DETAILED ACTION
Notice of Pre-AIA or AIA Status
The present application, filed on or after March 16, 2013, is being examined under the first inventor to file provisions of the AIA .
Examiner’s Comment
Upon further reconsideration, the requirement for restriction is withdrawn. Accordingly, all claims 1-18 will be examined; no claims are withdrawn.
Priority
The present application, 17871408, filed 07/22/2022 is a Continuation of PCT/EP2021/051930, filed 01/28/2021 claims foreign priority to EP20154407.9, filed 01/29/2020.
Information Disclosure Statement
The information disclosure statement (IDS) submitted on 09/01/2022 and 03/11/2026 are in compliance with the provisions of 37 CFR 1.97. Accordingly, the information disclosure statement is being considered by the examiner.
Drawings
The drawings are objected to under 37 CFR 1.83(a). The drawings must show every feature of the invention specified in the claims. Therefore, the following must be shown or the feature(s) canceled from the claim(s). No new matter should be entered.
A. multiplying a data vector a matrix as specified in claims 1-2 and 14-16
B. wherein the matrix is approximated by a plurality of matrices whose elements are positive or negative integer powers of two as specified in claims 1-2 and 14-16
C. wherein the matrix is approximated by a product of the plurality of matrices whose elements are positive or negative integer powers of two as specified in claims 5-6
D. a nonlinearity associated with the respective factors as specified in claim 8
E. wherein the power-2-decomposition is a sum- decomposition as specified in claims 9-10
The drawings are objected to as failing to comply with 37 CFR 1.84(p)(5) because they do not include the following reference sign(s) mentioned in the description:
104
1
,
104
2
and
104
3
mentioned in page 11 line 30.
Corrected drawing sheets in compliance with 37 CFR 1.121(d) are required in reply to the Office action to avoid abandonment of the application. Any amended replacement drawing sheet should include all of the figures appearing on the immediate prior version of the sheet, even if only one figure is being amended. Each drawing sheet submitted after the filing date of an application must be labeled in the top margin as either “Replacement Sheet” or “New Sheet” pursuant to 37 CFR 1.121(d). If the changes are not accepted by the examiner, the applicant will be notified and informed of any required corrective action in the next Office action. The objection to the drawings will not be held in abeyance.
Claim Objections
Claims 1, 3-13 and 17-18 are objected to under 37 C.F.R. 1.71(a) which requires “full, clear, concise, and exact terms” as to enable any person skilled in the art or science to which the invention or discovery appertains, or with which it is most nearly connected, to make and use the same. The following should be corrected.
A. In claim 1 line 2, “MIMO” should be spelled out for clarity of claim terminologies. Claims 14-15 recites a similar limitation and are objected for the same reasons. Claims 2-13 inherit the same deficiency as claim 1 by reason of dependence. Claims 17-18 inherit the same deficiency as claim 15 by reason of dependence.
B. In claim 12 line 2, “SNR” should be spelled out for clarity of claim terminologies.
C. In claim 12 line 6, “a further matrix” should read “the further matrix” instead because a further matrix is already introduced in line 5.
D. In claim 17 line 2, “transmit symbols” should read “the transmit symbols” instead because transmit symbols is already introduced in claim 15 from which the claim depends. Claim 18 inherit the same deficiency as claim 17 by reason of dependence.
E. In claim 17 line 2, “one or more receivers” should read “the one or more receivers” instead because one or more receivers is already introduced in claim 15 from which the claim depends. Claim 18 inherit the same deficiency as claim 17 by reason of dependence.
Claim Rejections - 35 USC § 112
The following is a quotation of 35 U.S.C. 112(b):
(b) CONCLUSION.—The specification shall conclude with one or more claims particularly pointing out and distinctly claiming the subject matter which the inventor or a joint inventor regards as the invention.
The following is a quotation of 35 U.S.C. 112 (pre-AIA ), second paragraph:
The specification shall conclude with one or more claims particularly pointing out and distinctly claiming the subject matter which the applicant regards as his invention.
Claims 1-15 and 17-18 rejected under 35 U.S.C. 112(b) or 35 U.S.C. 112 (pre-AIA ), second paragraph, as being indefinite for failing to particularly point out and distinctly claim the subject matter which the inventor or a joint inventor (or for applications subject to pre-AIA 35 U.S.C. 112, the applicant), regards as the invention.
Claim 1 recites “a matrix, like a precoding matrix” in line 5. It is unclear whether the narrower limitation of a precoding matrix is required or not because of the use of the use of exemplary phrase “like”. For purposes of examination, this is interpreted as required and all subsequent instances referring to the matrix are interpreted to refer to the precoding matrix. Claims 14-15 recite a similar limitation and are rejected for the same reasons. Claims 2-13 inherit the same deficiency as claim 1 by reason of dependence. Claims 17-18 inherit the same deficiency as claim 15 by reason of dependence.
Claim 2 recites “the inputs” in line 2. There is insufficient antecedent basis for this limitation in the claim. For purposes of examination, this is interpreted as inputs.
Claim 3 recites “e.g., when estimating a channel for transmitting the transmit symbols or for a coherence interval” in lines 2-3. It is unclear whether the narrower limitation of when estimating a channel for transmitting the transmit symbols or for a coherence interval is required or not because of the use of the use of exemplary phrase “e.g.”. For purposes of examination, this is interpreted as required.
Further, claim 3 recites “the artificial neural network” in line 4. There is insufficient antecedent basis for this limitation in the claim. Further clarification is required.
The term “substantially” in claim 4 is a relative term which renders the claim indefinite. The term “substantially” is not defined by the claim, the specification does not provide a standard for ascertaining the requisite degree, and one of ordinary skill in the art would not be reasonably apprised of the scope of the invention. Therefore, the phrase substantially the same as an amount of memory is indefinite.
Claim 6 recites “the power-2-decomposition” in line 3. There is insufficient antecedent basis for this limitation in the claim. A power-2-decomposition is introduced in claim 5, however, claim 6 does not depend on claim 5. For purposes of examination, claim 6 is interpreted to depend on claim 5. Claim 9 recites a similar limitation and is rejected for the same reasons. Claims 7-8 and 11-12 inherit the same deficiency as claim 6 by reason of dependence. Claim 10 inherit the same deficiency as claim 9 by reason of dependence.
Claim 7 recites “
E
0
”, “
V
k
” and “
Z
” in line 3. These terms are not defined in the claim. Therefore, it is unclear how these terms are to be interpreted. Claim 10 recites a similar limitation and is rejected for the same reasons. Further clarification is required.
Claim 8 recites “the respective factors”; and “the matrix A” in line 2. There is insufficient antecedent basis for these limitations in the claim. For purposes of examination, these are interpreted as respective factors and the matrix respectively.
Further, claim 8 recites “the matrix A may be approximated as follows”. It is unclear whether the subsequent limitation is required or optional because of the use of the phrase “may be”. For purposes of examination, this is interpreted as the matrix is approximated as follows.
Claim 9 recites “the approximated MxN precoding matrix” in line 5. There is insufficient antecedent basis for this limitation in the claim. For purposes of examination, this is interpreted as the approximated precoding matrix.
Claim 11 recites “the cardinality of
C
V
” in line 1. There is insufficient antecedent basis for this limitation in the claim. Further clarification is required.
Further, claim 11 recites “e.g., the same total amount of bits or a certain fraction of the total amount of bits, like ½ or ¼, as the matrix to be approximated”. It is unclear whether these narrower limitations are required or not because of the use of the use of exemplary phrase “e.g.” and “like”. For purposes of examination, these are interpreted as not required.
Claim 12 recites “the specific application” in line 3. There is insufficient antecedent basis for this limitation in the claim. Further clarification is required.
Further, claim 12 recites “wherein the decomposition may be terminated once an additional SNR achievable by a further matrix reaches of falls below a certain or predefined threshold” in lines 5-7. It is unclear whether the subsequent limitation is required or optional because of the use of the phrase “may be”. For purposes of examination, this is interpreted as wherein the decomposition is terminated once an additional SNR achievable by the further matrix reaches of falls below a certain or predefined threshold.
Claim 14 recites “the method” in line 2. There is insufficient antecedent basis for this limitation in the claim. For purposes of examination, this is interpreted as a method.
Claim 15 recites “wherein the apparatus is to receive data to be transmitted to the one or more receivers, and the apparatus is to acquire the transmit symbols to be transmitted by multiplying a data vector comprising the data to be transmitted by a matrix” in lines 3-5. These limitations are unclear because they merely state functions (that the apparatus must somehow receive data to be transmitted and acquire the transmit symbols to be transmitted by multiplying a data vector comprising the data to be transmitted by a matrix) that are not performed by any structure recited in the claim. The claim does not recite any structure of the apparatus. Therefore, it is unclear which structures are performing the claimed functions. Claims 17-18 inherit the same deficiency as claim 15 by reason of dependence.
Further, claim 15 is unclear because it recites a claim to a machine, i.e., an apparatus, however, the claim does not recite any components or parts of the apparatus. See MPEP 2106.03 I which states that “A machine is a "concrete thing, consisting of parts, or of certain devices and combination of devices”.
The following is a quotation of 35 U.S.C. 112(d):
(d) REFERENCE IN DEPENDENT FORMS.—Subject to subsection (e), a claim in dependent form shall contain a reference to a claim previously set forth and then specify a further limitation of the subject matter claimed. A claim in dependent form shall be construed to incorporate by reference all the limitations of the claim to which it refers.
The following is a quotation of pre-AIA 35 U.S.C. 112, fourth paragraph:
Subject to the following paragraph [i.e., the fifth paragraph of pre-AIA 35 U.S.C. 112], a claim in dependent form shall contain a reference to a claim previously set forth and then specify a further limitation of the subject matter claimed. A claim in dependent form shall be construed to incorporate by reference all the limitations of the claim to which it refers.
Claim 8 is rejected under 35 U.S.C. 112(d) or pre-AIA 35 U.S.C. 112, 4th paragraph, as being of improper dependent form for failing to further limit the subject matter of the claim upon which it depends, or for failing to include all the limitations of the claim upon which it depends.
Claim 8 recites “the matrix A may be approximated as follows:
A
~
=
∏
k
=
1
K
f
k
(
F
k
)
”. This limitation fails to include all the limitations of claim 6 upon which it depends because claim 6 requires the matrix to be approximated using
A
~
=
∏
k
=
1
K
(
F
k
)
, i.e., claim 8 is replacing the replacing the formula in claim 6 on how to approximate the matrix.
Applicant may cancel the claim(s), amend the claim(s) to place the claim(s) in proper dependent form, rewrite the claim(s) in independent form, or present a sufficient showing that the dependent claim(s) complies with the statutory requirements.
Claim Rejections - 35 USC § 101
35 U.S.C. 101 reads as follows:
Whoever invents or discovers any new and useful process, machine, manufacture, or composition of matter, or any new and useful improvement thereof, may obtain a patent therefor, subject to the conditions and requirements of this title.
Claims 1-18 are rejected under 35 U.S.C. 101 because the claimed invention is directed to an abstract idea without significantly more.
Under Step 1, claims 1-13 recite a series of steps and, therefore, is a process. Claim 14 recites a non-transitory digital storage medium and, therefore, is an article of manufacture. Claim 15 recites an apparatus and, therefore, is a machine. Claim 16 recites an artificial neural network and, therefore, is a machine. Claim 17 recites a transmitter and, therefore, is a machine. Claims 18 recites a system and, therefore, is a machine.
Under Step 2A prong 1, claim 1 recites
A method for providing transmit symbols to be transmitted by a transmitter to one or more receivers of a wireless MIMO communication system, the method comprising:
receiving data to be transmitted to the one or more receivers, and
acquiring the transmit symbols to be transmitted by multiplying a data vector comprising the data to be transmitted by a matrix, like a precoding matrix,
wherein the matrix is approximated by a plurality of matrices whose elements are positive or negative integer powers of two so that multiplying the data vector by the matrix comprises a series of sub-multiplications, each of the sub-multiplications being realized only by bit shifts and additions.
The above underlined limitations of multiplying a data vector by a matrix using a plurality of matrices whose elements are positive or negative integer powers of two to approximate the matrix such that the vector-matrix multiplication is implemented using bit shifts and additions amounts to processing mathematical calculations and falls within the “Mathematical Concepts” grouping of abstract ideas. See at least Equations (1, 6, 8a-8b, 12 and 15), page 18 and 21. Accordingly, the claim is directed to recite an abstract idea.
Under step 2A prong 2, the claim recites the following additional elements: providing transmit symbols to be transmitted by a transmitter to one or more receivers of a wireless MIMO communication system, and receiving data to be transmitted to the one or more receivers. However, the additional elements of “a transmitter”, “one or more receivers” and “a wireless MIMO communication system” are recited at a high-level of generality (i.e., as a generic wireless MIMO communication system comprising a generic transmitter for transmitting transmit symbols and a generic one or more receivers for receiving the transmit symbols) such that they amount to no more than merely reciting the words “apply it” (or an equivalent) with the judicial exception or merely as tools to implement the abstract idea. The additional elements of “providing transmit symbols to be transmitted by a transmitter to one or more receivers of a wireless MIMO communication system”, and “receiving data to be transmitted to the one or more receivers” are merely adding insignificant extra-solution activities and are also merely generally linking the use of a judicial exception to a particular technological environment or field of use. See MPEP 2106.05(h) for more information. The additional elements do not, individually or in combination, integrate the exception into a practical application. Accordingly, the claim is not integrated into a practical application.
Under step 2B, claim 1 does not include additional elements that, individually or in combination, are sufficient to amount to significantly more than the judicial exception. As discussed above with respect to integration of the abstract idea into a practical application, the additional elements of “a transmitter”, “one or more receivers” and “a wireless MIMO communication system” are recited at a high-level of generality (i.e., as a generic wireless MIMO communication system comprising a generic transmitter for transmitting transmit symbols and a generic one or more receivers for receiving the transmit symbols) such that they amount to no more than merely reciting the words “apply it” (or an equivalent) with the judicial exception or merely as tools to implement the abstract idea. The additional elements of “providing transmit symbols to be transmitted by a transmitter to one or more receivers of a wireless MIMO communication system”, and “receiving data to be transmitted to the one or more receivers” are merely adding insignificant extra-solution activities and are also merely generally linking the use of a judicial exception to a particular technological environment or field of use. See MPEP 2106.05(h) for more information. See MPEP 2106.05(d)(II) which states that the courts have recognized computer functions such as “Receiving or transmitting data over a network” and “Storing and retrieving information in memory” as well‐understood, routine, and conventional functions when they are claimed in a merely generic manner (e.g., at a high level of generality) or as insignificant extra-solution activity. The claim does not recite additional elements that alone or in combination amount to an inventive concept. Accordingly, the claim does not amount to significantly more than the abstract idea.
Under step 2A prong 1, claims 3-13 recite the same abstract idea as claim 1 by reason of dependence. Further, claims 3-13 recite further details of the abstract idea of how the matrix is approximated and/or how the plurality of matrices are determined and falls within the “Mathematical Concepts” grouping of abstract ideas. In particular claims 3-13 do not include additional elements that would require further analysis under step 2A prong 2 and step 2B. Accordingly, the claims are directed to recite an abstract idea.
Regarding claim 14, they are directed to a non-transitory digital storage medium having a computer program stored thereon to perform the method of claim 1. Claim 1 analysis applies equally to claim 14.
Regarding claim 15, it is directed to an apparatus configured to practice the method of claim 1. All steps performed by the apparatus of claim 15 are performed in the method of claim 1. Claim 1 analysis applies equally to claim 15.
Regarding claim 17, it is directed to a transmitter configured to practice the method for providing the transmit symbols of claim 1. All steps performed by the transmitter of claim 17 are performed in the method of claim 1. Claim 1 analysis applies equally to claim 17.
Regarding claim 18, it is directed to a wireless MIMO communication system comprising one or more transmitters configured to practice the method for providing the transmit symbols of claim 1 and one or more receivers to receive the transmit symbols. All steps performed by the wireless MIMO communication system of claim 18 are performed in the method of claim 1. Claim 1 analysis applies equally to claim 18.
Under Step 2A prong 1, claim 16 recites
An artificial neural network, comprising:
a plurality of inputs, some or all of the inputs to receive input values; and
a processor coupled to the inputs, the processor comprising a processing chain, the processing chain to process the input values, thereby acquiring output values,
wherein the processor is to multiply a data vector comprising the input values by a matrix so as to acquire the output values, and
wherein the matrix is approximated by a plurality of matrices whose elements are positive or negative integer powers of two so that multiplying the data vector by the matrix comprises a series of sub-multiplications, each of the sub-multiplications being realized only by bit shifts and additions.
The above underlined limitations of multiplying a data vector by a matrix using a plurality of matrices whose elements are positive or negative integer powers of two to approximate the matrix such that the vector-matrix multiplication is implemented using bit shifts and additions amounts to processing mathematical calculations and falls within the “Mathematical Concepts” grouping of abstract ideas. See at least Equations (1, 6, 8a-8b, 12 and 15), page 18 and 21. Accordingly, the claim is directed to recite an abstract idea.
Under step 2A prong 2, the claim recites the following additional elements: a plurality of inputs, some or all of the inputs to receive input values, and a processor coupled to the inputs, the processor comprising a processing chain. However, the additional elements of “a plurality of inputs”, “processor” and “a processing chain” are recited at a high-level of generality (i.e., as generic inputs for receiving input values; and as a generic processor comprising a processing chain for processing the input values to generate an output) such that they amount to no more than merely reciting the words “apply it” (or an equivalent) with the judicial exception or merely as tools to implement the abstract idea or no more than mere instructions using a generic computer component. The additional elements of “receive input values” is merely adding insignificant extra-solution activity, i.e. mere data gathering. The additional elements do not, individually or in combination, integrate the exception into a practical application. Accordingly, the claim is not integrated into a practical application.
Under step 2B, claim 16 does not include additional elements that, individually or in combination, are sufficient to amount to significantly more than the judicial exception. As discussed above with respect to integration of the abstract idea into a practical application, the additional elements of “a plurality of inputs”, “processor” and “a processing chain” are recited at a high-level of generality (i.e., as generic inputs for receiving input values; and as a generic processor comprising a processing chain for processing the input values to generate an output) such that they amount to no more than merely reciting the words “apply it” (or an equivalent) with the judicial exception or merely as tools to implement the abstract idea or no more than mere instructions using a generic computer component. The additional elements of “receive input values” is merely adding insignificant extra-solution activity, i.e. mere data gathering. See MPEP 2106.05(d)(II) which states that the courts have recognized computer functions such as “Receiving or transmitting data over a network” and “Storing and retrieving information in memory” as well‐understood, routine, and conventional functions when they are claimed in a merely generic manner (e.g., at a high level of generality) or as insignificant extra-solution activity. The claim does not recite additional elements that alone or in combination amount to an inventive concept. Accordingly, the claim does not amount to significantly more than the abstract idea.
Regarding claim 2, it is directed to a method practiced by the artificial neural network of claim 16. All steps performed by the method of claim 2 would be practiced by the artificial neural network of claim 16. Claim 16 analysis applies equally to claim 2.
Claim Rejections - 35 USC § 102
In the event the determination of the status of the application as subject to AIA 35 U.S.C. 102 and 103 (or as subject to pre-AIA 35 U.S.C. 102 and 103) is incorrect, any correction of the statutory basis (i.e., changing from AIA to pre-AIA ) for the rejection will not be considered a new ground of rejection if the prior art relied upon, and the rationale supporting the rejection, would be the same under either status.
The following is a quotation of the appropriate paragraphs of 35 U.S.C. 102 that form the basis for the rejections under this section made in this Office action:
A person shall be entitled to a patent unless –
(a)(1) the claimed invention was patented, described in a printed publication, or in public use, on sale, or otherwise available to the public before the effective filing date of the claimed invention.
(a)(2) the claimed invention was described in a patent issued under section 151, or in an application for patent published or deemed published under section 122(b), in which the patent or application, as the case may be, names another inventor and was effectively filed before the effective filing date of the claimed invention.
Claims 1, 3, 9-10 and 14 are rejected under 35 U.S.C. 102(a)(1) as being anticipated by Li et al. (NPL – “A global optimal zero-forcing Beamformer design with signed power-of-two coefficients”), hereinafter Li. Li is cited in the IDS submitted on 03/11/2026.
Regarding claim 1, Li teaches a method for providing transmit symbols to be transmitted by a transmitter to one or more receivers of a wireless MIMO communication system, the method comprising (Li section 1 “QOS based on cross-layer scheduling, and multi-user multiple-input multiple-output (MU-MIMO) systems to increase spectral efficiency”; section 2 and equations 1-3; transmit symbols – x; transmitter – component transmitting x; one or more receivers – component receiving x; wireless MIMO communication system – MIMO system; section 4 “the proposed method is used to solve two examples under different scenarios … the wavelength of the signal at which the wireless system operates”):
receiving data to be transmitted to the one or more receivers (Li section 2 and Equation 3; data - s), and
acquiring the transmit symbols to be transmitted by multiplying a data vector comprising the data to be transmitted by a matrix, like a precoding matrix (Li section 2 and Equation 3; matrix – W),
wherein the matrix is approximated by a plurality of matrices whose elements are positive or negative integer powers of two so that multiplying the data vector by the matrix comprises a series of sub-multiplications, each of the sub-multiplications being realized only by bit shifts and additions (Li section 2 and Equation 5 “the elements of W can be expressed in the form of sum of SPT terms as given below”; page 596 first paragraph “The beamforming weight vectors are expressed as the sum of signed power-of-two (SPT) terms. This expression is attractive for hardware implementation since multiplications can be effectively implemented by using shifters or adders”).
Regarding claim 3, Li teaches all the limitations of claim 1 as stated above. Further, Li teaches wherein the matrix is approximated by determining the plurality of matrices (Li section 2.1).
Regarding claim 9, Li teaches all the limitations of claim 1 as stated above. Further, Li teaches wherein the power-2-decomposition is a sum- decomposition, and the precoding matrix is approximated as follows:
A
~
=
∑
k
=
1
K
M
k
where
A
~
represents the approximated MxN precoding matrix,
M
k
represents a matrix of the decomposition with entries being either zero or a positive or negative integer power of 2, k
∈
{1,2, ... , K} (Li section 2.1 and Equation 5).
Regarding claim 10, Li teaches all the limitations of claim 9 as stated above. Further, Li teaches wherein the matrix is a MxN matrix, and the entries of
M
1
,
…
M
k
are of the form [
M
k
i
j
]
=
±
2
l
for
l
∈
E
0
∪
V
k
:
V
k
∈
Z
(Li section 2.1 and Equation 5).
Regarding claim 14, they are directed to a non-transitory digital storage medium having a computer program stored thereon to perform the method of claim 1. Claim 1 analysis applies equally to claim 14.
Claim Rejections - 35 USC § 103
In the event the determination of the status of the application as subject to AIA 35 U.S.C. 102 and 103 (or as subject to pre-AIA 35 U.S.C. 102 and 103) is incorrect, any correction of the statutory basis (i.e., changing from AIA to pre-AIA ) for the rejection will not be considered a new ground of rejection if the prior art relied upon, and the rationale supporting the rejection, would be the same under either status.
The following is a quotation of 35 U.S.C. 103 which forms the basis for all obviousness rejections set forth in this Office action:
A patent for a claimed invention may not be obtained, notwithstanding that the claimed invention is not identically disclosed as set forth in section 102, if the differences between the claimed invention and the prior art are such that the claimed invention as a whole would have been obvious before the effective filing date of the claimed invention to a person having ordinary skill in the art to which the claimed invention pertains. Patentability shall not be negated by the manner in which the invention was made.
Claims 15 and 17-18 are rejected under 35 U.S.C. 103 as being unpatentable over Li in view of Rusu (NPL – “Learning Multiplication-free Linear Transformations”). Rusu is submitted on the IDS submitted on 03/11/2026.
Regarding claim 15, Li teaches an apparatus for providing transmit symbols to be transmitted by a transmitter to one or more receivers of a wireless MIMO communication system (Li section 1 QOS based on cross-layer scheduling, and multi-user multiple-input multiple-output (MU-MIMO) systems to increase spectral efficiency”; section 2 and equations 1-3; transmit symbols – x; transmitter – component transmitting x; one or more receivers – component receiving x; wireless MIMO communication system – MIMO system; section 4 “the proposed method is used to solve two examples under different scenarios … the wavelength of the signal at which the wireless system operates”),
wherein the apparatus is to receive data to be transmitted to the one or more receivers (Li section 2 and Equation 3; data – s), and
the apparatus is to acquire the transmit symbols to be transmitted by multiplying a data vector comprising the data to be transmitted by a matrix, like a precoding matrix (Li section 2 and Equation 3; matrix – W),
wherein the matrix is approximated by (Li section 2 and Equation 5 “the elements of W can be expressed in the form of sum of SPT terms as given below”; page 596 first paragraph “The beamforming weight vectors are expressed as the sum of signed power-of-two (SPT) terms. This expression is attractive for hardware implementation since multiplications can be effectively implemented by using shifters or adders”).
Li does not explicitly teach wherein the matrix is approximated by a product of a plurality of matrices whose elements are positive or negative integer powers of two.
However, on the same field of endeavor, Rusu discloses a matrix that is approximated by a product of a plurality of matrices (Rusu Equation 10).
Accordingly, it would have been obvious to one of ordinary skill in the art before the effective filling date of the claimed invention, to modify Li using Rusu and approximate the matrix as a product of a plurality of matrices whose elements are positive or negative integer powers of two so that multiplying the data vector by the matrix comprises a series of sub-multiplications, each of the sub-multiplications being realized only by bit shifts and bit additions by replacing the sum-decomposition with a product-decomposition. One of ordinary skill in the art could have substituted the sum-decomposition for the product-decomposition, and the results of the substitution would have been predictable because both are power-of-two decomposition such that each of the sub-multiplications are still realized only by bit shifts and bit additions (Rusu section VII). See also MPEP 2141 III(B) for more information.
Therefore, the combination of Li as modified in view of Rusu teaches wherein the matrix is approximated by a product of a plurality of matrices whose elements are positive or negative integer powers of two so that multiplying the data vector by the matrix comprises a series of sub-multiplications, each of the sub-multiplications being realized only by bit shifts and bit additions.
Regarding claim 17, Li as modified in view of Rusu teaches all the limitations of claim 15 as stated above. Further, Li as modified in view of Rusu teaches a transmitter of a wireless MIMO communication system, comprising an apparatus of claim 15 for providing transmit symbols to be transmitted to one or more receivers of the wireless MIMO communication system (Li section 2 “To continue, a linear zero-forcing precoding transmitter is utilized”; page 596 first paragraph “each antenna of the transmitter has its own amplifier and their linear operation is important for modern efficient modulation”).
Regarding claim 18, Li as modified in view of Rusu teaches all the limitations of claim 17 as stated above. Further, Li as modified in view of Rusu teaches a wireless MIMO communication system, comprising one or more receivers, and one or more transmitters of claim 17 for transmitting data to the one or more receivers (Li section 1 first paragraph; section 2; section 4).
Claims 5-7 and 11 are rejected under 35 U.S.C. 103 as being unpatentable over Li as applied to claim 1 above, and further in view of Rusu.
Regarding claim 5, Li teaches all the limitations of claim 1 as stated above. Further, Li teaches wherein the matrix is approximated by positive or negative integer powers of two, and the finite resolution decomposition comprises a power-2-decomposition (section 2 and Equation 5).
Li does not explicitly teach wherein the matrix is approximated by a product of the plurality of matrices whose elements are positive or negative integer powers of two.
However, on the same field of endeavor, Rusu discloses a matrix that is approximated by a product of a plurality of matrices (Rusu Equation 10).
Accordingly, it would have been obvious to one of ordinary skill in the art before the effective filling date of the claimed invention, to modify Li using Rusu and approximate the matrix as a product of a plurality of matrices whose elements are positive or negative integer powers of two by replacing the sum-decomposition with a product-decomposition. One of ordinary skill in the art could have substituted the sum-decomposition for the product-decomposition, and the results of the substitution would have been predictable because both are power-of-two decomposition such that each of the sub-multiplications are still realized only by bit shifts and bit additions (Rusu section VII). See also MPEP 2141 III(B) for more information.
Therefore, the combination of Li as modified in view of Rusu teaches wherein the matrix is approximated by a product of the plurality of matrices whose elements are positive or negative integer powers of two.
Regarding claim 6, Li as modified in view of Rusu teaches all the limitations of claim 1 as stated above. Further, Li as modified in view of Rusu teaches wherein the power-2-decomposition is a product- decomposition, and the matrix is approximated as follows:
A
~
=
∏
k
=
1
K
(
F
k
)
, where
A
~
represents the approximated matrix,
F
k
represents a matrix of the decomposition with entries being either zero or a positive or negative integer power of 2, k
∈
{1,2, ... , K} (Rusu Equation 10 and section III.B; Li Equation 5).
Regarding claim 7, Li as modified in view of Rusu teaches all the limitations of claim 6 as stated above. Further, Li as modified in view of Rusu teaches wherein the matrix is a MxN matrix, and the entries of
F
1
,
…
F
k
are of the form [
F
k
i
j
]
=
±
2
l
for
l
∈
E
0
∪
V
k
:
V
k
∈
Z
(Rusu Equation 10 and section III.B; Li Equation 5).
Regarding claim 11, Li as modified in view of Rusu teaches all the limitations of claim 6 as stated above. Further, Li as modified in view of Rusu teaches wherein the cardinality of
C
V
is chosen so that the matrices of the decomposition occupy a predefined amount of bits, (Rusu section III.B).
Claim 8 is rejected under 35 U.S.C. 103 as being unpatentable over Li in view of Rusu as applied to claim 6 above, and further in view of Koker et al. (US 20220107914 A1), hereinafter Koker.
Regarding claim 8, Li as modified in view of Rusu teaches all the limitations of claim 6 as stated above. Further, Li as modified in view of Rusu teaches
A
~
=
∏
k
=
1
K
f
k
(
F
k
)
, where
A
~
represents the approximated matrix,
F
k
represents a matrix of the decomposition with entries being either zero or a positive or negative integer power of 2, k
∈
{1,2, ... , K},
F
k
(
∙
)
F
k
(Rusu Equation 10 and section III.B; Li Equation 5).
Rusu does not explicitly teach wherein the product-decomposition comprises a nonlinearity associated with the respective factors, and the matrix is approximated as follows:
A
~
=
∏
k
=
1
K
f
k
(
F
k
)
, where
A
~
represents the approximated matrix,
F
k
represents a matrix of the decomposition with entries being either zero or a positive or negative integer power of 2, k
∈
{1,2, ... , K}, and
F
k
(
∙
)
represents a nonlinearity to which
F
k
is subjected.
However, on the same field of endeavor, Koker discloses applying a nonlinear function ƒ(x) to an output of a matrix operation where
f
(
∙
)
represents a nonlinearity to which
x
is subjected (Koker paragraph [0201]).
Accordingly, it would have been obvious to one of ordinary skill in the art before the effective filling date of the claimed invention, to modify Li in view of Rusu and generalize the teaching of Koker by applying a respective nonlinear function
f
(
∙
)
to each respective matrix factor
F
k
to approximate the matrix in order to increase the nonlinear properties of the system (Koker paragraph [0201]).
Therefore, the combination of Li as modified in view of Rusu and Koker teaches wherein the product-decomposition comprises a nonlinearity associated with the respective factors, and the matrix is approximated as follows:
A
~
=
∏
k
=
1
K
f
k
(
F
k
)
, where
A
~
represents the approximated matrix,
F
k
represents a matrix of the decomposition with entries being either zero or a positive or negative integer power of 2, k
∈
{1,2, ... , K}, and
F
k
(
∙
)
represents a nonlinearity to which
F
k
is subjected.
Claim 12 is rejected under 35 U.S.C. 103 as being unpatentable over Li in view of Rusu as applied to claim 6 above, and further in view of Nabar et al. (US 8095097 B1), hereinafter Nabar.
Regarding claim 12, Li as modified in view of Rusu teaches all the limitations of claim 6 as stated above.
Li does not explicitly teach wherein the decomposition is terminated as soon as a SNR falls below a predefined or maximum SNR requirement on the approximated matrix of the specific application, or the number of matrices of the decomposition depends on an additional SNR achievable by a further matrix, wherein the decomposition may be terminated once an additional SNR achievable by a further matrix reaches of falls below a certain or predefined threshold.
However, on the same field of endeavor, Nabar discloses determining a signal-to-noise ratio (SNR) of a channel; determining whether the SNR meets a criterion/threshold; and transmitting a plurality of signals based if the criterion/threshold is met (Nabar Fig. 4 254-258; col 13 lines 22-25; and col 1 line 63 to col 14 line 2).
Accordingly, it would have been obvious to one of ordinary skill in the art before the effective filling date of the claimed invention, to modify Li in view of Rusu and generalize the teaching Nabar by determining a SNR requirement and terminating the decomposition once the SNR requirement is met (i.e., falls below a threshold) order to improve the SNR which results in a more reliable transmission (Nabar col 9 lines 50-51).
Therefore, the combination of Li as modified in view of Rusu and Nabar teaches wherein the decomposition is terminated as soon as a SNR falls below a predefined or maximum SNR requirement on the approximated matrix of the specific application, or the number of matrices of the decomposition depends on an additional SNR achievable by a further matrix, wherein the decomposition may be terminated once an additional SNR achievable by a further matrix reaches of falls below a certain or predefined threshold.
Claim 13 is rejected under 35 U.S.C. 103 as being unpatentable over Li as applied to claim 1 above, and further in view of Andreev (US 10096133 B1).
Regarding claim 13, Li teaches all the limitations of claim 1 as stated above.
Li does not explicitly teach wherein the matrix is approximated such that a distortion between the approximated matrix and the matrix is at or below a predefined threshold.
However, on the same field of endeavor, Adreev discloses approximating a matrix such that a distortion between the approximated matrix and the matrix is at or below a predefined threshold (Andreev col 8 line 56 to col 9 line 7).
Accordingly, it would have been obvious to one of ordinary skill in the art before the effective filling date of the claimed invention, to modify Li and generalize the teaching Andreev by approximating the matrix such that a distortion between the approximated matrix and the matrix is at or below a predefined threshold in order to reduce the error rate and increase the accuracy of the approximation (Andreev col 9 lines 18-23).
Therefore, the combination of Li as modified in view of Andreev teaches wherein the matrix is approximated such that a distortion between the approximated matrix and the matrix is at or below a predefined threshold.
Claims 2 and 16 rejected under 35 U.S.C. 103 as being unpatentable over Li et al. (US 11507814 B1), hereinafter L2, in view of Li.
Regarding claim 16, L2 teaches an artificial neural network, comprising:
a plurality of inputs, some or all of the inputs to receive input values (L2 Fig. 1B; plurality of inputs – PE inputs); and
a processor coupled to the inputs, the processor comprising a processing chain, the processing chain to process the input values, thereby acquiring output values (L2 Fig. 1B processor comprising a processing chain – PE array),
wherein the processor is to multiply a data vector comprising the input values by a matrix so as to acquire the output values (L2 col 10 lines 44-58; Figs. 3A-3C and col 15 lines 4-23).
L2 does not explicitly teach wherein the matrix is approximated by a plurality of matrices whose elements are positive or negative integer powers of two so that multiplying the data vector by the matrix comprises a series of sub-multiplications, each of the sub-multiplications being realized only by bit shifts and additions.
However, on the same field of endeavor, Li discloses multiplying a vector by a matrix to acquire output values wherein the matrix is approximated by a plurality of matrices whose elements are positive or negative integer powers of two so that multiplying the data vector by the matrix comprises a series of sub-multiplications, each of the sub-multiplications being realized only by bit shifts and additions (Li section 2; Equations 3 and 5 “the elements of W can be expressed in the form of sum of SPT terms as given below”; page 596 first paragraph “The beamforming weight vectors are expressed as the sum of signed power-of-two (SPT) terms. This expression is attractive for hardware implementation since multiplications can be effectively implemented by using shifters or adders”).
Accordingly, it would have been obvious to one of ordinary skill in the art before the effective filling date of the claimed invention, to modify L2 using Li and configure the PEs to multiply the data vector by the matrix using a plurality of matrices whose elements are positive or negative integer powers of two to approximate the matrix so that multiplying the data vector by the matrix comprises a series of sub-multiplications, each of the sub-multiplications being realized only by bit shifts and additions in order to implement a low complexity and low cost hardware implementation for performing the vector-matrix multiplication (Li page 596 first paragraph).
Therefore, the combination of L2 as modified in view of Li teaches wherein the matrix is approximated by a plurality of matrices whose elements are positive or negative integer powers of two so that multiplying the data vector by the matrix comprises a series of sub-multiplications, each of the sub-multiplications being realized only by bit shifts and additions.
Regarding claim 2, it is directed to a method practiced by the artificial neural network of claim 16. All steps performed by the method of claim 2 would be practiced by the artificial neural network of claim 16. Claim 16 analysis applies equally to claim 2.
Allowable Subject Matter
Claim 4 would be allowable if rewritten in independent form including all of the limitations of the base claim and any intervening claims and if rewritten to overcome the 35 U.S.C. 101 and 112(b) rejection discussed above.
None of the prior art references cited explicitly teach or suggest, in combination with other limitations of the claims, “an amount of memory occupied by the plurality of matrices is the same as an amount of memory occupied by the matrix” as recited in claim 4.
Conclusion
The prior art made of record and not relied upon is considered pertinent to applicant's disclosure.
McDanel et al. (NPL – “Full-stack Optimization for Accelerating CNNs Using Powers-of-Two Weights with FPGA Validation”) related to using power-of-two weight matrices such that convolution operations are replaced with shift and add operations. McDanel is cited in the IDS submitted on 03/11/2026.
Li et al. (NPL – “ADDITIVE POWERS-OF-TWO QUANTIZATION: A NONUNIFORM DISCRETIZATION FOR NEURAL NETWORKS”) related to using an additive power-of-two quantization such that multiplications are implemented as shift and add operations. Li is cited in the IDS submitted on 09/01/2022.
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/Carlo Waje/Examiner, Art Unit 2151 (571)272-5767
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