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`UNITED STATES PATENT AND TRADEMARK OFFICE
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`BEFORE THE PATENT TRIAL AND APPEAL BOARD
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`
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`ZTE (USA) INC.,
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`Petitioner
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`v.
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`BELL NORTHERN RESEARCH, LLC,
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`Patent Owner
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`
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`DECLARATION OF PAUL MIN, PH.D.
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`Case No. IPR2019-01438
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`ZTE, Exhibit 1015-0001
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`TABLE OF CONTENTS
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`I.
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`Introduction ...................................................................................................... 1
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`II.
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`Background/Qualifications .............................................................................. 1
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`III. Documents and Materials Considered ............................................................. 5
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`IV. Legal Principles ............................................................................................... 6
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`V.
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`Person of Ordinary Skill in the Art ................................................................12
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`VI.
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`’862 Patent .....................................................................................................13
`
`A.
`
`Summary .............................................................................................13
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`B.
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`C.
`
`Prosecution History .............................................................................16
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`Priority Date ........................................................................................17
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`VII. Technology Background ................................................................................17
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`A.
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`Beamforming .......................................................................................17
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`B.
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`Singular Value Decomposition (SVD) ................................................21
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`VIII. Claim Construction ........................................................................................25
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`IX.
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`Invalidity Opinions ........................................................................................27
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`A.
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`Li anticipates claims 9-12. ..................................................................27
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`1.
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`Application of Li to claims 9-12 ...............................................31
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`A.
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`Li in combination with Maltsev renders obvious claims 9-12. ...........58
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`1. Maltsev ......................................................................................58
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`2. Motivation to combine Li and Maltsev .....................................59
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`3.
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`Application of Li and Maltsev to claims 9-12 ..........................60
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`B.
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`Tong anticipates claims 9-12. ..............................................................81
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`Min Declaration
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`i
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`IPR2019-01438
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`ZTE, Exhibit 1015-0002
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`1.
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`2.
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`Tong ..........................................................................................81
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`Application of Tong to claims 9-12 ..........................................83
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`C.
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`Tong in combination with Reinhardt renders obvious claims 10. ......99
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`1.
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`Reinhardt ...................................................................................99
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`2. Motivation to combine Tong and Reinhardt ...........................101
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`3.
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`Application of Tong and Reinhardt to claim 10 .....................102
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`Min Declaration
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`ii
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`IPR2019-01438
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`ZTE, Exhibit 1015-0003
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`I.
`
`Introduction
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`1. My name is Paul Min, Ph.D. I submit this declaration on behalf of
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`ZTE (USA) Inc., (“Petitioner”), which I understand is challenging the validity of
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`claims 9-12 (“the challenged claims”) of U.S. Patent No. 8,416,862 (“the ’862
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`patent”) (Ex. 1001) in a petition for inter partes review.
`
`2.
`
`I have been asked to provide an opinion on the validity of the
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`challenged claims. In my opinion, U.S. Patent Application Publication No.
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`2006/0068718 (“Li”) (Ex. 1005) anticipates claims 9-12 of the ’862 patent.
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`Additionally, the combination of Li, U.S. Patent No. 7,570,696 (“Maltsev”) (Ex.
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`1006) renders obvious claims 9-12 of the ’862 patent.
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`3.
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`Furthermore, it is my opinion that, U.S. Patent Application
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`Publication No. 2008/0108310 (“Tong”) (Ex. 1007) anticipates claims 9-12 of the
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`’862 patent. Additionally, the combination of Tong and U.S. Patent No. 5,541,607
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`(“Reinhardt”) (Ex. 1014) renders obvious claim 10 of the ’862 patent.
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`II. Background/Qualifications
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`4.
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`I summarize in this section my educational background, career
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`history, publications, and other relevant qualifications. Appendix A to this
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`declaration is my curriculum vitae, which sets forth my qualifications.
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`5.
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`I received a B.S. degree in Electrical Engineering in 1982, an M.S.
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`degree in Electrical Engineering in 1984, and a Ph.D. degree in Electrical
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`Min Declaration
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`IPR2019-01438
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`ZTE, Exhibit 1015-0004
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`Engineering in 1987 from the University of Michigan in Ann Arbor. I received
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`several academic honors, including my B.S. degree with honors, a best graduate
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`student award and a best teaching assistant award during my M.S. study, and a best
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`paper award from a major international conference for reporting results from my
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`Ph.D. thesis.
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`6.
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`After receiving my Ph.D., I worked at Bellcore in New Jersey from
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`August 1987 until August 1990. At Bellcore, I was responsible for evolving the
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`public switched telephone network (PSTN) into a multi-services voice and data
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`network that incorporated packet switches, optical technologies, and wireless
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`technologies.
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`7.
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`In September 1990, I joined the faculty at Washington University in
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`St. Louis. In July 1996, I was promoted to an Associate Professor of Electrical
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`Engineering with tenure. I am currently a Senior Professor of Electrical and
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`Systems Engineering at Washington University. I have also served as the Chair of
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`the Graduate Curriculum (2000-2002) and the Chair of the Undergraduate
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`Curriculum (2011-2014) for the Department of Electrical and Systems
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`Engineering.
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`8.
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`At Washington University, I have conducted research in
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`communication, computing, and related electronic hardware and software. My
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`research group has pioneered a new paradigm for designing electronic circuits that
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`Min Declaration
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`IPR2019-01438
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`ZTE, Exhibit 1015-0005
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`can alleviate the speed and performance mismatch against optical technology. I
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`have received several grants from U.S. Federal Agencies, including the National
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`Science Foundation and the Defense Advanced Research Project Agency, and
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`numerous contracts from companies and organizations around the world.
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`9.
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`Specifically related to the technology matters in this litigation, I have
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`researched a variety of wireless communication technologies, including TDMA,
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`CDMA, WCDMA, OFDM, FDD, SC-FDMA, and TDD. I have an extensive
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`background and experience in each of these technologies.
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`10. As a faculty member at Washington University, I have taught a
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`number of courses in electronics, communication, and computing at both the
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`undergraduate and graduate levels. For example, I have taught communication
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`theory (Washington University ESE 471), transmission and multiplexing
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`(Washington University ESE 571), and signaling and control of communication
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`networks (Washington University ESE 572).
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`11.
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`I have supervised more than 50 graduate students, 12 of whom
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`received a doctoral degree under my guidance. A number of doctoral theses that I
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`have supervised relate specifically to wireless technology. My students and I have
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`published a number of peer-reviewed articles on resource allocation, scheduling,
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`modulation, mobility management, and multiplexing. Several of these articles
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`received accolades in the field. For example, in 2011, we received a best paper
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`Min Declaration
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`IPR2019-01438
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`ZTE, Exhibit 1015-0006
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`award in 3G WCDMA and 4G LTE related mobility and resource management at
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`the prestigious Mobility 2011 international conference.
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`12.
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`In addition to my responsibilities as a university faculty member, I
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`have founded two companies. In May 1997, I founded MinMax Technologies, Inc.,
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`a fabless semiconductor company that developed switch fabric integrated circuit
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`chips for the Internet. In March 1999, I founded Erlang Technology, Inc., a fabless
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`semiconductor company that focused on the design and development of integrated
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`circuit chips and software for the Internet. One of Erlang's products received a best
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`product of the year award in 2004 from a major trade journal for the electronics
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`industry.
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`13. Outside my own start-up companies, I have also served in various
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`technology and business advisor roles for other companies and organizations
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`around the world. I was the main technical author for one of two winning proposals
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`to the Korean government for CDMA wireless service licenses (1996). I was
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`responsible for designing a commercial scale IS-95 CDMA cellular network,
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`which I understand to be one of the earliest such networks deployed in the world. I
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`worked with numerous engineers and scientists around the world to implement this
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`commercial scale cellular network before IS-95 CDMA was widely accepted. This
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`provided me with extensive insight into various components of cellular technology,
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`which by and large are used in today's 3G and 4G networks. I have also been
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`Min Declaration
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`IPR2019-01438
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`ZTE, Exhibit 1015-0007
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`involved in a semiconductor company that specializes in semiconductor memories,
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`such as flash EEPROMs, as a board member and as a technical advisor (2007-
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`2011).
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`14.
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`I am a named inventor on ten U.S. patents, many of which are directly
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`related to resource allocation, packet processing, and network designing. I have
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`extensively published technical papers in international journals and at international
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`conferences as well as technical memoranda and reports, and I have given a
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`number of seminars and invited talks. Many of these papers are specifically within
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`the context of the 3GPP standards. I have organized several international
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`conferences and served as an international journal editor.
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`15.
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`I am a member of, and have been actively involved in, a number of
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`professional organizations. For example, I have served as the Chair of the St. Louis
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`Section of the IEEE, which has more than 3,000 members (2014), and a member of
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`the Eta Kappa Nu Honor Society for electrical engineers. I have also been an
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`Ambassador of the McDonnell International Scholars Academy (2007-2013).
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`16.
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`In my over 30 years of experience with telecommunications
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`technology, I have acquired significant knowledge about telecommunications
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`systems industry standards and standard setting organizations such as 3GPP.
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`III. Documents and Materials Considered
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`17. Appendix B to this declaration lists materials that I have considered in
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`IPR2019-01438
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`ZTE, Exhibit 1015-0008
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`rendering the opinions that I express in this declaration. In forming my opinions, I
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`have also relied on my experience and education.
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`IV. Legal Principles
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`18.
`
`I am not an attorney. I offer no opinions on the law. But counsel has
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`informed me of legal standards that apply to the issue of patent validity. I have
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`applied these standards in arriving at my conclusions.
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`19.
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`I understand that in an inter partes review the petitioner has the
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`burden of proving a proposition of unpatentability by a preponderance of the
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`evidence. I understand this standard is different from the standard that applies in a
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`district court, where I understand a challenger bears the burden of proving
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`invalidity by clear and convincing evidence.
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`20.
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`I understand that a patent claim is invalid based on anticipation if a
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`single prior art reference discloses all of the features of that claim, and does so in a
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`way that enables one of ordinary skill in the art to make and use the invention.
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`Each of the claim features may be expressly or inherently present in the prior art
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`reference. I understand that if the prior art necessarily functions in accordance
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`with, or includes a claim’s feature, then that prior art inherently discloses that
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`feature. I have relied on this understanding in expressing the opinions set forth
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`below.
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`21.
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`I understand that a prior art reference describes the claimed invention
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`Min Declaration
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`IPR2019-01438
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`ZTE, Exhibit 1015-0009
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`if it either expressly or inherently describes each and every feature set forth in the
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`claim; i.e., in determining whether a single item of prior art anticipates a patent
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`claim, one should take into consideration not only what is expressly disclosed in
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`that item, but also what is inherently present as a natural result of the practice of
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`the system or method disclosed in that item.
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`22.
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`I understand that to establish inherency, the evidence must make clear
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`that the missing descriptive matter is necessarily present in the item of prior art and
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`that it would be so recognized by persons of ordinary skill in the art. I also
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`understand that prior art use of the claimed patented invention that was accidental,
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`unrecognized, or unappreciated at the time of filing can still be an invalidating
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`anticipation.
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`23.
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`I understand that although multiple prior art references may not be
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`combined to show anticipation, additional references may be used to interpret the
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`allegedly anticipating reference and shed light on what it would have meant to
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`those skilled in the art at the time of the invention. These additional references
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`must make it clear that the missing descriptive matter in the patent claim is
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`necessarily present in the allegedly anticipating reference, and that it would be so
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`recognized by persons of ordinary skill in the art.
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`24.
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`I understand that a patent may not be valid even though the invention
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`is not identically disclosed or described in the prior art if the differences between
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`Min Declaration
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`IPR2019-01438
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`ZTE, Exhibit 1015-0010
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`the subject matter sought to be patented and the prior art are such that the subject
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`matter as a whole would have been obvious to a person having ordinary skill in the
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`art in the relevant subject matter at the time the invention was made.
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`25. To determine if a claim is obvious, the following factors should be
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`considered: (1) the level of ordinary skill in the art at the time the invention was
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`made; (2) the scope and content of the prior art; (3) the differences between the
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`claimed invention and the prior art; and (4) secondary considerations, including
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`evidence of commercial success, long-felt but unsolved need, unsuccessful
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`attempts by others, copying of the claimed invention, unexpected and superior
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`results, acceptance and praise by others, independent invention by others, and the
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`like.
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`26. For example, I understand that the combination of familiar elements
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`according to known methods is likely to be obvious when it does no more than
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`yield predictable results. I also understand that an obviousness analysis need not
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`seek out precise teachings directed to the specific subject matter of the challenged
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`claim because a court can take account of the inferences and/or creative steps that a
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`person of ordinary skill in the art would employ.
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`27.
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`I understand that the obviousness determination of an invention turns
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`on whether a hypothetical person with ordinary skill and full knowledge of all the
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`pertinent prior art, when faced with the problem to which the claimed invention is
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`Min Declaration
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`IPR2019-01438
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`ZTE, Exhibit 1015-0011
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`addressed, would be led naturally to the solution adopted in the claimed invention
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`or would naturally view that solution as an available alternative. Facts to be
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`evaluated in this analysis include:
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` The scope and contents of the prior art;
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` Differences between the prior art and the claims at issue;
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` The level of ordinary skill in the pertinent art; and
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` Evidence of objective factors suggesting or negating obviousness.
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` I understand that the following rationales may be used to determine whether
`a piece of prior art can be combined with other prior art or with other
`information within the knowledge of one of ordinary skill in the art:
`
` Combining prior art elements according to known methods to yield
`predictable results;
`
` Simple substitution of one known element for another to obtain predictable
`results;
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` Use of known techniques to improve similar devices (methods, or products)
`in the same way;
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` Applying a known technique to a known device (method, or product) ready
`for improvement to yield predictable results;
`
` “Obvious to try” - choosing from a finite number of identified, predictable
`solutions, with a reasonable expectation of success;
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` Known work in one field of endeavor may prompt variations of it for use in
`either the same field or a different one based on design incentives or other
`market forces if the variations would have been predictable to one of
`ordinary skill in the art; or
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` Some teaching, suggestion, or motivation in the prior art that would have led
`one of ordinary skill to modify the prior art reference or to combine prior art
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`Min Declaration
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`IPR2019-01438
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`ZTE, Exhibit 1015-0012
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`reference teachings to arrive at the claimed invention.
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`28.
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`I understand that when a work is available in one field of endeavor,
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`design incentives and/or other market forces, for example, can prompt variations of
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`it, either in the same field or a different one. Moreover, if a person of ordinary skill
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`can implement a predictable variation, I understand that that likely bars its
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`patentability.
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`29.
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`I understand that obviousness must be tested as of the time the
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`invention was made. I understand that the test for obviousness is what the
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`combined teachings of the prior art references would have suggested, disclosed, or
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`taught to one of ordinary skill in the art. In particular, it is my understanding that a
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`patent claim is invalid based upon obviousness if it does nothing more than
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`combine familiar elements from one or more prior art references or products
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`according to known methods to yield predictable results. For example, I understand
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`that where a technique has been used to improve one device, and a person of
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`ordinary skill in the art would have recognized that it would improve similar
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`devices in the same way, using that technique is obvious. I understand that
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`obviousness can be proved by showing that a combination of elements was
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`obvious to try, i.e.: that it does no more than yield predictable results; implements a
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`predictable variation; is no more than the predictable use of prior art elements
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`according to their established functions; or when there is design need or market
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`Min Declaration
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`IPR2019-01438
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`ZTE, Exhibit 1015-0013
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`pressure to solve a problem and there are a finite number of identified, predictable
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`solutions. I have been further informed that when a patent claim simply arranges
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`old elements with each element performing the same function it had been known to
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`perform and yields results no more than one would expect from such an
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`arrangement, the combination is obvious.
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`30.
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`I understand that another factor to be considered is common sense.
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`For example, I understand that common sense teaches that familiar items may have
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`obvious uses beyond their primary purposes, and, in many cases, a person of
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`ordinary skill will be able to fit the teachings of multiple patents together like
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`pieces of a puzzle.
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`31.
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`I understand that the Supreme Court articulated additional guidance
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`for obviousness in its KSR decision. My understanding is that the Supreme Court
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`said that technical people of ordinary skill look for guidance in other solutions to
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`problems of a similar nature, and that the obviousness inquiry must track reality,
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`and not legal fictions. I have relied on these understandings in expressing the
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`opinions set forth below.
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`32.
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`I understand that a new use of an old product or material cannot be
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`claimed as a new product; the apparatus or system itself is old and cannot be
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`patented. I further understand that, in general, merely discovering and claiming a
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`new benefit to an old process cannot render the process newly patentable.
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`Min Declaration
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`IPR2019-01438
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`ZTE, Exhibit 1015-0014
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`V.
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`Person of Ordinary Skill in the Art
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`33.
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`In order to determine the characteristics of a person of ordinary skill
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`in the art of the ’862 Patent, I have used April 21, 2005 as the relevant time frame.
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`My understanding is that this is the filing date of the earliest provisional
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`application to which the ’862 Patent claims priority. For purposes of this statement,
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`any reference to the filing date of the ’862 Patent is intended to refer to this April
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`21, 2005 priority date of the provisional application to which the ’862 Patent
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`claims priority. (I have not been asked to opine on whether the provisional
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`application is sufficient to establish the priority date for the ’862 Patent; I am using
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`this date in the following analysis because that is the priority date alleged by
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`BNR.)
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`34.
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`In determining the characteristics of a person of ordinary skill for the
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`’862 Patent, I have considered the state of the art of wireless mobile
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`communication systems at that time, the types of problems encountered with signal
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`fading, and the solutions that then existed such as antenna systems, including
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`MIMO, and beamforming techniques. I have also considered the then-existing
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`technology for wireless communication systems, such as cellular radio systems and
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`wireless local area network systems (e.g., IEEE 802.11 Wi-Fi systems), including
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`the sophistication of the technology involved. I have also considered the education
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`and experience of those working in the field at that time. I have also considered my
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`IPR2019-01438
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`ZTE, Exhibit 1015-0015
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`personal knowledge and experience with the field at that time, including those I
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`worked and interacted with regarding wireless mobile communication systems. I
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`have also considered the knowledge, education, and experience of those in
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`academia and industry at that time that were working, innovating, or performing
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`research in the field of wireless mobile communication systems, and in particular,
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`techniques to address signal fading problems.
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`35.
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`It is my opinion that a POSITA for the ’862 Patent at the time of this
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`filing date would have had a Bachelor’s degree in Electrical Engineering,
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`Computer Engineering, Computer Science, or a related field, and at least 2 to 4
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`years of experience in the field of wireless communication, or a person with
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`equivalent education, work, or experience in this field.
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`36. Based on my background and qualifications, I am currently and was
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`as of the priority date of the ’862 Patent at least a POSITA in the subject matter of
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`the ’862 patent.
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`VI.
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`’862 Patent
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`A.
`
`Summary
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`37. U.S. Patent No. 8,416,862 to Carlos Aldana, et al., is entitled
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`“Efficient Feedback of Channel Information in a Closed Loop Beamforming
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`Wireless Communication System” and was issued on April 9, 2013.
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`38. The ’862 Patent relates to wireless communications using
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`Min Declaration
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`IPR2019-01438
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`ZTE, Exhibit 1015-0016
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`beamforming. ’862 patent at 1:20–22. “FIG. 6 is a schematic block diagram of a
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`beamforming wireless communication where H=UDV* (H–represents the channel,
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`U is the receiver beamforming unitary matrix, and V* is the conjugate of the
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`transmitter beamforming unitary matrix.” ’862 patent at 12:47–51.
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`
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`39.
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`In the background section, the specification explains that a receiver
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`must provide feedback information “for a transmitter to properly implement
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`beamforming (i.e., determine the beamforming matrix [V]).” ’862 patent at 3:14–
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`19. “One approach for sending feedback from the receiver to the transmitter is for
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`the receiver to determine the channel response (H) and to provide it as the
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`feedback information.” ’862 patent at 3:19–22. Alternatively, “the receiver may
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`decompose the channel using singular value decomposition (SVD) and send
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`Min Declaration
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`IPR2019-01438
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`ZTE, Exhibit 1015-0017
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`information relating only to a calculated value of the transmitter’s beamforming
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`matrix (V) as the feedback information. In this approach, the receiver calculates (V)
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`based on H=UDV*, where H is the channel response, D is a diagonal matrix, and U
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`is a receiver unitary matrix.” ’862 patent at 3:26–33. The patent explains that each
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`of these prior art methods results in the size of the feedback information being too
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`large for practical applications. ’862 patent at 3:22–25, 3:33–35.
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`40. The ’862 Patent states that it discloses the following method for
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`feeding back transmitter beamforming information:
`
`A method for feeding back transmitter beamforming
`information from a receiving wireless communication
`device to a transmitting wireless communication device
`includes a receiving wireless communication device
`receiving a preamble sequence from the transmitting
`wireless device. The receiving wireless device estimates
`a channel response based upon the preamble sequence
`and
`then
`determines
`an
`estimated
`transmitter
`beamforming unitary matrix based upon the channel
`response and a receiver beamforming unitary matrix. The
`receiving wireless device then decomposes the estimated
`transmitter beamforming unitary matrix to produce the
`transmitter beamforming information and then wirelessly
`sends the transmitter beamforming information to the
`transmitting wireless device. The receiving wireless
`device may
`transform
`the estimated
`transmitter
`beamforming unitary matrix using a QR decomposition
`operation such as a Givens Rotation operation to produce
`the transformer beamforming information.
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`
`’862 patent at Abst.
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`Min Declaration
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`IPR2019-01438
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`ZTE, Exhibit 1015-0018
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`B.
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`Prosecution History
`
`41. The ’862 patent issued from U.S. Patent Application No. 11/237,341,
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`which was filed on September 28, 2005.
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`42. On August 5, 2008, the examiner rejected the pending claims based
`
`on the combination of U.S. Patent Application Publication Nos. 2002/0187753
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`(“Kim”) and 2004/0042558 (“Huang”). Ex. 1002 (’862 file history) at 0155. In
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`response, the applicant argued that the claim element “[a mechanism for
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`decomposing] the estimated transmitter beamforming unitary matrix (V)” in the
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`independent claims is missing. Ex. 1002 (’862 file history) at 0149.
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`43. The examiner also included a rejection based on U.S. Patent No.
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`5,541,607 (“Reinhardt”) in certain dependent claims, indicating that Reinhardt
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`disclosed “converting parameters from Cartesian to polar coordinates.” Ex. 1002
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`(’862 file history) at 0162. This rejection was traversed based on arguments made
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`with respect to the independent claims. Ex. 1002 (’862 file history) at 0149-50.
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`Applicant did not specifically address whether Reinhardt disclosed conversion
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`from Cartesian to polar coordinates in a transmitter beamforming system.
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`44. On January 23, 2009, the examiner issued a final rejection, based
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`again on Kim and Huang. Ex. 1002 (’862 file history) at 0136. In response, the
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`applicant appealed to the Patent Trial and Appeal Board and successfully
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`overturned the examiner’s rejections, leading to allowance and issuance of the ’862
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`Min Declaration
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`ZTE, Exhibit 1015-0019
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`patent on April 9, 2013. See Ex. 1002 (’862 file history) at 0120; id. at 0037.
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`C.
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`Priority Date
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`45. Application No. 11/237,341, which issued as the ’862 patent, is a
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`continuation-in-part of U.S. Patent Application No. 11/168,793, filed on June 28,
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`2005 and issued as U.S. Patent No. 7,738,583. Application No. 11/237,341 also
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`claims priority to U.S. Provisional Patent Application Nos. 60/673,451 (Ex. 1003),
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`filed on April 21, 2005 and 60/698,686 (Ex. 1004), filed on July 13, 2005.
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`46. For the purposes of this report, I have been told to assume that the
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`earliest priority date of the ’862 patent is April 21, 2005.
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`VII. Technology Background
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`47.
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`In order to aid the discussions that I have presented in this declaration,
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`I have provided below a brief technology background for the ’862 patent. A
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`POSITA would be familiar with the following concepts as of the priority date of
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`the ’862 patent.
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`A. Beamforming
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`48.
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`In wireless communication, a transmitter transmits radio frequency
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`(RF) signals over the wireless medium. A particular definition varies regarding the
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`term “radio frequency signal,” but generally the radio frequency signals relate to
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`the signals utilizing frequencies greater than the audible signals and less than the
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`visible signals. In this way, an RF signal may be in tens of kilohertz (khz = 103
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`ZTE, Exhibit 1015-0020
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`cycles per second) to tens of gigahertz (Ghz = 109 cycles per second). For example,
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`in the United States, the broadcast AM radio utilizes between about 530 khz and
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`1600 khz, and the broadcast FM radio utilizes between about 88 megahertz (Mhz =
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`106 cycles per second) and 108 Mhz.
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`49. When a transmitter transmits a sine wave (or tone) to a receiver at a
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`particular frequency, depending on the distance between the transmitter and the
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`receiver, the amplitude of the received sine wave varies. This can be seen by
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`considering a wave of water propagating on the water surface radially when a rock
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`hits the water. At any given time, the wave creates peaks and troughs on the
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`surface of the water, which can be seen at different locations.
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`50.
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`In wireless communication, an RF signal propagates as an
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`electromagnetic wave, which travels in a wireless medium at the speed of light. As
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`fast as the speed of light may be, it is still finite and for a different distance away
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`from the transmitter, it takes a different amount of time before the RF signal is
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`received.
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`51. Consider now two transmitters, each generating a sine wave at the
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`same frequency. A receiver located at certain distances away from the two
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`transmitters receives two different sine waves from the transmitters and depending
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`on the distance from each transmitter, the receiver observes a different magnitude
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`of the received signal from the individual transmitter.
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`ZTE, Exhibit 1015-0021
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`52.
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`If the two sine waves from the transmitters happen to coincide in
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`phase at the receiver, the combined wave has the magnitude equaling the sum of
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`the two sine wave amplitudes. For example, if the received signal from the first
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`transmitter is A1sin(ωt) and the received signal from the second transmitter is
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`A2sin(ωt), then the combined signal at the receiver becomes (A1 + A2)sin(ωt). If, on
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`the other hand, the two sine waves happen to coincide in opposite phase, the
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`combined wave has the magnitudes equaling the difference of the two sine wave
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`amplitudes. Following the above example, if the received signal from the first
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`transmitter is A1sin(ωt) and the received signal from the second transmitter is
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`A2sin(ωt + 180°) = -A2sin(ωt), then the combined signal at the receiver becomes
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`(A1 - A2)sin(ωt). The combination of two sine waves in phase is referred to as a
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`constructive combination and the combination of the two sine waves in opposite
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`phase is referred to as a destructive combination.
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`53. Again using the example of rocks hitting the water, when two rocks
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`hit the water at two locations at the same time, two waves start propagating
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`radially, and they meet and generate the combined wave patterns on the water
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`surface. Depending on the location on the water surface, the water waves may
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`show a greater peak or trough value (i.e., constructive combination) or show a
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`lesser displacement up or down (i.e., destructive combination).
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`54. When a transmitter transmits an RF signal, the strength of the received
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`ZTE, Exhibit 1015-0022
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`signal depends largely on the distance from the transmitter. This is because the
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`transmitter emits the RF signal radially much like the way a rock generates a wave
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`on the water surface. Consider now that a receiver is located at certain distances
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`away from multiple transmitters, each generating sine waves at the same
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`frequency. Since the distances to different transmitters are different, the sine waves
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`from the transmitters arrive at the receiver with different time delays. At this same
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`transmitter frequency, the time del