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一種新的聯(lián)合塊對(duì)角化卷積盲分離時(shí)域算法
來(lái)源：電子技術(shù)應(yīng)用2012年第2期
溫媛媛， 陳 豪
中國(guó)空間技術(shù)研究院 西安分院, 陜西 西安710000
摘要： 提出一種基于高階累積量聯(lián)合塊對(duì)角化的時(shí)域算法求解卷積混合盲信號(hào)分離問(wèn)題。引入白化處理，將混疊矩陣轉(zhuǎn)變成酉矩陣，混合信號(hào)轉(zhuǎn)變?yōu)榛ゲ幌嚓P(guān)的，進(jìn)而計(jì)算出其對(duì)應(yīng)的一系列高階累積量矩陣，通過(guò)最小化代價(jià)函數(shù)來(lái)實(shí)現(xiàn)高階累積量矩陣聯(lián)合塊對(duì)角化的目的，在時(shí)域中解決超定卷積盲分離問(wèn)題。實(shí)驗(yàn)表明，相比于經(jīng)典的自然梯度算法，所提方法的分離精度更高，且運(yùn)算速度也更快。
中圖分類號(hào)： TN912.3
文獻(xiàn)標(biāo)識(shí)碼： A
文章編號(hào)： 0258-7998(2012)02-0101-04
A new joint block diagonalization time-domain algorithm for convolutive blind separation
Wen Yuanyuan, Chen Hao
Xi’an Division of China Academy of Space Technology, Xi’an 710000, China
Abstract： This paper proposes a new time-domain joint block diagonalization algorithm based on the high-order cumulant for the blind source separation of convolutive mixtures. This paper adopts the whitening procedure to transform the mixing matrix into an unitary matrix. Computing the high-order cumulant matrixes of the mixing signals whitened, which can be transformed into block diagonal matrixes through minimizing the cost function. Simulations results illustrate that, the new method outperforms the classic natural gradient method in separation precision and operation speed, and can be efficiently applied to the blind source separation of convolutive mixtures.
Key words : blind source separation; convolutive mixtures; high-order cumulant; joint block diagonalization

    近年，盲信號(hào)分離BSS（Blind Source Separation）的研究已經(jīng)成為信號(hào)處理領(lǐng)域的一個(gè)研究熱點(diǎn)，涌現(xiàn)出許多盲分離的算法。盲信號(hào)分離是在源信號(hào)和傳輸信道參數(shù)未知的情況下，僅根據(jù)源信號(hào)的統(tǒng)計(jì)特性，從觀測(cè)信號(hào)中分離源信號(hào)的過(guò)程[1]。盲信號(hào)分離所研究的混疊模型主要分為瞬時(shí)混疊和卷積混疊兩類。瞬時(shí)盲分離已經(jīng)得到廣泛而成熟的研究，聯(lián)合塊（JBD）對(duì)角化是解決瞬時(shí)盲分離的有效方法[2-4]。然而，傳感器接收到的信號(hào)通常是源信號(hào)與多徑傳輸信道的卷積混疊信號(hào)，這使得卷積盲分離受到越來(lái)越多的關(guān)注[5-7]。

    與瞬時(shí)混疊模型相比，卷積混疊信號(hào)模型及其求解更為復(fù)雜。在現(xiàn)有方法中，基于高階統(tǒng)計(jì)量的時(shí)域算法[8-9]是解卷積混疊盲信號(hào)分離問(wèn)題的一類直觀且有效的方法。作為時(shí)域算法，它不需要解決頻域算法[10-11]中所固有的又不得不解決的尺度模糊和排列模糊問(wèn)題；同時(shí)，對(duì)一組高階累積量矩陣同時(shí)進(jìn)行JBD又可以有效地抑制高斯噪聲的影響。鑒于這兩點(diǎn)，本文提出一種基于高階累積量的JBD時(shí)域算法，來(lái)解決卷積混疊盲信號(hào)分離問(wèn)題。
1 問(wèn)題描述
    盲信號(hào)分離的目的是把通過(guò)一未知混合系統(tǒng)后的觀測(cè)信號(hào)分離開來(lái)。在卷積混合情況下，假設(shè)源信號(hào)通過(guò)一個(gè)線性有限脈沖響應(yīng)FIR濾波器，也就是說(shuō)觀測(cè)信號(hào)是由它們的延遲所組成的線性組合，即：
 



    用參考文獻(xiàn)[14]中所提到的自然梯度算法來(lái)分離卷積混合的源信號(hào),最后分離出來(lái)的信號(hào)波形如圖3所示。
    從兩種算法分離出的信號(hào)波形圖中很難明顯看出其性能的差別，下面通過(guò)兩個(gè)性能指標(biāo)來(lái)客觀地分析一

陣。在此基礎(chǔ)上通過(guò)使代價(jià)函數(shù)最小化的方法來(lái)使累積量矩陣成為塊對(duì)角矩陣，進(jìn)而實(shí)現(xiàn)盲分離。計(jì)算機(jī)仿真結(jié)果表明，本文算法與自然梯度算法相比有分離精度高及分離速度快的特點(diǎn)。

參考文獻(xiàn)
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