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.     

Performance analysis of switch‐and‐examine diversity systems with interference and Rayleigh fading channels

This paper studies the behavior of the low‐complexity switch‐and‐examine diversity combining (SEC) and switch‐and‐examine diversity combining with post‐examine selection (SECps) antenna selection schemes with interference. In this paper, we first derive the cumulative distribution function (CDF) of the end‐to‐end (e2e) signal‐to‐interference plus noise ratio at the selection scheme combiner output. This CDF is then used to derive closed‐form expressions for the e2e outage and symbol error probabilities for the independent nonidentically distributed and independent identically distributed cases of diversity branches. In the analysis, the channels of the desired user and the interferers are assumed to follow Rayleigh distribution. Furthermore, to have more details about the system insights, the performance is evaluated at the high signal‐to‐noise ratio (SNR) values where the diversity order and coding gain are derived and analyzed. The derived analytical and asymptotic results are validated via a comparison with Monte‐Carlo simulations. Main findings show that with interference power does not scale with average SNR; the system can still achieve performance gain when more receive antennas are used. This happens at the values of switching threshold that are close to average SNR. Also, results illustrate that the interference is noticeably affecting the gain achieved in system performance when more antennas are used. Furthermore, findings show that the SECps selection scheme outperforms the conventional SEC scheme when more antennas are added with the switching threshold is much larger than the average SNR. Finally, findings show that the SEC and SECps antenna selection schemes are efficient for systems which operate at the range of low SNR values and this makes them attractive candidates to be implemented in the emerging mobile broadband communication systems. Copyright © 2015 John Wiley & Sons, Ltd.     

Performance analysis of dual switched diversity over correlated Weibull fading channels with co‐channel interference

This paper studies the performance of switch and stay combining (SSC) diversity in the presence of co‐channel interference over correlated Weibull fading channels. SSC diversity based on signal‐to‐interference ratio (SIR) is a low‐complexity and a very efficient technique that reduces fading and co‐channel interference influence. New closed‐form expressions for the probability density function and cumulative distribution function of the output SIR's are derived. These formulas are used in a detailed analysis of the average output SIR and outage probability. The influence of fading severity and correlation coefficient on the optimum switching threshold and system performance is investigated. Monte Carlo simulations are performed to verify obtained theoretical results and determine average bit error rate in detecting binary phase‐shift keying (BPSK), differential BPSK and quadrature amplitude modulation signals. Copyright © 2011 John Wiley & Sons, Ltd.     

Switching rate and receiver performance of binary modulations with the selection‐and‐stay combining over independent and correlated Nakagami‐m fading channels

The dual‐branch selection‐and‐stay combining (SSTC) is analyzed for diversity reception on independent and correlated Nakagami‐m fading channels, where the conventional selection combining (SC) is employed only at the switching instance, and the receiver uses the selected branch till its signal‐to‐noise ratio (SNR) estimation is lower than a preset threshold. In this combining scheme, the receiver only needs to continuously estimate the SNR of the single selected branch. For the performance analysis of SSTC, the switching rate and the average bit error rates (BERs) of different binary coherent and non‐coherent modulations are evaluated. Numerical results based on the analysis and simulations are illustrated. According to the analysis and numerical results, the SSTC outperforms the existing switch‐and‐stay combining in the senses of the average BER and switching rate. Copyright © 2011 John Wiley & Sons, Ltd.     

Analysis of LDPC with optimum combining

Low density parity check (LDPC) codes have shown exceptionally good performance for single antenna systems over a wide class of channels. LDPC when implemented with a single input multiple output system with maximum ratio combining is optimum from the standpoint of maximising signal-to-noise ratio at combiner output without the presence of interferer. Optimum combining outperforms maximal ratio combining (MRC) in the presence of interferer(s). In this article, the performance of the LDPC codes with multiple receiver antennas with optimum combining in the presence of single interferer is investigated. The simulation results showed that LDPC codes of irregular construction are able to give high coding and diversity gain with optimum combining. The proposed LDPC optimum combined (LDPC–OC) system in Rayleigh fading channel in the presence of a single interferer improves the signal to interferer plus noise ratio by 2.62 dB with four receiver antennas and by 1.98 dB when the number of receiver antennas is three.     

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.     

A generalisation of the Rayleigh distribution with applications in wireless fading channels

The signal received in a mobile radio environment exhibits rapid signal level fluctuations which are generally Rayleigh‐distributed. These result from interference by multiple scattered radio paths between the base station and the mobile receptor. Fading‐shadowing effects in wireless channels are usually modelled by means of the Rayleigh–Lognormal distribution (RL), which has a complicated integral form. The K‐distribution (K) is similar to RL but it has a simpler form and its probability density function admits a closed form; however, due to the Bessel function, parameter estimates are not direct. Another possible approach is that of the Rayleigh‐inverse Gaussian distribution (RIG). In this paper, an alternative is presented, a generalisation of the Rayleigh distribution which is simpler than the RL, K and RIG distributions, and thus more suitable for the analysis and design of contemporary wireless communication systems. Closed‐form expressions for the bit error rate (BER) for differential phase‐shift keying (DPSK) and minimum shift keying (MSK) modulations with the proposed distribution are obtained. Theoretical results based on statistically well‐founded distance measurements validate the new distribution for the cases analysed. Copyright © 2011 John Wiley & Sons, Ltd.     

Performance of optimum wavelet for DS‐CDMA chip waveform over multi‐path Rayleigh fading channels

In this paper, the probability of error (P_e) expression of asynchronous direct sequence‐code division multiple access (DS‐CDMA) signals using band‐limited chip waveforms is derived over multi‐path Rayleigh fading channels. In receiver, a matched filter‐based rake receiver in conjunction with maximum ratio combiner (MRC) is considered. Numerical values for the P_e are calculated for various chip waveforms including an optimum wavelet waveform. Analytical results are verified by conducting simulations. Results show that the optimum wavelet‐based scheme outperforms time‐limited raised cosine, half sine, rectangular and band‐limited square‐root raised cosine chip waveform‐based schemes in terms of the P_e and the capacity defined as the number of users per Hertz for a same P_e level. Copyright © 2006 John Wiley & Sons, Ltd.     

Performance analysis of system with selection combining over correlated Weibull fading channels in the presence of cochannel interference

Selection diversity based on the signal to interference ratio (SIR) is a very efficient technique that reduces fading and channel interference influence. In this paper, system performances of selection combining and correlated Weibull channels are analyzed. Fading between the diversity branches and between interferers is correlated and Weibull distributed. Very useful closed-form expressions are obtained for the output SIR's probability density function (PDF) and cumulative distribution function which is main contribution of this paper. Outage probability, the average output SIR, and the average error probability for coherent, noncoherent modulation are derived. Numerical results presented in this paper point out the effects of fading severity and correlation on the system performances.     

Performance analysis of QAM in amplify-and-forward cooperative communication networks over Rayleigh fading channels

Performance analysis of quadrature amplitude modulation (QAM) schemes for cooperative amplify-and-forward (AF) dual-hop relaying system over independent and identically distributed (i.i.d.) Rayleigh fading channels are presented in this paper. Specifically, we derive closed-form lower-bound expressions of average symbol error rate (ASER) for general order rectangular QAM (RQAM) and cross QAM (XQAM) using well-known moment generating function (MGF) based approach with maximal ratio combining (MRC) scheme. Further, using best relay selection scheme (BRS), we also derive an ASER expression for XQAM. Numerical and simulated results are compared to validate the correctness of derived expressions. Furthermore, comparative analysis of RQAM and XQAM schemes is discussed which confirms that XQAM is better alternative over RQAM for transmission of odd number of bits per symbol for the considered system model. We also compare the ASER performance for MRC and BRS schemes in terms of SNR gain using different XQAM constellations. Moreover, the impact of system parameters on ASER is also highlighted.     

BER of OFDM in Rayleigh fading environments with selective diversity

This paper derives the analytical bit error rate (BER) of orthogonal frequency division multiplexing (OFDM) systems employing selective diversity in Rayleigh fading environments. First, the probability density function (pdf) of inter‐carrier interference (ICI) power in Rayleigh fading environments is derived. Second, the pdf of the signal‐to‐interference ratio (SIR) is then derived. The cumulative distribution function (cdf) and hence pdf of the SIR with selective diversity are then given in the third and fourth steps. Using the BER expressions of binary phase shift keying (BPSK) and differential BPSK (DBPSK) modulation in an added white Gaussian noise (AWGN), the corresponding BER expressions of OFDM systems can then be derived. Detailed discussions are given. Possible future work is also outlined. Copyright © 2009 John Wiley & Sons, Ltd.     

Exact BER analysis of M‐ary orthogonal signaling with MRC over Ricean fading channels

A new approach for analyzing the performance of coherent M‐ary orthogonal signaling with maximal ratio combining over Ricean fading channels is presented here. A new series representation for the bit‐error rate is derived, making it possible to compute error rates with guaranteed accuracy. Copyright © 2007 John Wiley & Sons, Ltd.     

Error performance of selection combining and switched combining systems in Rayleigh fading channels with imperfect channel estimation

In this paper, we present a general analysis of the performance of selection combining (SC), switch-and-stay combining (SSC), and switch-and-examine combining (SEC) systems in Rayleigh fading channels with imperfect channel estimation (ICE). The complex channel estimate and the actual fading are modeled as jointly Gaussian random variables. For SC systems with channel estimation error, closed-form expressions are obtained for the error rates of M/sub s/-ary pulse amplitude modulation (PAM) and rectangular-quadrature amplitude modulation (QAM), and simple single integral formulas with finite integration limits are derived for the symbol error probability of arbitrary two-dimensional (2-D) modulation formats. These error probability expressions are then applied to three types of channel estimation errors potentially encountered in practical systems to study their impact on the performance of selection diversity. Moreover, single integral formulas with finite integration limits are derived for the performance of SSC and SEC systems with minimum mean square error (MMSE) channel estimation. Optimum switching thresholds for 2-D modulation formats with MMSE based switched combining are acquired through numerical computation.     

Performance analysis of optimum combining in wirelesscommunications with Rayleigh fading and cochannel interference

Optimum combining for space diversity reception is studied in digital cellular mobile radio communication systems with Rayleigh fading and multiple cochannel interferers. This paper considers binary phase-shift keying (BPSK) modulation in a flat Rayleigh-fading environment when the number of interferences L is no less than the number of antenna elements N(L⩾N). The approach of this paper and its main contribution is to carry out the analysis in a multivariate framework. Using this approach and with the assumption of equal-power interferers, it is shown that the probability density function of the maximum signal-to-interference ratio (SIR) at the output of the optimum combiner has a Hotelling T² distribution. Closed form expressions using hypergeometric functions are derived for the outage probability and the average probability of bit error. Theoretical results are demonstrated by Monte Carlo simulations     

Performance analysis of system with L‐branch selection combining over correlated Weibull fading channels in the presence of cochannel interference

In this paper, the performance of L‐branch selection combining receiver over correlated Weibull fading channels in the presence of correlated Weibull‐distributed cochannel interference is analyzed. Closed‐form expressions for probability density function and cumulative distribution function of the signal‐to‐interference ratio at the output of the selection combining receiver present main contribution of this paper. Numerical results are also presented to show the effects of various parameters as the fading severity, correlation and number of branches on outage probability. Copyright © 2009 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.     

Performance analysis of coded space‐time adaptive detection in DS/CDMA systems over Rayleigh fading channels

In this paper, we study the use of channel coding in a direct‐sequence code‐division multiple‐access (DS‐CDMA) system that employs space‐time adaptive minimum‐mean square‐error (MMSE) interference suppression over Rayleigh fading channels. It is shown that the employment of adaptive antenna arrays at the receiver can assist in attenuating multiuser interference and at the same time speeds‐up the convergence rate of the adaptive receiver. In this work, we assess the accuracy of the theoretical results developed for the uncoded and convolutionally coded space‐time multiuser detector when applied to the adaptive case. It is found that the use of antenna arrays brings the receiver performance very close to its multiuser counterpart. Using performance error bounds, we show that a user‐capacity gain of approximately 200% can easily be achieved for the space‐time adaptive detector when used with a rate 1/2 convolutional code (CC) and a practical channel interleaver. This capacity gain is only 10% less than the gain achieved for the more complicated multiuser‐based receiver. Finally, we perform a comparison between convolutional and turbo coding where we find that the latter outperforms the former at all practical bit‐error rates (BER). Copyright © 2006 John Wiley & Sons, Ltd.     

Outage probability and error rate analysis of full duplex relay in asymmetric fading channels

Full duplex (FD) technique has evolved as a viable solution to address the spectrum scarce issue. It has gained research interest for its potential to double the wireless link capacity and enhance spectral efficiency (SE). In this paper, the end-to-end performance of an amplify-and-forward full duplex relay(FDR) in asymmetric Rayleigh–Rician fading channels is explored, unlike the other works that assume symmetric fading conditions in both the links. The asymmetric or mixed fading channels properly model the realistic communication scenarios like satellite/terrestrial wireless communication systems. In this work, we consider that the source-relay link experiences Rayleigh fading and the relay-destination link experiences Rician fading. The novel exact and lower bound closed form analytical expressions for outage probability (OP) and bit error rate (BER) for the considered FD system are derived. Moreover, the effect of severity of fading and the amount of residual self-interference (RSI) on the performance of FDR are also studied. In addition, MC simulations are carried out to validate the results. It is observed that the performance metrics, OP and BER, are highly dependent on the severity of fading and the amount of RSI. Furthermore, it is found that typically at the SNR of 10 dB, an improvement of approximately 27.6% in OP is obtained. Also, our work offers appreciable SNR gain, for example, for a BER of 10⁻², an SNR improvement of around 11 dB is achieved. These findings have been compared with the mixed Rayleigh–Rician fading channel conditions considering only half duplex(HD) mode. These parameter metrics are helpful in analyzing the performance of FD in various communication scenarios such as LoS/NLoS conditions and hence pave the way for more realistic FDR.     

协同通信系统中差分调制在Rayleigh衰落信道中的误码性能分析

根据源-中继-目的节点链路的等效信噪比模型,推导了检测传送和选择检测传送两种协议下目的节点瞬时信噪比的概率密度函数和特征函数,基于此推导了协同DMPSK调制近似误符号率的闭合表达式.推导结果不含积分表达式,方便计算,为系统设计和功率分配提供了理论基础.最后通过仿真验证了推导结果的正确性.