噪訊增強的無線通訊網路盲蔽式錯誤率估測器之設計與效能分析

Abstract

基於多筆資訊做資料偵測或融合的技術已經廣泛被使用在通訊系統上。本論文考慮一廣義的無線網路框架，在此框架中，我們假設訊號會經過不同的鏈結(link)到達接收器，而鏈結的種類包含了直接鏈結(從傳送端到接收端)以及兩步(two-hop)鏈結(從傳送端經由中繼站到達接收器)。在兩步鏈結中，中繼端會把收到的訊號作解碼並傳送重新編碼過後的訊號到接收端。在此框架中，資料偵測或融合的技術通常需要各鏈結的錯誤率資訊。舉例來說，在二元相位調變(binary phase-shift keying)合作式通訊系統中，最佳資料偵測需要知道遠端鏈結(從傳送端到中繼站的鏈結，縮寫為SR鏈結)的錯誤率資訊。同樣地，在資料融合中心(fusion center)，基於多感測測量值的最佳資料融合也是需要各遠端鏈結的錯誤率資訊。 為了在接收端盲蔽式地估測遠端的二進位調變(binary modulation)錯誤率，我們首先把估測問題轉換成解非線性聯立方程式的問題。每一個方程式皆反映成功匹配機率(success matching probability)和兩鏈結的錯誤率關係。其中，我們定義成功匹配機率是給定一傳送訊號下兩鏈結做出相同決策的機率。為了要讓此非線性聯立方程式有解，其基本的要求是要有足夠的鏈結數目。當鏈結數目不夠時，我們需要部分的資訊才能求出解，部分的資訊可能包含了從傳送端到接收端的鏈結(SD鏈結)錯誤率或是從中繼站到接收端的鏈結(RD鏈結)錯誤率。而事實上，我們發現當我們沒有從中繼站到接收端的鏈結錯誤率資訊時，即使有再多的鏈結數目亦是無法求出合理解來，這是因為從傳送端經中繼站到接收端的錯誤率會是SR鏈結和RD鏈結錯誤率的對稱函數。 為了解決上述的問題以及增加收斂速度，我們提出基於蒙地卡羅(Monte-Carlo)的估測器。具體來說，我們在接收端加入噪訊(noise)到接收訊號。在第一種方式中，我們加入噪訊是為了產生虛擬的SD鏈結或是RD鏈結，藉由這樣的方法，我們可以在即使只有一中繼站情況下亦可以得到有解的非線性聯立方程式問題。此方法我們稱為虛擬鏈結估測器(virtual link aided estimatior)。在第二種方法中，我們加入噪訊使得收到訊號的機率分佈作改變，藉由機率分佈的改變可以使得估測器的效能有所改善。 事實上，第二種方法顯示出隨機震盪（stochastic resonance）的現象，也就是說注入適當的噪訊可以改善均方根估測誤差（mean squared estimation error），此外我們發現到存在最佳的注入噪訊量使得估測效能最佳。針對此現象，我們做了一系列的分析並找出最佳的注入噪訊量為何，並藉由模擬驗證我們分析的正確性。模擬結果也顯示出訊號偵測器配合提出的盲蔽式估測器會和最佳偵測器有差不多的錯誤率效能。 對於非二進位調變通訊網路，成功匹配機率和鏈結符碼錯誤率(symbol error rate)的關係不再成立，因此，上述提到的方法不再能夠直接使用於此情況。在參考文獻[34]中，此問題被轉換成一個非線性最佳化問題，雖然其問題理論上可以解，但是其複雜度會非常的高如果中繼站數目或是M-ary 調變的M值不小的時候。針對此問題，我們基於二位元表示法提出次佳的接收機以及其對應所需的錯誤率估測器。由於我們可以找到解的數學表示式，其複雜度會遠比上述所提的方法還要低得多。為了進一步改善偵測器的收斂速度，我們亦提出一噪訊增強的估測器。模擬的結果顯示我們提出的偵測器伴隨相對應的估測器會和最佳估測器有相似的效能。在均方估測錯誤(mean square estimation error)效能的評估上，我們亦可以觀察到隨機震盪的現象

Data detection or fusion based on multiple received copies containing the same information arises in many applications. We consider the scenario that each copy is transmitted from the same source through a different wireless link to the same destination node (DN). These links include single-hop, direct source-to-destination (SD) links and two-hop links that require an intermediate decode-and-forward (DF) node to relay the source signal. Detection or fusion under such a circumstance often need channel side information (CSI) about the link reliability. For example, maximum likelihood (ML) detection of binary modulated signals in a DF based cooperative communication network (CCN), information about the bit error rates (ERs) of the hidden source-relay (SR) links is needed. Similarly, optimal data fusion based on multiple sensor measurements requires that the ERs of various SR links be available at the fusion center.

To estimate multiple ERs blindly at the DN in a binary modulated network, we convert the estimation problem into one of solving a system of nonlinear equations. Each equation arises from the fact that the success matching probability (SMP) that a bit transmitted over two independent links connecting the same source and destination results in identical destination decisions is nonlinearly related to the ERs of the two associated links. However, the number of distinct link pairs must be larger than the number of ERs to be estimated so that the system is not an underdetermined one. Various degrees of channel side information (CSI) about the ERs of the SD and relay-destination (RD) links is called for to remove the ambiguity arising from the insufficient number of links in the network and from that due to the symmetric nature of a cascaded source-relay-destination (SRD) link's ER as a function of its component SR and RD links' ERs.

We propose novel Monte-Carlo-based estimators that overcome all these shortcomings and accelerate the convergence speed. Our proposals involve injecting noise into the samples received by the DN. The injected noise in the first solution, called the virtual link aided (VLA) estimator, help creating virtual SD and RD links to release all CSI requirements, resolve the symmetric ambiguity and provide estimates for ERs of all component links. Using multitude of VLs, we can enhance the VLA scheme's performance and reduce the number of RNs required. The role the injected noise plays in another solution, called the importance-sampling-inspired (ISI) estimator, is different: it is used to modify link output statistics to improve the VLA estimator's convergence rate.

The latter approach exhibits a stochastic resonance effect, i.e., its mean squared estimation error (MSEE) performance is enhanced by injecting proper noise, and there exists an optimal injected noise power level that achieves the maximum improvement. The stochastic resonance effects are analyzed, and numerical examples are provided to display our estimators' MSEE behaviors, as well as to show that the ER performance of the optimal detector using the proposed estimators is almost as good as that with perfect ER information.

For nonbinary modulation based networks, a relation between the SMP of a link pair and the associated symbol error rates does not exist, hence the nonlinear system based moments approach is not directly applicable. A nonlinear optimization approach which we call LJW blind estimator [34] had been proposed. Unfortunately it requires prohibitively high computational complexity unless M and the relay numbers are small. We propose a suboptimal detector based on bit-level representation and a corresponding blind estimator to estimate the error rate of sensor nodes. The complexity of our estimator is much lower than that of LJW as we are able to obtain a closed-form salutation instead of employing an iterative algorithm for solving a nonlinear optimization. To further improve the convergence rate, we propose a noise-enhanced estimator. Simulation results show that the proposed suboptimal detector using the proposed blind estimator render negligible performance loss with respect to that of the optimal detector. A stochastic resonance phenomenon is observed in the estimator's mean square estimation error performance.