Analysis of UWB communication over IEEE 802.15.3a channel by superseding lognormal shadowing by Mixture of Gamma distributions

https://doi.org/10.1016/j.aeue.2015.09.003Get rights and content

Abstract

In this paper, we calculate the bit error rate (BER) of the ultra-wide band (UWB) wireless communication system over IEEE 802.15.3a channel model by superseding the lognormal (LN) shadow fading distribution to the Mixture of Gamma (MG) distributions. In general, shadow fading is the effect of random fluctuation of received signal power around the mean path loss and it is modeled as LN distribution. In this work, we approximate the LN shadow fading distribution to the MG distributions, because of intractable, indefinite mathematical expression of the characteristic function (CF) and moment generating function (MGF) of the LN distribution, which are required to evaluate BER of the UWB communication system. To estimate the approximate MG distributions parameters, we use rth moment algorithm with least square non-linear curve fitting criteria. This work employs the L-fingers RAKE receiver which is needed to collect the total energy at the receiver in the UWB system. The results show that 5-MG distributions is the good fit for LN shadow fading distribution of the UWB communication system. The proposed analytical BER is closely matched to the simulated BER for all the four IEEE 802.15.3a channel models. It verifies the accuracy of the approximation considered in this BER analysis.

Introduction

The low cost and high data rate features have drawn the considerable interest towards the Ultra-wide band (UWB) wireless indoor communication system. UWB offers frequency spectrum of 3.1–10.6 GHz as assigned by the Federal Communication Commission (FCC). FCC has put a constraint on maximum allowable transmitted power spectral density (PSD <  −41.3 dBm) of the UWB signal to limit the interference with the existing wireless systems. The standardized channel model for short range high data rate UWB system is termed as IEEE 802.15.3a [1]. In the IEEE 802.15.3a channel model all the multipath components (MPCs) and shadow fading are lognormally distributed. It also offers the ability to resolve all the MPCs separately, makes it different from the conventional narrow band indoor channel model.

The mathematical expression of Lognormal (LN) distribution poses higher computational complexities and intractable integrals while conducting the performance analysis. Different approaches are available in the literature to overcome the computational complexities posed by the LN distribution during the performance analysis of the UWB system [2], [3], [4]. In Ref. [2], the author used Wilkinson's method to approximate the sum of LN random variables (RVs) by another LN-RV. In Ref. [3], the author has approximated the sum of LN random variables (RVs) by the linear weighted sum of LN distributions via Pearson type IV distribution. In Ref. [4], the author has approximated the total received SNR by the different distributions depending upon the severeness of the fading. These distributions are namely Coxian, Mixture of Gamma (MG) and LN distributions. All these works have not considered the shadow fading effect during the error performance analysis of the UWB system. The shadow fading effect is a pivotal parameter to be taken into account during the error performance analysis as it is very much part of the indoor UWB wireless communication system.

The present work considers the shadow fading effect during the error performance analysis. In Ref. [5], the author suggested that LN distribution can be approximated by the Gamma distribution. In Ref. [6], the author has opined that MG distributions is the good approximation of the composite channels and many other RVs. It also offers a tractable mathematical expression of moment generating function (MGF), characteristic function (CF) and cumulative distribution function (CDF). Those remarkable properties of MG distributions motivate us to approximate LN shadow fading distribution by it in the present work. We also evaluate the CF based error performance analysis of the UWB system using the above approximation.

The rest of this paper is organized as follows. The IEEE 802.15.3a UWB channel model is described in Section 2. MG distributions and estimation of its parameters is presented in Section 3. We derived an analytical BER expression of the UWB communication system over IEEE 802.15.3a channel model in Section 4. Section 5 discussed the estimation of the number of mixing coefficients of MG distributions. Section 6 presents the simulation and numerical results. Finally, conclusion is drawn in Section 7.

Section snippets

IEEE 802.15.3a UWB channel model

IEEE 802.15.3a is a standard channel model for high data rate, short distance UWB wireless communications systems. All the MPCs and shadow fading of the IEEE 802.15.3a channel model are LN distributed. The multi-cluster signals and MPCs in each cluster are also subjected to the independent LN fading. Due to this, it is modeled by the modified Saleh-Valenzuela (S-V) channel model. The channel impulse response (CIR) of IEEE 802.15.3a channel is given as [7]

h(t)=X∑m=0M∑r=0Rαr,mδt−Tm−τr,m,where αr,m

Mixture of Gamma (MG) distributions

Linear weighted sum of Gamma distribution offers tractable mathematical expression of MGF, CF and CDF. It also offers a good approximation of composite fading channel and many other RVs. The probability density function (PDF) of MG distributions is given as [8]

fMG(x)=∑i=1nPixαi−1Γαiβiαie−x/βi,where n denotes the number of mixing coefficients, Pi is the mixing coefficient of the ith Gamma distribution with Pi > 0 and ∑i=1nPi=1. αi and βi are the shape and scale parameters of the ith Gamma

Performance analysis

In this paper, we evaluate the error performance of the UWB wireless communication system by approximating the LN shadow fading distribution by MG distributions. The conditional error probability (CEP) of the UWB system using L-fingers RAKE receiver is given as [9]Peγ=Q1−ρrγ,where γ=EbN0ɛ is the received SNR, Eb is the bit energy, N0 is the noise power spectral density and ɛ is the total received energy. ρr = 0 or 1 for orthogonal and antipodal signal respectively. The average bit error

Estimation of number of mixing coefficients (n)

The number of mixing coefficients (n) of the MG distributions is a pivotal parameter to closely approximate it with the shadow fading distribution. The mean square error (MSE) between the exact and approximated distributions is defined asMSE=Efexact(x)−fapp(x)2.We have calculated MSE between the square of LN shadow fading distribution X2∼ln{N(0,2σxdB)} and the approximate distribution (MG) of the square of LN shadow fading for different values of n of MG distributions. It is shown in Fig. 1.

Numerical results and discussions

For the simulation purpose we set mean μ = 0 and standard deviation σx = 3 dB for the LN shadow fading X∼ln{N(0,3dB)}, therefore the mean and standard deviation of X2 are 0, 6 dB respectively X2∼ln{N(0,6dB)}. To approximate the square of LN shadow fading by the MG distributions, we set n = 1, 3, 5. The shape, scale and weight parameters of the MG distributions are given in Table 3. We plot PDF & CDF of the square of LN shadow fading distribution and its approximation (MG). It is shown in Fig. 2, Fig. 3

Conclusions

In this paper, we evaluate the ABER of UWB wireless communication over the IEEE 802.15.3a channel model considering the shadow fading whose distribution is approximated by MG distributions. The proposed analytical results closely match with the simulation results. This verify the accuracy of the approximation used in ABER analysis of the UWB system. The proposed approach to calculate the ABER is accurate and faster than the existing approaches. Our computer (Intel(R) Core(TM) i5-3470 CPU 3.20 

Anand Agrawal received his M.Tech. degree in Digital Communication Engineering from National Institute of Technology (NIT) Bhopal, India, in 2010 and the B.E. degree in Electronics and Communication Engineering (ECE) from Samrat Ashok Technological Institute (SATI), Vidisha, India, in 2008. He is currently a Ph.D. Candidate in the Department of Electronics and Electrical Engineering at Indian Institute of Technology Guwahati, India. His research interests are in the areas of Cooperative

References (11)

  • J. Foerster

    Channel modeling sub-committee report final, IEEE P802.15-02/368r5-SG3a

    (2002)
  • H. Liu

    Error performance of a pulse amplitude and position modulated ultra-wideband system over lognormal fading channels

    IEEE Commun Lett

    (2003)
  • M.D. Renzo et al.

    Approximating the linear combination of log-normal RVs via pearson type IV distribution for UWB performance analysis

    IEEE Trans Commun

    (2009)
  • C. Abou-Rjeily

    Performance analysis of UWB systems over the IEEE 802.15.3a channel model

    IEEE Trans Wireless Commun

    (2011)
  • A. Abdi et al.

    On the utility of Gamma PDF in modeling shadow fading (slow fading)

There are more references available in the full text version of this article.

Anand Agrawal received his M.Tech. degree in Digital Communication Engineering from National Institute of Technology (NIT) Bhopal, India, in 2010 and the B.E. degree in Electronics and Communication Engineering (ECE) from Samrat Ashok Technological Institute (SATI), Vidisha, India, in 2008. He is currently a Ph.D. Candidate in the Department of Electronics and Electrical Engineering at Indian Institute of Technology Guwahati, India. His research interests are in the areas of Cooperative communication, UWB wireless communication systems and MIMO.

Rakhesh Singh Kshetrimayum received the Ph.D. degree from the School of Electrical and Electronic Engineering (EEE), Nanyang Technological University (NTU) Singapore in 2005 and the B.Tech. degree in Electrical Engineering (EE) from the Indian Institute of Technology (IIT) Bombay in 2000. Currently, he is an Associate Professor in the department of EEE, IIT Guwahati. His current areas of research interests are in printed antennas and circuits, UWB communications and MIMO wireless communications. He has published over 80 journal and conference papers; authored and co-authored three books.

View full text
Copyright © 2015 Elsevier GmbH. All rights reserved.