US5283813A — Methods and apparatus particularly useful for bli…

Claim 1

Independent Claim 150 words

A method for controlling an equalizer to be coupled to an unknown system having an input and an output which equalizer receives the output of the unknown system in order to produce a response recovering the input to said system, characterized by iteratively adjusting the equalizer such that the unknown system combined with the equalizer behaves essentially as a linear system whose (t,n) taps, for some combinations of t and n, are iteratively adjusted according to the following rule: ##EQU27## where s t ,n denotes the (t,n) tap before the iteration, s' t ,n denotes the (t,n) tap after the iteration, I is a preselected integer greater than or equal to one, α i i=1,2. . . I are preselected scalars that may vary from iteration to iteration, and p i , q i i=1,2, . . . I are preselected non-negative integers such that p i +q i ≧2.

Claim 2

Independent Claim 150 words

A method for controlling an equalizer to be coupled to an unknown system having an input and an output which equalizer receives the output of the unknown system in order to produce a response recovering the input to said system, characterized by iteratively adjusting the equalizer such that the unknown system combined with the equalizer behaves essentially as a linear system whose (t,n) taps, for some combinations of t and n, are iteratively adjusted according to the following rule: ##EQU27## where s t ,n denotes the (t,n) tap before the iteration, s' t ,n denotes the (t,n) tap after the iteration, I is a preselected integer greater than or equal to one, α i i=1,2. . . I are preselected scalars that may vary from iteration to iteration, and p i , q i i=1,2, . . . I are preselected non-negative integers such that p i +q i ≧2.

Claim 3

Dependent Claim 55 words

The method according to claim 1 wherein the unknown system combined with the equalizer behaves essentially as a linear shift invariant system whose taps are interatively adjusted according to the following rule: ##EQU28## where s n denotes the n th tap before the iteration and s' n denotes the n th tap after the iteration.

Claim 4

Dependent Claim 37 words

The method according to claim 2, wherein I=1, such that s'.sub.n =αs.sub.n.sup.p (s.sub.n *).sup.q where α is a scalar that may vary from iteration to iteration, and p and q are preselected non-negative integers such that p+q≧2.

Claim 5

Dependent Claim 122 words

The method according to claim 3, wherein the equalizer is a linear shift invariant system whose taps are iteratively adjusted such that: c'=αR.sup.-1 d where c' is the column tensor whose n th element, c' n is the n th tap of the equalizer after the iteration, R is the tensor whose (n,m) element is: R.sub.nm =cum(y.sub.t-mi ;y.sub.t-n *) where y t is the input to the equalizer, and d is the column tensor whose n th element is: d.sub.n =cum(z.sub.t :p; z.sub.t *q;y.sub.t-n *) where z t is the output of the equalizer given by: ##EQU29## where c n is the n th tap of the equalizer before the iteration, and the subscripts n and m belong to a pre-specified set.

Claim 6

Dependent Claim 16 words

The method according to claim 4 wherein the elements of d are computed as follows: ##EQU30##

Claim 7

Dependent Claim 145 words

The method according to claim 3 wherein the equalizer is a linear shift invariant system whose transfer function is iteratively adjusted such that: ##EQU31## where C'(w) is the transfer function of the equalizer after the iteration, C(w) is the transfer function of the equalizer before the iteration, S y 1 ,0 (w) is the (1,0)-order spectrum (power spectrum) of y t , S y p ,q (w 1 , w 2 , . . . , w p+q ) is the (p,q)-order spectrum of y t where p and q are preselected non-negative integers such that p+q≧2, S a 1 ,0 (w) and S a p ,q (w 1 , w 2 , . . . , w p+q ) are preselected functions, and where w and w 1 , w 2 , . . . w p+q-1 belong to a prespecified set of frequencies.

Claim 8

Dependent Claim 32 words

The method according to claim 3 wherein α is selected at some iterations such that cum(z.sub.t ;z.sub.t *)=η.sub.t where z t is the output of the equalizer and η t is preselected.

Claim 9

Dependent Claim 22 words

The method according to claim 1 wherein the cumulants/spectra of additive noises at some iterations are subtracted from the respective data cumulants/spectra.

Claim 10

Dependent Claim 27 words

The method according to claim 1 wherein the cumulants/spectra are replaced by their estimates based on the available data at the input and output of the equalizer.

Claim 11

Dependent Claim 19 words

The method according to claim 1 wherein the iterations are performed sequentially such that the equalizer is adjusted sequentially.

Claim 12

Dependent Claim 62 words

The method according to claim 10 wherein t is one-dimensional, and the equalizer is adjusted sequentially as follows: ##EQU32## is the vector equalizer taps after t iterations, ##EQU33## where Q 0 is a preselected matrix; c.sup.(0) is a preselected vector; L 1 and L 2 are preselected numbers; and β t , γ t , δ t are preselected sequences of numbers.

Claim 13

Dependent Claim 21 words

The method according to claim 11 wherein c.sup.(t) =c.sup.(t-1) +β.sub.t Q.sub.t y.sub.t *z.sub.t (|z.sub.t |.sup.2 -ρ.sub.t) where ρ t is preselected.

Claim 14

Dependent Claim 150 words

Apparatus to be coupled to an unknown system having an input and an output for producing a response recovering the input to said system, comprising an equalizer receiving the output of the unknown system and a processor for iteratively adjusting the equalizer such that the unknown system combined with the equalizer behaves essentially as a linear system whose (t, n) taps, for some combinations of t and n, are iteratively adjusted according to the following rule: ##EQU34## where s t ,n denotes the (t, n) tap before the iteration, s' t ,n denotes the (t, n) tap after the iteration, I is a preselected integer greater than or equal to one, α i i=1,2 . . . I are preselected scalars that may vary from iteration to iteration, and p i , q i i=1,2, . . . I are preselected non-negative integers such that p i +q i ≧2.

Claim 15

Dependent Claim 150 words

Apparatus to be coupled to an unknown system having an input and an output for producing a response recovering the input to said system, comprising an equalizer receiving the output of the unknown system and a processor for iteratively adjusting the equalizer such that the unknown system combined with the equalizer behaves essentially as a linear system whose (t, n) taps, for some combinations of t and n, are iteratively adjusted according to the following rule: ##EQU34## where s t ,n denotes the (t, n) tap before the iteration, s' t ,n denotes the (t, n) tap after the iteration, I is a preselected integer greater than or equal to one, α i i=1,2 . . . I are preselected scalars that may vary from iteration to iteration, and p i , q i i=1,2, . . . I are preselected non-negative integers such that p i +q i ≧2.

Claim 16

Dependent Claim 54 words

Apparatus according to Claim 13 wherein the unknown system combined with the equalizer behaves essentially as a linear shift invariant system whose taps are iteratively adjusted according to the following rule: ##EQU35## where s n denotes the n th tap before the iteration and s' n denotes the n th tap after the iteration.

Claim 17

Dependent Claim 36 words

Apparatus according to claim 14, wherein I=1, such that s'.sub.n =αs.sub.n.sup.p (s.sub.n *).sup.q where α is a scalar that may vary from iteration to iteration, and p and q are preselected non-negative integers such that p+q≧2.

Claim 18

Dependent Claim 120 words

Apparatus according to claim 15, wherein the equalizer is a linear shift invariant system whose taps are iteratively adjusted such that: c'=αR.sup.-1 d where c' is the column tensor whose n th element, c' n is the n th tap of the equalizer after the iteration, R is the tensor whose (n,m) element is: R.sub.nm =cum(y.sub.t-m ;y.sub.t-n *) where y t is the input to the equalizer, and d is the column tensor whose n th element is: d.sub.n =cum(z.sub.t :p;z.sub.t *:q;y.sub.t-n *) where z t is the output of the equalizer given by: ##EQU36## where c n is the n th tap of the equalizer before the iteration, and the subscripts n and m belong to a pre-specified set.

Claim 19

Dependent Claim 15 words

Apparatus according to claim 16 wherein the elements of d are computed as follows: ##EQU37##

Claim 20

Dependent Claim 144 words

Apparatus according to claim 15 wherein the equalizer is a linear shift invariant system whose transfer function is iteratively adjusted such that: ##EQU38## where C'(w) is the transfer function of the equalizer after the iteration, C(w) is the transfer function of the equalizer before the iteration, S y 1 ,0 (w) is the (1,0)-order spectrum (power spectrum) of y t , S y p ,q (w 1 , w 2 , . . . , w p+q ) is the (p,q)-order spectrum of y t where p and q are preselected non-negative integers such that p+q≧2, S a 1 ,0 (w) and S a p ,q (w 1 , w 2 , . . . , w p+q ) are preselected functions, and where w and w 1 , w 2 , . . . w p+q-1 belong to a prespecified set of frequencies.

Claim 21

Dependent Claim 31 words

Apparatus according to claim 15 wherein α is selected at some iterations such that cum(z.sub.t ;z.sub.t *)=η.sub.t where z t is the output of the equalizer and η t is preselected.

Annuity Stage	Window Opens	Payment Deadline	Surcharge Period Until	Estimated Fee	Status
3.5 Years (Year 4)	1997-01-31	1997-08-02	1998-02-01	$2000.00	Window Closed / Lapsed
7.5 Years (Year 8)	2001-01-31	2001-08-02	2002-02-01	$3760.00	Window Closed / Lapsed
11.5 Years (Year 12)	2005-01-31	2005-08-02	2006-02-01	$7700.00	Window Closed / Lapsed

Methods and apparatus particularly useful for blind deconvolution

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