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US 2004/0174931 A1Published application
Equalizers
AssigneeIndustry-Academic Cooperation Foundation, Yonsei University
InventorChulhee Lee
Life of this patent
Estimating the term…
Abstract
The linear equalizer is implemented utilizing second-order statistics, assuming two classes that have normal distributions, which improves the convergence speed and performance significantly. The idea and teaching of the present invention is also extended with equalization viewed as a multi-class classification problem. Furthermore, the idea and teaching of the present invention is extended to blind equalization.
Claims4
A linear equalizer for a linear dispersive channel with known channel characteristics, characterized by
- 24 y ( n ) = ∑ k = - L 1 L 2 α k x ( n - k ) + e ( n ) ,
- comprising the steps of:
- (a) constructing a vector from received signals as follows:
- Y(n)=[y(n−L1),y(n−L1+1), . . . ,y(n+L2−1),y(n+L2)]T;
- (b) computing a weight vectors as follows:
- w=ΣY−1(μY1−μY2)
- where
- 25 μ X 1 = [ 0 , … , 0 ⏟ L 1 zeros , 1 , 0 , … , 0 ⏟ L 2 zeros ] T , μ X 2 = [ 0 , … , 0 ⏟ L 1 zeros , - 1 , 0 , … , 0 ⏟ L 2 zeros ] T , ΣX1=1−μX1μX1T, μY1=AμX1, μY2=AμX3, ΣY=AΣX1AT+σe2I, 26 A = [AutoLeftMatch] [ a - L 1 a - L 1 + 1 … a L 2 - 1 a L 2 … 0 0 0 0 a - L 1 a - L 1 + 1 … a L 2 - 1 a L 2 … 0 0 … … … … … … … … … 0 0 … a - L 1 a - L 1 + 1 … a L 2 - 1 a L 2 0 0 0 0 … a - L 1 a - L 1 + 1 … a L 1 - 1 a L 21 ] ,
- I is an identity matrix, and
- σe2 is the noise power;
- and
- (c) determining a received signal according to the following rule:
- if wTY(n)>0, then decide that state 1 is transmitted,
- if wTY(n)<0, then decide that state −1 is transmitted.
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A linear equalizer with unknown channel characteristics, comprising the steps of:
- (a) constructing a class 1 vector from training signals when an input signal corresponding to y(n) is state 1, as follows:
- Y1(n)=[y(n−L1),y(n−L1+1), . . . ,y(n), . . . ,y(n+L2−1),y(n+L2)]T;
- (b) constructing a class 2 vector from training signals as follows when an input signal corresponding to y(n) is state −1:
- Y−1(n)=[y(n−L1),y(n−L1+1), . . . ,y(n), . . . ,y(n+L2−1),y(n+L2)]T;
- (c) computing a weight vectors as follows:
- w={circumflex over (Σ)}Y−1({circumflex over (μ)}Y1−{circumflex over (μ)}Y2)
- where
- 27 μ ^ Y 1 = 1 N 1 ∑ i = 1 N 1 Y 1 ( i )
- ( N1:
- the number of training vectors belonging to state 1),
- 28 ∑ = Y 1 ^ 1 N 1 ∑ i = 1 N 1 ( Y 1 ( i ) - μ ^ Y 1 ) ( Y 1 ( i ) - μ ^ Y 1 ) T ,
- 29 μ ^ Y 2 = 1 N 2 ∑ i = 1 N 2 Y 2 ( i )
- (N2:
- the number of training vectors belonging to state −1),
- 30 ∑ = Y 2 ^ 1 N 2 ∑ i = 1 N 2 ( Y 2 ( i ) - μ ^ Y 2 ) ( Y 2 ( i ) - μ ^ Y 2 ) T ,
- and
- {circumflex over (Σ)}Y=({circumflex over (Σ)}Y1+{circumflex over (Σ)}Y2)/2;
- and
- (d) determining a received signal according to the following rule:
- if wTY(n)>0, then decide that state 1 is transmitted,
- if wTY(n)<0, then decide that state −1 is transmitted.
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A blind linear equalizer, comprising the steps of:
- (a) assigning initial parameters {Njinitial, μjinitial, Σjinitial} where Njinitial is the initially assumed number of training samples of class ωj, μjinitial the initial estimator of the mean vector of class ωj, and Σjinitial the initial estimator of the covariance matrix of class ωj;
- (b) estimating the mean vector and covariance of class ωj as follows:
- 31 μ ^ j ( N j ) = 1 N j SUMY j ( N j ) , Σ ^ j ( N j ) = 1 N j - 1 SUMYY j ( N j ) - N j N j - 1 μ ^ j ( N j ) μ ^ j ( N j ) T ,
- where
- Nj=Njinitial+Njinitial,
- Njinitial is the actual number of samples that are classified as class ωj,
- 32 SUMY j ( N j ) = SUMY j initial + ∑ i = N j initial + 1 N j Y j ( i ) , and SUMYY j ( N j ) = SUMYY j initial + ∑ i = N j initial + 1 N j Y j ( i ) Y j ( i ) T ;
- (c) determining a received signal according to the following rule:
- if gj(Y(n))>gk(Y(n)) for all k≠j, then decide ωj where gj(Y(n))=−1n(|{circumflex over (Σ)}j|)−(Y(n)−{circumflex over (μ)}j){circumflex over (Σ)}Yj−1(Y(n)−{circumflex over (μ)}j)T;
- (d) updating the parameters as follows:
- SUMYj (Nj+1)=SUMYj (Nj)+Yj(Nj+1), SUMYYj(Nj+1)=SUMYYj(Nj)+Yj(Nj+1)Yj(Nj+1)T, NjNj+1
- where Yj(Nj+1) is Y(n) that is the current incoming vector, which is classified as class ωj,
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A linear equalizer that views equalization as a multiclass classification problem by considering a plurality of bits simultaneously, comprising the steps of:
- (a) constructing a received vector from received training signals as follows:
- Y(n)=[y(n−L1),y(n−L1+1), . . . ,y(n), . . . ,y(n+L2−1), y(n+L2)]T;
- (a) assigning said received vector to one of the classes, each of which has a unique bit pattern of said plurality of bits and thereby generating a set of training vectors for each class;
- (c) estimating a mean vector from said set of vectors for each class as follows:
- 33 μ ^ γ j = 1 N j ∑ i = 1 N j Y j ( i )
- where
- {circumflex over (μ)}Y1 is an estimated mean vector of class ωj,
- Yj(i) is the i-th training vector of class ωj, and
- Nj is the number of vectors corresponding to class ωj;
- (d) estimating a covariance matrix from said set of vectors for each class as follows:
- 34 Σ ^ γ j = 1 N j ∑ i = 1 N j ( Y j ( i ) - μ ^ Y j ) ( Y j ( i ) - μ ^ Y j ) T
- where {circumflex over (Σ)}Yj is an estimated covariance matrix of class ωj;
- and
- (e) determining a received signal according to the following rule:
- if gj(Y(n))>gk(Y(n)) for all k≠j, then decide ωj where gj(Y(n))=−1n(|{circumflex over (Σ)}j|)−(Y(n)−{circumflex over (μ)}j){circumflex over (μ)}Yj−1(Y(n)−{circumflex over (μ)}j)T,
- {circumflex over (μ)}j is said estimated mean vector of class ωj, and
- {circumflex over (Σ)}j is said estimated covariance matrix of class ωj.
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Dependencies are inferred from the claim text.