Non-WSSUS水聲通訊通道之降階追蹤

Abstract

許多水聲通訊通道常具有時變之交互相關 ( cross-tap correlation) 的特性，此種通訊通道的脈沖響應 (Channel Impulse Response; CIR) 具有隨時間改變的二階統計值以及時變的交互相關特性，通稱為non-WSSUS通道。傳統的通道估測/追蹤演算法，並不針對此特殊的種通道特性做任何的處理，且一般數位通訊，包含水聲通訊，均假設通道滿足uncorrelated scattering (US) 的假設。 本文的主旨，在於提出針對non-WSSUS淺水水聲通道之降階估測/追蹤的演算法。Non-WSSUS淺水水聲通道具備以下幾種特殊的特性：因有限的頻寬及tap間的交互相關性，使得用來描述通道的變數taps，雖具備相對大的維度，但卻僅有較低的自由度 (DOF) ; 此外，因為通道介質的不均勻性或因為水面的波浪影響，使得此種交互相關的結構隨時間而改變。 本文主要的發現，在於可將通道脈沖響應參數化成不同訊號成分貢獻的加總，每筆貢獻可視為訊號子空間基底向量 (signal subspace basis) 乘上一複數變量，稱之為通道成分 (channel components) ; 本文所提出的通道追蹤方式，根基於此參數化的解析 (decomposition)，並以不同的方式處理此兩種參數，文中所提出的方法，以一種被稱為子空間追蹤的演算法 (subspace tracking algorithm)，追蹤變化速度較慢的訊號子空間基底向量的時變特性，至於變化較快的通道成分變量，可視為具備交互相關的通道響應投影到訊號子空間基底上的分量，這些投影的分量 (即通道成分) 則成為互不相關 (uncorrelated) 的變量，這些快速變化且互不相關的通道成分變量，可以數種不同的方式追蹤，例如，使用基於通道模型 (model base) 的追蹤方法 (如：使用卡曼濾波器; Kalman Filter) ; 使用傳統的LMS或RLS 等追蹤演算法或是根基於子空間基底向量重組的演算法 (channel reconstruction)。這些方法藉由在較低維度的訊號子空間進行通道成分以及基底追蹤 (或重組)。相較於傳統的演算法 (如RLS )，除了可以降低計算的複雜度外並且可以大幅提升通道追蹤的性能，這些演算法的實際性能，則經由實海實驗資料加以驗證。 此研究的主要貢獻，在於了解通道的物理特性如何影響通訊演算法的設計及探討可能的改進空間，並可將此發現運用在其他具有維度-變化量相互衝突的問題上。

Many underwater acoustic channels exhibit time-varying cross-path (cross-tap) correlated scattering (CS) property; such channels, with time-varying 2nd order statistics, are known as non-WSSUS channels. Traditional channel estimation algorithms do not exploit/compensate this time-varying correlation property. Despite uncorrelated scattering (US) has been the standard assumption for digital communications including underwater acoustic communications; this thesis develops methods for tracking non-WSSUS shallow-water acoustic communication channels. Such channel has few distinct features: large dimension yet limited number of degrees of freedom (DOF) due to limited bandwidth and inter-tap correlations; these correlation structure are time-varying due to medium inhomogeneity and motion sea surface. The key observation is that the channel impulse responses can be parameterized as the sum of contributions, each related to a different multipath component, characterized by a signal subspace basis and complex weighting amplitude known as channel components. The channel tracking methods proposed in this thesis relies on this parameterization and differs in the way they handle these two parameters. The proposed techniques perform an unstructured tracking of the slow variations of the signal subspace through one of the so-called subspace tracking algorithms. The fast time-varying channel components are tracked separately, e.g., using the model (Kalman filter) based approach. By tracking only a small number of degrees of freedom in the signal subspace, significant savings in computations and significant tracking performance improvements can be achieved compared with the conventional recursive least square (RLS) algorithm. Performance is demonstrated with at sea data. The study contributes to a better understanding of the channel physical constraints on algorithm design and potential performance improvement. It may also be generalized to other applications where dimensionality and variability collide.