針對無線感測器網路的訊息中繼考慮通道參數不匹配的低冗餘波束形成設計

Abstract

於低訊號冗餘合作式通訊系統中的高效能訊號處理演算法在實現節能的第四代中繼網路中扮演著重要的角色。在這篇論文中，我們研究在無線感測器網路中針對訊息中繼來考慮在通道參數不匹配的情況下的低冗餘合作式波束形成設計。在我們所考慮的系統中，為了達到降低傳送通道狀態資訊的訊號冗餘，每一個中繼端會將其測得之訊源與中繼端的鏈結訊雜比量化成一位元的訊息。為了反映無線感測器網路嚴格的傳送功率限制，每一個訊雜比的量化訊息在傳輸過程中因此假設為不理想的，於數學上視為經由一個帶有非零交叉機率的二元對稱通道來傳送。當接收端接收這些可能有位元翻轉的一位元訊雜比訊息，且假設中繼端與接收端間鏈結的通道估測是完美的，則我們首先可以考慮藉由最大化接收訊號的訊雜比期望值所得的波束形成系數設計，其中此訊雜比公式是針對二元對稱通道中位元翻轉的統計特性所求得的期望值。接著，我們進一步延伸考慮中繼端與接收端間鏈結的通道估測可能會產生誤差的情況，在數學上我們以獨立同分佈的高斯隨機變數才表示。在這兩種情況下，我們可以透過針對訊雜比不確定性或是通道狀態資訊不確定性作平均，以分別推導出具封閉形式的條件平均接收訊雜比。因為如此推導出來的訊雜比公式對波束形成系數來說是一高度非線性函數，所以針對這兩種訊雜比公式，我們分別進一步地推導出各自的可分析下界以利於分析。藉由最大化各自的訊雜比下界，相應的亞最佳波束形成系數解即可透過解廣義特徵值問題來求得。最後，電腦模擬結果用以檢驗我們提出方法的成效。

High-performance signal processing algorithms for cooperative communication systems with reduced signaling overhead play a key role toward realizing energy-efficient relay networks for 4G and beyond. In this thesis, we study the problem of low-overhead cooperative beamforming design for information relaying in wireless sensor networks (WSNs) by taking account of the effect of mismatched inter-node channel state information (CSI). In the considered system, each relay node quantizes the signal-to-noise ratio (SNR) of the source-to-relay (S-R) link into one bit in order to reduce the signaling overhead dedicated to CSI transmission. To reflect the severe transmit power limitation of WSNs, the transmission link of the quantized SNR message is assumed to be non-ideal, and is modeled by a binary symmetric channel (BSC) with a non-zero crossover probability. With the flipped one-bit SNR messages received at the destination and assuming that the relay-to-destination (R-D) link channel estimation is perfect, we first study the beamforming design based on maximization of the expected receive SNR, averaged with respect to the bit-flipping distributions of BSC's. Next, the proposed approach is extended to the scenario wherein the R-D link channel estimation errors occur, and are modeled as i.i.d. Gaussian random variables. In both cases, we derive closed-form expressions for the conditional receive SNR averaged over the distributions of the SNR/CSI uncertainty. Since the SNR measures thus obtained are highly nonlinear functions of the beamforming coefficients, we further derive for each case a tractable SNR lower bound to facilitate analyses. By conducting maximization with respect to the derived SNR lower bounds, suboptimal beamformers can be obtained via solving generalized eigenvalue problems. Computer simulations are used to illustrate the performances of the proposed schemes.