本文主要在於推導出一個接收傳感器陣列光圈的上行接收信號的四階空間相關係數函數。
這個推導在數學上是嚴謹的且建構在移動發射器、基地接收天線和散射體通道的理想幾何關係。散射體的空間位置是建模於二維空間的卜瓦松分佈，受高斯強度影響。假定傳感器被定位在任意四個位置上。最後的公式為封閉的形式，僅與少數參數相關。研究結果為Wang, Guo, Wong 和Piterbarg (2012) 傳感器位於直線上的延伸。

This paper derives the uplink received signal’s fourth-order spatial-correlation coefficient function across a receiving sensor-array’s aperture. This derivation is mathematically rigorous and is based on idealized geometric relationships among the mobile transmitter, the basestation’s receiving antennas, and the scatterers of the channel. The scatterers’ spatial locations are modeled as Poisson distributed, with a Gaussian intensity over a two-dimensional space. Sensors are assumed to locate on the four arbitrary locations. The final formula is in closed form, explicit in terms of the simple geometric model’s few independent parameters. The results extend the collinear sensor case ofWang, Guo,Wong and Piterbarg (2012).

Contents
論文審定書 i
誌謝 ii
摘要 vi
Abstract v
1 Introduction 1
2 The Proposed ”Geometric Model” 1
3 A General Formula of ρ(4) 5
3.1 Phase-Differences of Four Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
3.2 Spatial Fourth-Order Correlation-Coefficient Function of Four Sensors . . . . . . . 6
3.3 Special Cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8
4 Simulation Study 9
4.1 Simulation Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9
4.2 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10
5 Conclusion 11
References 12
Appendix A 15
Appendix B 20

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