到達方位角、時間延遲、載波頻率、極性、起始方位角、衰減量、多重弦波頻率和衰減因子等多維度參數的聯合估測，常被應用在信號源定位、接收機設計、雷達顯像、多重輸入多重輸出系統、核磁共振造影及無線通訊頻道探測等信號處理領域。為使估測方法能符合實際應用之要求，本論文特提出許多基於階層式信號拆解技術之高效能且低複雜度的多維度參數估測演算法。
基於階層式信號拆解技術，演算法應用許多低維度之子空間估測方法，以階層樹狀結構來進行各個特定維度的參數估量，在各維度參數應用子空間法進行估測的過程之間，交錯使用投影濾波或空間波束形成對所估測信號做適當的分群，藉以削減雜訊影響提升估量的精準度。在信號拆解的架構下，不僅可將參數相近的信號進行拆解分群，也可進一步提升參數估測的效能。因此，信號在同一維度之參數即使相近，也可以被正確的估測。此外，由於使用階層式的樹狀架構，受估測的參數可自動達成配對，可消弭配對錯誤造成的危害和額外的運算負擔。
本論文所探討和研究的主題發展出高效率且高正確度之子空間估測演算法，包括到達方位角-時間延遲的聯合估測，入射信號於矩形陣列之二維方位角-載波頻率的聯合估測、使用同心交錯耦極天線陣列進行二維方位角-極性的聯合估測和多維度諧波檢索等。本論文應用大量的電腦模擬來進行演算法的效能驗證，與比其他文獻所論述的方法相比，本論文提出的演算法除了可顯著降低運算複雜度外，也提供符合的估測效能，達到高性能和低複雜度兼顧的目標。

Joint estimation of multidimensional parameters, such as direction-of-arrival (DOA), delay, carrier frequency, polarization, direction-of-departure (DOD), fading, and multidimensional sinusoidal frequency and decaying factor, arises in various facets of signal processing applications such as source location, receiver design, radar imaging, multiple-input-multiple output (MIMO) systems, nuclear magnetic resonance spectroscopy and wireless channel sounding. To be more amenable to practical applications, in this dissertation, we propose several efficacious, yet low complexity algorithms for the multidimensional parameter estimation using a novel Hierarchical Signal Separation (HISS) technique.

Based on the HISS, several of lower-dimensional subspace-based algorithms are employed in a hierarchical tree structure to estimate the parameters in each specific dimension. In between every other subspace-based algorithm, a set of filtering/beamforming processes is invoked to partition the signals into appropriate groups and to remove the additive noise to enhance the estimation accuracy. Such a signal separation scheme not only partitions the signals with close parameters into separate groups, but it also enhances the parameter estimation accuracy. Consequently, signals can be well resolved even with very close parameters in the same dimension. In addition, the parameter estimation proceeds in a hierarchical tree structure, so
the estimated parameters are automatically paired without extra computational overhead.

Our investigations of this dissertation include the development of the efficient, yet high accuracy subspace-based algorithms for joint DOA and delay estimation in the Frequency Hopping (FH) systems, joint two-dimensional (2-D) angle and carrier frequency estimation of the signals impinging on a uniform rectangular array (URA), joint 2-D angle and polarization estimation using co-centered crossed dipole (CCD) pairs, and multidimensional harmonic retrieval (MHR). Conducted simulations show that the developed algorithms, calling for drastically reduced computations, can provide satisfactory performance compared with previous works, and thus strike a better tradeoff between performance and complexity.

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