Selection Combining Diversity Research Articles

Subcarrier Intensity Modulated Free-Space Optical Communications in K-Distributed Turbulence Channels

In this paper, the bit error rate (BER) performance of a subcarrier intensity-modulated (SIM) free-space optical (FSO) communications system using binary phase shift keying (BPSK) is investigated over a K-distributed turbulence channel. First, the performance is analyzed employing a negative exponential turbulence model, and an exact closed-form expression is derived for the BER. Then, it is shown that the probability density function (PDF) of the K distribution can be approximated accurately by a finite sum of weighted negative exponential PDFs. Based on this interesting result and by using the closed-form expression, which is derived for the case of a negative exponential model, an approximate, closed-form expression for the BER of the BPSK-based SIM FSO over a K channel is derived. Moreover, to improve the BER performance, spatial diversity using selection combining (SC) is considered. It is shown that the PDF of the resulting channel irradiance corresponding to the SC diversity scheme over a K channel can be approximated accurately by a finite linear combination of negative exponential functions. The derived approximate PDF accurately estimates the PDF of the channel irradiance for arbitrary values of diversity order and is valid for a wide range of channel parameters. Then, an approximate, closed-form expression is derived for the average BER of the BPSK-based SIM FSO system employing the SC diversity technique over a K channel. Numerical results presented in this paper show that the derived approximate expressions are very accurate and can be used as efficient tools for performance analysis of the system.

BER of Differentially Detected π/4-DQPSK with Selection Combining in Nakagami-m Fading

Nakagami’s m distribution is a versatile statistical model to characterize small-scale multipath fading in wireless channels. On the other hand, selection combining (SC) is a widely practiced diversity technique to mitigate the detrimental effects of multipath fading. Thus, when SC is applied over Nakagami fading channel, the error performance improvement for any given modulation format is of considerable interest. Since the last decade, π/4-shifted differential quadrature phase shift keying (π/4-DQPSK) modulation has attracted much attention as it is used for high-capacity code division multiple access (CDMA) based digital cellular systems. One of the major reasons behind this is the provision for differential detection which allows production of low complexity mobile units. In this paper, we present analytical expressions for bit error rate (BER) of π/4-DQPSK modulation with L-branch SC diversity in Nakagami-m fading channels perturbed by additive white Gaussian noise (AWGN). The derived end expressions are in closed form and contain finite series of Gaussian hypergeometric function. This makes evaluation of error rates much more straightforward compared to earlier approaches that required single or even double numerical integration. Some special instances such as the nondiversity case and Rayleigh fading case are also investigated and plotted along with the main findings. For different fading parameter (m) values and for different diversity orders (L), simulated results are shown to be in excellent agreement with the derived analytical results. All the results are, however, limited to integer values of fading severity parameter m.

Performance evaluation of half-duplex relay-based opportunistic cooperation diversity

Cooperative diversity is proposed as a means to improve the wireless transmission performance, which can effectively combat the wireless fading through sharing the antennas between source and relay nodes. In this paper, considering the practicability, we investigate the use of half-duplex relay, rather than full-duplex relay, for the opportunistic cooperation diversity. Two combining methods, namely selection diversity combining (SDC) and maximum ratio combining (MRC), are utilized for the implementation of the half-duplex relay-based opportunistic cooperation. Closed-form expressions of outage probability are derived for the proposed opportunistic cooperation as well as the known deterministic cooperation over Rayleigh fading channels. Numerical results show that the opportunistic cooperation is superior to the traditional deterministic cooperation in terms of outage probability and, moreover, the MRC-based case outperforms the SDC-based case no matter which duplex mode relay (i.e., half-duplex and full-duplex) is used for the opportunistic cooperation.

Switching rates of two-branch selection diversity in correlated Doppler fading

The switching rate of a correlated dual branch selection diversity combiner in Rayleigh and Rician fading is derived in noise-free conditions. Balanced and unbalanced branches are considered. Numerical results are presented for a space-diversity system with horizontally spaced omnidirectional antennas at a mobile station.

Switching rates of dual selection diversity in noisy fading channels

The effect of noise on the switching rate of a dual branch selection diversity combiner in noisy fading channels is examined. A closed-form solution is derived for independent and identically distributed (i.i.d.) and independent and nonidentically distributed (i.n.d.) fading channels. The switching rate in noisy fading channels is compared to that in noise-free conditions.

Outage analysis of opportunistic cooperation over rayleigh fading channels

Cooperation is emerging as a promising technology to combat the wireless fading and enhance the channel capacity. However,cooperative transmission can not be guaranteed to perform better always than direct transmission, since the statistics of both direct and relay channels are varied due to large scale fading. Therefore, we design an opportunistic criterion to automatically determine which transmission mode should be adopted depending on the channel quality from the source to the cooperative relay, as opposed to the deterministic cooperation regardless of relay channel conditions. According to the proposed criterion, we further present two opportunistic cooperation schemes, namely, the SDC (selection diversity combining) -based and the MRC (maximum ratio combining) -based opportunistic cooperation, and develop the closed-form expressions of outage probability for the proposed schemes over Rayleigh fading channels. For the purpose of comparison, we also analyze the outage probability for the known deterministic cooperation and coded cooperation. Numerical results show that our schemes outperform the traditional schemes in terms of outage probability, especially when the relay channel conditions worsen. In addition, we compare the MRC-based opportunistic cooperation with the SDC-based opportunistic cooperation, showing the superiority of the former scheme.

Stochastic approach for output SINR computation at SC diversity systems with correlated Nakagami‐m fading

AbstractIn this paper, we derive the cumulative distribution function of the signal‐to‐interference + ,noise ratio (SINR) achieved by the selection combining (SC) diversity receiver operating over correlated Nakagami‐m channel in the presence of co‐channel interference. Numerical and simulation results are presented to show the effects of fading severity and signal and interference imbalance on the system's performance. Copyright © 2009 John Wiley & Sons, Ltd.

Switching rates of two-branch selection diversity in κ-μ and α-μ distributed fadings

An analytical expression for the switching rate of a dual branch selection diversity combiner in kappa-mu and alpha-mu distributed fadings is derived. Independent and identically distributed (i.i.d.) kappa-mu as well as alpha-mu fading channels are considered. The switching rates for dual i.i.d. Rayleigh, Rician and Nakagami-m fading channels are special cases of the switching rate for dual i.i.d. kappa-mu fading channels. Similarly, the general switching rates for dual alpha-mu fading channels also include special cases such as Rayleigh, Nakagami-m, and Weibull fading channels.

Spectral efficiency evaluation for selection combining diversity (SCD) scheme over slow fading

In this paper we derive closed-form expressions for the single-user capacity of selection combining diversity (SCD) system, taking into account the effect of imperfect channel estimation at the receiver. The channel considered is a slowly varying spatially independent flat Rayleigh fading channel. The complex channel estimate and the actual channel are modelled as jointly Gaussian random variables with a correlation that depends on the estimation quality. Three adaptive transmission schemes are analysed: 1) optimal power and rate adaptation opra; 2) constant power with optimal rate adaptation ora; and 3) channel inversion with fixed rate cifr. Furthermore, we derive in this paper analytical results for capacity statistics including moment generating function (MGF), complementary cumulative distribution function (CDF) and probability density function (PDF). These statistics are valid for arbitrary number of receive antennas. Our numerical results show the effect of Gaussian channel estimation error on the achievable spectral efficiency.

The Criterions with LCR and AFD of Dual-Branch SC Diversity over Specified Wireless Radio Fading Channels

In this paper we proposed the results of average LCR (level crossing rate) and AFD (average fading duration) criterions applied to evaluate the performance of dual-branch SC (selection combining) reception in the specified fading channels characterized as statistical distributions with correlated-Rayleigh and correlated-Rice models. Moreover, in order to unify and clarify the criterions of performance formulas with average LCR and AFD for SC diversity over different kinds of fading models, include such as Rayleigh, Rice, Nakagami-m, and Weibull distributions etc., almost all of the ever researched and published results from discussing about the LCR and AFD of SC diversity are comprehensively collected in this report. On the other hand, for the purpose of comparison, there are a large number of LCR and AFD performance formulas for SC diversity and the generalized fading statistic models are extracted and tabulated together, in which the cases of correlated and independent proprieties between diversity branches are taken into consideration too (some of the formulas are illustrated by the assumption of dual-branch SC diversity).

Evaluation on the Selective Combining for the Detection of M-ary DPSK Signals over Nakagami Fading Channels

The performances of M-ary DPSK(MDPSK) for diversity reception theoretically are derived, using an L-branch selection combining(SC) in frequency-nonselective slow Nakagami fading channels. For integer values of the Nakagami fading parameter m, An exact closed-form symbol error rate(SER) multichannel performance that can be easily evaluated via numerical integration is presented. Finally, we compare these analyses with numerical analyses with integral-form expressions for the performance of MDPSK signals under the effect of two-branch SC diversity over slow and nonselective Rician fading channels with additive white Gaussian noise(AWGN).

A unified approach to average LCR and AFD performance of SC diversity in generalized fading environments

The average level crossing rate (LCR) and average fading duration (AFD) criterions are applied to analyze the selection combining (SC) diversity for wireless communication systems over correlated-Rayleigh and correlated-Rice fading in this paper. The scenarios of the fading channel models are characterized as 4 generalized and experimental distributions, e.g., Rayleigh, Rice, Nakagami- m, and Weibull distributed statistics. Moreover, both of independent and correlated proprieties between branches are also involved for consideration. For purpose of unifying and clarifying the average LCR and AFD performance formulas results from the evaluation for SC diversity, it is not only the results from our research presented, but some of the published results are also cited and illustrated by numerical evaluation again in this study.

SER of selection diversity MFSK with channel estimation errors

The performance of the selection diversity combiner in slowly and flatly fading channels is studied. Unlike most previous works where perfect knowledge of the signal amplitude and the noise power is assumed, in this analysis, knowledge of the signal amplitude and the noise power is obtained by using practical estimators that introduce estimation errors. The average symbol error rate of the combiner is derived for noncoherent M-ary frequency shift keying signals, independent and non-identically distributed diversity branches and unequal noise powers. The effect of estimation errors on the performance of the combiner is evaluated and illustrated by numerical examples. An interesting and useful conclusion is that it is disadvantageous to employ signal-to-noise ratio as a branch selection criterion when the branch noise powers are known a priori to be equal

Average LCR and AFD for SC Diversity Over Correlated Weibull Fading Channels

The analytic methods of average LCR (Level Crossing Rate) and AFD (Average Fading Duration) are applied in the analysis for the SC (Selection Combining) diversity, which works over the correlated Weibull statistics channel. The dual branch SC diversity was used to prove the accuracy of the derived theoretical formula in this paper. We adopt different probability density functions (pdf) and cumulate distribution functions (CDF) to show the Moreover, the numerical results obtained from computer are verified to the published researches.

Performance analysis of linear diversity-combining schemes on Rayleigh fading channels with binary signaling and Gaussian weighting errors

In this paper, we analyze the error probability performance of maximal-ratio combining (MRC), equal-gain combining (EGC), selection combining (SC), and generalized-selection combining (GSC) diversity schemes with coherent binary phase-shift keying (BPSK) signaling on Rayleigh fading channels with Gaussian channel-estimation errors. We first show that, with weighting errors, averaging the conditional probability of error with the density function of the instantaneous signal-to-noise ratio (SNR) at the output of the combiner yields a lower bound on the exact probability of error. Later, we derive the exact probability of error for MRC, EGC, SC, and GSC diversity schemes and show that, for the case of nonnegative values of the in-phase correlation coefficient between the actual and the estimated channel gains, the exact probability of error with weighting errors is the same as that of the case with perfect channel estimation, but with the average SNR per diversity branch /spl gamma/~, for the case of perfect channel estimation, replaced by the effective SNR /spl gamma/~/sub /spl rho//, due to weighting errors. The effective SNR is a function of both /spl gamma/~ and /spl rho/, the magnitude of the normalized cross correlation between the actual and the estimated channel gains. Finally, we show that, as /spl rho//spl rarr/0, the average probability of error approaches 0.5, irrespective of the order of diversity and the diversity-combining rule.

Performance Analysis of Coded Communication Systems on Nakagami Fading Channels With Selection Combining Diversity

In this paper, we develop analytical tools for the performance analysis of coded, coherent communication systems on independent and identically distributed Nakagami-m fading channels with selection combining (SC) diversity. First, we derive an exact expression for the moment generation function (MGF) of the signal-to-noise ratio (SNR) of a code symbol at the output of the selection combiner. Next, based on Gauss-Chebyshev quadrature and Gauss-Laguerre quadrature rules, we propose a simple to compute, yet accurate, numerical solution for the pairwise error probability (PEP) of coded M-phase-shift keying (PSK) signals. Using the PEP expressions, we present the union bound-based bit-error performance of trellis-coded modulation schemes and turbo codes. Finally, we derive an exact expression for the computational cutoff rate of a coded system with M-PSK signaling and SC diversity, and show that the cutoff rate expression is a simple function of the MGF of the SNR at the output of the diversity combiner.

Level Crossing Rate and Average Fade Duration of the Select-and-Hold Policy of Selection Diversity Combining in a Rayleigh Fading Channel

The select-and-hold policy (SAH) is a general form of selection diversity combining (SDC). In this letter, we provide closed-form expressions for average level crossing rate and average fade duration for Nth-order SAH-SDC. The diversity branches are assumed to be independent and identical Rayleigh fading channels. A useful guideline for choice of the holding time is also obtained.

Average probability of packet error with diversity reception over arbitrarily correlated fading channels

AbstractClosed form expressions for the average probability of packet error (PPE) are presented for no diversity, maximum ratio combining (MRC), selection combining (SC) and switch and stay combining (SSC) diversity schemes. The average PPE for the no diversity case is obtained in two alternative expressions assuming arbitrarily correlated Nakagami and Rician fading channels. For the MRC case, L diversity branches are considered and the channel samples are assumed to follow Nakagami distribution and to be arbitrarily correlated in both time and space. For the SC diversity scheme with L diversity branches, two bounds on the average PPE are derived for both slow and fast fading channels. The average PPE in this case is obtained in an infinite integral form for Nakagami channels while it is reduced to a closed form expression for the Rayleigh case. The average PPE is also derived in the case of SSC diversity with dual branches for both slow and fast Rayleigh fading channels. The new formulas are applicable for all modulation schemes where the conditional probability of error has an exponential dependence on the signal‐to‐noise ratio. The average PPE is then used to obtain a modified expression for the throughput for network protocols. In general, the diversity gain exhibits a little diminishing effect as the number of diversity branches increases. In addition, the system is found to be more sensitive to the space correlation than to the time correlation. The effects of different system parameters and diversity schemes are studied and discussed. Specific figures about the system performance are also provided. Copyright © 2004 John Wiley & Sons, Ltd.

New method of performance analysis for diversity reception with correlated rayleigh-fading signals

Fang et al. (2000) attempted to simplify the procedures of performance analysis for maximal ratio combining (MRC), selection combining (SC), and equal gain combining (EGC) diversity systems of two correlated Rayleigh-fading channels by using a known transformation technique. It was then found by Loyka et al. (for comment see ibid., vol. 52, no. 3, p. 725-726 (2003)) that this transformation technique is correct for MRC, but leads to some performance-prediction deviations for SC and EGC diversity systems compared to the results produced by other reported approaches. Because the transformation process redistributes the signal energy among different antennas, the bit error ratio (BER) achieved after the transformation may be different from that without transformation. For SC and EGC, the transformation technique can provide the same BER as that achieved without the transformation technique when the correlation is not strong and the signal-to-noise ratio (SNR) is large (p/sup 2/ < 0.8 and SNR > 8 dB, for example). In the case of small SNR and strong correlation, desirable performance gain in BER can be achieved by the transformation technique for the SC diversity system. However, the transformation technique produces an undesirable performance loss in terms of the BER for the EGC diversity system. It is not sufficient to use one example, as in Loyka et al. (fig. 2), to assess when the transform technique for SC predicts performance that deviates from reported approaches.

A one-shot LDD with pre-SDC/post-MRC for random CDMA over asynchronous Rayleigh channels

It is well known that conventional detectors of direct sequence-code division multiple access systems are interference-limited. Multiuser detection has been considered as a promising approach to combat this problem. Since an optimal multiuser detector is too complex to implement, several suboptimal multiuser detector techniques have been developed. The one-shot linear decorrelating detector (LDD) was proposed to reduce the computational complexity and delay required in the conventional LDD, but it still require high complexity. Another one-shot LDD with low complexity was proposed. To improve its performance, this detector uses a maximal ratio combining (MRC) at the two outputs of the left piece of the present bit and the right piece of the next bit in an one-shot window; this detector is called as a one-shot LDD with post-MRC. In spite of the aid of MRC, the performance of the one-shot LDD with post-MRC is worse than the one-shot LDD. To overcome this problem, we propose the one-shot LDD with pre-SDC/post-MRC that employs selection diversity combining (SDC) with multiple antenna elements in front of the one-shot LDD with post-MRC. In asynchronous random code division multiple access systems over fading channels, the largest signal-to-noise ratio (SNR) of SDC, near-far resistance (NFR) of the one-shot LDD, and the output SNR of MRC are random variables. We derive the probability density functions (PDFs) for these random variables and calculate the bit error rate) of the proposed detector using the obtained PDFs. In a comparison of mathematical analysis and computer simulation results, we observe good agreement.