粒子群趨動交叉熵法於多輸入多輸出信號偵測之應用

Abstract

多輸入多輸出(MIMO)之無線通訊系統中，多根傳送天線同時傳送資料至多根接收天線，接收端如何由收到的混合信號辨別出不同天線傳送的資料，並正確地估計資料內容一直是多輸入多輸出系統的重要議題。近幾年來，多種常見的信號偵測法如逼零(zero-forcing)偵測法、最小均方誤差(minimum-mean-square-error)檢測法及垂直分層空時碼(V-BLAST)等均不斷地被應用及改善。

本文提出一種用於正交振幅調變(QAM)之多輸入多輸出系統的信號偵測方法。交叉熵(cross-entropy)法為一種近似於蒙地卡羅(Monte-Carlo)的迭代式最佳化問題解法。藉由兩機率密度函數之間距離(Kullback-Leibler distance)的最小化找出權重取樣分佈機率(importance sampling density)，進而求出最佳點所在位置。應用此方法於多輸入多輸出系統之信號偵測上，其位元錯誤率(BER)在低信號雜信比(SNR)時與最大似然法之位元錯誤率(Maximum Likelihood method)幾乎相同，然而在高信號雜信比範圍卻存在錯誤平台(error floor)現象。為改善此現象，我們引入粒子群驅動演算法(particle swarm algorithm)主要概念修正所提出之偵測方法。粒子群驅動演算法是一種以群體為基底的迭代式演算法，每個粒子藉著前一次迭代過程中所提供之資訊決定移動軌跡，在可行解搜尋區域(feasible solution space)往最佳點所在位置移動。將此概念融合於所提出之交叉熵偵測法，在尋找權重取樣分佈機率過程中加入一股驅動力量使其不致陷入區域最佳解，並將其稱之為粒子群趨動交叉熵法偵測器。此偵測法的位元錯誤率於高信號雜訊比範圍具有極顯著之改善。此外，我們亦針對通道估計誤差修正此偵測法提出一穩健偵測器。

Many solutions for detecting signals transmitted over flat-faded multiple input multiple output (MIMO) channels have been proposed, e.g., the zero-forcing (ZF), minimum mean squared error (MMSE), lattice reduction and V-BLAST algorithms, to name a few. However, these approaches suffer from either unsatisfactory performance or high complexity.

We present an alternative method for detecting quadrature amplitude modulated (QAM) MIMO signals. This method tries to estimate the probability distribution of the candidate signal location by sampling over a neighborhood of the received waveform. The proposed random sampling based iterative distribution estimator is similar to the class of Monte-Carlo based optimization approach and if the distance used in measuring the distance between a tentative distribution and the optimal distribution is the Kullback-Leibler distance (cross entropy) then our solution is identical to the one known as the Cross-Entropy (CE) method. The CE method is motivated by the search for an efficient rare-event simulation solution. The problem is equivalent to finding the optimal importance sampling density. The desired density is obtained by iterative random search in the space of exponential distributions with the CE metric.

The proposed CE-based detector yields bit-error-rate (BER) performance which is close to that achievable by the Maximum-Likelihood (ML) detector when the signal-to-noise ratio (SNR) is relatively low. Unfortunately the performance curves exhibit error floors in high SNR region. To improve the performance in high SNR region, we borrow the concept of particle swarm optimization (PSO) in designing our detector. PSO is a population-based iterative search algorithm which moves a number of particles through the feasible solution space towards the optimal solution with the information obtained in previous iterations. The modified iterative detector incorporates extra terms, which are generated by a PS-like process and represent a driving force to pull the iterative optimization process from being trapped in local minimums, in updating of the importance density and is called the particle-swarm-driven cross-entropy (PSD-CE) MIMO detector. The PSD-CE detector gives significant BER performance improvement in medium-to-high SNR region. We also consider the case when channel state information is imperfect and suggest a robust detector structure based on a modified score function.