On the rates of convergence of the wireless multi-access interference distribution to the normal distribution

It is of prime importance to reveal the structure of wireless multi-access interference distributions to compute many performance bounds and metrics for wireless networks such as transmission capacity, outage probability and bit-error-rate. However, at the present, there are no closed form expressions for the multi-access interference distributions in wireless networks apart from a very special case. This paper presents a principled methodology towards the resolution of this bottleneck by establishing rates of convergence of the multi-access interference distribution to a Gaussian distribution for any given bounded power-law decaying path-loss function G. In particular, it is shown that the interference distribution converges to the Gaussian distribution with the same mean and variance at a rate √1/λ, where λ>0 is the intensity of the homogenous planar Poisson point process generating node locations.

[1]  V. Schmidt,et al.  NORMAL CONVERGENCE OF MULTIDIMENSIONAL SHOT NOISE AND RATES OF THIS CONVERGENCE , 1985 .

[2]  E.S. Sousa,et al.  Performance of a spread spectrum packet radio network link in a Poisson field of interferers , 1992, IEEE Trans. Inf. Theory.

[3]  Malvin Carl Teich,et al.  Power-law shot noise , 1990, IEEE Trans. Inf. Theory.

[4]  Louis H. Y. Chen,et al.  Stein's method for normal approximation , 2005 .

[5]  John A. Gubner,et al.  Computation of Shot-Noise Probability Distributions and Densities , 1996, SIAM J. Sci. Comput..

[6]  H. Vincent Poor,et al.  On unbounded path-loss models: effects of singularity on wireless network performance , 2009, IEEE Journal on Selected Areas in Communications.

[7]  P. Billingsley,et al.  Probability and Measure , 1980 .

[8]  P. Rousseeuw,et al.  Wiley Series in Probability and Mathematical Statistics , 2005 .

[9]  Dimitrios Hatzinakos,et al.  Analytic alpha-stable noise modeling in a Poisson field of interferers or scatterers , 1998, IEEE Trans. Signal Process..

[10]  Martin Haenggi,et al.  Interference and Outage in Clustered Wireless Ad Hoc Networks , 2007, IEEE Transactions on Information Theory.

[11]  Stephen V. Hanly,et al.  Calculating the outage probability in a CDMA network with spatial Poisson traffic , 2001, IEEE Trans. Veh. Technol..

[12]  R. Durrett.  Probability: Theory and Examples , 1993 .

[13]  Jeffrey G. Andrews,et al.  Transmission capacity of wireless ad hoc networks with outage constraints , 2005, IEEE Transactions on Information Theory.

[14]  Jeffrey G. Andrews,et al.  Stochastic geometry and random graphs for the analysis and design of wireless networks , 2009, IEEE Journal on Selected Areas in Communications.

[15]  John A. Silvester,et al.  Optimum Transmission Ranges in a Direct-Sequence Spread-Spectrum Multihop Packet Radio Network , 1990, IEEE J. Sel. Areas Commun..

[16]  Jeffrey G. Andrews,et al.  WLC02-1: Bounds on the SIR Distribution for a Class of Channel Models in Ad Hoc Networks , 2006, IEEE Globecom 2006.

[17]  S. Musa,et al.  Co-Channel Interference of Spread Spectrum Systems in a Multiple User Environment , 1978, IEEE Trans. Commun..

[18]  Jeffrey G. Andrews,et al.  Transmission Capacity of Wireless Ad Hoc Networks With Successive Interference Cancellation , 2007, IEEE Transactions on Information Theory.