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## On the error rate analysis of dual-hop amplify-and- forward relaying in Generalized-K fading channels (2010)

Venue: | Journal of Electrical and Computer Engineering |

Citations: | 2 - 0 self |

### Citations

1259 |
Table of integrals, series, and products
- Gradshteyn, Ryzhik
- 2000
(Show Context)
Citation Context ... results are given in Section 4, while concluding remarks are given in Section 5. 2. Statistics of the Generalized-K Distribution We assume that the fading environment is such that the signal envelope X in a receive antenna is a generalized-K distributed random variable with pdf given by [9] fX(x) = 4m (k+m)/2 Γ(m)Γ(k)Ω(k+m)/2 xk+m−1 × Kk−m ( 2 ( m Ω )1/2 x ) , x ≥ 0, (1) where k and m are the distribution’s shaping parameters,Ω = E[X2]/k is the mean power with E[·] denoting expectation, Γ(·) is the Gamma function, and Kk−m(·) is the (k − m)th order modified Bessel function of the second kind [14]. The instantaneous received SNR per symbol of a single receiver is γ = X2Es/N0, where Es is the symbol energy and N0 is the single-sided power spectral density of the additive white Gaussian noise (AWGN). The corresponding average received SNR per symbol is given as γ = kΩ · Es/N0. The pdf of γ is given by fγ ( γ ) = 2Ξ(k+m)/2 Γ(m)Γ(k) γ(k+m)/2−1Kk−m ( 2 √ Ξγ ) , γ ≥ 0, (2) DestinationSource Relay N Relay 1 γ0 γ12γ11 γN2γN1 γout ... Figure 1: Cooperative dual-hop relay transmission scheme with MRC at the destination. with Ξ = (km)/γ. The cdf of γ, defined as Fγ(γ) = ∫ γ 0 fγ(x)dx, has been ob... |

164 |
End-to-end performance of transmission systems with relays over Rayleigh-fading channels,”
- Hasna, Alouini
- 2003
(Show Context)
Citation Context ... has been shown to provide high data rate coverage and mitigate channel impairments in next generation wireless systems. Amplify-and-forward relay techniques have attracted a lot of attention recently as they provide a simple way to implement collaborative/cooperative wireless communication systems. For dual-hop nonregenerative systems, the end-to-end signal-to-noise ratio (SNR) at the receiving node depends on the amplification gain employed at the relays. For relays with channel side information (CSI) of the first link, the end-to-end SNR of a single dual-hop relay link has been obtained in [1]. For this relay transmission scenario, analytical performance results have been obtained by approximating the end-to-end SNR by the harmonic mean of the SNRs of the two hops [2], their geometric mean [3], and the minimum SNR of the two hops [4, 5]. Among the proposed approximations for the endto-end SNR of dual-hop transmission, the harmonic mean and the minimum SNR bounds have been shown to result in tight performance bounds [2, 4], whereas the geometric mean bound has been shown to give accurate results for low and medium values of the SNR per hop [3, 4]. Using one of the above proposed upp... |

55 | Performance analysis of cooperative diversity wireless networks over Nakagami-m fading channel
- Ikki, Ahmed
- 2007
(Show Context)
Citation Context ...llaborative/cooperative wireless communication systems. For dual-hop nonregenerative systems, the end-to-end signal-to-noise ratio (SNR) at the receiving node depends on the amplification gain employed at the relays. For relays with channel side information (CSI) of the first link, the end-to-end SNR of a single dual-hop relay link has been obtained in [1]. For this relay transmission scenario, analytical performance results have been obtained by approximating the end-to-end SNR by the harmonic mean of the SNRs of the two hops [2], their geometric mean [3], and the minimum SNR of the two hops [4, 5]. Among the proposed approximations for the endto-end SNR of dual-hop transmission, the harmonic mean and the minimum SNR bounds have been shown to result in tight performance bounds [2, 4], whereas the geometric mean bound has been shown to give accurate results for low and medium values of the SNR per hop [3, 4]. Using one of the above proposed upper bounds for the total SNR, the performance of dual-hop relaying has been studied in terms of outage probability and average bit error rate (BER) for various symmetrical fading conditions, such as Rayleigh [1], Nakagami-m [2–4], Weibull [5], and g... |

44 |
Harmonic mean and end-toend performance of transmission systems with relays,”
- Hasna, Alouini
- 2004
(Show Context)
Citation Context ... of attention recently as they provide a simple way to implement collaborative/cooperative wireless communication systems. For dual-hop nonregenerative systems, the end-to-end signal-to-noise ratio (SNR) at the receiving node depends on the amplification gain employed at the relays. For relays with channel side information (CSI) of the first link, the end-to-end SNR of a single dual-hop relay link has been obtained in [1]. For this relay transmission scenario, analytical performance results have been obtained by approximating the end-to-end SNR by the harmonic mean of the SNRs of the two hops [2], their geometric mean [3], and the minimum SNR of the two hops [4, 5]. Among the proposed approximations for the endto-end SNR of dual-hop transmission, the harmonic mean and the minimum SNR bounds have been shown to result in tight performance bounds [2, 4], whereas the geometric mean bound has been shown to give accurate results for low and medium values of the SNR per hop [3, 4]. Using one of the above proposed upper bounds for the total SNR, the performance of dual-hop relaying has been studied in terms of outage probability and average bit error rate (BER) for various symmetrical fading ... |

37 | On the performance analysis of digital communications over Generalized-K fading channels,”
- Bithas, Sagias, et al.
- 2006
(Show Context)
Citation Context ...nd slow fading on the received signal. This fading model corresponds to a Nakagami-Gamma composite distribution and is controlled by two shaping parameters m and k, where m is the Nakagami parameter for the short-term fading and k is the parameter of the gamma distribution for the received average power due to shadowing [9]. Note that the K distribution [10] is derived as a special case of the generalized-K distribution by letting m = 1 (i.e., Rayleigh short-term fading). A number of results on the performance analysis of communication links in this fading model can be found in the literature [11, 12]. 2 Journal of Electrical and Computer Engineering Recently, analytical expressions for the error rate performance of dual-hop relaying over generalized-K fading channels were given in terms of convergent infinite series in [13], using the minimum SNR upper bound for the end-toend SNR and averaging the conditional BER over the derived probability density function (pdf) of the total SNR. However, these expressions are restricted to a single dual-hop relay system and result in some truncation error depending on the number of terms employed. Furthermore, the expressions in [13] cannot be evaluate... |

33 |
Error rates in generalized shadowed fading channels,”
- Shankar
- 2004
(Show Context)
Citation Context ...unds [2, 4], whereas the geometric mean bound has been shown to give accurate results for low and medium values of the SNR per hop [3, 4]. Using one of the above proposed upper bounds for the total SNR, the performance of dual-hop relaying has been studied in terms of outage probability and average bit error rate (BER) for various symmetrical fading conditions, such as Rayleigh [1], Nakagami-m [2–4], Weibull [5], and generalized Gamma [6] fading, as well as for asymmetrical links [7, 8], although most analyses have been restricted to single dual-hop relay links. The generalized-K fading model [9] has also attracted considerable attention as one of the most general wireless fading models that can characterize the combined effects of fast and slow fading on the received signal. This fading model corresponds to a Nakagami-Gamma composite distribution and is controlled by two shaping parameters m and k, where m is the Nakagami parameter for the short-term fading and k is the parameter of the gamma distribution for the received average power due to shadowing [9]. Note that the K distribution [10] is derived as a special case of the generalized-K distribution by letting m = 1 (i.e., Rayleig... |

29 |
K distribution: an appropriate substitute for Rayleigh-lognormal distribution in fadingshadowing wireless channels,”
- Abdi, Kaveh
- 1998
(Show Context)
Citation Context ...st analyses have been restricted to single dual-hop relay links. The generalized-K fading model [9] has also attracted considerable attention as one of the most general wireless fading models that can characterize the combined effects of fast and slow fading on the received signal. This fading model corresponds to a Nakagami-Gamma composite distribution and is controlled by two shaping parameters m and k, where m is the Nakagami parameter for the short-term fading and k is the parameter of the gamma distribution for the received average power due to shadowing [9]. Note that the K distribution [10] is derived as a special case of the generalized-K distribution by letting m = 1 (i.e., Rayleigh short-term fading). A number of results on the performance analysis of communication links in this fading model can be found in the literature [11, 12]. 2 Journal of Electrical and Computer Engineering Recently, analytical expressions for the error rate performance of dual-hop relaying over generalized-K fading channels were given in terms of convergent infinite series in [13], using the minimum SNR upper bound for the end-toend SNR and averaging the conditional BER over the derived probability den... |

11 | Performance analysis of the dual-hop asymmetric fading channel,”
- Suraweera, Karagiannidis, et al.
- 2009
(Show Context)
Citation Context ...al-hop transmission, the harmonic mean and the minimum SNR bounds have been shown to result in tight performance bounds [2, 4], whereas the geometric mean bound has been shown to give accurate results for low and medium values of the SNR per hop [3, 4]. Using one of the above proposed upper bounds for the total SNR, the performance of dual-hop relaying has been studied in terms of outage probability and average bit error rate (BER) for various symmetrical fading conditions, such as Rayleigh [1], Nakagami-m [2–4], Weibull [5], and generalized Gamma [6] fading, as well as for asymmetrical links [7, 8], although most analyses have been restricted to single dual-hop relay links. The generalized-K fading model [9] has also attracted considerable attention as one of the most general wireless fading models that can characterize the combined effects of fast and slow fading on the received signal. This fading model corresponds to a Nakagami-Gamma composite distribution and is controlled by two shaping parameters m and k, where m is the Nakagami parameter for the short-term fading and k is the parameter of the gamma distribution for the received average power due to shadowing [9]. Note that the K ... |

10 | Diversity reception over generalized-K (KG) fading channels,”
- Bithas, Mathiopoulos, et al.
- 2007
(Show Context)
Citation Context ...nd slow fading on the received signal. This fading model corresponds to a Nakagami-Gamma composite distribution and is controlled by two shaping parameters m and k, where m is the Nakagami parameter for the short-term fading and k is the parameter of the gamma distribution for the received average power due to shadowing [9]. Note that the K distribution [10] is derived as a special case of the generalized-K distribution by letting m = 1 (i.e., Rayleigh short-term fading). A number of results on the performance analysis of communication links in this fading model can be found in the literature [11, 12]. 2 Journal of Electrical and Computer Engineering Recently, analytical expressions for the error rate performance of dual-hop relaying over generalized-K fading channels were given in terms of convergent infinite series in [13], using the minimum SNR upper bound for the end-toend SNR and averaging the conditional BER over the derived probability density function (pdf) of the total SNR. However, these expressions are restricted to a single dual-hop relay system and result in some truncation error depending on the number of terms employed. Furthermore, the expressions in [13] cannot be evaluate... |

9 | BER analysis of collaborative dual-hop wireless transmissions,”
- Tsiftsis, Karagiannidis, et al.
- 2004
(Show Context)
Citation Context ...they provide a simple way to implement collaborative/cooperative wireless communication systems. For dual-hop nonregenerative systems, the end-to-end signal-to-noise ratio (SNR) at the receiving node depends on the amplification gain employed at the relays. For relays with channel side information (CSI) of the first link, the end-to-end SNR of a single dual-hop relay link has been obtained in [1]. For this relay transmission scenario, analytical performance results have been obtained by approximating the end-to-end SNR by the harmonic mean of the SNRs of the two hops [2], their geometric mean [3], and the minimum SNR of the two hops [4, 5]. Among the proposed approximations for the endto-end SNR of dual-hop transmission, the harmonic mean and the minimum SNR bounds have been shown to result in tight performance bounds [2, 4], whereas the geometric mean bound has been shown to give accurate results for low and medium values of the SNR per hop [3, 4]. Using one of the above proposed upper bounds for the total SNR, the performance of dual-hop relaying has been studied in terms of outage probability and average bit error rate (BER) for various symmetrical fading conditions, such as Raylei... |

9 | Closed-form error analysis of the non-identical Nakagami-m relay fading channel,”
- Suraweera, Karagiannidis
- 2008
(Show Context)
Citation Context ...al-hop transmission, the harmonic mean and the minimum SNR bounds have been shown to result in tight performance bounds [2, 4], whereas the geometric mean bound has been shown to give accurate results for low and medium values of the SNR per hop [3, 4]. Using one of the above proposed upper bounds for the total SNR, the performance of dual-hop relaying has been studied in terms of outage probability and average bit error rate (BER) for various symmetrical fading conditions, such as Rayleigh [1], Nakagami-m [2–4], Weibull [5], and generalized Gamma [6] fading, as well as for asymmetrical links [7, 8], although most analyses have been restricted to single dual-hop relay links. The generalized-K fading model [9] has also attracted considerable attention as one of the most general wireless fading models that can characterize the combined effects of fast and slow fading on the received signal. This fading model corresponds to a Nakagami-Gamma composite distribution and is controlled by two shaping parameters m and k, where m is the Nakagami parameter for the short-term fading and k is the parameter of the gamma distribution for the received average power due to shadowing [9]. Note that the K ... |

7 |
Performance analysis of dualhop relaying communications over generalized gamma fading channels,”
- Ikki, Ahmed
- 2007
(Show Context)
Citation Context ...sed approximations for the endto-end SNR of dual-hop transmission, the harmonic mean and the minimum SNR bounds have been shown to result in tight performance bounds [2, 4], whereas the geometric mean bound has been shown to give accurate results for low and medium values of the SNR per hop [3, 4]. Using one of the above proposed upper bounds for the total SNR, the performance of dual-hop relaying has been studied in terms of outage probability and average bit error rate (BER) for various symmetrical fading conditions, such as Rayleigh [1], Nakagami-m [2–4], Weibull [5], and generalized Gamma [6] fading, as well as for asymmetrical links [7, 8], although most analyses have been restricted to single dual-hop relay links. The generalized-K fading model [9] has also attracted considerable attention as one of the most general wireless fading models that can characterize the combined effects of fast and slow fading on the received signal. This fading model corresponds to a Nakagami-Gamma composite distribution and is controlled by two shaping parameters m and k, where m is the Nakagami parameter for the short-term fading and k is the parameter of the gamma distribution for the received ave... |

5 |
Performance analysis of dual hop relaying over non-identical weibull fading channelsw,”
- Ikki, Ahmed
- 2009
(Show Context)
Citation Context ...llaborative/cooperative wireless communication systems. For dual-hop nonregenerative systems, the end-to-end signal-to-noise ratio (SNR) at the receiving node depends on the amplification gain employed at the relays. For relays with channel side information (CSI) of the first link, the end-to-end SNR of a single dual-hop relay link has been obtained in [1]. For this relay transmission scenario, analytical performance results have been obtained by approximating the end-to-end SNR by the harmonic mean of the SNRs of the two hops [2], their geometric mean [3], and the minimum SNR of the two hops [4, 5]. Among the proposed approximations for the endto-end SNR of dual-hop transmission, the harmonic mean and the minimum SNR bounds have been shown to result in tight performance bounds [2, 4], whereas the geometric mean bound has been shown to give accurate results for low and medium values of the SNR per hop [3, 4]. Using one of the above proposed upper bounds for the total SNR, the performance of dual-hop relaying has been studied in terms of outage probability and average bit error rate (BER) for various symmetrical fading conditions, such as Rayleigh [1], Nakagami-m [2–4], Weibull [5], and g... |

1 |
On the performance analysis of digital modulations in generalized-K fading channels,” submitted to IET Communications,
- Efthymoglou
- 2010
(Show Context)
Citation Context ...antaneous received SNR per symbol of a single receiver is γ = X2Es/N0, where Es is the symbol energy and N0 is the single-sided power spectral density of the additive white Gaussian noise (AWGN). The corresponding average received SNR per symbol is given as γ = kΩ · Es/N0. The pdf of γ is given by fγ ( γ ) = 2Ξ(k+m)/2 Γ(m)Γ(k) γ(k+m)/2−1Kk−m ( 2 √ Ξγ ) , γ ≥ 0, (2) DestinationSource Relay N Relay 1 γ0 γ12γ11 γN2γN1 γout ... Figure 1: Cooperative dual-hop relay transmission scheme with MRC at the destination. with Ξ = (km)/γ. The cdf of γ, defined as Fγ(γ) = ∫ γ 0 fγ(x)dx, has been obtained in [15] for integer values of m and arbitrary values of k, as Fγ ( γ ) = 1− 2 ( Ξγ )k/2 Γ(k) m−1∑ r=0 1 r! ( Ξγ )r/2 Kk−r ( 2 √ Ξγ ) , γ ≥ 0. (3) Moreover, the MGF of γ, defined as Mγ(−s) =∫∞ 0 e −sγ fγ(γ)dγ, is given by [15] Mγ(−s) = 1 Γ(m)Γ(k) G 1,2 2,1 ( s Ξ ∣∣∣∣∣ 1− k, 1−m0 ) , (4) where G(·) is the Meijer’s G-function [14, equation (9.301)]. 3. End-to-End Error Rate Analysis We consider a dual-hop relay system with N relays as well as a direct link between the source and the destination, as shown in Figure 1. The output SNR, assuming MRC at the destination receiving end, can be written as γout =... |