無線光通道容量分析

Abstract

本篇論文探討無線光通道的容量大小。此通道有下列幾項特性: 輸入端的是以光的強度當做記量的單位，所以其值為非負值 ; 輸出端會受到雜訊的影響，在此我們把此雜訊假設成相加白色高斯雜訊，因為在接收端會受到許多不同獨立來源的雜訊，所以我們把它假設成白色高斯雜訊 ; 此外，電池電力的限制和使用上眼睛安全的問題，我們必須有平均能量與峰值能量大小的限制。

我們的任務是改善之前所提出的上下限，讓上下限間的距離變得更靠近，我們就可夾擊出真正的通道容量。首先我們先利用數值分析的方式求出一個數值的通道容量下限，然後跟之前的結果比較。之後在根據先前的比較，用理論分析的方式去求得公式。

我們所得到的數值下限與之前論文所推導出的上限在低訊雜比(SNR) 的情況下相當接近，如果我們放鬆對平均能量的限制，我們可以得到更好結果。而我們理論分析出來的下限，在中雜訊比的地方有明顯的改善。

In this thesis we study the free-space optical communication channeld. This channel is characterized by inputs that are nonnegative representing transmitted optical intensity, and by outputs that are corrupted by additive white Gaussian noise, because in free space the disturbances arise from many independent sources. Due to battery and safety reasons the inputs are simultaneously constrained on both their average and peak power. Our task is trying to find upper and lower bounds on the capacity of this channel. We use a numerical approach to compute the channel capacity and compare it with previous bounds. Based on the result of this comparison, we try to derive improved analytical lower bounds on capacity. Our numerical lower bounds are very close to previous upper bounds in lower SNR region (below 5 dB) with improving performance if we loosen the average-power constraint. Our analytical lower bounds are good in medium SNR region (between 5 dB and 15 dB).