Performance analysis of uplink spatial multiplexing MIMO MT‐CDMA over multipath fading channels

In this paper, we consider multiple‐input multiple‐output (MIMO) multi‐tone code division multiple access (MT‐CDMA) uplink transmission over multipath fading channels. The zero‐forcing vertical Bell Laboratories layered space‐time architecture (ZF V‐BLAST) algorithm and maximum ratio combining scheme are applied at the receiver. The average bit error rate (BER) expression is derived provided that the number of receive antennas is not less than that of transmit antennas. The BER expression is verified by simulations. Numerical results show that the numbers of transmit and receive antennas have significant effects on the BER performance of the considered system. Spatial and path diversity show different capabilities to improve the BER performance. The MIMO MT‐CDMA system based on the ZF V‐BLAST algorithm is capable of achieving a better BER performance and a higher capacity than the conventional MT‐CDMA system. Copyright © 2011 John Wiley & Sons, Ltd.     

Fast turbo codes with space‐time block codes in fast fading channels

In this paper, space‐time block coding has been used in conjunction with Turbo codes to provide good diversity and coding gains. A new method of dividing turbo encoder and decoder into several parallel encoding and decoding blocks is considered. These blocks work simultaneously and yield a faster coding scheme in comparison to classical Turbo codes. The system concatenates fast Turbo coding as an outer code with Alamouti's G2 space‐time block coding scheme as an inner code, achieving benefits associated with both techniques including acceptable diversity and coding gain as well as short coding delay. In this paper, fast fading Rayleigh and Rician channels are considered for discussion. For Rayleigh fading channels, a fixed frame size and channel memory length of 5000 and 10, respectively, the coding gain is 7.5 dB and bit error rate (BER) of 10^?4 is achieved at 7 dB. For the same frame size and channel memory length, Rician fading channel yields the same BER at about 4.5 dB. Copyright © 2013 John Wiley & Sons, Ltd.     

Cross‐layer design for MIMO systems over spatially correlated and keyhole Nakagami‐m fading channels

Cross‐layer design is a generic designation for a set of efficient adaptive transmission schemes, across multiple layers of the protocol stack, that are aimed at enhancing the spectral efficiency and increasing the transmission reliability of wireless communication systems. In this paper, one such cross‐layer design scheme that combines physical layer adaptive modulation and coding (AMC) with link layer truncated automatic repeat request (T‐ARQ) is proposed for multiple‐input multiple‐output (MIMO) systems employing orthogonal space‐‐time block coding (OSTBC). The performance of the proposed cross‐layer design is evaluated in terms of achievable average spectral efficiency (ASE), average packet loss rate (PLR) and outage probability, for which analytical expressions are derived, considering transmission over two types of MIMO fading channels, namely, spatially correlated Nakagami‐m fading channels and keyhole Nakagami‐m fading channels. Furthermore, the effects of the maximum number of ARQ retransmissions, numbers of transmit and receive antennas, Nakagami fading parameter and spatial correlation parameters, are studied and discussed based on numerical results and comparisons. Copyright © 2009 John Wiley & Sons, Ltd.     

Diagonal block space-time code design for diversity and coding advantage over flat fading channels

The potential promised by multiple transmit antennas has raised considerable interest in space-time coding for wireless communications. In this paper, we propose a systematic approach for designing space-time trellis codes over flat fading channels with full antenna diversity and good coding advantage. It is suitable for an arbitrary number of transmit antennas with arbitrary signal constellations. The key to this approach is to separate the traditional space-time trellis code design into two parts. It first encodes the information symbols using a one-dimensional (M,1) nonbinary block code, with M being the number of transmit antennas, and then transmits the coded symbols diagonally across the space-time grid. We show that regardless of channel time-selectivity, this new class of space-time codes always achieves a transmit diversity of order M with a minimum number of trellis states and a coding advantage equal to the minimum product distance of the employed block code. Traditional delay diversity codes can be viewed as a special case of this coding scheme in which the repetition block code is employed. To maximize the coding advantage, we introduce an optimal construction of the nonbinary block code for a given modulation scheme. In particular, an efficient suboptimal solution for multilevel phase-shift-keying (PSK) modulation is proposed. Some code examples with 2-6 bits/s/Hz and two to six transmit antennas are provided, and they demonstrate excellent performance via computer simulations. Although it is proposed for flat fading channels, this coding scheme can be easily extended to frequency-selective fading channels.     

Performance of multi level‐turbo coding with neural network‐based channel estimation over WSSUS MIMO channels

This paper presents the performance of the transmit diversity‐multi level turbo codes (TD‐MLTC) over the multiple‐input–multiple‐output (MIMO) channels based on the wide sense stationary uncorrelated scattering (WSSUS). The multi level‐turbo code (ML‐TC) system contains more than one turbo encoder/decoder block in its structure. At the transmitter side, the ML‐TC uses the group partitioning technique that partitions a signal set into several levels and encodes each level separately by a proper component of the encoder to improve error performance. The binary input sequence is passed through the MLTC encoder and mapped to 4‐PSK and then fed into the transmit diversity scheme for high data transmission over wireless fading channels. At the receiver side, distorted multi‐path signals are received by multiple receiver antennae. WSSUS MIMO channel parameters are estimated by using an artificial neural network and an iterative combiner. Input sequence of the first level of the MLTC encoder is estimated at the first level of MLTC decoder. Subsequently, the other input sequences are computed by using the estimated input bit streams of the previous levels. 4‐PSK two‐level turbo codes are simulated for 2T_x?1R_x and 2T_x?2R_x antenna configurations over WSSUS MIMO channels. Here, TD‐MLTC and its efficient implementations are discussed and simulation results are given. Copyright © 2008 John Wiley & Sons, Ltd.     

Space-time overlays for convolutionally coded systems

We consider the design of space-time overlays to upgrade single-antenna wireless communication systems to accommodate multiple transmit antennas efficiently. We define the overlay constraint such that the signal transmitted from the first antenna in the upgraded system is the same as that in the single-antenna system. The signals transmitted from the remaining antennas are designed according to space-time coding principles to achieve full spatial diversity in quasi-static flat fading channels. For both binary phase-shift keying (BPSK) and quaternary phase-shift keying modulation systems, we develop an algebraic design framework that exploits the structure of existing single-dimensional convolutional codes in designing overlays that achieve full spatial diversity with minimum additional decoding complexity at the receiver. We also investigate a concatenated coding approach for a BPSK overlay design in which the inner code is an orthogonal block code. This approach is shown to yield near optimal asymptotic performance for quasi-static fading channels. We conclude by offering a brief discussion outlining the extension of the proposed techniques to time-varying block fading channels.     

Space–time coding and signal processing for high data rate wireless communications

The information capacity of wireless communication systems can be increased dramatically by employing multiple transmit and receive antennas [Foschini GJ, Gans MJ. On limits of wireless communications in a fading environment when using multiple antennas. Wireless Communications Magazine 1998; 6 311–335. Telatar E. Capacity of Multi‐Antenna Gaussian Channels, Technical Memorandum, AT&T Bell Laboratories, 1995.] An effective approach to increasing data rate over wireless channels is to employ coding techniques appropriate to multiple transmit antennas, that is space–time coding. Space–time codes introduce temporal and spatial correlation into signals transmitted from different antennas, in order to provide diversity at the receiver, and coding gain over an uncoded system. The spatial–temporal structure of these codes can be exploited to further increase the capacity of wireless systems with a relatively simple receiver structure. This paper provides an overview of space–time coding techniques and the associated signal processing framework. Copyright © 2001 John Wiley & Sons, Ltd.     

空时编码OFDM与多维波束形成组合方案

针对MIMO-OFDM系统提出了一种简单灵活的空时分组码与多维特征波束形成组合方案,以充分利用MIMO信道的二阶统计信息。该方案在保证空时编码分集度的同时能最大化系统的编码增益,空时分组码的选取并不受实际发射天线数的限制,因此可以在分集度、编码增益以及系统码率之间进行灵活的折中。理论分析和仿真结果同时表明,当实际发射天线数大于空时码所需天线数时,系统的编码增益随着实际发射天线数的增加大致呈线性增长,发射天线阵列间相关性越强,增长速度越快。     

A comparative study on the performance of MIMO‐STBC subject to Weibull fading channels

In this paper, we investigate the analytical performance of the multiple‐input multiple‐output system (MIMO) with orthogonal space‐time block codes (STBCs) subject to Weibull fading channels (WFC). Space‐time block code technique provides an efficient pattern for wireless transmission over various fading channels using multiple transmit antennas. Two approximating methods of the sum of independent Weibull random variables are studied. For each approach, we derive accurate approximate expressions for several performance metrics of MIMO‐STBC system operating under independent and nonidentical WFC. The proposed approximations are expressed in terms of 2 generalized hypergeometric functions, namely, Fox's H and Meijer's G functions. All the derived approximate expressions prove high accuracy, while compared with the simulation results established via Monte Carlo method and Kolmogorov‐Smirnov test as well. Although the 2 approaches have approximately the same accuracy, the second method approximate expressions are much less complex than those of the first method.     

Optimal space-time coding under iterative processing

In this paper, we deal with the design of a full-rate space-time block coding (STBC) scheme optimized for linear iterative decoding over fast fading multiple-input multiple-output (MIMO) channel. A general and simple coding scheme called diagonal threaded space-time (DTST) code is presented for an arbitrary number of transmit and receive antennas. Theoretical analysis shows that DTST code associated with linear iterative decoding tends towards full diversity performance while providing maximum MIMO multiplexing gain. Simulation results confirm the ability of DTST to outperform the state-of-the-art STBC and conventional spatial data multiplexing schemes under iterative processing.     

Noncoherent space-frequency coded MIMO-OFDM

Recently, the use of coherent space-frequency coding in orthogonal frequency-division multiplexing (OFDM)-based frequency-selective multiple-input multiple-output (MIMO) fading channels has been proposed. Acquiring knowledge of the fading coefficients in a MIMO channel is already very challenging in the frequency-flat (fast) fading case. In the frequency-selective case, this task becomes significantly more difficult due to the presence of multiple paths, which results in an increased number of parameters to be estimated. In this paper, we address code design for noncoherent frequency-selective MIMO-OFDM fading links, where neither the transmitter nor the receiver knows the channel. We derive the code design criteria, quantify the maximum achievable diversity gain, and provide explicit constructions of full-diversity (space and frequency) achieving codes along with an analytical and numerical performance assessment. We also demonstrate that unlike in the coherent case, noncoherent space-frequency codes designed to achieve full spatial diversity in the frequency-flat fading case can fail completely to exploit not only frequency diversity but also spatial diversity when used in frequency-selective fading environments. We term such codes "catastrophic.".     

Generalized OSTBC‐based subcarrier intensity‐modulated MIMO optical wireless communication system

In this paper, we analyze an optical wireless communication (OWC) system having a source and a destination node, equipped with multiple transmit and receive apertures, respectively. We utilize generalized orthogonal space‐time block codes (OSTBCs) of any arbitrary order and subcarrier intensity modulation scheme for data transmission over gamma–gamma (GG) fading optical links using M ‐ary phase‐shift keying (PSK) constellation. A symbol‐wise decoding is utilized, and the closed‐form expression of the approximate average symbol error rate (SER) of multi‐aperture‐based OWC system is obtained for the generalized OSTBC and an arbitrary M ‐PSK constellation. Using the derived SER expression, we analytically evaluate the diversity order and the coding gain of the OWC system with GG atmospheric turbulence. It has been shown by the numerical results that the maximum possible diversity is achieved by using the symbol‐wise maximum likelihood decoding in the destination. Copyright © 2016 John Wiley & Sons, Ltd.     

Robust full-diversity full-rate quasi-orthogonal STBC for four transmit antennas

A novel quasi-orthogonal space-time block code (QSTBC) with full-diversity full-rate transmission and double-symbol decoding is proposed for a system with four transmit antennas, which is constructed by linearly combining two optimally power-scaled component Alamouti codes. Compared with the existing QSTBC with optimal constellation rotation, the proposed code provides excellent robustness, in terms of bit error rate performance, against spatially correlated and/or time-selective fading channels.     

Performance analysis of MIMO systems with multiuser diversity

In this paper, we present a comprehensive performance analysis for multiple‐input multiple‐output (MIMO) systems with multiuser diversity over Rayleigh fading channels. We derive exact closed‐form expressions of the outage probability and the average bit error rate (BER) for different MIMO schemes, including the selective combining (SC), maximum ratio combining (MRC) and space‐time block codes (STBC). We also provide the explicit upper bounds on the BER performance. Finally, the mathematical formalism is verified by numeric results that study the interaction between the antenna diversity and the multiuser diversity. It is observed that the system performance is deteriorated as the number of transmit antennas increases in multiuser scenario, which is unlike the case in single‐user systems. Copyright © 2007 John Wiley & Sons, Ltd.     

多天线对角空频编码传输

将平坦衰落信道的对角代数空时码(DAST)推广到频率选择性衰落信道,提出了对角空频分组码(DSF).基于多输入多输出天线和正交频分复用(OFDM),DSF码将满秩的旋转信号星座和子载波分组结合起来,以对角发送方式(每时刻只有一个天线发射)发射旋转信息符号向量的每个分量.成对错误概率分析表明:在频率选择性信道中,通过选择最佳的旋转矩阵,这种DSF-OFDM系统能实现满分集增益和最大的编码增益.系统采用了球型解码器对DSF码实施最大似然解码,它的解码复杂性是中等的,并且,解码算法的复杂性与信号星座的维数无关.此外,和先前所提出的一些方法相比,提出的空频码还具有频谱效率高(1symbol/s/Hz)的性能特点.     

在频率选择性相关信道中的空频分组编码技术

本文提出了频率选择性瑞利衰落信道中的对角空频分组码(DSF)，研究了码的性能。分析表明，在各天线对间的信道相互独立，系统有NT个发射天线，NR个接收天线和信道冲击响应长度是L时，DSF码可实现分集增益NRNTL。此外，相关的发射天线阵列会使DSF码分集增益下降，但是对码的性能影响不大，特别是在较长的多路径信道上。因此，DSF码对于相关的衰落信道显示出优越的鲁棒性能。最终仿真结果证实了本文的分析。     

On channel orthogonalization using space-time block coding with partial feedback

Orthogonal space-time block codes (OSTBCs) yield full diversity gain even while requiring only a linear receiver. Such full-rate (rate-one) orthogonal designs are available for complex symbol constellations only for N=2 transmit antennas. In this paper, we propose a new family of full-rate space-time block codes (STBCs) using a single parameter feedback for communication over Rayleigh fading channels for N=3,4 transmit antennas and M receive antennas. The proposed rate-one codes achieve full diversity, and the performance is similar to maximum receiver ratio combining. The decoding complexity of these codes are only linear even while performing maximum-likelihood decoding. The partial channel information is a real phase parameter that is a function of all the channel gains, and has a simple closed-form expression for N=3,4. This feedback information enables us to derive (channel) orthogonal designs starting from quasi-orthogonal STBCs. The feedback complexity is significantly lower than conventional closed-loop transmit beamforming. We compare the proposed codes with the open-loop OSTBCs and also with the closed-loop equal gain transmission (EGT) scheme which uses equal power loading on all antennas. Simulated error-rate performances indicate that the proposed channel orthogonalized STBCs significantly outperform the open-loop orthogonal designs, for the same spectral efficiency. Moreover, even with significantly lower feedback and computational complexity, the proposed scheme outperforms the EGT technique for M>N.     

On the design of space-time and space-frequency codes for MIMO frequency-selective fading channels

The authors introduced an algebraic design framework for space-time coding in flat-fading channels . We extend this framework to design algebraic codes for multiple-input multiple-output (MIMO) frequency-selective fading channels. The proposed codes strive to optimally exploit both the spatial and frequency diversity available in the channel. We consider two design approaches: The first uses space-time coding and maximum likelihood decoding to exploit the multi-path nature of the channel at the expense of increased receiver complexity. Within this time domain framework, we also propose a serially concatenated coding construction which is shown to offer a performance gain with a reasonable complexity iterative receiver in some scenarios. The second approach utilizes the orthogonal frequency division multiplexing technique to transform the MIMO multipath channel into a MIMO flat block fading channel. The algebraic framework is then used to construct space-frequency codes (SFC) that optimally exploit the diversity available in the resulting flat block fading channel. Finally, the two approaches are compared in terms of decoder complexity, maximum achievable diversity advantage, and simulated frame error rate performance in certain representative scenarios.     

Design of concatenated space-time block codes using signal space diversity and the Alamouti scheme

New full-rate space-time block codes achieving full diversity for quadrature amplitude modulation (QAM) using an even number of transmit antennas over quasi-static Rayleigh fading channels are proposed. The proposed codes are constructed by serially concatenating unitary rotating precoders with the Alamouti code. The coding advantage of the proposed code for a codeword pair corresponding to any distinct input pair is shown to be greater than or equal to that of the ST-CR code.     

On the design of algebraic space-time codes for MIMO block-fading channels

The availability of multiple transmit antennas allows for two-dimensional channel codes that exploit the spatial transmit diversity. These codes were referred to as space-time codes by Tarokh et al. (see ibid., vol.44, p.744-765, Mar. 1998) Most prior works on space-time code design have considered quasi-static fading channels. We extend our earlier work on algebraic space-time coding to block-fading channels. First, we present baseband design criteria for space-time codes in multi-input multi-output (MIMO) block-fading channels that encompass as special cases the quasi-static and fast fading design rules. The diversity advantage baseband criterion is then translated into binary rank criteria for phase shift keying (PSK) modulated codes. Based on these binary criteria, we construct algebraic space-time codes that exploit the spatial and temporal diversity available in MIMO block-fading channels. We also introduce the notion of universal space-time codes as a generalization of the smart-greedy design rule. As a part of this work, we establish another result that is important in its own right: we generalize the full diversity space-time code constructions for quasi-static channels to allow for higher rate codes at the expense of minimal reductions in the diversity advantage. Finally, we present simulation results that demonstrate the excellent performance of the proposed codes.