Bit error rate for rectangular QAM with arbitrary constellation mapping in Nakagami‐m channels

We present closed‐form expressions for the bit error rate (BER) of rectangular quadrature amplitude modulation (QAM) in Nakagami‐m fading channels. The presented formulas, which are valid for arbitrary bits‐to‐symbols mapping, thus may be used when non‐Gray mapping is employed, are particularly useful in the low signal‐to‐noise ratio (SNR) range and/or for small values of the parameter m. The advantage of the proposed expressions over the known bounding techniques is illustrated through numerical simulations. Copyright © 2006 John Wiley & Sons, Ltd.     

Nakagami-m衰落信道下空时分组码的性能估计

基于等效单输入单输出SISO (Single-input Single-output) 模型,利用矩量母函数 (MGF) 分析法,空时分组码STBC (Space-Time Block Coding) 的误符号率是可以得到其准确闭式表达式的.对于独立同分布Nakagami-m衰落信道下的空时分组码的性能进行了研究,给出了采用M-PSK 和M-QAM调制方案的不同空时分组编码矩阵误符号率的闭式解以及基于闭式解的解析性能结果,通过蒙特卡洛仿真验证了闭式解的准确性.还从调制方案的角度对于几种新的空时分组码的性能进行了一些新的讨论.     

Space‐time ring‐TCM codes with CPM based on the decomposed model for transmission over Rayleigh fading channels

Space–time (ST) coding is a proved technique for achieving high data rates in 3G mobile systems that combines coding, modulation and multiple transmitters and receivers. A novel algorithm is proposed for ST ring trellis‐coded modulation (ST‐RTCM) systems with continuous‐phase modulation (CPM) when the channel coefficients are known to the receiver. This algorithm is based on the CPM decomposed model, which exploits the memory properties of this modulation method, resulting in a straightforward implementation of joint ST coding and CPM, which is particularly suitable for ring codes. This new scheme is used to investigate the performance of the delay diversity code with CPM over slow Rayleigh fading channels, in particular with MSK which is one of the most widely used modulation methods of continuous phase. Furthermore, a feedback version of delay diversity allowed by the decomposition is tested in 1REC and 1RC systems. This feedback configuration is seen to provide good results for low signal‐to‐noise ratios. Simulations results are also provided for multilevel ST‐RTCM codes that achieve a higher throughput than MSK‐coded systems. Additionally the serial concatenation of an outer Reed–Solomon code with an ST‐RTCM code is shown, this combination further reduces the error probability and achieves even more reliable communications. Copyright © 2005 John Wiley & Sons, Ltd.     

Symbol error rate calculation and data pre‐distortion for 16‐QAM transmission over nonlinear memoryless satellite channels

This paper presents a simplified mathematical approach to evaluate the performance of any given circular constellation of 16‐level quadrature amplitude modulation (16‐QAM) in terms of symbol error rate (SER). Following this approach, with the aim to work with memoryless nonlinear satellite channels, a model is derived as a generalized form for both linear and nonlinear channels in the presence of down link additive white Gaussian noise (AWGN). The analysis provides means to calculate the optimal ring ratio (RR) and phase difference (PD) for several possible candidates of 16‐QAM circular constellations. The effects of RR and PD on the SER performance are investigated in the analysis. To overcome the nonlinear distortion, data pre‐distortion is taken into account in the study. The paper gives a general procedure for data pre‐distortion implementation for all circular 16‐QAM constellations. The analytical formulation has been extended for total degradation (TD) performance measure as a function of input back‐off (IBO) of the nonlinear amplifier. A SER performance‐comparison between different constellations for 16‐QAM systems has also been presented in this paper. The analytical results are validated by simulation. Copyright © 2006 John Wiley & Sons, Ltd.     

Analysis of transmit antenna selection/orthogonal space‐time block coding with receive selection and combining in the presence of feedback errors

Examining the effect of imperfect transmit antenna selection (TAS) caused by the feedback link errors on the performance of hybrid TAS/orthogonal space‐time block coding (OSTBC) with single receive antenna selection (i.e., joint transmit and receive antenna selection (JTRAS)/OSTBC) and TAS/OSTBC (with receive maximal‐ratio combining‐like combining structure) over slow and frequency‐flat Nakagami‐m fading channels is the main objective of this paper. Under ideal channel estimation and delay‐free feedback assumptions, statistical expressions and several performance metrics related to the post‐processing signal‐to‐noise ratio are derived by defining a unified system model concerning both JTRAS/OSTBC and TAS/OSTBC schemes. Exact analytical expressions for outage probability (OP) and bit/symbol error rates of M‐ary modulations are presented in order to provide a detailed examination on the OP and error performances of the unified system that experiences feedback errors. Also, the asymptotic diversity order analysis, which shows that the diversity order of the investigated schemes is equal to the diversity order provided by OSTBC transmission itself, is included in the paper. Moreover, we have validated the theoretical results via Monte Carlo simulations. Copyright © 2014 John Wiley & Sons, Ltd.     

Diversity order analysis of orthogonal space–time block coding over keyhole fading channels with antenna selection

Although there are many research results for the keyhole fading channels in the current literature, fewer results have investigated the antenna selection scheme and quantified the diversity order. In this letter, we first derive some simple statistics of the output signal‐to‐noise ratio for the orthogonal space–time block coding over keyhole fading channels. On the basis of these results, we derive an approximate BER expression for the keyhole MIMO channels with receive antenna selection scheme. Results show that the diversity order with receive antenna selection is min{n_R,n_T}for n_R ≠ n_T, which means that the full diversity order with antenna selection is maintained. Finally, numerical results demonstrate the accuracy of our analytical expressions and the tightness of approximate formulas. Copyright © 2012 John Wiley & Sons, Ltd.     

Analysis of diversity schemes employing antenna selection in the presence of channel estimation errors and feedback delay

The main objective of this paper is to provide an extensive and complete examination on the effect of practical impairments such as channel estimation errors (CEEs) and feedback delay (FD) on the performance of diversity schemes over Nakagami‐m fading channels. Under erroneous channel estimation and outdated feedback cases, statistical expressions and several performance metrics related to the post‐processing signal‐to‐noise ratio (SNR) are derived for four different diversity schemes: transmit antenna selection (TAS)/orthogonal space–time block coding, TAS/maximal‐ratio transmission (MRT), MRT/receive antenna selection (RAS), and joint transmit and RAS. Exact analytical expressions for outage probability and average error rates of M‐ary modulations are derived in order to provide insightful perspectives on the capacity and error performance of diversity schemes that experience both CEE and FD. The asymptotic diversity order of the investigated diversity schemes are derived via a high‐SNR approximation approach. In order to assess the real‐world performance of the investigated diversity schemes and to observe their robustness or sensitivities in practical imperfections, various configurations are considered together with several performance comparisons. Also, Monte Carlo simulations are performed in order to validate the theoretical results. Copyright © 2014 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.     

衰落信道上空频分组码的性能分析

对于任意抽头数的多输入多输出(MIMO)频率选择性Nakagami衰落信道,利用矩生成函数(MGF)方法和高斯Q函数的指数近似表达式,推导采用矩形M进制正交幅度调制(MQAM)的空频分组编码(SFBC)正交频分复用(OFDM)系统的平均误符号率(SER)性能的精确和近似解析表达式。数值计算和仿真结果证明了理论分析的正确性和近似分析的准确性。     

Performance comparison of dual‐hop hybrid decode‐or‐amplify‐forward relay schemes for M‐ary quadrature amplitude modulation burst transmission over Rayleigh fading channels

This paper shows the analytical performance expressions of M‐ary quadrature amplitude modulation burst symbol transmission for hybrid decode‐or‐amplify‐forward (HDAF) relay schemes over quasi‐static Rayleigh‐fading channels. First, we derive the probability density function of the received instantaneous signal‐to‐noise ratio as the simplified form, which is related to all the possible occurrence probabilities of error‐events for M‐ary quadrature amplitude modulation burst transmission. On the basis of the derived probability density function, we express average bit error probability, average symbol error probability, and average burst error rate as closed forms, which can be also applied to both amplify‐and‐forward and adaptive decode‐and‐forward (ADF) schemes. The analysis and simulation results show that HDAF scheme for burst transmission can achieve the performance of ADF scheme with symbol‐by‐symbol transmission, which is the achievable lower bound. Furthermore, the outage probability, the normalized channel capacity, and the goodput performance are also derived as closed forms. The analysis shows the superiority of HDAF scheme to ADF scheme. Comparison with simulations confirms that the derived analytical expressions are accurate over all signal‐to‐noise ratio regions and for different numbers of relays and modulation orders.     

On the error probability of quasi‐orthogonal space–time block codes

In this paper, we derive the exact pairwise error probabilities (PEPs) of various quasi‐orthogonal space–time block codes (QO‐STBCs) using the moment generating function. By classifying the exact PEPs of QO‐STBCs into three types, we derive the closed‐form expression for each type of PEP. Based on these closed‐form expressions, we obtain the union bounds on the symbol error probability and bit error probability for QPSK modulation. Through simulation, it is shown that these union bounds are quite tight. Copyright © 2008 John Wiley & Sons, Ltd.     

On the performance of two‐way relay channels using space–time codes

In this paper, we explore the advantages of network coding and space–time coding in improving the performance of two‐way‐relayed communications where two terminals absent of direct links exchange information through a single relay in between. Network coding allows embracing the interference from other terminals thereby turning it into a capacity boost. The application of space–time codes yields higher capacity by exploiting the spatial diversity. The joint performance of both techniques is studied in this paper. Specifically, we consider the class of decode‐and‐forward (DF) relaying strategy, evaluated in terms of symbol error rate using BPSK and QPSK modulations by both theoretical analysis and simulation. Based on our results, DF outperforms the amplify‐and‐decode and partial‐decode‐and‐forward protocols. Copyright © 2011 John Wiley & Sons, Ltd.     

Performance evaluation of multiuser diversity in multiuser two‐hop cooperative multi‐relay wireless networks using maximal ratio combining over Rayleigh fading channels

Multiuser diversity (MUD) cooperative wireless networks combine the features of the MIMO systems without confronting the physical layer constraints by providing multiple copies of the transmitted signal from the source to the destination with the help of the relay node. Cooperative wireless networks have attracted the full attention in the last few years and are implemented widely in many wireless communication systems to adapt for the fading impairments, provide higher data rates, and improve the performance of the wireless communication systems. In this paper, we present an informative study for the reason of evaluating the performance of the MUD in the multiuser two‐hop cooperative multi‐relay networks using maximal ratio combining. Furthermore, we derive tight closed‐form expressions of outage probability and symbol error probability for the amplify‐and‐forward and fixed decode‐and‐forward protocols with the MUD. Additionally, we conduct a simulation study to show to what extent our analytical and simulation results agree with each other. It is worthy to mention that our analytical and simulation results agree fairly with each other under high average signal‐to‐noise ratio, whereas they show that our proposed system with multiple relays provides significant improvements over those previously proposed systems having only one relay. Copyright © 2013 John Wiley & Sons, Ltd.     

Bit error probability of the M‐QAM scheme under η‐μ fading and impulsive noise in a communication system using spatial diversity

This paper presents a new and exact expression for the bit error probability (BEP) of the square M‐ary quadrature amplitude modulation (M‐QAM) scheme, with the channel under double gated additive white Gaussian noise (G²AWGN) and η‐μ fading in a communication system using the spatial diversity technique. The expression for the BEP is written in terms of the Appell function. The BEP curves are presented under different values of the number of branches of the maximum ratio combining (MRC) receiver, order of the constellation M, and parameters that characterize mathematically the channel, corroborated by simulations performed with Monte Carlo method.     

Multiuser receiver scheme for full‐rate space–time coded CDMA system with imperfect estimation

By introducing a full‐rate space–time coding (STC) scheme, a synchronous CDMA (code division multiple access) system with full‐rate STC is given, and the corresponding uplink performance is investigated in Rayleigh fading channel with imperfect estimation. Considering that existing STC‐CDMA system has high decoding complexity, low‐complexity multiuser receiver schemes are developed for perfect and imperfect estimations, respectively. The schemes can make full use of the complex orthogonality of STC to reduce the high decoding complexity of the existing scheme, and have linear decoding complexity compared with the existing scheme with exponential decoding complexity. Moreover, the proposed schemes can achieve almost the same performance as the existing scheme. Compared with full‐diversity STC‐CDMA, the given full‐rate STC‐CDMA can achieve full data rate, low complexity, and partial diversity, and form efficient spatial interleaving. Thus, the concatenation of channel coding can effectively compensate for the performance loss due to partial diversity. Simulation results show that the full‐rate STC‐CDMA has lower bit error rate (BER) than full‐diversity STC‐CDMA systems under the same system throughput and concatenation of channel code. Moreover, the system BER with imperfect estimation are worse than that with perfect estimation due to the estimation error, which implies that the developed multiuser receiver schemes are valid and reasonable. Copyright © 2010 John Wiley & Sons, Ltd.     

Performance and diversity analysis of decode‐and‐forward cooperative system over Nakagami‐m fading channels

In this paper, we derive the upper bound of bit‐error rate (BER) performance and diversity gain for a decode‐and‐forward (DF) cooperative system. Either maximal‐ratio combining (MRC) or cooperative MRC (C‐MRC) is employed at the receiver in the presence of independent, non‐identical Nakagami‐m fading. Both analytical and simulation results show that C‐MRC takes advantage of spatial diversity more efficiently and thus achieves the same or better performance and diversity order as compared to MRC. Copyright © 2009 John Wiley & Sons, Ltd.     

Performance analysis of MIMO cognitive amplify‐and‐forward relay networks with orthogonal space–time block codes

In this paper, we study the performance of multiple‐input multiple‐output cognitive amplify‐and‐forward relay networks using orthogonal space–time block coding over independent Nakagami‐m fading. It is assumed that both the direct transmission and the relaying transmission from the secondary transmitter to the secondary receiver are applicable. In order to process the received signals from these links, selection combining is adopted at the secondary receiver. To evaluate the system performance, an expression for the outage probability valid for an arbitrary number of transceiver antennas is presented. We also derive a tight approximation for the symbol error rate to quantify the error probability. In addition, the asymptotic performance in the high signal‐to‐noise ratio regime is investigated to render insights into the diversity behavior of the considered networks. To reveal the effect of network parameters on the system performance in terms of outage probability and symbol error rate, selected numerical results are presented. In particular, these results show that the performance of the system is enhanced when increasing the number of antennas at the transceivers of the secondary network. However, increasing the number of antennas at the primary receiver leads to a degradation in the secondary system performance. Copyright © 2014 John Wiley & Sons, Ltd.     

On the blind channel identifiability of multiple‐input multiple‐output space–time block code systems using Joint Approximate Diagonalization of Eigenmatrices

Channel identifiability for multiple‐input multiple‐output space–time block code (MIMO‐STBC) systems using Joint Approximate Diagonalization of Eigenmatrices (JADE) is studied in this paper. Compared with the previous blind MIMO‐STBC channel estimation methods in literature, the method proposed in this paper is more suitable for non‐cooperative scenario because it needs less prior information and can be applied to a general class of STBCs. The main contribution of the paper consists in the theoretical proof that, although the sources transmitted by different antennas of MIMO‐STBC systems are not independent, they can be retrieved from the received data by directly using JADE in most cases. The conclusion is also demonstrated by a simulation. This shows that the classical JADE algorithm can be applied to a wider range of situations rather than strictly independent sources. Copyright © 2013 John Wiley & Sons, Ltd.     

A new subspace method for blind estimation of selective MIMO‐STBC channels

In this paper, a new technique for the blind estimation of frequency and/or time‐selective multiple‐input multiple‐output (MIMO) channels under space‐time block coding (STBC) transmissions is presented. The proposed method relies on a basis expansion model (BEM) of the MIMO channel, which reduces the number of parameters to be estimated, and includes many practical STBC‐based transmission scenarios, such as STBC‐orthogonal frequency division multiplexing (OFDM), space‐frequency block coding (SFBC), time‐reversal STBC, and time‐varying STBC encoded systems. Inspired by the unconstrained blind maximum likelihood (UML) decoder, the proposed criterion is a subspace method that efficiently exploits all the information provided by the STBC structure, as well as by the reduced‐rank representation of the MIMO channel. The method, which is independent of the specific signal constellation, is able to blindly recover the MIMO channel within a small number of available blocks at the receiver side. In fact, for some particular cases of interest such as orthogonal STBC‐OFDM schemes, the proposed technique blindly identifies the channel using just one data block. The complexity of the proposed approach reduces to the solution of a generalized eigenvalue (GEV) problem and its computational cost is linear in the number of sub‐channels. An identifiability analysis and some numerical examples illustrating the performance of the proposed algorithm are also provided. Copyright © 2009 John Wiley & Sons, Ltd.     

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.