可調基底之稀疏貝式學習:演算法與應用

Abstract

稀疏貝式學習法利用貝式推理來求解，是一種被廣泛使用的壓縮感測法。在這種做法中，基底函數通常會被使用來以形成轉換矩陣。對於特定的應用上，可能存在一個模型已知參數卻未知的基底，可以把信號轉換到稀疏域。傳統的稀疏貝式學習法，基底的參數通常是假設已知的。這樣的假設可能不適用於真實世界，因而會大大影響傳統稀疏貝式學習法的效能。本篇論文提出了一個可調基底之稀疏貝式學習法，藉由輪流反覆地估測基底參數與系統參數來解決此問題。我們亦探討可能的應用。 首先我們將之應用於感知無線系統，探討合作式頻譜估測的問題。我們知道感知無線系統裏除了頻譜的稀疏性外，空間的稀疏性也能被利用來進一步加強頻帶的使用效率。為了達到此目的，次級使用者必須知道首要使用者基地台的位置以及信號強度分布。在此我們將此問題指稱為無線信號源的定位與功率傳播分布圖的重建。傳統的方式是利用一個路徑損耗模型來近似使用者基地台的功率衰減，並且假設使用者基地台的位置坐落於某些格點上。然而，路徑損耗模型的參數必須事先得知，並且估測的精準度會受限於格點的解析度。我們首先利用拉普拉斯函數來模式化使用者基地台的功率衰減，並且提出可調基底之稀疏貝式學習法來適當地估測相對應的參數。利用我們提出的方式，只需要知道少量的事前資訊。 為了進一步提升效能，我們結合了信號源數量檢測法，使得使用者基地台的數目可以精準地被估測。模擬結果顯示即使空間中的量測比例很低，我們所提出的演算法仍然有令人滿意的效能。雖然所提出的可調基底之稀疏貝式學習法可以有效地重建感知無線系統下的功率傳播分布圖，但它只能一次只能針對某一個單一頻帶重建，並沒有考慮到頻帶間的相關性。為了彌補這個不足，我們延伸拉普拉斯函數到多頻帶環境下。對一個多頻帶的拉普拉斯函數，我們採用區塊稀疏貝式學習法來有效的使用不同頻帶間的相關性。可調基底之稀疏貝式學習法因此被延伸成為可調基底之區塊稀疏貝式學習法，以同時重建多個頻帶的功率傳播分布圖。模擬顯示可調基底之區塊稀疏貝式學習法效能優於獨立使於不同頻帶之可調基底之稀疏貝式學習法。 最後，我們應用所提出的可調基底之區塊稀疏貝式學習法於第三代夥伴合作計劃長期演進系統下之定位問題。觀察到達時間差法被用來估計使用者元件的位置。它利用從三個不同基地台所估測到的到達時間來當作觀測值。對應於某基地台的到達時間可以藉由所估測時域信號響應的第一個係數延遲來得到。觀察到達時間差法主要的問題是在於藉由通道估測法求得之到達時間其估測精準度會受限於接收機取樣器的量化效應。由於無線通道普遍來說是稀疏的，我們可以將時域通道響應的估測模式化成一個壓縮感測的問題。用波形整形濾波器響應當作基底，我們可以利用所提出的可調基底之區塊稀疏貝式學習法來做通道估測，使用這種作法估得之到達時間將不受量化效應的影響。模擬顯示所提之可調基底區塊稀疏貝式學習法可顯著的提升到達時間估測精準度同時也改善定位效能。

Sparse Bayesian learning (SBL) is a widely used compressive sensing (CS) method that finds the solution by Bayesian inference. In this approach, a basis function is specified to form the transform matrix. For a particular application, it may exist a proper basis, with known model function and unknown parameters, which can convert the signal to a sparse domain. In conventional SBL, the parameters of the basis are assumed to be known as priori. This assumption may not be valid in real-world applications, and the efficacy of conventional SBL approaches can be greatly affected. In this dissertation, we propose a basis-adaptive-sparse-Bayesian-learning (BA-SBL) framework, which can estimate the basis and system parameters, alternatively and iteratively, to solve the problem. Possible applications are also explored. We start the work with the cooperative spectrum sensing problem in cognitive radio (CR) systems. It is known that in addition to spectrum sparsity, spatial sparsity can also be used to further enhance spectral utilization. To achieve that, secondary users (SUs) must know the locations and signal-strength distributions of primary-users’ base-stations (PUBSs), which is referred to as radio source positioning and power-propagation-map (PPM) reconstruction. Conventional approaches approximate PUBSs’ power decay with a path-loss model (PLM) and assume PUBSs’ locations on some grid points. However, the parameters of the PLM have to be known in advance and the estimation accuracy is bounded by the resolution of the grid points. We first employ a Laplacian function to model the PUBS power decay profile and propose a BA-SBL scheme to estimate corresponding parameters. With the proposed method, little priori information is required. To further enhance the performance, we incorporate source number detection methods such that the number of the PUBSs can be precisely detected. Simulations show that the proposed algorithm has satisfactory performance even when the spatial measurement rate is low. While the proposed BA-SBL scheme can effectively reconstruct the PPM in CR systems, it can only be applied in one frequency band at a time, and the frequency-band dependence is not considered. To fill the gap, we then extend the Laplacian function to the multiple-band scenario. For a multi-band Laplacian function, its correlation between different bands is taken into consideration by a block SBL (BSBL) method. The BA-SBL is then modified and extended to a basis-adaptive BSBL (BA-BSBL) scheme, simultaneously reconstructing the PPMs of multiple frequency bands. Simulations show that BA-BSBL outperforms BA-SBL applied to each band, independently. Finally, we apply the proposed BA-BSBL procedure to the positioning problem in the 3rdgeneration-partnership-project (3GPP) long-term-evolution (LTE) systems. The observed-timedifference-of-arrival (OTDOA) method is used to estimate the location of user-element (UE). It uses the estimated time-of-arrivals (TOAs) from three different base stations (BSs) as the observations. The TOA corresponding to a BS can be obtained by the first-tap delay of the time-domain channel response. The main problem of conventional OTDOA methods is that the precision of TOA estimation, obtained by a channel estimation method, is limited by the quantization effect of the receiver’s sampler. Since wireless channels are generally spare, we can then formulate the time-domain channel estimation as a CS problem. Using the pulseshaping-filter response as the basis, we apply the proposed BA-BSBL procedure to conduct the channel estimation, and the TOA can be estimated without quantization. Simulations show that the proposed BA-BSBL algorithm can significantly enhance the precision of TOA estimation and then improve the positioning performance.