Space-time Codes Research Articles

Space-Time Media-Based Modulation

Media-based modulation (MBM), which utilizes radiation patterns of a reconfigurable antenna to convey information, appears as a promising index modulation (IM) scheme for beyond 5G networking. In this paper, we present a general framework for MBM from the perspective of space-time coding, and introduce a novel space-time coded IM concept, which is called space-time media-based modulation (ST-MBM). The proposed scheme is based on one of the prominent IM solutions, space shift keying, along with Hurwitz–Radon family of matrices in order to achieve transmit diversity gain with a single radio frequency (RF) chain by utilizing the unique RF mirror activation principle of MBM. We derive the theoretical pairwise error probability of the ST-MBM scheme for correlated and uncorrelated channel states and obtain the average bit error probability. Additionally, a lower bound is derived for the mutual information of the ST-MBM scheme to gain insights into the information theoretical bounds of the proposed scheme. Furthermore, extensive computer simulations are provided to show the superior error performance of the ST-MBM scheme over the state-of-the-art multiple-input multiple-output-based transmission systems.

Space–Time Line Codes With Power Allocation for Regenerative Two-Way Relay Systems

In this paper, a general two-way relay (TWR) transmission method is proposed under per-antenna power constraints by combining space-time line codes (STLCs) with transmit power allocation for two source nodes. We introduce a general STLC-based encoding scheme for a decode-and-forward TWR and derive the detection signal-to-interference-plus-noise ratio (SINR) values at two source nodes. An optimal encoder structure with power allocation is proposed in terms of maximizing the minimum SINRs, and it is verified that the optimal encoder is identical to the superposition of two conventional STLCs. An iterative method is proposed to find the optimal power allocation for detection at two source nodes. Moreover, a low-complexity suboptimal encoder is proposed for practical implementation. Numerical simulations present that the proposed STLC-based transmission method outperforms a conventional eigen-beamforming scheme with nulling and an STLC-based scheme with equal power allocation, in terms of the average bit error rate of source nodes, regardless of the distribution of source nodes, the number of TWR antennas, and the transmit power.

On the Performance of Spatial Modulations Over Multimode Optical Fiber Transmission Channels

In this paper, we analyze the performance of coded and uncoded spatial modulations over multi-mode fiber optic channels with the mode-dependent loss (MDL) under the maximum likelihood (ML) and zero-forcing (ZF) detection schemes. We focus on the multi-dimensional modulations that satisfy certain orthogonality criteria such as the Threaded Algebraic Space-Time (TAST) codes. In particular, we link the post-detection signal-to-noise ratio (SNR) to the orthogonality defect factor (ODF) of the equivalent channel matrix by deriving their closed-form expressions as well as characterizing their statistical properties. Using the post-detection SNR and ODF properties, we develop upper and ad-hoc tight bounds on the error probabilities, which illustrate how these “orthogonal” spatial modulations mitigate the MDL under both the ML and ZF detection schemes. The obtained properties also allow us to propose a modification to the detection algorithm such that it still achieves an essentially optimal performance but at a much smaller cost than exhaustive or tree search algorithms. The theoretical results are validated numerically and by simulations.

Machine Learning Based Blind Decoding for Space–Time Line Code (STLC) Systems

In this correspondence paper, a novel machine learning (clustering) based blind decoding method is proposed for the space-time line code (STLC) systems without the information of modulation size and channels. The number of clusters, which is equivalent to the modulation size, is estimated from the received signals by using a k-mean cluster validation metrics, such as silhouette score and Davies-Bouldin index, and the cluster indices are directly mapped to the transmitted binary information bits. To improve the clustering performance, received signal normalization and the initial centroids of the clusters are designed by exploiting the combined STLC signal structure. From the numerical results, it is verified that the proposed blind decoding method can achieve near-coherent decoding performance with either small-size modulation, low noise at the receiver, or a large number of transmit antennas.

Performance analysis of bi-directional relay selection strategy for wireless cooperative communications

This paper proposes a new two-way double-relay selection strategy for wireless cooperative communication systems with its bit error rate (BER) performance analysis. In this work, two relays are first chosen to maximize the overall system performance in terms of BER. Then, either the two-phase or three-phase protocol is performed to achieve two-directional communications between the communicating terminals through the selected relay nodes that apply orthogonal space-time coding (STC) scheme in a distributed fashion to improve the overall system performance with linear decoding complexity. In other words, the proposed strategy offers an improvement in the reliability of the system and enjoys very low decoding complexity by enabling a symbol-wise decoder. On the other hand, another improvement in the performance at the communication terminals is achieved by performing a network coding method at the selected relay nodes. Furthermore, we offer also analytical approximation of the BER performance for the proposed strategy where the simulation results match perfectly the analytical ones. From the simulation results section, the proposed strategy shows a substantially improved BER performance as compared to the current ones.

Space-time coding waveform design for MIMO radar transmit beamforming with minimum MFL

In this paper, we utilize a space-time coding (STC) scheme to synthesize the multiple-input multiple-output (MIMO) radar transmit beampattern and meanwhile consider the matched filtering loss (MFL) of equivalent signal in waveform design. To solve the MFL optimization problem, we propose a simulated annealing based (SA-based) algorithm to effectively find the optimal solution of STC waveform matrix. Our STC method for waveform design has suppressed the fluctuation of equivalent signal so that has the advantage of achieving the minimum MFL nearly, compared to the conventional methods for constant-envelope constraint waveform design (e.g. cyclic algorithm (CA) method). Simulation results demonstrate the effectiveness of the proposed algorithm.

Double Full Diversity Massive Unitary Space–Time Codes for MIMO Channels

In this paper, we consider a flat fading noncoherent wireless communication system with double transmitter antennas and massive multiple receiver antennas, in which the channel coherence time is divided into four orthogonal time slots, and these are used within a complete transmission cycle. For such a system, we systematically design a family of noncoherent unitary space–time codes. Then, within this family and with the noncoherent maximum likelihood (ML) detector, we propose the design of an optimal unitary space-time code that minimizes the worst-case pairwise error probability (PEP) subject to a constraint on total transmission bits. A closed-form optimal solution is attained by first characterizing the optimal structure for any fixed bits on each parameter space and then finding an optimal bit assignment that further minimizes the worst-case PEP. Also, asymptotic PEP performance analysis on such an optimal code further shows that it enables full receiver-diversity gain when the number of the receiver antennas goes to infinity, with the increasing rate of the coding gain in terms of signal-to-noise ratio (SNR) being the number of the transmitter antennas. In other words, it also provides full diversity gain, i.e., the product of the number of the receiver antennas and the number of the transmitter antennas, when SNR goes to infinity. Therefore, we call such a code double full diversity code. One of the significant advantages of the proposed optimal design for our considered massive multiple-input multiple-output system is that it has no error floor with SNR increasing. Another significant advantage is that it enables a fast ML detector.

Blind Joint MIMO Channel Estimation and Decoding

We propose a method for multiple-input multiple-output (MIMO) decoding when channel-state information (CSI) is unknown to both the transmitter and receiver. The proposed method requires some structure in the transmitted signal for the decoding to be effective, in particular that the underlying sources are drawn from a hypercubic space. Our proposed technique fits a minimum volume parallelepiped to the received samples. This problem can be expressed as a non-convex optimization problem that can be solved with high probability by gradient descent. Our blind decoding algorithm can be used when communicating over unknown MIMO wireless channels using either binary phase-shift keying or MPAM modulation. We apply our technique to jointly estimate MIMO-channel gain matrices and decode the underlying transmissions with only knowledge of the transmitted constellation and without the use of pilot symbols. Our results provide theoretical guarantees that the proposed algorithm is correct when applied to MIMO systems with four or fewer transmit antennas. Empirical results show small sample size requirements, making this algorithm suitable for block-fading channels with coherence times typically seen in practice. Our approach has a loss of less than 3 dB compared to zero forcing with perfect CSI, imposing a similar performance penalty as space-time coding techniques without the loss of rate incurred by those techniques.

Pulse Position-Based Spatial Modulation for Molecular Communications

Multiple-input-multiple-output (MIMO) approaches have been recently introduced to molecular communications (MC) in order to increase the communication throughput. For MIMO systems, index modulation (IM) suggests encoding information bits using the indices of the available antennas, rather than employing spatial multiplexing or performing other space-time coding schemes. Recent works have shown that utilizing the available MIMO antennas with the IM-based approaches improve the error performance of a molecular MIMO system, courtesy of molecular-IM’s robustness against inter-symbol interference and inter-link interference (ILI). Inspired by IM’s prospects on the MC, this letter proposes a novel family of the IM-based schemes to the MC realm. The proposed schemes combine position-based constellations with antenna indices to encode bits in and yield reliable error performances due to their robustness against the ILI.

MIMO multi-relay systems with tensor space-time coding based on coupled nested Tucker decomposition

In this paper, we propose a two-hop MIMO multi-relay system with tensor space-time coding (TSTC) at the source and the relays. The multiple relays use orthogonal channels (parallel relaying) to increase the diversity order, assuming that all the relays can communicate directly with the destination. The signals received at destination form a fifth-order tensor that satisfies a new tensor model, called coupled nested Tucker decomposition (CNTD). This model is a generalization of the nested Tucker decomposition (NTD) and extends the coupling concept, introduced for PARAFAC models, to Tucker-based decompositions. The CNTD consists of a coupling of NTD models that share a common factor, resulting in the concatenation of a generalized Tucker model with a Tucker one. This tensor modeling is exploited to derive a semi-blind receiver for jointly estimating the information symbols and the channels. The uniqueness property of the proposed tensor model and the identifiability conditions of the receiver are established. Monte Carlo simulation results are provided to illustrate the effectiveness of the proposed system and the advantage of exploiting cooperative diversity based on tensor modeling.

A Simple ML Detection for Coded Generalized Frequency Division Multiplexing in MIMO Channels

Generalized frequency division multiplexing (GFDM) is a promising multicarrier scheme, which has shown to be a good candidate to meet the rising demands of 5G networks. The inherent self-interference of GFDM prohibits the direct utilization of maximum likelihood (ML) detection of space-time coding (STC) in multi-input multi-output (MIMO) channels. Recently, a modified version of GFDM, called coded GFDM (CGFDM), has been proposed, which solves the problem of interference mitigation. In this paper, a simple near-optimal ML detection of Alamouti STC is proposed for MIMO CGFDM. Simulation results show that without sacrificing bandwidth efficiency, the proposed scheme outperforms the current MIMO GFDM detection techniques in terms of BER and computational complexity.

Multi-dimensional ambiguity function for subarray-based space-time coding radar

Space-time coding radar has been recently proposed and investigated. It is a radar framework which can perform transmit beamforming at the receiver. However, the range resolution decreases when the number of the transmit element increases. A subarray-based space-time coding (sub-STC) radar is explored to alleviate the range resolution reduction. For the proposed radar configuration, an identical waveform is transmitted and it introduces a small time offset in different subarrays. The multidimensional ambiguity function of sub-STC radar is defined by considering resolutions in multiple domains including the range, Doppler, angle and probing direction. Analyses on properties of the multi-dimensional ambiguity function of the sub-STC radar with regard to the spatial coverage, resolution performance and low sidelobes are also given. Results reveal that the range resolution and low sidelobes performance are improved with the proposed approach.

OAM Mode Selection and Space–Time Coding for Atmospheric Turbulence Mitigation in FSO Communication

Orbital angular momentum (OAM) multiplexing has recently received considerable interest in free space optical (FSO) communications. Propagating OAM modes through free space may be subject to atmospheric turbulence (AT) distortions that cause intermodal crosstalk and power disparities between OAM modes. In this paper, we are interested in multiple-input-multiple-output (MIMO) coherent FSO communication systems using the OAM. We propose a selection criterion for the OAM modes to minimize the impact of the AT. To further improve the obtained performance, we propose a space-time (ST) coding scheme at the transmitter. Through numerical simulations of the error probability, we show that the penalty from AT is completely absorbed for the weak AT regime, and considerable coding gains are obtained in the strong AT regime.

Closed-Form Receiver for Multi-Hop MIMO Relay Systems with Tensor Space-Time Coding

A multi-hop multi input multi output (MIMO) relay system with tensor coding at the source and relays is proposed in this paper. The tensor of signals received at destination satisfies a high-order nested Tucker decomposition (HONTD), generalizing an existing tensor decomposition. Exploiting this HONTD model allows to derive a closed-form semi-blind receiver for jointly estimating the information symbols and the individual channels. Identifiability conditions and ambiguity relations are derived. Monte Carlo simulation results are provided to evaluate the performance of the proposed receiver in terms of channels and symbols estimation, and the impact of the number of relays is illustrated.

Galois extensions, positive involutions and an application to unitary space-time coding

We show that under certain conditions every maximal symmetric subfield of a central division algebra with positive unitary involution \begin{document}$ (B, \tau) $\end{document} will be a Galois extension of the fixed field of \begin{document}$ \tau $\end{document} and will real split \begin{document}$ (B, \tau) $\end{document} . As an application we show that a sufficient condition for the existence of positive involutions on certain crossed product division algebras over number fields, considered by Berhuy in the context of unitary space-time coding, is also necessary, proving that Berhuy's construction is optimal.

Diagonal Space Time Block Coded Spatial Modulation

In this paper, a new Spatial Modulation (SM) scheme, called Diagonal Space Time Coded Spatial Modulation (DS-SM), is designed by embedding the Diagonal Space Time Code in SM. The DS-SM scheme still inherits advantages of SM while enjoying further benefits from spatial constellation (SC) designs. Based on rank and determinant criteria, a new set of four SC codewords is proposed for the DS-SM system with 4 transmit antennas to achieve the fourth-order diversity. Then a general design procedure for an even number of transmit antennas, larger than 4, is developed by cyclically shifting two rows of the SC codewords. Simulation results show that DS-SM surpasses several existing SM schemes at the same spectral efficiency and antenna configuration. DS-SM also exhibits better performance over the benchmark systems under spatially correlated channels. Complexity of DS-SM is also analyzed and compared with other SM schemes.

Bandwidth Efficiency Improvement for Differential Alamouti Space-Time Block Codes Using M-QAM

We propose a technique that enhances the bandwidth efficiency of the two transmit antenna differential space-time block code (DSTBC) by use of space-time block code (STBC) expansion and trellis coding. STBC expansion is realized by expanding the conventional Alamouti STBC using unitary matrix transformation. This is followed by trellis code-aided mapping of additional bits to space-time codes of the expanded set. Trellis code-aided mapping of additional bits enhances the bandwidth efficiency of the proposed DSTBC scheme. The proposed scheme sends more information bits in each transmitted space-time code than the conventional differential detection-aided DSTBC (CDD-DSTBC) scheme, and yet retains the same error performance. For each additional bit sent with the transmitted space-time codeword, the proposed scheme using 16QAM achieves a 12.5% increase in bandwidth efficiency, while the scheme using 64QAM realises an 8.3% increase. Simulation results demonstrate that the error performance of the proposed scheme tightly matches that of CDD-DSTBC with improvement in bandwidth efficiency. The bandwidth efficiency is enhanced at the expense of a moderate increase of the computational complexity at the receiver.

Differential Space-Time Coding Dispensing With Channel Estimation Approaches the Performance of Its Coherent Counterpart in the Open-Loop Massive MIMO-OFDM Downlink

In this paper, we propose a simple yet powerful mapping scheme that converts any conventional square-matrix-based differential space-time coding (DSTC) into a nonsquare-matrix-based DSTC. This allows DSTC schemes to be used practically in open-loop large-scale multiple-input multiple-output scenarios. Our proposed scheme may be viewed as the differential counterpart of coherent spatial modulation (SM), of the generalized SM, of Bell Laboratories layered space-time architecture, and of subcarrier-index modulation. The fundamental impediment of the existing DSTC schemes is the excessive complexity imposed by the unitary constraint. Specifically, the transmission rate of conventional DSTC schemes decays as the number of transmit antennas increases. Our proposed scheme eliminates this impediment and thus achieves a significantly higher transmission rate. We introduce four novel construction methods for the nonsquare codewords, some of which include an arbitrary number of nonzero elements in each codeword column. Our analysis shows that the proposed encoding technique reduces the complexity of both the inverse Fourier transform and the detection processes. Our proposed scheme is shown to approach the performance of its coherent counterpart for low-mobility scenarios, where the number of transmit antennas is increased up to 256.

A New Approach to Space-Time Coding through Gram-Schmidt Procedure

A New Approach to Space-Time Coding through Gram-Schmidt Procedure

A Novel Robust and Low-Complexity Spacetime Codes for Industry 4.0 Systems

This paper proposes different robust and low-complexity space time codes which provide more reliability for industrial automation. An innovative synchronized uplink system configuration for an Industrial Environment is proposed. Mathematical framework for estimating the channel phase of each Slave Node (SN) is developed. Furthermore, the channel is practically estimated based on an innovative method using parallel sequence spread spectrum (PSSS) implemented in Universal Software Radio Peripheral (USRP). The proposed space time codes are applied in the uplink of an industrial communication system where the channel is modelled using Quasi Deterministic Radio Channel Generator (Quadriga) which follows a geometry-based stochastic approach. Simulation results exposed that the proposed codes surpass Alamouti code for Industrial Automation. The bit error rate (BER) performance demonstrates that the achieved coding gain for the proposed codes is higher than Alamouti code leading to more robust communication. Furthermore, a low complexity decoders based on minimum mean squared error (MMSE) and zero forcing (ZF) algorithms are designed at the receiver side. The proposed codes give a predominant execution against the state-of-the-art space time codes for Industry 4.0.