Ridha Bouallegue

Multiple-input multiple-output (MIMO) systems are playing an important role in the recent wireless communication. The complexity of the different systems models challenge different researches to get a good complexity to performance balance. Lattices Reduction Techniques and Lenstra-Lenstra-Lovàsz (LLL)\ud algorithm bring more resources to investigate and can contribute to the complexity reduction purposes.In this paper, we are looking to modify the LLL algorithm to reduce the computation operations by exploiting the structure of the upper triangular matrix without “big” performance degradation. Basically, the first columns of the upper triangular matrix contain many zeroes, so the algorithm will perform several \ud \ud \ud operations with very limited income. We are presenting a performance and complexity study and our\ud proposal show that we can gain in term of complexity while the performance results remains almost the\ud same. \u

Several methods have been proposed to approximate the sum of lognormal RVs. However the accuracy of each method relies highly on the region of the resulting distribution being examined, and the individual lognormal parameters, i.e., mean and variance. There is no such method which can provide the needed accuracy for all cases. This paper propose a universal yet very simple approximation method for the sum of Lognormals based on log skew normal approximation. The main contribution on this work is to propose an analytical method for log skew normal parameters estimation. The proposed method provides highly accurate approximation to the sum of lognormal distributions over the whole range of dB spreads for any correlation coefficient. Simulation results show that our method outperforms all previously proposed methods and provides an accuracy within 0.01 dB for all cases.

Several methods have been proposed to approximate the sum of correlated lognormal RVs. However the accuracy of each method relies highly on the region of the resulting distribution being examined, and the individual lognormal parameters, i.e., mean and variance. There is no such method which can provide the needed accuracy for all cases. This paper propose a universal yet very simple approximation method for the sum of correlated lognormals based on log skew normal approximation. The main contribution on this work is to propose an analytical method for log skew normal parameters estimation. The proposed method provides highly accurate approximation to the sum of correlated lognormal distributions over the whole range of dB spreads for any correlation coefficient. Simulation results show that our method outperforms all previously proposed methods and provides an accuracy within 0.01 dB for all cases.

Sums of lognormal random variables (RVs) occur in many important problems in wireless communications especially in interferences calculation. Several methods have been proposed to approximate the lognormal sum distribution. Most of them requires lengthy Monte Carlo simulations, or advanced slowly converging numerical integrations for curve fitting and parameters estimation. Recently, it has been shown that the log skew normal distribution can offer a tight approximation to the lognormal sum distributed RVs. We propose a simple and accurate method for fitting the log skew normal distribution to lognormal sum distribution. We use moments and tails slope matching technique to find optimal log skew normal distribution parameters. We compare our method with those in literature in terms of complexity and accuracy. We conclude that our method has same accuracy than other methods but more simple. To further validate our approach, we provide an example for outage probability calculation in lognormal shadowing environment based on log skew normal approximation.