US5761088A
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Method and apparatus for channel identification using incomplete or noisy information
Assignee: Philips North America LLC
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Filing: 1995-12-18
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Granted: 1998-06-02
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Expires: 2015-12-18
Abstract
Abstract A method and apparatus for channel identification utilizing two Least-Squares (LS) estimators. Each LS estimator is used for calculating a sequence of channel values, further for determining an estimated channel impulse response, over an entire frequency band thereof in light of the fact that information is incomplete or unreliable over part of the frequency band. Each LS estimator operates for the case when the estimated channel impulse response span is less than the span of a known test signal, the test signal having been transmitted over the channel for use in identifying the channel. In a TV ghost-cancellation system for removal of channel induced distortion from received signals, each LS estimator is used to compute channel impulse response coefficients, wherein the system includes ghost-cancellation filters responsive to the channel impulse response for removing the effects of the channel from the signals.
Inventors
- 👤 Samir N. Hulyalkar
- 👤 Zhi-Yuan Guan
Bibliographic Details
Application Number
—
Jurisdiction
US
Data Source
google_patents
Last Synchronized
2026-11-06 03:55
CPC Classifications
H; H04; H04N; H04N5/00; H04N5/14; H04N5/21; H04L; H04L25/00; H04L25/02; H04L25/0202; H04L25/024; H04L25/0242; H04L25/0212; H04L25/0224; H04L25/0228; H04N5/211
Claims Analysis
Total Claims: 53
Claim 1
Independent Claim
145 words
A method of communication channel identification comprising the steps of: transmitting a test signal x over a communication channel to be identified, the test signal x having a signal span; receiving a signal y, wherein signal y comprises test signal x after test signal x has passed through the communication channel; and calculating a sequence of channel values corresponding to an estimated channel impulse response, the channel impulse response providing an estimate of the communication channel, wherein the sequence of channel values comprises a sampled discrete channel of a finite number of non-zero indices in an interval defmed by -L, M!, wherein the channel impulse response has an impulse response span equal to M+L, the impulse response span being less than the span of the test signal x, wherein said step of calculating the sequence of channel values further comprises using a least-squares (LS) estimator.
Claim 2
Independent Claim
145 words
A method of communication channel identification comprising the steps of: transmitting a test signal x over a communication channel to be identified, the test signal x having a signal span; receiving a signal y, wherein signal y comprises test signal x after test signal x has passed through the communication channel; and calculating a sequence of channel values corresponding to an estimated channel impulse response, the channel impulse response providing an estimate of the communication channel, wherein the sequence of channel values comprises a sampled discrete channel of a finite number of non-zero indices in an interval defmed by -L, M!, wherein the channel impulse response has an impulse response span equal to M+L, the impulse response span being less than the span of the test signal x, wherein said step of calculating the sequence of channel values further comprises using a least-squares (LS) estimator.
Claim 3
Dependent Claim
124 words
The method of communication channel identification according to claim 1, wherein calculating the sequence of channel values still further comprises using a least-squares (LS) estimator h A given by h.sub.A =T.sup.† y, where T.sup.† is a Moore-Penmore (approximate) inverse of T and T is a Toeplitz matrix given by ##EQU7## further wherein x n , for n=0 to (N+L-1), is a finite sequence of sampled values of a reference test signal X REF , wherein the reference test signal X REF comprises the test signal x uncorrupted by the communication channel, further wherein N equals the number of sampled values of the finite sequence of x n , and still further wherein y is a finite sequence of sampled values of the received signal.
Claim 4
Dependent Claim
137 words
The method of communication channel identification according to claim 1, wherein calculating the sequence of channel values still further comprises using a least-squares (LS) estimator h B given by h.sub.B =(T.sup.T T).sup.† T.sup.T y, where (T T T).sup.† T T is approximately equal to T.sup.†, wherein T.sup.† is a Moore-Penmore (approximate) inverse of T and T is a Toeplitz matrix given by ##EQU8## further wherein x n , for n=0 to (N+L-1), is a finite sequence of sampled values of a reference test signal X REF , wherein the reference test signal X REF comprises the test signal x uncorrupted by the communication channel, further wherein N equals the number of sampled values of the finite sequence of x n , and still further wherein y is a finite sequence of sampled values of the received signal.
Claim 5
Dependent Claim
41 words
The method of communication channel identification according to claim 1, wherein said step of calculating the sequence of channel values further comprises generating a number of singular-value-decomposition (SVD) singular values and truncating an optimal number of SVD singular values to zero.
Claim 6
Dependent Claim
62 words
The method of communication channel identification according to claim 4, wherein truncating the optimal number of SVD singular values to zero comprises the steps of (i) truncating a first number of smallest singular values and then (ii) continuing to truncate an increasing number of smallest singular values until a minimum squared-estimation error (SE) of a performance of the LS estimator is obtained.
Claim 7
Dependent Claim
31 words
The method of communication channel identification according to claim 4, wherein truncating the optimal number of SVD singular values to zero comprises truncating singular values of less than 1×10 -4 .
Claim 8
Dependent Claim
124 words
The method of communication channel identification according to claim 4, wherein calculating the sequence of channel values still further comprises using a least-squares (LS) estimator h A given by h.sub.A =T.sup.† y, where T.sup.† is a Moore-Penmore (approximate) inverse of T and T is a Toeplitz matrix given by ##EQU9## further wherein x n , for n=0 to (N+L-1), is a finite sequence of sampled values of a reference test signal X REF , wherein the reference test signal X REF comprises the test signal x uncorrupted by the communication channel, further wherein N equals the number of sampled values of the finite sequence of x n , and still further wherein y is a finite sequence of sampled values of the received signal.
Claim 9
Dependent Claim
62 words
The method of communication channel identification according to claim 7, wherein truncating the optimal number of SVD singular values to zero comprises the steps of (i) truncating a first number of smallest singular values and then (ii) continuing to truncate an increasing number of smallest singular values until a minimum squared-estimation error (SE) of a performance of the LS estimator is obtained.
Claim 10
Dependent Claim
31 words
The method of communication channel identification according to claim 7, wherein truncating the optimal number of SVD singular values to zero comprises truncating singular values of less than 1×10 4 .
Claim 11
Dependent Claim
137 words
The method of communication channel identification according to claim 4, wherein calculating the sequence of channel values still further comprises using a least-squares (LS) estimator h B given by h.sub.B =(T.sup.T T).sup.† T.sup.T y, where (T T T).sup.† T T is approximately equal to T.sup.†, wherein T.sup.† is a Moore-Penmore (approximate) inverse of T and T is a Toeplitz matrix given by ##EQU10## further wherein x n , for n=0 to (N+L-1), is a finite sequence of sampled values of a reference test signal X REF , wherein the reference test signal X REF comprises the test signal x uncorrupted by the communication channel, further wherein N equals the number of sampled values of the finite sequence of x n , and still further wherein y is a finite sequence of sampled values of the received signal.
Claim 12
Dependent Claim
62 words
The method of communication channel identification according to claim 10, wherein truncating the optimal number of SVD singular values to zero comprises the steps of (i) truncating a first number of smallest singular values and then (ii) continuing to truncate an increasing number of smallest singular values until a minimum squared-estimation error (SE) of a performance of the LS estimator is obtained.
Claim 13
Dependent Claim
31 words
The method of communication channel identification according to claim 10, wherein truncating the optimal number of SVD singular values to zero comprises truncating singular values of less than 1×10 -4 .
Claim 14
Independent Claim
179 words
An apparatus for communication channel identification comprising: means for receiving a signal y, wherein signal y comprises a test signal x after test signal x has passed through a communication channel to be identified, test signal x having been transmitted over the communication channel and further having a signal span; means for storing a reference test signal X REF , wherein the reference test signal X REF comprises the test signal x uncorrupted by the communication channel; and means responsive to the received signal y and the reference test signal x REF for calculating a sequence of channel values corresponding to an estimated channel impulse response, the channel impulse response providing an estimate of the communication channel, wherein the sequence of channel values comprises a sampled discrete channel of a finite number of non-zero indices in an interval defmed by -L, M!, wherein the channel impulse response has an impulse response span equal to M+L, the impulse response span being less than the span of the test signal x, wherein said calculating means further comprises a least-squares (LS) estimator.
Claim 15
Independent Claim
179 words
An apparatus for communication channel identification comprising: means for receiving a signal y, wherein signal y comprises a test signal x after test signal x has passed through a communication channel to be identified, test signal x having been transmitted over the communication channel and further having a signal span; means for storing a reference test signal X REF , wherein the reference test signal X REF comprises the test signal x uncorrupted by the communication channel; and means responsive to the received signal y and the reference test signal x REF for calculating a sequence of channel values corresponding to an estimated channel impulse response, the channel impulse response providing an estimate of the communication channel, wherein the sequence of channel values comprises a sampled discrete channel of a finite number of non-zero indices in an interval defmed by -L, M!, wherein the channel impulse response has an impulse response span equal to M+L, the impulse response span being less than the span of the test signal x, wherein said calculating means further comprises a least-squares (LS) estimator.
Claim 16
Dependent Claim
104 words
The apparatus for communication channel identification according to claim 13, wherein the LS estimator of said calculating means comprises a LS estimator h A given by h.sub.A =T.sup.† y, where T.sup.† is a Moore-Penmore (approximate) inverse of T and T is a Toeplitz matrix given by ##EQU11## further wherein x n , for n=0 to (N+L-1), is a finite sequence of sampled values of the reference test signal X REF , further wherein N equals the number of sampled values of the finite sequence of X n , and still further wherein y is a finite sequence of sampled values of the received signal.
Claim 17
Dependent Claim
116 words
The apparatus for communication channel identification according to claim 13, wherein the LS estimator of said calculating means comprises a LS estimator h B given by h.sub.B =(T.sup.T T).sup.† T.sup.T y, where (T T T).sup.† T is approximately equal to T.sup.†, wherein T.sup.† is a Moore-Penmore (approximate) inverse of T and T is a Toeplitz matrix given by ##EQU12## further wherein x n , for n=0 to (N+L-1), is a finite sequence of sampled values of a reference test signal x REF , further wherein N equals the number of sampled values of the finite sequence of x n , and still further wherein y is a finite sequence of sampled values of the received signal.
Claim 18
Dependent Claim
39 words
The apparatus for communication channel identification according to claim 13, wherein said calculating means further comprises means for generating a number of singular-value-decomposition (SVD) singular values and means for truncating an optimal number of SVD singular values to zero.
Claim 19
Dependent Claim
51 words
The apparatus for communication channel identification according to claim 16, wherein the truncating means (i) truncates a first number of smallest singular values and then (ii) continues to truncate an increasing number of smallest singular values until a minimum squared-estimation error (SE) of a performance of the LS estimator is obtained.
Claim 20
Dependent Claim
23 words
The apparatus for communication channel identification according to claim 16, wherein the truncating means truncates singular values of less than 1×10 -4 .
Claim 21
Independent Claim
104 words
The apparatus for communication channel identification according to clain 16, wherein the LS estimator of said calculating means comprises a LS estimator h A given by h.sub.A =T.sup.† y, where T.sup.† is a Moore-Pemnore (approximate) inverse of T and T is a Toeplitz matrix given by ##EQU13## further wherein x n , for n=0 to (N+L-1), is a finite sequence of sampled values of a reference test signal x REF , further wherein N equals the number of sampled values of the finite sequence of x n , and still further wherein y is a finite sequence of sampled values of the received signal.
Claim 22
Independent Claim
104 words
The apparatus for communication channel identification according to clain 16, wherein the LS estimator of said calculating means comprises a LS estimator h A given by h.sub.A =T.sup.† y, where T.sup.† is a Moore-Pemnore (approximate) inverse of T and T is a Toeplitz matrix given by ##EQU13## further wherein x n , for n=0 to (N+L-1), is a finite sequence of sampled values of a reference test signal x REF , further wherein N equals the number of sampled values of the finite sequence of x n , and still further wherein y is a finite sequence of sampled values of the received signal.
Claim 23
Dependent Claim
51 words
The apparatus for communication channel identification according to claim 19, wherein the truncating means (i) truncates a first number of smallest singular values and then (ii) continues to truncate an increasing number of smallest singular values until a minimum squared-estimation error (SE) of a performance of the LS estimator is obtained.
Claim 24
Dependent Claim
23 words
The apparatus for communication channel identification according to claim 19, wherein the truncating means truncates singular values of less than 1×10 -4 .
Claim 25
Dependent Claim
117 words
The apparatus for communication channel identification according to claim 16, wherein the LS estimator of said calculating means comprises a LS estimator h B given by h.sub.B =(T.sup.T T).sup.† T.sup.T y, where (T T T).sup.† T T is approximately equal to T.sup.†, wherein T.sup.† is a Moore-Penmore (approximate) inverse of T and T is a Toeplitz matrix given by ##EQU14## further wherein x n , for n=0 to (N+L-1), is a finite sequence of sampled values of a reference test signal X REF , further wherein N equals the number of sampled values of the finite sequence of x n , and still further wherein y is a finite sequence of sampled values of the received signal.
Claim 26
Dependent Claim
51 words
The apparatus for communication channel identification according to claim 22, wherein the truncating means (i) truncates a first number of smallest singular values and then (ii) continues to truncate an increasing number of smallest singular values until a minimum squared-estimation error (SE) of a performance of the LS estimator is obtained.
Claim 27
Dependent Claim
23 words
The apparatus for communication channel identification according to claim 22, wherein the truncating means truncates singular values of less than 1×10 -4 .
Claim 28
Independent Claim
195 words
A method of removing channel-induced distortion from signals, said method comprising the steps of: receiving the signals, wherein the signals include a signal y, further wherein signal y comprises a test signal x after test signal x has passed through and been distorted by a communication channel, test signal x having been transmitted over the communication channel and further having a signal span; identifying the communication channel in real time, wherein said identifying step comprises calculating a sequence of channel values corresponding to an estimated channel impulse response, the channel impulse response providing an estimate of the communication channel, wherein the sequence of channel values comprises a sampled discrete channel of a finite number of non-zero indices in an interval defmed by -L, M!, wherein the channel impulse response has an impulse response span equal to M+L, the impulse response span being less than the span of the test signal x, wherein calculating the sequence of channel values further comprises using a leastsquares (LS) estimator; and filtering the received signals in real time, in response to the sequence of channel values corresponding to the estimated channel impulse response, to remove channel-induced distortion from the signals.
Claim 29
Independent Claim
195 words
A method of removing channel-induced distortion from signals, said method comprising the steps of: receiving the signals, wherein the signals include a signal y, further wherein signal y comprises a test signal x after test signal x has passed through and been distorted by a communication channel, test signal x having been transmitted over the communication channel and further having a signal span; identifying the communication channel in real time, wherein said identifying step comprises calculating a sequence of channel values corresponding to an estimated channel impulse response, the channel impulse response providing an estimate of the communication channel, wherein the sequence of channel values comprises a sampled discrete channel of a finite number of non-zero indices in an interval defmed by -L, M!, wherein the channel impulse response has an impulse response span equal to M+L, the impulse response span being less than the span of the test signal x, wherein calculating the sequence of channel values further comprises using a leastsquares (LS) estimator; and filtering the received signals in real time, in response to the sequence of channel values corresponding to the estimated channel impulse response, to remove channel-induced distortion from the signals.
Claim 30
Dependent Claim
125 words
The method of removing channel-induced distortion from signals according to claim 25, wherein calculating the sequence of channel values further comprises using a least-squares (LS) estimator h A given by h.sub.A =T.sup.† y, where T.sup.† is a Moore-Penmore (approximate) inverse of T and T is a Toeplitz matrix given by ##EQU15## further wherein x n , for n=0 to (N+L-1), is a finite sequence of sampled values of a reference test signal X REF , wherein the reference test signal X REF comprises the test signal x uncorrupted by the communication channel, further wherein N equals the number of sampled values of the finite sequence of x n , and still further wherein y is a finite sequence of sampled values of the received signal.
Claim 31
Dependent Claim
138 words
The method of removing channel-induced distortion from signals according to claim 25, wherein calculating the sequence of channel values further comprises using a least-squares (LS) estimator h B given by h.sub.B =(T.sup.T T).sup.† T.sup.T y, where (T T T).sup.† T T is approximately equal to T.sup.†, wherein T.sup.† is a Moore-Penmore (approximate) inverse of T and T is a Toeplitz matrix given by ##EQU16## further wherein x n , for n=0 to (N+L-1), is a finite sequence of sampled values of a reference test signal x REF , wherein the reference test signal x REF comprises the test signal x uncorrupted by the communication channel, further wherein N equals the number of sampled values of the finite sequence of x n , and still further wherein y is a finite sequence of sampled values of the received signal.
Claim 32
Dependent Claim
40 words
The method of removing channel-induced distortion from signals according to claim 25, wherein calculating the sequence of channel values further comprises generating a number of singular-value-decomposition (SVD) singular values and truncating an optimal number of SVD singular values to zero.
Claim 33
Dependent Claim
64 words
The method of removing channel-induced distortion from signals according to claim 28, wherein truncating the optimal number of SVD singular values to zero comprises the steps of (i) truncating a first number of smallest singular values and then (ii) continuing to truncate an increasing number of smallest singular values until a minimum squared-estimation error (SE) of a performance of the LS estimator is obtained.
Claim 34
Dependent Claim
33 words
The method of removing channel-induced distortion from signals according to claim 28, wherein truncating the optimal number of SVD singular values to zero comprises truncating singular values of less than 1×10 -4 .
Claim 35
Dependent Claim
126 words
The method of removing channel-induced distortion from signals according to claim 28, wherein calculating the sequence of channel values still further comprises using a least-squares (LS) estimator h A given by h.sub.A =T.sup.† y, where T.sup.† is a Moore-Penmore (approximate) inverse of T and T is a Toeplitz matrix given by ##EQU17## further wherein x n , for n=0 to (N+L-1), is a finite sequence of sampled values of a reference test signal X REF , wherein the reference test signal X REF comprises the test signal x uncorrupted by the communication channel, further wherein N equals the number of sampled values of the finite sequence of x n , and still further wherein y is a finite sequence of sampled values of the received signal.
Claim 36
Dependent Claim
64 words
The method of removing channel-induced distortion from signals according to claim 31, wherein truncating the optimal number of SVD singular values to zero comprises the steps of (i) truncating a first number of smallest singular values and then (ii) continuing to truncate an increasing number of smallest singular values until a minimum squared-estimation error (SE) of a performance of the LS estimator is obtained.
Claim 37
Dependent Claim
33 words
The method of removing channel-induced distortion from signals according to claim 31, wherein truncating the optimal number of SVD singular values to zero comprises truncating singular values of less than 1×10 4 .
Claim 38
Dependent Claim
139 words
The method of removing channel-induced distortion from signals according to claim 28, wherein calculating the sequence of channel values still further comprises using a least-squares (LS) estimator h B given by h.sub.B =(T.sup.T T).sup.† T.sup.T y, where (T T T).sup.† T T is approximately equal to T.sup.†, wherein T.sup.† is a Moore-Penmore (approximate) inverse of T and T is a Toeptitz matrix given by ##EQU18## further wherein x n , for n=0 to (N+L-1), is a finite sequence of sampled values of a reference test signal X REF , wherein the reference test signal X REF comprises the test signal x uncorrupted by the communication channel, further wherein N equals the number of sampled values of the finite sequence of x n , and still further wherein y is a finite sequence of sampled values of the received signal.
Claim 39
Dependent Claim
64 words
The method of removing channel-induced distortion from signals according to claim 34, wherein truncating the optimal number of SVD singular values to zero comprises the steps of (i) truncating a first number of smallest singular values and then (ii) continuing to truncate an increasing number of smallest singular values until a minimum squared-estimation error (SE) of a performance of the LS estimator is obtained.
Claim 40
Dependent Claim
33 words
The method of removing channel-induced distortion from signals according to claim 34, wherein truncating the optimal number of SVD singular values to zero comprises truncating singular values of less than 1×10 -4 .
Claim 41
Independent Claim
237 words
An apparatus for removing channel-induced distortion from signals, said means for receiving the signals, wherein the signals include a signal y, further wherein signal y comprises a test signal x after test signal x has passed through and been distorted by a communication channel, test signal x having been transmitted over the communication channel and further having a signal span; means for storing a reference test signal x REF , wherein the reference test signal X REF comprises a copy of the test signal x uncorrupted by the comlmunication channel; means responsive to the received signal y and the reference test signal X REF for identifying the communication channel in real time, wherein said identifying means comprises means for calculating a sequence of channel values corresponding to an estimated channel impulse response, the channel impulse response providing an estimate of the communication channel, wherein the sequence of channel values comprises a sampled discrete channel of a finite number of non-zero indices in an interval defined by -L, M!, wherein the channel impulse response has an impulse response span equal to M+L, the impulse response span being less than the span of the test signal x, wherein said calculating means further comprises a least-squares (LS) estimator; and means for filtering the received signals in real time, in response to the sequence of channel values corresponding to the estimated channel impulse response, to remove channel-induced distortion from the signals.
Claim 42
Independent Claim
237 words
An apparatus for removing channel-induced distortion from signals, said means for receiving the signals, wherein the signals include a signal y, further wherein signal y comprises a test signal x after test signal x has passed through and been distorted by a communication channel, test signal x having been transmitted over the communication channel and further having a signal span; means for storing a reference test signal x REF , wherein the reference test signal X REF comprises a copy of the test signal x uncorrupted by the comlmunication channel; means responsive to the received signal y and the reference test signal X REF for identifying the communication channel in real time, wherein said identifying means comprises means for calculating a sequence of channel values corresponding to an estimated channel impulse response, the channel impulse response providing an estimate of the communication channel, wherein the sequence of channel values comprises a sampled discrete channel of a finite number of non-zero indices in an interval defined by -L, M!, wherein the channel impulse response has an impulse response span equal to M+L, the impulse response span being less than the span of the test signal x, wherein said calculating means further comprises a least-squares (LS) estimator; and means for filtering the received signals in real time, in response to the sequence of channel values corresponding to the estimated channel impulse response, to remove channel-induced distortion from the signals.
Claim 43
Dependent Claim
106 words
The apparatus for removing channel-induced distortion from signals according to claim 37, wherein the LS estimator of said calculating means comprises a LS estimator h A given by h.sub.A =T.sup.† y, where T.sup.† is a Moore-Penmore (approximate) inverse of T and T is a Toeplitz matrix given by ##EQU19## further wherein x n , for n=0 to (N+L-1), is a finite sequence of sampled values of the reference test signal X REF , further wherein N equals the number of sampled values of the finite sequence of x n , and still further wherein y is a finite sequence of sampled values of the received signal.
Claim 44
Dependent Claim
119 words
The apparatus for removing channel-induced distortion from signals according to claim 37, wherein the LS estimator of said calculating means comprises a LS estimator h B given by h.sub.B =(T.sup.T T).sup.† T.sup.T y, where (T T T).sup.† T T is approximately equal to T.sup.†, wherein T.sup.† is a Moore-Penmore (approximate) inverse of T and T is a Toeplitz matrix given by ##EQU20## further wherein x n , for n=0 to (N+L-1), is a finite sequence of sampled values of a reference test signal x REF , further wherein N equals the number of sampled values of the finite sequence of x n , and still further wherein y is a finite sequence of sampled values of the received signal.
Claim 45
Dependent Claim
41 words
The apparatus for removing channel-induced distortion from signals according to claim 37, wherein said calculating means further comprises means for generating a number of singular-value-decomposition (SVD) singular values and means for truncating an optimal number of SVD singular values to zero.
Claim 46
Dependent Claim
53 words
The apparatus for removing channel-induced distortion from signals according to claim 40, wherein the truncating means (i) truncates a first number of smallest singular values and then (ii) continues to truncate an increasing number of smallest singular values until a minimum squared-estimation error (SE) of a performance of the LS estimator is obtained.
Claim 47
Dependent Claim
25 words
The apparatus for removing channel-induced distortion from signals according to claim 40, wherein the truncating means truncates singular values of less than 1×10 -4 .
Claim 48
Dependent Claim
104 words
The apparatus for removing channel-induced distortion from signals according to claim 40, wherein the LS estimator of said calculating means comprises a LS estimator h A given by h.sub.A =T.sup.† y, where T.sup.† is a Moore-Penmore (approximate) inverse of T and T is a Toeplitz matrix given by ##EQU21## further wherein x n , for n=0 to (N+L-1), is a finite sequence of sampled values of a reference test signal xRu, further wherein N equals the number of sampled values of the finite sequence of x n , and still further wherein y is a finite sequence of sampled values of the received signal.
Claim 49
Dependent Claim
53 words
The apparatus for removing channel-induced distortion from signals according to claim 43, wherein the truncating means (i) truncates a first number of smallest singular values and then (ii) continues to truncate an increasing number of smallest singular values until a minimum squared-estimation error (SE) of a performance of the LS estimator is obtained.
Claim 50
Dependent Claim
25 words
The apparatus for removing channel-induced distortion from signals according to claim 43, wherein the truncating means truncates singular values of less than 1×10 -4 .
Claim 51
Dependent Claim
119 words
The apparatus for removing channel-induced distortion from signals according to claim 40, wherein the LS estimator of said calculating means comprises a LS estimator h B given by h.sub.B =(T.sup.T T).sup.† T.sup.T y, where (T T T).sup.† T T is approximately equal to T.sup.†, wherein T.sup.† is a Moore-Penmore (approximate) inverse of T and T is a Toeplitz matrix given by ##EQU22## further wherein x n , for n=0 to (N+L-1), is a finite sequence of sampled values of a reference test signal x REF , further wherein N equals the number of sampled values of the finite sequence of x n , and still further wherein y is a finite sequence of sampled values of the received signal.
Claim 52
Dependent Claim
53 words
The apparatus for removing channel-induced distortion from signals according to claim 46, wherein the truncating means (i) truncates a first number of smallest singular values and then (ii) continues to truncate an increasing number of smallest singular values until a minimum squared-estimation error (SE) of a performance of the LS estimator is obtained.
Claim 53
Dependent Claim
25 words
The apparatus for removing channel-induced distortion from signals according to claim 46, wherein the truncating means truncates singular values of less than 1×10 -4 .
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