The Folded Normal Distribution: A New Model for the Small-Scale Fading in Line-of-Sight (LOS) Condition

In this paper, a novel form of the folded normal (FN) distribution has been proposed to model the small-scale fading in wireless communications. From a multiple-input multiple-output (MIMO) measurement campaign conducted in a lab environment with the line-of-sight (LOS) conditions at both the 60 and the 94 GHz bands, the authors obtain the parameters of the Rician, FN, and <inline-formula> <tex-math notation="LaTeX">$\kappa $ </tex-math></inline-formula>-<inline-formula> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula> distributions. These parameters have been calculated by using the least square (LS) approximation and with techniques of statistical inference. The FN distribution provides the best fitting to the experimental results using the Kolmogorov–Smirnov (K–S) test for the inferred estimators with values of the fulfillment of 100% and 69.82% at the 60 and 94 GHz bands, respectively, for a significance level of 1%.

[1]  J. Reig,et al.  Fading Evaluation in the 60GHz Band in Line-of-Sight Conditions , 2014 .

[2]  Theodore S. Rappaport,et al.  Indoor Office Wideband Millimeter-Wave Propagation Measurements and Channel Models at 28 and 73 GHz for Ultra-Dense 5G Wireless Networks , 2015, IEEE Access.

[3]  Moon-Soon Choi,et al.  Statistical Characteristics of 60 GHz Wideband Indoor Propagation Channel , 2005, 2005 IEEE 16th International Symposium on Personal, Indoor and Mobile Radio Communications.

[4]  R. S. Cole,et al.  An experimental study of the propagation of 55 GHz millimeter waves in an urban mobile radio environment , 1994 .

[5]  Robert W. Heath,et al.  Measurements of the 60 GHz UE to eNB Channel for Small Cell Deployments , 2017, IEEE Wireless Communications Letters.

[6]  M.D. Yacoub,et al.  The α-η-μ and α-κ-μ Fading Distributions , 2006, 2006 IEEE Ninth International Symposium on Spread Spectrum Techniques and Applications.

[7]  Michel Daoud Yacoub,et al.  The symmetrical n-k distribution , 2004, 2004 IEEE 15th International Symposium on Personal, Indoor and Mobile Radio Communications (IEEE Cat. No.04TH8754).

[8]  Theodore S. Rappaport,et al.  Propagation Models and Performance Evaluation for 5G Millimeter-Wave Bands , 2018, IEEE Transactions on Vehicular Technology.

[9]  E. H. Moore A unified approach to the detection of fluctuating pulsed signals in noise , 1967, IEEE Trans. Inf. Theory.

[10]  K. Pahlavan,et al.  On the modeling of fading multipath indoor radio channels , 1989, IEEE Global Telecommunications Conference, 1989, and Exhibition. 'Communications Technology for the 1990s and Beyond.

[11]  Theodore S. Rappaport,et al.  Millimeter-Wave Cellular Wireless Networks: Potentials and Challenges , 2014, Proceedings of the IEEE.

[12]  R. Elandt The Folded Normal Distribution: Two Methods of Estimating Parameters from Moments , 1961 .

[13]  R. McNicol The fading of radio waves of medium and high frequencies , 1949 .

[14]  Jose-Maria Molina-Garcia-Pardo,et al.  Small‐scale distributions in an indoor environment at 94 GHz , 2017 .

[15]  José-María Molina-García-Pardo,et al.  Experimental Study of MIMO-OFDM Transmissions at 94 GHz in Indoor Environments , 2017, IEEE Access.

[16]  Michel Daoud Yacoub,et al.  The α-μ distribution: a general fading distribution , 2002, PIMRC.

[17]  Markus Rupp,et al.  Position-Specific Statistics of 60 GHz Vehicular Channels During Overtaking , 2019, IEEE Access.

[18]  L. S. Nelson,et al.  The Folded Normal Distribution , 1961 .

[19]  Theodore S. Rappaport,et al.  New analytical models and probability density functions for fading in wireless communications , 2002, IEEE Trans. Commun..

[20]  M.D. Yacoub,et al.  The κ-μ distribution and the η-μ distribution , 2007, IEEE Antennas and Propagation Magazine.

[21]  H. P. Groll,et al.  Propagation properties of an indoor-channel at 94 GHz , 1998, ICMMT'98. 1998 International Conference on Microwave and Millimeter Wave Technology. Proceedings (Cat. No.98EX106).

[22]  Rafael Timóteo de Sousa Júnior,et al.  On the capacity analysis of κ-μ and α-μ fading channels for millimeter waves , 2015 .

[23]  Theodore S. Rappaport,et al.  Investigation of Prediction Accuracy, Sensitivity, and Parameter Stability of Large-Scale Propagation Path Loss Models for 5G Wireless Communications , 2016, IEEE Transactions on Vehicular Technology.

[24]  A. Kajiwara Indoor propagation measurements at 94 GHz , 1995, Proceedings of 6th International Symposium on Personal, Indoor and Mobile Radio Communications.

[25]  Davy P. Gaillot,et al.  Channel sounding and indoor radio channel characteristics in the W-band , 2016, EURASIP J. Wirel. Commun. Netw..

[26]  Mohamed-Slim Alouini,et al.  Coded Communication over Fading Channels , 2005 .

[27]  Claude Oestges,et al.  Measurement-based analysis of specular and dense multipath components at 94 GHz in an indoor environment , 2018 .

[28]  M. Nakagami The m-Distribution—A General Formula of Intensity Distribution of Rapid Fading , 1960 .

[29]  Kushal K. Talukdar,et al.  Estimation of the parameters of the Rice distribution , 1991 .