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Method of inverting nearly Toeplitz or block Toeplitz matrices
Method of inverting nearly Toeplitz or block Toeplitz matrices
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机译:反转几乎Toeplitz矩阵或块Toeplitz矩阵的方法
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摘要
A method of computing an inversion (X) of a nearly Toeplitz n by n matrix (A). A perturbation matrix (E) is first determined such that the sum of the nearly Toeplitz matrix (A) and the perturbation matrix (E) is a Toeplitz matrix (T). The inversion is solved by solving the equation X=T−1(B+EX), where B is a vector or matrix of dimension n by m. An initial estimate X(0) is selected and estimates of the inversion X are iteratively computed through the recursion X(n−1)=T−1(B+EX(n)). The initial estimate X(0) may be equal to an inversion (T−1) of the Toeplitz matrix (T). The present invention may be utilized in a radio receiver to efficiently compute (1) a least-squares (LS) channel estimate, (2) minimum mean squared error (MMSE) prefilter coefficients for a decision feedback equalizer (DFE), or (3) an autoregressive (AR) noise-spectrum estimation from a finite number of observed noise samples.
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机译:一种计算近似Toeplitz n x n矩阵(A)的求逆的方法。首先确定扰动矩阵(E),以使近似托普利兹矩阵(A)和扰动矩阵(E)之和为托普利兹矩阵(T)。通过求解方程X = T -1 Sup>(B + EX)来求解反演,其中B是n乘m的向量或矩阵。选择初始估计值X (0) Sup>,然后通过递归X (n-1) Sup> = T -1 up>迭代计算反演X的估计值。 Sup>(B + EX (n) Sup>)。初始估计X (0) Sup>可以等于Toeplitz矩阵(T)的反演(T -1 Sup>)。本发明可以在无线电接收机中利用以有效地计算(1)最小二乘(LS)信道估计,(2)用于判决反馈均衡器(DFE)的最小均方误差(MMSE)预滤波器系数,或(3) )根据有限数量的观察到的噪声样本进行自回归(AR)噪声频谱估计。
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