Simple tight approximations of the error performance for dual-hop MIMO relay systems in Rayleigh fading

In this paper we present tight approximations of the error performance for the entire signal-to-noise ratio (SNR) range of practical interest for an amplify and forward (AF) relaying system with channel state information (CSI) at the relay and destination, which employs multiple antennas at the nodes and orthogonal space–time block coding (OSTBC) transmission over a flat Rayleigh fading. Additionally, for a high value SNR range, we simplified the tight approximation expression in the simple asymptotic expression. The comparison of the error performance obtained by those two approximations with the error performance obtained by numeric integration of moment generating functions (MGF) and by Monte Carlo simulations shows close matching of the results.     

Uplink performance of CWP-MC-CDMA with Space Diversity Combining technique over Rayleigh fading channel

In this paper, a Complex Wavelet Packet （CWP-MC-CDMA） system uplink model is proposed, based Multi-Carrier Code Division Multiple Access based on the analysis of the principle of MC-CDMA and the use of the optimized complex wavelet packet. Considering that the base station can adopt multiple re- ceiver antennas in the uplink, we employ the Space Diversity Combining （SDC） technique to improve the sys- tem pertbrmance via multiple antennas. The uplink performance of proposed CWP-MC-CDMA system with SDC technique is investigated over Rayleigh lading channel, and corresponding bit error rate analysis is given in detail. The system can avoid the decrease of spectrum efficiency of conventional MC-CDMA due to inserting cyclic prefix. Theoretical analysis and simulation result show that the application of SDC technique can improve the CWP-MC-CDMA system ability to combat spatial lading and various interferences effectively. Moreover, the proposed system based on SDC technique has superior Bit Error Rate （BER） performance over the Discrete Fourier Transform （DFT） and SDC based MC-CDMA system and the real wavelet packet and SDC based MC-CDMA system.     

A general moment generating function for MRC diversity over fading channels with Gaussian channel gains

For maximal ratio combining (MRC) diversity over correlated fading channels with Gaussian channel gains, we utilize unitary diagonalization of the channel covariance matrix to decorrelate the physical channels into uncorrelated virtual channels to obtain the moment generating function (MGF) of the received signal‐to‐noise ratio (SNR). The MGF thus obtained has a compact form and can be universally applied to various popular fading models. In addition to the advantage of simple derivation procedure, this general MGF can be readily modified to express various scenarios of channel power distributions as well as joint fading models. To demonstrate these advantages, we use the generalized Ricean fading as a specific example to compare our derivation and our MGF expression with an existing work in the literature. Again, we present numerical simulations for MRC reception of binary phase shift keying (BPSK) signals over Nakagami fading to compare with existing results appearing in the literature. Copyright © 2006 John Wiley & Sons, Ltd.     

Outage probability and channel capacity for the Nth best relay selection AF relaying over INID Rayleigh fading channels

Cooperative diversity systems have recently been proposed as a way to form virtual antenna schemes without utilizing collocated multiple antennas. In this paper, we consider the Nth best opportunistic amplify‐and‐forward (AF) cooperative diversity systems. The AF type can be regarded as one on the basis of modified channel state information. Wireless channels between any pair of nodes (i.e., direct and dual hop links) are assumed quasi‐static independent and nonidentically distributed (INID) Rayleigh fading. The best opportunistic AF (OAF) scheme requires two phases of transmission. During the first phase, the source node transmits a signal to all relays and the destination. In the second phase, the best relay is only selected on the basis of highest signal‐to‐noise ratio (SNR) scheme to forward the source signal to the destination. Therefore, the indirect link (i.e., source‐selected relay destination) can give the highest received SNR. However, the best relay selection cannot be available so that we might choose the second, third, or generally the Nth best relay. In this paper, we derive the approximated outage probability and channel capacity for the Nth best OAF relay systems over INID Rayleigh fading channels. At first, the indirect link's received SNR is approximated as harmonic mean upper bound. With this information, we obtain the given relay's Nth best selection probability as the closed form. Finally, both outage probability and channel capacity are derived as the closed forms. Simulation results are finally presented to validate the analysis. Copyright © 2011 John Wiley & Sons, Ltd.     

More tractable average error rate expression for the Nth best relay selection scheme of DF relaying over Rayleigh fading channels

In this paper, we derive another exact average error rate expression for the Nth best decode‐and‐forward relay systems over Rayleigh fading channels. On the basis of error‐events at relay nodes, the Nth best relay's selection probability is expressed as a more tractable form in which the number of summations and the length of each summation are specified. Then, exact average error performance metrics are obtained as two well‐known forms. The first is expressed with a moment generating function, and the other is presented as a closed form. Simulation results are finally presented to validate that the derived analytical expression can be a general frame work covering all Rayleigh fading channel conditions. Copyright © 2012 John Wiley & Sons, Ltd.     

Erased-Chase decoding for RS-coded MPSK signaling over a Rayleigh fading channel

In this paper, a novel dual-metric, the maximum and minimum Squared Euclidean Distance Increment （SEDI） Brought by changing the hard decision symbol, is introduced to measure the reliability of the received M-ary Phase Shift Keying （MPSK） symbols over a Rayleigh fading channel. Based on the dual-metric, a Chase-type soft decoding algorithm, which is called erased-Chase algorithm, is developed for Reed-Solomon （RS） coded MPSK schemes. The proposed algorithm treats the unreliable symbols with small maximum SEDI as erasures, and tests the non-erased unreliable symbols with small minimum SEDI as the Chase-2 algorithm does. By introducing optimality test into the decoding procedure, much more reduction in the decoding complexity can be achieved. Simulation results of the RS（63, 42, 22）-coded 8-PSK scheme over a Rayleigh fading channel show that the proposed algorithm provides a very efficient tradeoff between the decoding complexity and the error performance. Finally, an adaptive scheme for the number of erasures is introduced into the decoding algorithm.     

Switch‐and‐examine combining with different new switch statistics for diversity over Rayleigh fading channels

Three schemes of multibranch switch‐and‐examine combining (MSEC) with switch statistics different from the signal‐to‐noise ratio used in the traditional MSEC are analyzed. For each diversity branch, with its fading factor a and low‐passed received signal r, the switch statistics for the three MSEC schemes considered in the paper are | r | , | ar | , and a linear combination of a and | r | , respectively. To illustrate the performances of the MSEC schemes, the average BER of each MSEC scheme with BPSK signaling is evaluated for independent and identically distributed Rayleigh fading channels. For performance optimization, the optimal switch thresholds of the MSEC schemes are obtained. Numerical results based on the analysis and simulations are presented for performance illustrations. Copyright © 2012 John Wiley & Sons, Ltd.     

Parallel interference cancellation employing RAKE receiver with selection diversity for multiuser asynchronous DS/CDMA detectors in multipath Rayleigh fading channels

In this paper, we propose and analyse parallel CCI multistage cancellation by combining RAKE and selection diversity. In order to account for channel variations, adaptive implementation of decision thresholds at the RAKE output is suggested. It is shown to provide significant improvement over either hard or soft decision techniques especially in the near‐far situation. Investigation of the system robustness to imperfect channel parameter estimation is also presented. The communication channel is modelled as slowly varying Rayleigh fading discrete multipath channel. Copyright © 2002 John Wiley & Sons, Ltd.     

Performance evaluation of HDAF relaying systems for pilot and data symbol burst transmission over quasi‐static Rayleigh fading channels

This paper analyzes averaged symbol error probabilities of burst transmission consisting of pilot and data symbols for hybrid adaptive decode‐or‐amplify‐forward (HDAF) relaying systems. Under the assumption of quasi‐static Rayleigh fading channels with independent and non‐identically distribution, we consider a channel estimation scheme based on pilot symbols and show how channel estimation error affects received signal‐to‐noise ratio (SNR) and symbol error probability (SEP). Firstly, all the possible detection error‐events are presented for all the relay nodes, and their probabilities are derived as forms related with data symbol burst transmission. For the given error event, we analyze the conditional SEP as an exact form and then, the averaged SEP (ASEP) is approximately derived as a closed‐form. The simulation results verify that our derived ASEP expression is accurate over all the regions of SNR. Utilizing the proposed expressions, we can evaluate ASEP performance of HDAF relay systems easily and fast. Copyright © 2015 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.     

Exact closed‐form symbol error rate of arbitrary rectangular M‐QAM over Rayleigh fading for two‐branch transmit diversity

By using a ‘pre‐averaging method’, we successfully derive an exact closed‐form symbol error rate (SER) expression for the particular case of two transmit‐one receive antenna diversity system employing arbitrary rectangular M‐QAM signalling over flat Rayleigh fading. Fading between branches are assumed independent. Both identical and distinct branch powers are considered. The closed‐form SER obtained is in terms of elemental functions containing no unevaluated integrals nor lengthy and complicated transcendental functions. Simulation results show that square M‐QAM outperforms rectangular M‐QAM for a given size M. Monte Carlo simulation results are found in excellent agreements with theoretical results. Copyright © 2006 John Wiley & Sons, Ltd.     

Enhanced switch combining for spatial diversity with a switch window over correlated Nakagami‐m fading channels

On the basis of a mixture of the selection combining and switch‐and‐stay combining schemes, the enhanced switch combining (ESC) scheme is proposed for antenna diversity over multiple correlated Nakagami‐m fading channels, where a switch window with upper and lower switch thresholds are used. Compared with the existing select‐and‐stay combining or switch with post‐examining, the ESC scheme reduces simultaneous multiantenna observations and hence saves processing time and energy from multibranch observations, while achieving matched receiver performance. Thus, ESC also has better performance than switch‐and‐examine combining (SEC). To assess the reduction of simultaneous observations, a dual‐observation rate is defined. Moreover, the ESC unifies some well‐known switch‐based combining schemes (for example selection combining, switch‐and‐stay combining, or SEC) in the sense that, by adjusting switch thresholds, these combining schemes become different special cases of ESC. The CDF, PDF, and moment generating function of the combined signal‐to‐noise ratio for ESC are derived for general fading channels. Then, the outage probability and the average BER of different binary modulations over correlated Nakagami‐m fading channels are evaluated. Numerical results from analysis and simulation are presented to demonstrate ESC performance. Copyright © 2012 John Wiley & Sons, Ltd.     

An approximate analytical framework for performance analysis of equal gain combining technique over independent Nakagami,Rician and Weibull fading channels

In this paper, an approximate analytical method for performance analysis of equal gain combiner (EGC) receiver over independent Nakagami and Rician fading channels is presented. We use a convergent infinite series approach which makes it possible to describe the probability of error of EGC receiver in the form of an infinite series. In this paper, we develop a new approximation method for computation of the required coefficients in this series which lets us to derive simple analytical closed-form expressions with good accuracy compared with the exact results existing in the literatures. Our proposed approximation method only needs the mean and the variance of the fading envelope, which are known for various fading distributions, and hence, bypasses the required integration over the fading envelope distribution while computing the required coefficients. This feature lets us to extend our approximation method for performance analysis of EGC receiver over independent Weibull fading channels where the required integration has not any closed-form or tabulated solutions. To give an application of our developed method, we analyze the probability of error of an EGC receiver for binary, coherent PSK (CPSK) modulation over independent Nakagami, Rician and weibull fading channels and study the effect of the fading conditions on the system performance.