Performance analysis of wireless communication system in general fading environment subjected to shadowing and interference
- Goran Stamenović†^{1},
- Stefan R Panić†^{2}Email author,
- Dejan Rančić†^{1},
- Časlav Stefanović†^{2} and
- Mihajlo Stefanović†^{1}
https://doi.org/10.1186/1687-1499-2014-124
© Stamenović et al.; licensee Springer. 2014
Received: 30 September 2013
Accepted: 9 July 2014
Published: 8 August 2014
Abstract
In this paper, performance analysis of wireless communication over α−η−μ fading channels has been investigated. First, analysis has been carried out for the case when communication is subjected to the influence of co-channel interference. Closed-form expressions have been derived for the probability density function and cumulative distribution function of the received signal-to-interference ratio. Outage probability has been obtained for this case, in the function of various values of system parameters, and also for the case when selection diversity has been presented at the reception. Further, simultaneous multipath fading and shadowing occurrence has been analyzed, through deriving novel composite Gamma long-time faded α−η−μ fading distribution. First-order statistical parameters have been obtained in closed form, for this novel composite distribution, and capitalizing on them, standard performance measures have been efficiently evaluated, graphically presented and discussed in the function of system parameters.
Keywords
α−η−μ distribution Co-channel interference Signal-to-interference ratio Selection combining Novel fading/shadowing composite model Average bit error rateIntroduction
Every wireless communication system design must take into account three major channel propagation impairments: short-term fading (multipath propagation), long-term fading (shadowing) and the corruptive effect of co-channel interference [1].
The non-linear properties of propagation medium have been considered extensive recently [2, 3]. Various short-term fading distributions like Nakagami-m, Ricean and Rayleigh assume a resultant homogenous diffuse scattering field, from randomly distributed scatters. However, surfaces are often spatially correlated and they characterize non-linear environment. Exploring the fact that the resulting envelope would be a non-linear function of the sum of multipath components, novel general α−η−μ distribution for short-term fading model was recently presented. Probability density function (PDF) is presented in the form of three parameters α, η and μ, which are related to the non-linearity of the environment, the number of multipath clusters in the environment and the scattered wave power ratio between the in-phase and quadrature components of each cluster of multipath, respectively [3].
Since it is a general fading distribution, the α−η−μ model includes as special cases other short-term fading distributions, like Rayleigh, Nakagami-q (Hoyt), Nakagami-m, η−μ, Weibull and one-side Gaussian distribution. By setting parameter α to value α=2, it reduces to η−μ distribution. Further, from the η−μ fading distribution, the Nakagami-m model could be obtained in two cases: first, for η→1, with parameter m being expressed as m=μ/2 and second, for η→0, with parameter m being expressed as m=μ. It is well-known that η−μ distribution reduces to the Hoyt distribution, for the case when μ=1, with parameter b defined as b=(1−η)/(1+η). By equating the in-phase and quadrature component variances, namely by setting η=1, the Rayleigh distribution is derived from Hoyt. Also the Weibull distribution could be obtained as a special case of the α−η−μ model by setting corresponding values to the parameters η=1 and μ=1. Major contribution of this analysis is then the above-mentioned generality.
Here, analytical framework for performance analysis of wireless communication system subjected to co-channel interference (CCI) over α−η−μ fading channels will be presented. Signal-to-interference (SIR)-based analysis will be provided and closed-form expressions will be provided for received SIR PDF and cumulative distribution function (CDF). From this statistics, outage probability (OP) values will be obtained in the function of system parameters. Even OP improvement will be observed through a prism of space diversity reception techniques appliance, particularly selection combining (SC) reception.
Number of composite channel models have been used in literature for the wireless communication systems analysis, for the case when multipath fading and shadowing occur simultaneously. Such are the η−μ/gamma [4], the κ−μ/gamma [5], the K[6], and the generalized- K (KG) [7] distribution models. Similar work has been presented in [8, 9]. Non-linear, non-homogenous, shadowed propagation have been analyzed in [10], but for the case when dominant, line-of-sight (LOS) component is taken into account. Starting from general α−η−μ distribution, closed-form statistics (PDF, CDF and n-th order moments expressions) will be introduced, for novel composite distribution. That is another contribution of this work since this composite distribution has not been reported in literature so far. Obtained mathematical form will allow simple performance analysis of wireless communication systems, operating in composite fading environments. This performance analysis is also accompanied by graphically presented numerical results, which show the influence of various communication system parameters (fading and shadowing parameters), on the standard performance criterions.
Transmission subjected to co-channel interference
In modern wireless communication systems, a tendency to preserve the available spectrum is present. Preserving of available spectrum could be obtained by reusing allocated frequency channels in areas, which are as geographically close to each other as possible. However, distance for reusing channels is limited by the level of CCI. CCI is defined as the interfering signal that has the same carrier frequency as the desired information signal, namely two or more channel signals from different locations, but operating at the same carrier frequency, due to frequency reuse interfere. In this section, we will analyze how CCI as a general distortion affects well-accepted criterions of wireless system performances. These effects will be observed in the function of instantaneous and average signal-to-interference ratios (SIRs). SIR-based performance analysis is a very effective performance criterion since SIR can be measured in real time both in base and mobile stations. An interference-limited system will be discussed, so the effect of noise would be ignored.
with Ω_{ d }=E[ R^{ α }], denoting the desired signal average power, while I_{ n }(.) is the n-th order modified Bessel function of the first kind ([11], Eq. (8.406)). As mentioned, parameter μ_{ d } defines the number of multipath clusters, through which desired signal propagates, while parameter η_{ d } defines the ratio of the in-phase and the in-quadrature component variances in desired signal [3]. Desired signal propagation environment non-linearity is defined with parameter α.
with Ω_{ c }=E[ r^{ α }], denoting the CCI signal average power. Parameters α, η_{ c } and μ_{ c } are describing CCI signal propagation in the same manner as parameters α, η_{ d } and μ_{ d } are describing propagation of desired signal.
Number of terms need to be summed in double-infinite series of Equation 5
λ/S=−10 dB | λ/S=0 dB | λ/S=10 dB | |||
---|---|---|---|---|---|
μ_{ d }=1.5; μ_{ c }=1.5 | |||||
α=2 | η_{ d }=0.8 | η_{ c }=0.8 | 4 | 3 | 3 |
α=2 | η_{ d }=1.6 | η_{ c }=1.6 | 6 | 5 | 5 |
α=1.5 | η_{ d }=0.8 | η_{ c }=0.8 | 3 | 3 | 3 |
α=1.5 | η_{ d }=1.6 | η_{ c }=1.6 | 5 | 5 | 4 |
μ_{ d }=2; μ_{ c }=2 | |||||
α=2 | η_{ d }=0.8 | η_{ c }=0.8 | 4 | 3 | 3 |
α=2 | η_{ d }=1.6 | η_{ c }=1.6 | 6 | 5 | 5 |
α=1.5 | η_{ d }=0.8 | η_{ c }=0.8 | 4 | 4 | 4 |
α=1.5 | η_{ d }=1.6 | η_{ c }=1.6 | 6 | 5 | 5 |
Number of terms need to be summed in infinite series of Equation 11
R/Ω=−10 dB | R/Ω=0 dB | R/Ω=10 dB | ||
---|---|---|---|---|
c=1 | ||||
μ=1.5 | η=1.6 | 6 | 6 | 5 |
μ=1.5 | η=0.8 | 4 | 3 | 3 |
μ=2 | η=1.6 | 7 | 6 | 6 |
μ=2 | η=0.8 | 3 | 3 | 3 |
c=1.5 | ||||
μ=1.5 | η=1.6 | 6 | 5 | 5 |
μ=1.5 | η=0.8 | 3 | 3 | 3 |
μ=2 | η=1.6 | 9 | 8 | 6 |
μ=2 | η=0.8 | 4 | 3 | 3 |
System performances
Selection combining
where corresponding CDF’s for the uncorrelated input branches are defined with (5).
Numerical results
Further, performance improvement obtained by the appliance of selection combining (SC) reception technique was presented at this figure. Improvement obtained with the usage of dual-branch SC diversity is visible, since for the same system parameter values, significantly lower OP values are reached.
Based on (4) and (5), other well-known performance criteria, such as, i.e. ABER, and output moments could be efficiently evaluated and graphically presented for this scenario.
Transmission subjected to shadowing
In order to superimpose the influence of multipath fading, modelled by general α−η−μ distribution, with shadowing process modelled with Gamma distribution, for the first time in the literature, we will present in this section novel composite fading distribution. As multipath fading and shadowing simultaneously occur in wireless transmission, there is a need to derive general model which would accurately describe this composite random process.
where ${G}_{m,n}^{p,q}\left[{}_{{\left(b\right)}_{q}}^{{\left(a\right)}_{p}}\mid x\right]$ stands for Meijer’s G-function ([11], Eq. (9.301)). Rapid convergence of this expression could be seen from Table 2.
System performances
where P_{ e }(t) denotes conditional error probability, whose functional dependency is determined by the type of modulation scheme performed. For some non-coherent modulation schemes, it stands ${P}_{e}\left(t\right)=\frac{1}{2}exp(-\mathit{\text{gt}})$, with g denoting modulation constant, (g=1 for BDPSK and g=1/2 for NCFSK), while for some coherent modulation schemes, it stands ${P}_{e}\left(t\right)=\frac{1}{2}\text{erfc}\left(\sqrt{\mathit{\text{gt}}}\right)$ with g denoting modulation constant (g=1 for CPSK and g=1/2 for CFSK) and erfc (x) being complementary error function ([11], Eq. (8.250.4)).
where r denotes random envelope process, γ_{th} stands for the average received signal-to-noise ratio (SNR) and B stands for the bandwidth of a channel.
Numerical results
Conclusion
This paper has considered wireless communication in a general fading environment, which can be reduced to other types of fading environments like Rayleigh, η−μ, Nakagami-q (Hoyt), Nakagami-m, Weibull. Obtained closed-form expressions for PDF and CDF of SIR for the interference-limited system case and closed-form expressions for first-order statistics (PDF, CDF, moments of various order) of newly introduced composite fading/shadowing model allow simple unconstrained analysis and accurate wireless system planning and performance evaluation. Some of the performance measures are evaluated and discussed in the paper.
Notes
Declarations
Authors’ Affiliations
References
- Lee WCY: Mobile Communications Engineering. Mc-Graw-Hill, New York; 2001.Google Scholar
- Papazafeiropoulos AK, Kotsopoulos SA: Second-order statistics for the envelope of α − κ − μ fading channels. IEEE Comm. Lett 2010, 14(4):291-293.View ArticleGoogle Scholar
- Fraidenraich G, Yacoub MD: The α − η − μ and α − κ − μ fading distributions. In Proceedings of the IEEE Ninth International Symposium on Spread Spectrum Techniques and Applications. Manaus-Amazon, Brasil, 28–31 Aug.; 2006:16-20.Google Scholar
- Sofotasios PC, Freear S: The η − μ /gamma composite fading model. In IEEE International Conference in Wireless Information Technology and Systems (ICWITS ‘10). Honolulu, HI, 28 Aug. 2010-3 Sept. 2010), vol. 2,; 872-877.Google Scholar
- Sofotasios PC, Freear S: The κ − μ /gamma extreme composite distribution: a physical composite fading model. In IEEE Wireless Communications and Networking Conference (WCNC ‘11). (Cancun, Mexico, 28–31 March.; 2011.Google Scholar
- Abdi A, Kaveh M: K distribution: an appropriate substitute for Rayleigh-lognormal distribution in fading-shadowing wireless channels. Electron. Lett 1998, 34(9):851-852. 10.1049/el:19980625View ArticleGoogle Scholar
- Bithas PS, Sagias NC, Mathiopoulos PT, Karagiannidis GK, Rontogiannis AA: On the performance analysis of digital communications over generalized-K fading channels. IEEE Commun. Lett 2006, 5(10):353-355.View ArticleGoogle Scholar
- Al-Ahmadi S, Yanikomeroglu H: On the approximation of the generalized- K distribution by a gamma distribution for modeling composite fading channels. IEEE Trans. Wireless Commun 2010, 9(2):706-713.View ArticleGoogle Scholar
- Ansari IS, AlAhmadi S, Yilmaz F, Alouini MS: A new formula for the BER of the binary modulations with dual-branch selection over generalized-K composite fading channels. IEEE Trans. Commun 2011, 59(10):2654-2658.View ArticleGoogle Scholar
- Sofotasios PC, Freear S: The α − κ − μ /gamma composite distribution: a generalized non-linear multipath/shadowing fading model. In Proceedings of the IEEE INDICON ‘11. Hyderabad, India, 16–18 Dec.; 2011.Google Scholar
- Gradshteyn IS, Ryzhik IM: Table of Integrals, Series, and Products. Academic Press, New York; 2000.MATHGoogle Scholar
- Trigui I, Laourine A, Affes S, Stephenne A: Performance analysis of mobile radio systems over composite fading/shadowing channels with co-located interferences. IEEE Trans. Wireless Commun 2009, 8(7):3449-3453.View ArticleGoogle Scholar
- Stefanovic M, Minic S, Nikolic S, Panic S, Peric M, Radenkovic D, Gligorijevic M: The CCI effect on system performance in kappa-mu fading channels. TTEM 2012, 7(1):88-92.Google Scholar
- Stefanovic M, Milovic D, Mitic A, Jakovljevic M: Performance analysis of system with selection combining over correlated Weibull fading channels in the presence of cochannel interference. AEU - Int. J. Electron. Commun 2008, 62(Issue 9):695-700.View ArticleGoogle Scholar
- Panajotovic A, Stefanovic M, Draca D: Performance analysis of system with selection combining over correlated Rician fading channels in the presence of cochannel interference. AEU - Int. J. Electron. Commun 2009, 63(12):1061-1066. 10.1016/j.aeue.2008.08.001View ArticleGoogle Scholar
- Petrovic I, Stefanovic M, Spalevic P, Panic SR, Stefanovic D: Outage analysis of selection diversity over Rayleigh fading channels with multiple co-channel interferers. Telecommun. Syst 2013, 52(1):39-50. doi:10.1007/s11235-011-9438-z 10.1007/s11235-011-9438-zView ArticleGoogle Scholar
- Abdi A, Kaveh M: On the utility of the gamma PDF in modeling shadow fading (slow fading). In Proceedings of the IEEE Vehicular Technology Conference (VTC’99). Houston, 16–20 May 1999), vol. 3; 2308-2312.Google Scholar
- Shankar PM: Analysis of microdiversity and dual channel macrodiversity in shadowed fading channels using a compound fading model. Int. J. Electron. Commun. (AEU) 2008, 62: 445-449. 10.1016/j.aeue.2007.06.008MathSciNetView ArticleGoogle Scholar
- The Wolfram Functions Site [Online] Available: . Accessed 01 Dec 2012 http://functions.wolfram.com Available: . Accessed 01 Dec 2012
- Adamchik VS, Marichev OI: The algorithm for calculating integrals of hypergeometric type functions and its realization in REDUCE system. In Proceedings of the International Conference on Symbolic and Algebraic Computation. Tokyo, Japan, 20–24 Aug. 1990; 212-224.Google Scholar
- Sekulovic N, Stefanovic M, Denic D, Aleksic D: Performance analysis of SINR-based selection diversity over correlated Rayleigh fading channels. IET Commun 201, 5(2):127-134.MathSciNetView ArticleGoogle Scholar
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