless communication systems. The practical motivation for tensor modeling comes from the fact that one can simultaneously benefit from multiple (more than two) signal diversities, like space, time and frequency diversities, for instance. In the context of cooperative wireless communications, few results have been published on tensor-based receivers, and most of them are limited to a single relay scenario. In previous works [5]–[8], the problem of channel estimation for multiple input multiple output (MIMO) relaying systems was considered under a supervised approach. The works [5]–[7] considered one-way two-hop systems, while [8] addressed two-way MIMO relaying systems. In [9] and [10], three-hop relaying systems were studied. Recent works proposed semi-blind receivers for joint symbol and channel estimation. For instance, one can cite the PARAFAC-PARATUCK [11] and the nested PARAFAC receivers [12], [13]. However, the generalization of tensor-based semi-blind receivers to the multi-hop relaying scenario has not been addressed so far to the best of authors' knowledge.

Multimedia Relay Resource Allocation for Energy Efficient Wireless Networks: High-Layer Content Prioritization With Low-Layer Diversity Cooperation

With the popularity of versatile mobile multimedia applications and the pressing need to reduce energy consumption in future wireless networks, new challenges have been posed to maintain adequate coverage, quality of service, and reliability for big-scale multimedia traffic. Specifically, in this paper we introduce a cooperative multimedia relay framework and investigate premium-regular-diversity-based multimedia resource allocation treatment approaches. We also comparatively study five generic wireless multimedia relay scenarios including direct transmission, single relay, multiple pure relays, relay cooperation with space-time coding, and relay coordination with distributed beamforming. The key contribution of the new relay resource allocation framework is that packet importance priority diversity at the application layer is jointly considered with spatial diversity and relay coordination protocols at lower layers. Premium packets and regular packets of multimedia streams are adaptively allocated to relay nodes, and transmission resources are optimally allocated with regards to energy budget. Extensive simulation results demonstrate that the proposed resource allocation paradigm using multirelay coordination has significant video quality enhancement and energy saving potentials to support future big-data wireless multimedia traffic.

On the Design of Maximal-Rate Shape-Preserving $2\times 2$ and $3\times 3$ Space-Time Codes for Noncoherent Energy-Detection-Based PPM Communications

In this paper, we propose novel $2\times 2$ and $3\times 3$ noncoherent space-time (ST) codes for impulse-radio ultra-wideband communications with pulse position modulation (PPM). The code design is based on existing coherent ST codes, where the associated constellation is confined in order to achieve full diversity with analog energy detectors. A comprehensive performance analysis guides this confinement and highlights the maximum rates that can be achieved by this specific layered code word structure with two and three transmit antennas. The proposed codes attain these maximum rates without introducing any expansion to the unipolar PPM signal set.

New Constructions of Asymptotically Optimal Codebooks With Multiplicative Characters

In practical applications, such as direct spread code division multiple access communications, space-time codes and compressed sensing, and codebooks with small inner-product correlation are required. It is extremely difficult to construct codebooks achieving the Levenshtein bound. In this paper, two new constructions of infinitely many codebooks with multiplicative characters of finite fields are presented. These constructions produce complex codebooks asymptotically achieving the Levenshtein bound and codebooks asymptotically achieving the Welch bound. The codebooks presented in this paper have new parameters.

Channel quantization-based physical-layer network coding for two-way relay STBC system

Wireless multiple-input multiple-output (MIMO) two-way relay systems have received increasing attention recently. In a simple two-hop relay system, physical-layer network coding (PNC) is an effective scheme for relay to map the transmitted symbols from two terminal nodes into the network coded symbol. This paper considers a two-hop two-way relay system which uses the Alamouti space-time code for signaling between all nodes and channel quantization for PNC mapping at the relay. Specifically, based on the concept of CQ-PNC we derive a PNC mapping rule for two pairs of network coded symbols. An adaptive mapping scheme based on minimum residual interference power is introduced to reduce the effect of quantization error. Finally, a relay selection method based on minimum residual interference power is proposed as a means to increase the system performance.

Performance Analysis for Two-Way Network-Coded Dual-Relay Networks With Stochastic Energy Harvesting

In this paper, we consider an energy harvesting (EH) two-way (TW) dual-relay network, including one non-EH relay and one EH relay equipped with a finite-sized battery. In the network, a space-time transmission protocol with space-time network coding is designed, and an optimal transmission policy for the EH relay is proposed by using a stochastic solar EH model. In this optimal policy, the long-term paired-wise error probability (PEP) of the system is minimized by adapting the EH relay’s transmission power to the knowledge of its current battery energy, channel fading status, and causal solar EH information. The designed problem is formulated as a Markov decision process framework, and the conditional capability of the contribution to PEP by the EH relay is adopted as the reward function. We uncover a monotonic and limited difference structure for the expected total discounted reward. Furthermore, a non-conservative property and a monotonic structure of the optimal policy are revealed. Based on the optimal policy and its special structures, the expectation, lower and upper bounds, and asymptotic approximation of the PEP are computed and an interesting result on the system diversity performance is revealed, i.e., the full diversity order can be achieved only if the EH capability index, a metric to quantify the EH node’s capability of harvesting and storing energy, approaches to infinity; otherwise, the EH diversity order is only equal to one, and the coding gain of the network is increasing with the EH capability index at this time. Furthermore, a full diversity criterion for the EH TW dual-relay network is proposed. Finally, computer simulations confirm our theoretical analysis and show that our proposed optimal policy outperforms other compared policies.