Design Of Space-time Codes Research Articles

Space-Time Coding Design for RIS-Assisted Integrated Sensing and Communication System

Space-Time Coding Design for RIS-Assisted Integrated Sensing and Communication System

A Better Than Alamouti OSTBC for MIMO Backscatter Communications

Backscatter communications have received increasingly attention in Internet of Things (IoT) due to its advantages of requiring no internal battery and almost zero maintenance. However, the drawback of backscatter communications is that, its channel fades deeper than conventional channel. To improve the performance, multiple-input multiple-output (MIMO) techniques have been investigated for backscatter communications. By considering duty cycle, a particular behavior of backscatter communications, as a new performance criterion, we propose a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2 \times 2$ </tex-math></inline-formula> orthogonal space-time block code for MIMO backscatter communications. The new code is a rotation of the classical Alamouti code, and in MIMO backscatter channels, this simple rotation will incur an improved duty cycle for both linear and nonlinear energy harvester models, as well as a same, or even better symbol error rate performance. We provide both rigorous mathematical proofs and numerical simulations to show the above results. An interesting thing is that, this new code does not outperform Alamouti code in conventional MIMO channels, which indicates that the space-time code design criteria for conventional channels is not the optimal one for backscatter channels, and existing space-time codes should be reconsidered and/or redesigned to achieve a higher performance in MIMO backscatter communications.

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.

Distance Hardening in Large MIMO Systems

Asymptotic analysis plays an important role in the performance evaluation and technology design of large multiple-input multiple-output (MIMO) systems. This paper investigates an asymptotic property of large MIMO systems, called distance hardening . It involves distance metrics defined in terms of many factors, such as the channel matrix and the difference matrix of two arbitrary transmitted codewords. The asymptotic property is revealed by the use of the Chernoff bounding method and expressed in an analogous way to the well-known channel hardening. More specifically, we first derive Chernoff bounds on the tail probabilities of distance metrics, in which we are interested. Then, we formulate the asymptotic property based on a generalized definition of the hardening phenomena by referring to a formal definition of the channel hardening. The distance hardening is shown to have implications for space-time code design, MIMO detection, and millimeter wave MIMO systems. Numerical simulations are conducted to verify our theoretical development.

Multi-Resolution Multicasting Over the Grassmann and Stiefel Manifolds

We consider the design of space-time codes for the multiple-input multiple-output multicast communication systems with two classes of receivers. The first class comprises high-resolution (HR) receivers which have access to reliable channel state information (CSI) and can perform coherent detection, and the second class comprises low-resolution (LR) receivers which do not have access to CSI and can only perform non-coherent detection. We propose a layered encoding structure in which LR information available to both classes of receivers is encoded using Grassmannian constellations, and an incremental component, which is available only to the HR receivers, is encoded in the particular bases of the transmitted Grassmannian constellation points, thereby giving rise to constellations on the Stiefel manifold. The proposed structure enables reliable coherent communication of the HR information without compromising the reliability with which the basic LR information is non-coherently communicated. To effect rate-efficient communication of the incremental, HR layer, we use optimization methods on the Stiefel manifold to develop a novel technique for designing the unitary constellations directly. This approach alleviates the restriction imposed by the traditional techniques in which unitary space-time codes are constructed from scalar constellations. As such, this approach enables better control of the distance spectrum of the developed constellations and more effective utilization of the degrees of freedom that underlie the Stiefel manifold. For the LR receivers, we use maximum likelihood detection, whereas for the HR receivers, we develop a computationally-efficient two-step sequential detector which detects the LR information prior to detecting the incremental component superimposed on it. The detectors and the layered structure with the aforementioned constellations enable full diversity and maximum degrees of freedom to be achieved on the Grassmann and Stiefel manifolds.

Space-Time Coding: an Overview

This work provides an overview of the fundamental aspects and of some recent advances in space-time coding (STC). Basic information theoretic results on Multiple-Input Multiple-Output (MIMO) fading channels, pertaining to capacity, diversity, and to the optimal Diversity Multiplexing Tradeoff (DMT), are reviewed. The code design for the quasi-static, outage limited, fading channel is recognized as the most challenging and innovative with respect to traditional “Gaussian” coding. Then, a survey of STC constructions is presented. This culminates with the description of families of codes that are optimal with respect to the DMT criterion and have error performance that is very close to the information theoretic limits. The paper concludes with some important recent topics, including open problems in STC design.

Random network coding in MIMO system

Random network coding (RNC) has emerged as a promising technology. In this paper, we seek to answer the question that how RNC benefits cellular systems. A novel RNC-based space–time code (STC) scheme is proposed for the data transmission in MIMO system. In this scheme, RNC is integrated with the STC design for MIMO system. And then, the improved diversity order and multiplexing gain of the RNC-based STC scheme are analyzed and derived. This RNC-based STC scheme can also have benefit of RNC on some practical applications. After that, a general RNC-based STC protocol which describes the data transmission flow in practical system is designed for MIMO transmission. Finally, the performance of RNC-based STC scheme is evaluated through both link-level and system-level simulations. The simulation results show that RNC can provide extra diversity gain, multiplexing gain, or reduce the decoding complexity, and improve the bandwidth efficiency and user fairness in cellular system with MIMO.

A Space-Time Code Design for Omnidirectional Transmission in Massive MIMO Systems

Omnidirectional space-time coding has been proposed recently for massive multiple-input multiple-output (MIMO) systems to broadcast common information. In these systems, signals across all transmit antennas have constant power and their discrete Fourier transforms have constant power as well, where the number of discrete frequencies is the number of transmit antennas. When the number of transmit antennas is large, i.e., it is a massive MIMO system, signals received at these discrete angles have constant mean power at any instant time. Furthermore, spatial diversity can be achieved. In this letter, we propose a different design of such a transmission, where the sum of received signal powers in a few consecutive time slots is constant at any angle (not just discrete angles). The other two properties mentioned above, namely, constant transmission power across antennas at any instant time and achieving spatial diversity, are still maintained. Furthermore, it has the fast symbol-wise maximum-likelihood decoding.

Space Time Coding Techniques in MIMO: A Review

This paper explore the basic approaches used for of space-time coding technique. The emerging field of wireless evaluation such as Multiple Input Multiple Output (MIMO) and Antenna diversity plays an important role in space-time code design. Spatial diversity techniques by the means of multiple transmitting and receiving antennas and the performance of MIMO systems has been discussed for different space-time coding structures such as Alamouti, OSTBC3, OSTBC4 etc. Space-time coding techniques rely on the construction of matrices and the signal is to be transmitted at different period of time from multiple of antennas. These code structures utilises the diversity schemes to improve the bit error rate and thus to achieve higher data rates without bandwidth expansion. Keywords: BER, Multiple Input Multiple Output (MIMO), OSTBC3, OSTBC4, SNR, Spatial Diversity, STBC, STTC

Evaluation of Bit Error Probability for CPM MIMO Systems in Rayleigh Channel

Space time codes (STC) design employing continuous phase modulation (CPM) is well suitable for a multi-antenna system with low power and compact spectrum. Although STC design criteria for CPM MIMO system have been developed to date, the evaluation of performances with CPM MIMO system requires more general results like linear modulations such as PSK, QAM and so on. In this paper, Laurent decomposition is first applied and the conclusions of PAM signals in MIMO systems are extended to CPM MIMO systems. Thereby the average exact bound of bit error probability is derived. Further, space time block codes with CPM MIMO are introduced and its decoding is simplified for Monte-Carlo simulation. Finally, analytical and simulated results have confirmed the performances of CPM MIMO system.

Threaded Space Time Code Design for CPM with Joint Decoding

In the letter, a system of continuous phase modulation (CPM) with threaded space time codes (TSTC) is proposed for multiple-input multiple-output systems. In the system, source bits are coded via outer coder of Reed Solomon (RS). The codeword of which is suitable for TSTC design. Then inner coder mainly converts binary symbols into M-ary symbols for purpose of CPM. At receiver, Joint soft decoding approach is considered. Finally simulation results are provided for VBLAST, DBLAST, and TSTC as comparison.

Algebraic space-time codes based on division algebras with a unitary involution

In this paper, we focus on the design of unitary space-time codes achieving full diversity using division algebras, and on the systematic computation of their minimum determinant.We also give examples of such codes with high minimum determinant. Division algebras allow to obtain higher rates than known constructions based on finite groups.

Space–Time Trellis Codes for Two-Way Relay MIMO Channels With Single-Antenna Relay Nodes

In this paper, the analysis and design of space-time trellis codes (STTCs) for two-way relay channels (TWRCs) with multiantenna source and destination and single-antenna relay nodes, assuming perfect channel state information (CSI) at the destination nodes, is considered. We derive a pairwise error probability (PEP) expression for the performance of STTCs in this type of channels. A simple upper bound on the PEP is then derived and used to find optimum STTCs. We prove that the designed STTCs based on the derived criterion achieve full diversity and significant coding gain in TWRCs, particularly at high signal-to-noise ratios (SNRs).

Space-Time Block Code Designs for Two-User MIMO X Channels

In this paper, we study space-time block code (STBC) designs for two-user MIMO X channels to achieve full diversity when the inter-user interference is cancelled by the group zero-forcing receiver. To do so, we first propose a design criterion and then propose a systematic design to satisfy the criterion so that it achieves full diversity. The code rate approaches one when encoding length gets large. We prove that full diversity can be achieved by the proposed STBC without the channel information at the transmitters. Simulation results are provided to demonstrate the theory.

Design of distributed collaborative space‐time block codes for two‐way relaying networks

Utilising the recently-developed unique factorisation of signals and distributed Alamouti coding, a distributed collaborative space-time block code design is presented for a two-way amplify-and-forward (AF) relaying network, where all nodes are equipped with a single antenna. Two asymptotic pairwise error probability (PEP) formulae are firstly derived for both fixed-gain AF and variable-gain AF over Rayleigh channels with the maximum-likelihood detector. Then, subject to the constraints on a fixed transmission bit rate and unity average transmission energy, the optimal constellation combinations with the optimal coefficients are attained by minimising the dominant term of PEP. It is shown that the PEP and the average block error rate of the newly-designed code are superior to those of the conventional distributed Alamouti code while the prior still has linear-decoding complexity.

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

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

Analysis of Different Space Time Block Codes with Linear Receiver for Various Modulation Technique

Space-time coding is designed with two-dimensional signal matrices to be transmitted over a period of time from a number of antennas. The structure of the signal enables to exploit diversity in the spatial and temporal dimensions to obtain improved bit error performance and higher data rates without bandwidth expansion. So it is clear that transmit diversity plays an integral role in space-time code design. The objective of this paper is to provide the description of different type of space time block codes and to provide the performance analysis of these codes without channel knowledge at the transmitter with different schemes for four transmit and one receive antenna. Here a new space time block code is proposed and compared with other codes.

Energy-Efficient Full Diversity Collaborative Unitary Space-Time Block Code Designs via Unique Factorization of Signals

In this paper, a novel concept called a uniquely factorable constellation pair (UFCP) is proposed for the systematic design of a noncoherent full diversity collaborative unitary space-time block code by normalizing two Alamouti codes for a wireless communication system having two transmitter antennas and a single receiver antenna. It is proved that such a unitary UFCP code assures the unique identification of both channel coefficients and transmitted signals in a noise-free case as well as full diversity for the noncoherent maximum likelihood receiver in a noise case. To further improve error performance, an optimal unitary UFCP code is designed by appropriately and uniquely factorizing a pair of energy-efficient cross quadrature amplitude modulation (QAM) constellations to maximize the coding gain subject to a transmission bit rate constraint. After a deep investigation of the fractional coding gain function, a technical approach developed in this paper to maximizing the coding gain is to carefully design an energy scale to compress the first three largest energy points in the corner of the QAM constellations in the denominator of the objective as well as carefully design a constellation triple forming two UFCPs, with one collaborating with the other two so as to make the accumulated minimum Euclidean distance along the two transmitter antennas in the numerator of the objective as large as possible, and at the same time, to avoid as many corner points of the QAM constellations with the largest energy as possible to achieve the minimum of the numerator. In other words, the optimal coding gain is attained by intelligent constellations collaboration and efficient energy compression. Computer simulations demonstrate that error performance of the optimal unitary UFCP code presented in this paper outperforms those of the differential code and the signal-to-noise-ratio-efficient training code.

Single‐symbol decodable space‐time block code for multi‐input–multi‐output systems with four transmit antennas

This study presents an orthogonal design of space-time block code (STBC) that is single symbol decodable and enables full diversity and full rate transmission in a quasi-static channel environment. In the proposed scheme, full diversity is achieved by use of constellation rotation and co-ordination interpolation as is the case for the co-ordinate interleaved orthogonal design, whereas the transmission matrix of the proposed code consists of orthogonal columns with all non-zero elements, alleviating the concern about high peak-to-average power ratio. In particular, the proposed code offers lower complexity of channel estimation, and exhibits lower symbol error rate than the conventional quasi-orthogonal STBC when an maximum-likelihood decision-directed channel estimator is assumed. The advantages of the proposed code over the conventional codes are demonstrated through computer simulations. In addition, the selection of the angle of rotation for the proposed design is also presented, regarding the impact of channel estimation error.

Space-Time Code Design for MIMO Detection Based on Kullback-Leibler Divergence

The focus of the paper is on the design of space-time codes for a general multiple-input, multiple-output detection problem, when multiple observations are available at the receiver. The figure of merit used for optimization purposes is the convex combination of the Kullback-Leibler divergences between the densities of the observations under the two hypotheses, and different system constraints are considered. This approach permits to control the average sample number (i.e., the time for taking a decision) in a sequential probability ratio test and to asymptotically minimize the probability of miss in a likelihood ratio test: the solutions offer an interesting insight in the optimal transmit policies, encapsulated in the rank of the code matrix, which rules the amount of diversity to be generated, as well as in the power allocation policy along the active eigenmodes. A study of the region of achievable divergence pairs, whose availability permits optimization of a wide range of merit figures, is also undertaken. A set of numerical results is finally given, in order to analyze and discuss the performance and validate the theoretical results.