關於獨立對數常態隨機變數和之分配函數估計的探討與改進

在蜂巢式行動無線電系統中，單一個干擾訊號的強度可以用一個對數常態隨機變數來表示，而共頻道干擾常會被表示成多個對數常態隨機變數的和。由於對數常態和的分布並沒有 analytic expression，通常會用單一個對數常態隨機變數來近似。基於這個假設，常用的近似方法有 Fenton-Wilkinson 方法和 Schwartz-Yeh 方法。在觀察了對數常態的機率密度函數圖形後，我們提出了眾數法。與傳統方法相比，眾數法的機率密度函數圖形與真實分布更為接近。之後我們又結合了 Fenton-Wilkinson 和 Schwartz-Yeh 兩種方法，提出了混合近似法。混合近似法的誤差比 Fenton-Wilkinson 方法小很多，且在計算速度上會比 Schwartz-Yeh 方法快。

關鍵字

對數常態和；共頻道干擾；眾數法；混合近似法

並列摘要

In wireless communications, sums of lognormal random variables occur in many problems because signal shadowing is well modeled by the lognormal distribution. Since the lognormal sum distribution is known to have no analytic expression, a lognormal sum is usually approximated by a single lognormal random variable. In this paper, we provides two methods of lognormal sum approximation. One is based on the probability density function of lognormal random variables, and the other is a combination of Fenton-Wilkinson method and Schwartz-Yeh method. Numerical examples are provided to compare these approximations.

並列關鍵字

lognormal sum ； cochannel interference ； moment matching

參考文獻

N. C. Beaulieu, A. A. Abu–Dayya, and P. J. McLane, “Estimating the distribution of a sum of independent lognormal random variables,” IEEE Trans. Commun., vol. 43, pp.2869–2873, Dec. 1995.

N. C. Beaulieu and Q. Xie, “An optimal lognormal approximation to lognormal sum distributions,” IEEE Trans. Veh. Technol., vol. 53, pp.479–489, March 2004.

L. F. Fenton, “The sum of lognormal probability distributions in scatter transmission systems,” IRE Trans. Commun. Syst., vol. CS-8, pp. 57–67, 1960.

M. Pratesi, F. Santiccu and F. Graziosi, “Generalized moment matching for the linear combination of lognormal RVs: application to outage analysis in wireless systems,” IEEE Trans. Wireless. Commun., vol. 5, pp.1122–1132, May 2006.

S. C. Schwartz and Y. S. Yeh, “On the distribution function and moments of power sums with lognormal components,” Bell Syst. Tech. J., vol. 61, no. 7, pp. 1441–1462, 1982.

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關於獨立對數常態隨機變數和之分配函數估計的探討與改進

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