Linear Dispersion Codes Research Articles

Constant-Envelope Space-Time Shift Keying

From the power amplifier's perspective, the peak-to-average power ratio (PAPR) is of essential importance, especially for both single-RF and reduced-RF multiple-input multiple-output (MIMO) single-carrier schemes. In this context, many of the diversity-oriented index modulation schemes—including the full-RF space-time shift keying (STSK) and the single-RF asynchronous STSK (ASTSK) that invoke randomized signals—exhibit eroded energy-efficiency. To circumvent this problem, we propose a holistic signal construction approach for single-RF, reduced-RF, and full-RF MIMO setups, which always achieve both perfect 0 dB PAPR transmission and inter-channel interference (ICI) free signal detection. More explicitly, first of all , we conceive a new family of single-RF constant-envelope ASTSK (CE-ASTSK), which is capable of substantially outperforming conventional spatial modulation (SM) in both Rayleigh fading and Ricean fading associated with increasing line-of-sight (LoS) power. Second , we propose the new full-RF CE-STSK concept, which is capable of outperforming the orthogonal space-time block codes (STBCs) without either increasing PAPR or imposing ICI. This is particularly beneficial because the conventional linear dispersion code (LDC) approaches always compromise the orthogonality of STBC and hence impose ICI. Third , we also conceive the reduced-RF versions of CE-STSK, which outperform both generalized spatial modulation (GSM) and space-time block coded spatial modulation (STBC-SM). Finally , the proposed schemes are intrinsically amalgamated with turbo detection assisted channel coding, which further confirms the superiority of CE-ASTSK and CE-STSK over SM and STBC in the single-RF and full-RF modes, respectively.

A Novel Linear Antenna Synthesis for Linear Dispersion Codes Based on an Innovative HYBRID Genetic Algorithm

As far as taking-away of the symmetry constraints is concerned, as a scientifically symmetry problem, the global synthesis for antenna arrays that produce the desired radiation pattern is also a highly nonlinear optimization issue in fact. Besides this, the built criteria offer the reasonable power patterns. The consequent synthesis could be implemented by looking for a nominal pattern. When the criteria are already sufficient, it can simply do the whole synthesis process. To utilize multiple antennae, a method to choose a transmit antenna for the linear dispersion codes (LDC-TAS) is implemented in this paper. The authors used the max–min-post- signal to noise ratio (SNR) criteria to select these optimal transmitting antennae while this dependent, linear receiver is applied to the varying and slow channel. The simulated results illustrate that this max–min-post-SNR criterion outperforms the Bell Labs layered space time transmitting antenna selection (BLAST-TAS) applying the same spectral efficiency than space–time block codes (STBC)-TAS in the environment with low SNR. Furthermore, once the M antennae are selected under the selection criteria, a max–min-post-SNR rule, a novel linear antenna synthesis to linear dispersion codes on the basis of an innovative HYBRID (of mixed characters or solutions) genetic algorithm has been presented and evaluated to formulate and address the optimal problem to non-uniformly spaced and linear arrays. The restricted side-lobes level, the main-lobe width, and the shaped beam pattern are contemporarily concerned via maximizing a pretty suitable cost function through the innovational advanced genetic-algorithm-based algorithm. The method proposed in this paper can provide flexibility and a simple insertion of the a priori knowledge under a small computing pressure. At last, a computing simulation is completed well and the results are shown. It should be noticed that some extensions of the presented method could also be easily utilized without an obvious increase in the algorithm complexity.

Performance Analysis of Joint Relay and Transmit–Receive Antenna Selection for Low Density Parity Check-Asynchronous Distributed Space Time Block Coded Cooperative Diversity System

In this work we propose a joint relay and transmit–receive antenna selection method for amplify and forward asynchronous distributed space time block coded (ADSTBC) system. To the LDPC coded signal received from the source at the relays, we apply linear dispersion codes which are optimized over the delay profile of the system to produce the ADSTBC. Selection of the best transmit–receive antenna pair between source and selected relays, and that of between the selected relays and destination is done on the basis of instantaneous signal to noise ratio (SNR) of the respective paths. The relays and transmit-receive antenna pairs are selected by maximizing the end-to-end instantaneous SNR. Performance analysis of the system is done on the basis of pair wise error probability and outage probability (Pout).

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.

Two Decades of MIMO Design Tradeoffs and Reduced-Complexity MIMO Detection in Near-Capacity Systems

A pair of salient tradeoffs have driven the multiple-input multiple-output (MIMO) systems developments. More explicitly, the early era of MIMO developments was predominantly motivated by the multiplexing-diversity tradeoff between the Bell Laboratories layered space-time and space-time block coding. Later, the linear dispersion code concept was introduced to strike a flexible tradeoff. The more recent MIMO system designs were motivated by the performance-complexity tradeoff, where the spatial modulation and space-time shift keying concepts eliminate the problem of inter-antenna interference and perform well with the aid of low-complexity linear receivers without imposing a substantial performance loss on generic maximum-likelihood/max a posteriori -aided MIMO detection. Against the background of the MIMO design tradeoffs in both uncoded and coded MIMO systems, in this treatise, we offer a comprehensive survey of MIMO detectors ranging from hard decision to soft decision. The soft-decision MIMO detectors play a pivotal role in approaching to the full-performance potential promised by the MIMO capacity theorem. In the near-capacity system design, the soft-decision MIMO detection dominates the total complexity, because all the MIMO signal combinations have to be examined, when both the channel’s output signal and the a priori log-likelihood ratios gleaned from the channel decoder are taken into account. Against this background, we provide reduced-complexity design guidelines, which are conceived for a wide-range of soft-decision MIMO detectors.

Impact of Cooperative Space-Time/Frequency Diversity in OFDM Based Wireless Sensor Systems over Mobile Multipath Channels.

Cooperative linear dispersion coding (LDC) can support arbitrary configurations of source nodes and destination nodes in virtual multi-input multi-output (MIMO) systems. In this paper, we investigate two spatial diversity applications of cooperative LDC for orthogonal frequency division multiplexing (OFDM) based wireless sensor systems in order to achieve space-time/frequency (ST/SF) diversity gains when transmitting over time-/frequency-selective fading channels. Cooperative LDC-aided ST/SF-OFDM is flexible in configuring various numbers of cooperative source nodes and time-slots or frequency-tones. Our results show that the ST-OFDM scheme is sensitive to exploiting diversity gains, subject to the impact of varying channel Doppler spreads; while the performance of SF-OFDM is mainly subject to delay spread. Specifically, when the system involves more than two cooperative nodes, the cooperative LDC-aided ST/SF-OFDM outperforms the cooperative orthogonal block codes (e.g. Tarokh's codes) aided ST/SF-OFDM, when communicating over a higher Doppler/delay spread.

Distributed Concatenated Recursive Alamouti-Circulant STBC for Two-Way Multi-Relay Networks

A general distributed multi-antenna two-way relaying network with multiple relays is considered in this paper. We first obtain a tight lower bound of pairwise error probability (PEP) of a maximum likelihood detector for the general distributed linear dispersion code for a half-duplex amplify-and-forward two-way relaying network (TWRN) consisting of two sources with each having single antenna and $N$ relays with each having two antennas. Furthermore, by jointly considering signal precoding at the sources and signal processing at the relays, a general distributed concatenated recursive Alamouti-circulant space-time block code is proposed for the considered TWRNs. Our design ensures that the equivalent channel matrices at both source nodes are the so-called the recursive Alamouti-circulant matrices, with each block being a product of the two Alamouti channel matrices. Based on a lower–upper bound strategy and an induction method, asymptotic PEP formula is attained to show that given the optimal angle rotation matrix and the precoding matrix, the code can meet the lower bound of the diversity gain, as well as the maximum coding gain. In addition, the proposed rate one code turns to be effectively decodable.

Diversity‐multiplexing trade‐off of linear dispersion coded multi‐input–multi‐output systems

In this study, the authors study the diversity-multiplexing trade-off (DMT) of multi-input–multi-output (MIMO) systems in which linear dispersion (LD) codes are used. They first focus on an LD-coded 2 × 2 MIMO systems at the high signal-to-noise ratio (SNR) regime. By using the joint eigenvalue density, the outage probability is presented in a very compact expression, which establishes the DMT framework at this regime. Simulation results show that the derived expression for the outage probability is sufficiently accurate at high SNR regimes but less accurate in the transition region. Finally, for the special case of multi-input–single-output, they derive both the outage probability and the DMT framework inexact and closed form formulas at all SNRs, including finite SNRs.

Performance analysis of randomised space–time block codes for amplify‐and‐forward cooperative relaying

In recent studies (Verde et al.), capitalising on randomised space–time block coding (STBC), a decentralised coding method has been developed for amplify-and-forward (A&F) relays, which can closely achieve the performance of a centralised A&F linear dispersion coding (LDC) scheme and notebly outperform the decentralised A&F LDC counterpart, by requiring a reduced amount of signalling and processing overhead. However, A&F relaying process introduces correlation among the noise samples at the destination which, along with the non-Gaussian nature of the relaying channel and the fact that the relays are located in different positions, significantly complicates the performance analysis of the system. In this study, a theoretical performance analysis of the randomised STBC A&F rule is carried out in terms of average pairwise error probability to evaluate its attainable diversity order. Numerical results are provided to corroborate the analytical findings.

Study on an Adaptive Distributed Linear Dispersion Code

An adaptive distributed linear dispersion code is proposed in this article. In the first place, each relay code selects modulation type adaptively according to channel capacity. Then the candidate dispersion matrixes are selected based on the channel state weight. Finally the best transmission scheme is selected according to the system information rate and reliability. Simulation results show that the proposed adaptive coding scheme gives a more good performance.

Novel Distributed Quasi-Orthogonal Space-Time Block Codes for Two-Way Two-Antenna Relay Networks

A half-duplex amplify-and-forward two-way relay network consisting of two single-antenna sources and N relays with each having two antennas is considered in this paper. For such a system, a tight lower bound of pairwise error probability (PEP) of a maximum likelihood (ML) detector for any distributed linear dispersion code with a fixed average amplifier is derived, revealing that diversity gain function cannot decay faster than ln <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</sup> SNR/SNR <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2N</sup> , where rm SNR is signal to noise ratio. Particularly for the network having two relays, a novel distributed quasi-orthogonal space-time block code (QO-STBC) is proposed with two significant advantages. One is that the equivalent channel matrices at both source nodes turn out to be the block-circulant matrices, with each block being a product of the two Alamouti channel matrices. The other is that the equivalent noises at the both source nodes are Gaussian and white. Therefore, like QO-STBC for a multi-antennas system, the proposed code for the relay system still maintains low-decoding complexity for the ML detector. Asymptotic PEP formula is attained to show that the proposed code enables the optimal diversity gain function, i.e., meeting the lower bound of diversity gain, and the optimal coding gain. In addition, a near optimal power allocation that maximizes the received SNR of the worse link is presented and examined through comprehensive computer simulations for various kinds of asymmetric relay channels.

간섭 제거와 수신 성능 향상을 위한 전처리기법을 적용한 LDC기반의 다중 사용자 다중 입출력 시스템

본 논문에서는 다중사용자 다중입출력 시스템에서 대역폭 효율의 감소 없이 페이딩에 대한 수신 성능을 향상시키는 부호화 알고리듬을 제안한다. 기존의 다중사용자 다중입출력 방식으로 사용되는 공간분할다중화 방식은 페이딩 경로에 취약하며, 이를 극복하기 위한 시공간블록부호화 방식은 전송량이 떨어지는 단점이 있다. 이러한 문제점을 개선하기 위하여 제안 부호화 알고리듬은 페이딩 환경에 강인하고 전송량이 송신 안테나 개수에 비례하여 증가하는 LDC(linear dispersion code) 기법을 이용하여 송신 심벌을 부호화하고, 예측한 채널 이득의 특이값 분해 값을 LDC 부호화 심벌에 전처리하여 성능을 개선한다. 그리고 컴퓨터 모의실험을 통하여 기존 알고리듬과 제안하는 알고리듬의 성능을 비교 평가한다.

Cooperative Performance and Diversity Gain of Wireless Relay Networks

In this paper, the error rate performance and diversity gain of amplify-and-forward (AF) wireless relay networks are studied. The distributed space-time block code (DSTBC) in a synchronous relay network with multiple relay nodes is considered. The distributed linear dispersion code is used at the relays. The symbol (or codeword) error rate is studied in terms of upper and lower bounds through rigorous derivations, and the diversity gain of the DSTBC is derived, for any number of relay nodes. As a corollary, a necessary and sufficient condition is obtained for achieving full cooperative diversity. Arbitrary coding matrices at the relays, path loss and general linear power allocation are considered. Finally, the orthogonal frequency division multiplexing (OFDM)-based space-time transmission scheme in asynchronous cooperative networks is also discussed.

Design of Delay-Tolerant Linear Dispersion Codes

In cooperative communication networks, owing to the nodes' arbitrary geographical locations and individual oscillators, the system is fundamentally asynchronous. This will damage some of the key properties of the space-time codes and can lead to substantial performance degradation. In this paper, we study the design of linear dispersion codes (LDCs) for such asynchronous cooperative communication networks. Firstly, the concept of conventional LDCs is extended to the delay-tolerant version and new design criteria are discussed. Then we propose a new design method to yield delay-tolerant LDCs that reach the optimal Jensen's upper bound on ergodic capacity as well as minimum average pairwise error probability. The proposed design employs stochastic gradient algorithm to approach a local optimum. Moreover, it is improved by using simulated annealing type optimization to increase the likelihood of the global optimum. The proposed method allows for flexible number of nodes, receive antennas, modulated symbols and flexible length of codewords. Simulation results confirm the performance of the newly-proposed delay-tolerant LDCs.

차세대 통신 시스템을 위한 향상된 하이브리드 MIMO 기법

In this paper, a terrestrial transmission system is proposed for the next generation digital television (DTV) system by applying a hybrid multi-input multi-output (MIMO) technology based on linear dispersion codes (LDCs). The digital video broadcasting-2nd generation terrestrial (DVB-T2) system adopted a space time block code (STBC) for improving receive performance. However, the data rate of STBC is not increased in proportion to the transmitter. The hybrid STBC scheme utilizes several STBC transmission blocks for increasing data rate. It is possible to increase the data rate and performance in the receiver by utilizing LDC. The performances of the proposed and conventional hybrid STBC schemes are evaluated through computer simulations.

SCLDGM coded modulation for MIMO systems with spatial multiplexing and space‐time block codes

AbstractWe analyze Multiple‐Input Multiple‐Output (MIMO) coded modulation systems where either Bit‐Interleaved Coded Modulation (BICM) with spatial multiplexing or concatenation of channel coding and Space‐Time Block Codes (STBCs) is used at transmission, assuming iterative Turbo‐like decoding at reception. We optimize Serially‐Concatenated Low‐Density Generator Matrix (SCLDGM) codes (a subclass of LDPC codes) for each system configuration, with the goal of assessing its ability to approach the capacity limits in either ergodic or quasi‐static channels. Our focus is on three relevant STBCs: the Orthogonal Space‐Time Block Codes (OSTBCs) for two transmit antennas (i.e., the Alamouti code), which enables optimum detection with low complexity; the Golden code, which provides a capacity increase with respect to the input constellation; and Linear Dispersion (LD) codes, which enable practical detection in asymmetrical antenna configurations (i.e., more transmit than receive antennas) for cases in which optimum detection is infeasible. We conclude that BICM without concatenation with STBCs is in general the best option, except for Alamouti‐coded 2×1 and Golden‐coded 2×2 MIMO systems. Copyright © 2009 John Wiley &amp; Sons, Ltd.

Hybrid ARQ in Multiple-Antenna Slow Fading Channels: Performance Limits and Optimal Linear Dispersion Code Design

This paper focuses on studying the fundamental performance limits and linear dispersion code design for the MIMO-ARQ slow fading channel. The optimal average rate of well-known HARQ protocols is analyzed. The optimal design of space-time coding for the MIMO-ARQ channel is discussed. Information-theoretic measures are used to optimize the rate assignment and derive the optimum design criterion, which is then used to evaluate the optimality of existing space-time codes. A different design criterion, which is obtained from the error probability analysis of space-time coded MIMO-HARQ, is presented. Examples are studied to reveal the gain of ARQ feedback in space-time coded MIMO systems.

On Soft Decision Value Calculation for Linear-Dispersion Codes with SC-FDMA

The capability of error correction codes is largely dependent on the calculation of soft decision values. In this letter, linear-dispersion (LD) code is applied to single-carrier frequency-division multiple access (SC-FDMA) and the closed-form expression of soft decision values is derived. It is shown that the calculation of soft decision values generally depends on both time and space within an SC-FDMA symbol, as opposed to single-antenna transmission. In addition, a sufficient condition to guarantee the independence from time and space is presented.

Linear Dispersion Codes for Limited Feedback Channels with Feedback Impairments

Linear dispersion codes (LDCs) are an attractive tool for attaining spatial diversity in OFDM systems with multiple transmit antennas. To reach the potential gains, in each situation, the selection of a proper set of codes depends, in general, on the existence of a reliable feedback channel. We propose LDCs for multiple-input multiple-output (MIMO) channels with a fixed amount of feedback. The proposed scheme selects the LDC from a set of LDCs that minimizes the error probability based on the instantaneous channel conditions. The determination of the best set of LDCs is described as a constrained optimization problem. We present several good sets of LDCs, obtained from an optimization algorithm. Through simulation results we show that the proposed schemes outperform previously reported comparable results, yet at the price of increased complexity. We also show the performance gains that can be reached in practice with LDC, by critically evaluating the feedback channel impairments, such as errors and signalling delays, and also considering the effect of signalling overhead on the achievable throughput.

Generalized Space-Time Shift Keying Designed for Flexible Diversity-, Multiplexing- and Complexity-Tradeoffs

In this paper, motivated by the recent concept of Spatial Modulation (SM), we propose a novel Generalized Space-Time Shift Keying (G-STSK) architecture, which acts as a unified Multiple-Input Multiple-Output (MIMO) framework. More specifically, our G-STSK scheme is based on the rationale that P out of Q dispersion matrices are selected and linearly combined in conjunction with the classic PSK/QAM modulation, where activating P out of Q dispersion matrices provides an implicit means of conveying information bits in addition to the classic modem. Due to its substantial flexibility, our G-STSK framework includes diverse MIMO arrangements, such as SM, Space-Shift Keying (SSK), Linear Dispersion Codes (LDCs), Space-Time Block Codes (STBCs) and Bell Lab's Layered Space-Time (BLAST) scheme. Hence it has the potential of subsuming all of them, when flexibly adapting a set of system parameters. Moreover, we also derive the Discrete-input Continuous-output Memoryless Channel (DCMC) capacity for our G-STSK scheme, which serves as the unified capacity limit, hence quantifying the capacity of the class of MIMO arrangements. Furthermore, EXtrinsic Information Transfer (EXIT) chart analysis is used for designing our G-STSK scheme and for characterizing its iterative decoding convergence.