On the Statistical Properties of Capacity Outage Intervals in OSTBC-MIMO Rayleigh Fading Channels

This paper deals mainly with the study of the asymptotic probability density functions (PDFs) of the outage durations of the instantaneous capacity of orthogonal space-time block code (OSTBC) multiple-input multiple-output (MIMO) systems over Rayleigh channels. Drawing upon known statistical properties for the asymptotic behavior of chi-squared processes at low levels, we provide approximate solutions for the PDF, the cumulative distribution function (CDF), and the kth-order moments of the outage intervals of the underlying capacity processes. Then, as an application of the derived PDF, the performance assessment of capacity simulators is reported. Following this, we introduce the newly defined average-to-trough capacity ratio (ATCR) metric, and investigate its PDF and CDF. The validity of the derived results is confirmed by specializing them to already known ones, although they have been obtained by using a rather different approach. The accuracy and applicability of the asymptotic analysis to practical values of capacity thresholds have been examined by means of computer simulations. The theoretical results presented contribute to the statistical characterization of outage events, the study of which has mainly been limited to the analysis of the probability, the occurrence rate, and the average duration of outages.

[1]  Ignacio Santamaría,et al.  Closed-form approximation for the outage capacity of orthogonal STBC , 2005, IEEE Communications Letters.

[2]  Robert J. Adler,et al.  Extrema and level crossings of χ2 processes , 1986, Advances in Applied Probability.

[3]  D. Rajan.  Probability, Random Variables, and Stochastic Processes , 2017 .

[4]  A. Robert Calderbank,et al.  Space-Time block codes from orthogonal designs , 1999, IEEE Trans. Inf. Theory.

[5]  Matthias Pätzold,et al.  The Influence of Spatial Correlation and Severity of Fading on the Statistical Properties of the Capacity of OSTBC Nakagami-m MIMO Channels , 2009, VTC Spring 2009 - IEEE 69th Vehicular Technology Conference.

[6]  Andrea Giorgetti,et al.  MIMO capacity, level crossing rates and fades: The impact of spatial/temporal channel correlation , 2003, Journal of Communications and Networks.

[7]  Neji Youssef,et al.  On the probability density functions of outage and inter-outage durations of the capacity of Rayleigh fading channels , 2009, IEEE Transactions on Wireless Communications.

[8]  Jean-Paul M. G. Linnartz,et al.  Threshold crossing rate and average non-fade duration in a Rayleigh-fading channel with multiple interferers , 1989 .

[9]  David Tse,et al.  Fundamentals of Wireless Communication , 2005 .

[10]  G. Rama Krishna,et al.  DIVERSITY analysis in MIMO systems using OSTBC(Orthogonal Space Time Block Codes , 2012 .

[11]  Sofiène Affes,et al.  On the capacity of log-normal fading channels , 2009, IEEE Transactions on Communications.

[12]  Matthias Pätzold.  Mobile Radio Channels: Pätzold/Mobile Radio Channels , 2011 .

[13]  Rohit U. Nabar,et al.  Introduction to Space-Time Wireless Communications , 2003 .

[14]  Matthias Pätzold,et al.  Two new sum-of-sinusoids-based methods for the efficient generation of multiple uncorrelated rayleigh fading waveforms , 2009, IEEE Transactions on Wireless Communications.

[15]  S. O. Rice,et al.  Distribution of the duration of fades in radio transmission: Gaussian noise model , 1958 .

[16]  Shuangquan Wang,et al.  Instantaneous Mutual Information and Eigen-Channels in MIMO Mobile Rayleigh Fading , 2012, IEEE Transactions on Information Theory.

[17]  Andrea J. Goldsmith,et al.  Capacity limits of MIMO channels , 2003, IEEE J. Sel. Areas Commun..

[18]  D. Slepian,et al.  Large Excursions of Gaussian Processes , 1959 .

[19]  Matthias Pätzold,et al.  Statistical Analysis of the Channel Capacity Outage Intervals in Massive MIMO Systems with OSTBC over Rayleigh Fading Channels , 2015, 2015 IEEE 81st Vehicular Technology Conference (VTC Spring).

[20]  Sofiène Affes,et al.  The Inverse Gaussian Distribution in Wireless Channels: Second-Order Statistics and Channel Capacity , 2012, IEEE Transactions on Communications.

[21]  Mohamed-Slim Alouini,et al.  On the Computation of the Higher Order Statistics of the Channel Capacity for Amplify-and-Forward Multihop Transmission , 2014, IEEE Transactions on Vehicular Technology.

[22]  Karl Pearson F.R.S..  X. On the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling , 2009 .

[23]  Lee M. Garth,et al.  Level crossing rates for MIMO channel eigenvalues: implications for adaptive systems , 2005, IEEE International Conference on Communications, 2005. ICC 2005. 2005.

[24]  Riaz Esmailzadeh.  Broadband Wireless Communications Business: An Introduction to the Costs and Benefits of New Technologies , 2006 .

[25]  L. Slater,et al.  Confluent Hypergeometric Functions , 1961 .

[26]  Athanasios Papoulis,et al.  Probability, Random Variables and Stochastic Processes , 1965 .

[27]  George K. Karagiannidis,et al.  Cooperative Diversity With Mobile Nodes: Capacity Outage Rate and Duration , 2010, IEEE Transactions on Information Theory.

[28]  Julia Abrahams,et al.  A Survey of Recent Progress on Level-Crossing Problems for Random Processes , 1986 .

[29]  Matthias Pätzold,et al.  Exact Closed-Form Expressions for the Distribution, the Level-Crossing Rate, and the Average Duration of Fades of the Capacity of OSTBC-MIMO Channels , 2009, IEEE Transactions on Vehicular Technology.

[30]  Dongwoo Kim,et al.  Test procedures and performance assessment of mobile fading channel simulators , 2004, 2004 IEEE 59th Vehicular Technology Conference. VTC 2004-Spring (IEEE Cat. No.04CH37514).

[31]  Matthias Pätzold,et al.  Optimal Sampling Period and Required Number of Samples for OSTBC-MIMO Rayleigh Fading Channel Capacity Simulators , 2014, 2014 IEEE 80th Vehicular Technology Conference (VTC2014-Fall).

[32]  W. C. Jakes,et al.  Microwave Mobile Communications , 1974 .

[33]  Aymen Omri,et al.  Enhanced Alamouti decoding scheme for DVB-T2 systems in SFN channels , 2011, 2011 IEEE 22nd International Symposium on Personal, Indoor and Mobile Radio Communications.

[34]  Siavash M. Alamouti,et al.  A simple transmit diversity technique for wireless communications , 1998, IEEE J. Sel. Areas Commun..

[35]  Matthias Patzold,et al.  On the statistical properties of the capacity of OSTBC Nakagami-lognormal MIMO channels , 2010, 2010 4th International Conference on Signal Processing and Communication Systems.

[36]  Mohammed Aboud Kadhim,et al.  Improvement of Fixed WiMAX OSTBC – OFDM Transceiver Based Wavelet Signals by Non-Linear Precoding Using SDR Platform , 2013 .