多步迭代降维方法研究

doi:1000-436X(2007)09-0068-06

Abstract

Abstract:

On the background of joint space-time anti-jammer processing for GPS receiver,multistage Wiener filter-ing(MWF) algorithm and auxiliary vector filtering(AVF) algorithm was deeply analyzed as two typical multistage itera-tive rank-reduced method in this article and their immanent relationship was pointed out.A new algorithm was proposed which has a forward recursion on the data level and a backward iterative.Compared with MWF and AVF,the proposed algorithm has a better performance,reduces the computation complexity and selects the filter rank more easily.It suits with practical realization of joint space-time anti-jammer processing for GPS receiver.Numerical simulation demon-strates that the proposed method is effect and efficient.

Key words: multistage iterative, multistage Wiener filtering, auxiliary vector filtering, rank-reduced algorithm

Yi GUO,Er-yang ZHANG,Rong-jun SHEN. Study on the multistage iterative rank-reduced method[J]. Journal on Communications, 2007, 28(9): 68-73.

Figures/Tables 6

初始化： $d_{0} (k) = S^{H} X_{M N × 1} (k)$ , $X_{0} (k) = X_{M N × 1} (k) - S d_{0} (k)$ ，
$t = E {d_{0}^{} (k) X_{0} (k)} / ‖ E {d_{0}^{} (k) X_{0} (k)} ‖$ ，
$d_{1} (k) = t_{1}^{H} X_{0} (k)$ ， $X_{1} (k) = X_{0} (k) - t_{1} d_{1} (k)$ ，
$r_{0, 1} = 0$ ， $r_{1, 1} = {d_{1} (k) d_{1}^{*} (k)}$ ， $c_{f i r s t}^{(1)} = r_{1.1}^{- 1}$ ， $c_{l a s t}^{(1)} = r_{1.1}^{- 1}$
迭代：For j=2,3,…,MN?1
$t_{j} = E {d_{j - 1}^{} (k) X_{j - 1} (k)} / ‖ E {d_{j - 1}^{} (k) X_{j - 1} (k)} ‖$ ，
$d_{j} (k) = t_{j}^{H} X_{j - 1} (k)$ ， $X_{j} (k) = X_{j - 1} (k) - t_{j} d_{j} (k)$ ，
$r_{j, j} = E {d_{j} (k) d_{j}^{} (k)}$ ， $r_{j - 1, j} = E {d_{j - 1} (k) d_{j}^{} (k)}$ ，
$β_{j} = r_{j, j} - {[r_{j - 1, j}]}^{2} c_{l a s t, j - 1}^{(j - 1)}$ ，
$c_{f i r s t}^{(j)} = [\begin{matrix} e_{f i r s t}^{(j - 1)} \\ 0 \end{matrix}] + β_{j}^{- 1} c_{l a s t, 1}^{{(j - 1)}^{}} [\begin{matrix} {\| r_{j - 1, j} \|}^{2} c_{l a s t}^{(j - 1)} \\ - r_{j - 1, j}^{} \end{matrix}]$ ，
$c_{l a s t}^{(j)} = β_{j}^{- 1} [\begin{matrix} - r_{j - 1, j} c_{l a s t}^{(j - 1)} \\ 1 \end{matrix}]$ ，
$M S E^{(j)} = σ_{d_{0}}^{2} - {‖ r_{X_{0} d_{0}} ‖}_{2}^{2} c_{f i r s t, 1}^{(j)}$
If $M S E^{(D)} ＜ M S E_{t h r e s h o l d}$ ,
Then D=j，跳出
End
权值计算： $T_{D} = [t_{1}, t_{2}, \dots t_{D}]$ ，
$W_{M W F_s i m p l e} = T_{D} W_{D} = {‖ r_{X_{0} d_{0}} ‖}_{2} T_{D} c_{f i r s t}^{(D)}$

References 1

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多步迭代降维方法	前向分析滤波递推计算量（乘法）	后向综合滤波及求权值计算量（乘法）
原AVF方法	O[(MN)²D]	O[(MN)²]（实时性好）
原MWF方法	O[(MN)²D]	O(MND)（实时性差）
改进方法	O(MND)	O(MND)（实时性好）

Study on the multistage iterative rank-reduced method

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