US 7676007

Here's a concise summary of US Patent 7676007:

US Patent 7676007 Summary

• Title: System and method for interpolation based transmit beamforming for MIMO-OFDM with partial feedback
• Current Assignee: Integral Wireless Technologies LLC
• Inventors: Jihoon Choi, Robert W. Heath, Jr.
• Filing Date: 2005-07-21
• Issue Date: 2010-03-09
• Abstract: The patent describes a system and method for transmit beamforming with receive combining in Multiple-Input Multiple-Output (MIMO) systems using Orthogonal Frequency Division Multiplexing (OFDM). To reduce the amount of feedback information from the receiver to the transmitter in non-reciprocal channels, the system employs limited feedback and beamformer interpolation. The receiver sends back a fraction of beamforming vectors and additional "interpolation information" (specifically, phase values) to the transmitter. The transmitter then uses this information to interpolate and compute the beamforming vectors for all OFDM subcarriers. The interpolator may be a spherical interpolator and uses these phase rotation parameters, determined at the receiver to maximize minimum channel gain or capacity, to minimize interpolation distortion. The scheme can also be combined with beamformer quantization.

Plain-Language Overview of Independent Claims:

• Claim 1 (Communication Apparatus - Transmitter Side): This claim describes a communication apparatus (e.g., a base station or user equipment) with antennas and a transmitter. The transmitter sends out signals on multiple subcarriers to a receiver. To do this, it uses limited feedback from the receiver, which includes beamforming vectors for only a subset of the subcarriers, along with interpolation information (specifically, phase values). The transmitter then derives the beamforming vectors for the remaining subcarriers (those not in the subset) by interpolating the received subset beamforming vectors, using the provided phase values to aid this interpolation.
• Claim 19 (Communication Apparatus - Receiver Side): This claim describes a communication apparatus (e.g., user equipment) with antennas and a receiver. The receiver receives signals from a transmitter, decodes them, and then determines and provides beamforming vectors for a subset of the subcarriers and interpolation parameters to the transmitter. These interpolation parameters are specifically designed for the transmitter to use to derive the beamforming vectors for the subcarriers not included in the subset. The receiver achieves this by subsampling the subcarriers, selecting a portion, and generating the interpolation parameters from the evaluated beamforming vectors for that selected subset.
• Claim 25 (Communication Apparatus - Receiver Side, Precoding): This claim describes a receiver apparatus that receives signals via OFDM on multiple subcarriers. It decodes these signals and then provides precoding vectors for some of the subcarriers and interpolation parameters to the transmitter. These parameters enable the transmitter to derive precoding vectors for the other subcarriers through interpolation. Crucially, the interpolation information provided by the receiver includes phase values.
• Claim 28 (Communication Apparatus - Transmitter Side, Precoding): This claim describes a transmitter apparatus with antennas that uses OFDM to send signals on multiple subcarriers. It includes a "precode matrix reconstruct unit" that generates precoding matrices based on channel information from the receiver. This channel information specifically contains precoding vectors for a subset of subcarriers and interpolation parameters. The unit then derives the precoding vectors for the subcarriers not in the subset by interpolating the provided subset precoding vectors, and this interpolation is based on the interpolation parameters. The receiver, in turn, is responsible for subsampling, selecting the subset, evaluating the precoding vectors for that subset, and generating the interpolation parameters.
• Claim 40 (Method - Transmitter Side): This claim describes a method for a transmitter to send signals. The method involves receiving limited feedback from a receiver, which includes beamforming vectors for a subset of subcarriers and interpolation information. The transmitter then derives beamforming vectors for the subcarriers not in the subset by interpolating the received subset beamforming vectors using the interpolation parameters. Finally, it provides output signals based on the input signals and these derived beamforming vectors, with the interpolation specifically using phase values from the feedback.
• Claim 41 (Method - Receiver Side): This claim describes a method for a receiver to receive signals. It involves receiving signals from a transmitter, decoding them, and then generating beamforming vectors for a subset of subcarriers and interpolation parameters. These are then provided to the transmitter, enabling it to derive beamforming vectors for other subcarriers. The key here is that the interpolation parameters include phase values.
• Claim 42 (Method - Transmitter Side, Precoding): This claim describes a method for a transmitter to send signals. It involves receiving limited feedback from a receiver, which includes interpolation information and precoding vectors for a subset of subcarriers. The transmitter then derives precoding vectors for the subcarriers not in the subset by interpolating the provided subset precoding vectors using the interpolation parameters. Finally, it provides output signals based on input signals and these derived precoding vectors. The limited feedback information also includes phase values.
• Claim 43 (Method - Receiver Side, Precoding): This claim describes a method for a receiver to receive signals. It involves receiving signals from a transmitter, decoding them, and then generating precoding vectors for a subset of subcarriers and interpolation parameters. These are then provided to the transmitter, enabling it to derive precoding vectors for other subcarriers. The interpolation parameters include phase values.

USPTO and CAFC 2026 Docket Search:

A search of USPTO and CAFC dockets for patent number US7676007 reveals the following:

USPTO Status:

• The patent US7676007B1 is Active and is set to expire on 2028-08-29. This information is directly from the Google Patents record, which sources its legal status from the USPTO.
• The current assignee is Integral Wireless Technologies LLC.

CAFC 2026 Dockets:

• A review of the CAFC 2026 scheduled cases, specifically for May 2026, did not show any direct listings for patent number 7676007.
• The CAFC website provides general case information and resources, but a direct search for specific patent numbers in their dockets requires navigating their search functionalities. No specific litigation related to 7676007 was found in the provided CAFC search results for 2026.

Therefore, as of April 26, 2026, the patent US7676007B1 is active and assigned to Integral Wireless Technologies LLC, with no specific CAFC 2026 docket entries found in the provided search results directly naming this patent number.

As a patent attorney, I have conducted a search for litigation involving US Patent 7676007.

Based on the available information from the Google Patents record and general search results, there are no specific litigation cases identified with detailed outcomes or current statuses readily available for US Patent 7676007 as of April 26, 2026. The Google Patents record indicates "Family has litigation" and lists several US cases filed in various district courts (Texas Western, Texas Eastern, Florida Southern), but these entries only provide links to Unified Patents or Darts-ip records and do not detail specific plaintiffs, defendants, case numbers, filing dates, or outcomes directly within the patent record itself. To obtain this level of detail would require access to paid databases like PACER.

Therefore, while there is an indication of litigation activity related to the patent family, specific details for US Patent 7676007 were not found in the public search results that could be definitively linked to specific plaintiffs, defendants, case numbers, filing dates, and outcomes.

Proceedings overview

As of May 25, 2026, there are no AIA trial proceedings (Inter Partes Reviews, Post-Grant Reviews, or Covered Business Method reviews) on file for US Patent 7676007 according to the USPTO Open Data Portal API. A comprehensive web search also yielded no public records of such proceedings for this patent. This indicates that the patent, while subject to noted litigation in district courts, has not yet faced validity challenges before the Patent Trial and Appeal Board.

Recommended next steps

Since no PTAB activity currently exists for US Patent 7676007, the following steps are recommended:

• For a potential defendant: The absence of PTAB activity means that all claims of US7676007 are currently untested in an AIA trial. If facing assertion, a defendant has the full range of prior art and statutory grounds (including §§ 102, 103, and 112) available for a potential IPR or PGR challenge, subject to the statutory time bars (e.g., one year from service of a complaint for IPR). This represents a significant opportunity to challenge the patent's validity before the PTAB without the estoppel constraints that would arise from prior proceedings.
• Monitor for future filings: It is advisable to set up alerts to monitor for any newly filed IPR, PGR, or CBM petitions against US7676007. As the patent remains active until 2028-08-29, and given its history of district court litigation, future PTAB challenges remain possible.

Inventors

• Jihoon Choi: Unspecified employer at the time of filing; likely a researcher or student at a university given the initial assignment to The University of Texas System.
• Robert W. Heath, Jr.: Unspecified employer at the time of filing; likely a researcher or faculty member at The University of Texas System.

Original assignee

The entity named on the issued patent is BOARD OF REGENTS, THE UNIVERSITY OF TEXAS SYSTEM.

The University of Texas System is a public university system primarily focused on education and research, not typically involved in shipping products embodying telecommunications claims in a commercial sense. Their primary line of business is higher education and academic research.

Their current status is operating.

Assignment timeline

Based on the legal events listed in the Google Patents record for US7676007B1:

• 2005-11-23 (executed) / recorded (date not specified in provided text) — Reel N/A
  • Conveyance: Assignment of Assignors Interest
  • Assignor: Robert W. Heath, Jr. and Jihoon Choi (Inventors)
  • Assignee: BOARD OF REGENTS, THE UNIVERSITY OF TEXAS SYSTEM
  • Correspondent: Not specified in provided text.
  • Context: Transfer of inventor rights to a university system.
• 2008-05-09 (executed) / recorded (date not specified in provided text) — Reel N/A
  • Conveyance: Assignment of Assignors Interest
  • Assignor: THE BOARD OF REGENTS, THE UNIVERSITY OF TEXAS SYSTEM
  • Assignee: INTELLECTUAL VENTURES HOLDING 40 LLC
  • Correspondent: Not specified in provided text.
  • Context: Transfer of patent rights from a university system to a patent monetization entity.
• 2024-10-09 (executed) / recorded (date not specified in provided text) — Reel 16812/0438
  • Conveyance: Corrective Assignment
  • Assignor: Robert W. Heath, Jr. and Jihoon Choi (Inventors)
  • Assignee: THE BOARD OF REGENTS, THE UNIVERSITY OF TEXAS SYSTEM
  • Correspondent: Not specified in provided text.
  • Context: Corrective assignment to address a previous inventor execution date error.
• 2024-10-10 (executed) / recorded (date not specified in provided text) — Reel N/A
  • Conveyance: Assignment of Assignors Interest
  • Assignor: INTELLECTUAL VENTURES HOLDING 40 LLC
  • Assignee: INTELLECTUAL VENTURES ASSETS 199 LLC
  • Correspondent: Not specified in provided text.
  • Context: Internal transfer between Intellectual Ventures entities.
• 2024-10-16 (executed) / recorded (date not specified in provided text) — Reel N/A
  • Conveyance: Assignment of Assignors Interest
  • Assignor: INTELLECTUAL VENTURES ASSETS 199 LLC
  • Assignee: INTEGRAL WIRELESS TECHNOLOGIES LLC
  • Correspondent: Not specified in provided text.
  • Context: Transfer of patent rights from Intellectual Ventures to another entity.

Timeline diagram

timeline
    title Ownership of US 7676007
    2005 : Filed by Individual inventors
         : Assigned to UT System
    2008 : Assigned to Intellectual Ventures Holding 40 LLC
    2010 : Patent granted
    2024 : Corrective assignment to UT System
         : Assigned to Intellectual Ventures Assets 199 LLC
         : Assigned to Integral Wireless Technologies LLC

NPE / troll-pattern signals

1. Shell-entity transfer — Present.

   • 2008-05-09 assignment from THE BOARD OF REGENTS, THE UNIVERSITY OF TEXAS SYSTEM to INTELLECTUAL VENTURES HOLDING 40 LLC. Intellectual Ventures is a known patent monetization entity, and "Holding" in the name suggests a non-operating entity.
   • 2024-10-10 assignment from INTELLECTUAL VENTURES HOLDING 40 LLC to INTELLECTUAL VENTURES ASSETS 199 LLC. This is an internal transfer within a known NPE.
   • 2024-10-16 assignment from INTELLECTUAL VENTURES ASSETS 199 LLC to INTEGRAL WIRELESS TECHNOLOGIES LLC. The current assignee, Integral Wireless Technologies LLC, has a name consistent with a licensing-focused entity, and given the chain, it's highly likely to be a shell entity for patent assertion.

2. Known asserter in the chain — Present.

   • 2008-05-09 assignment to INTELLECTUAL VENTURES HOLDING 40 LLC. Intellectual Ventures is explicitly listed as a known asserter.
   • 2024-10-10 assignment to INTELLECTUAL VENTURES ASSETS 199 LLC, another Intellectual Ventures entity.

3. Repeat correspondent across the chain — Unclear. The provided Google Patents data does not include correspondent information for most assignments, except for the reel/frame number of one corrective assignment. Therefore, recurrence cannot be determined.

4. Cascading transfers — Present.

   • There are three assignments occurring in quick succession in 2024:
     • 2024-10-09 (Corrective Assignment to UT System)
     • 2024-10-10 (IV Holding 40 LLC to IV Assets 199 LLC)
     • 2024-10-16 (IV Assets 199 LLC to Integral Wireless Technologies LLC)
       These three events within a week suggest a deliberate restructuring or transfer leading up to potential assertion, especially given the involvement of Intellectual Ventures.

5. Pre-litigation transfer — Unclear. While the Google Patents record indicates "Family has litigation" and lists several US cases filed in 2025 and 2026, the exact filing dates of these lawsuits are after the 2024 assignments. Without precise lawsuit filing dates directly linked to this patent, it's hard to definitively say if the 2024 transfers were within 6 months before the first suit specifically naming US7676007. However, the proximity in time (2024 assignments, 2025/2026 lawsuits) is suggestive.

6. Bankruptcy fire-sale — Not present. The original assignee (UT System) did not file for bankruptcy. The transfer from UT System to Intellectual Ventures was an assignment, not explicitly part of a bankruptcy proceeding.

7. Privateering — Unclear. While Intellectual Ventures is known for privateering, the context of the transfer from a university to IV, and then to Integral Wireless Technologies, does not explicitly indicate an operating company initiating assertion against competitors.

8. Defensive aggregator (anti-NPE) — Not present. The chain does not terminate at any known defensive aggregators like RPX, AST, LOT Network, Unified Patents, or Open Invention Network.

Verdict

NPE — high confidence

This verdict is based on the presence of multiple strong signals. The patent was assigned to Intellectual Ventures Holding 40 LLC on 2008-05-09, a well-known patent assertion entity. This was followed by a series of cascading transfers within Intellectual Ventures entities, culminating in its assignment to Integral Wireless Technologies LLC on 2024-10-16, a company whose name and position in the chain strongly suggest a licensing-only operation. The rapid succession of assignments in October 2024 further indicates a structured approach to patent monetization. Refer to USPTO Assignment Center search for US7676007 for verification.

To identify the most relevant prior art for US Patent 7676007, I will examine the "Cited By" section of the patent on Google Patents, as this generally includes references considered by the patent examiner. Prior art is information publicly available before a patent's effective filing date that could impact its patentability.

Upon reviewing US Patent 7676007, the "Cited By" section lists several publications and patents. It is crucial to distinguish between "References Cited" (prior art identified during prosecution by the applicant or examiner) and "Cited By" (later patents that cite this patent). For a prior art analysis, we focus on the "References Cited" by US7676007.

The full patent text explicitly incorporates several references by reference. These typically represent prior art that the inventors themselves or the examiner deemed relevant. I will focus on these directly cited references first, as they are explicitly acknowledged within the patent's detailed description.

Here are the most relevant prior art references explicitly mentioned and incorporated by reference within US7676007, along with an analysis of their potential anticipation:

References related to Codebooks for Beamforming (cited in "MIMO-OFDM Systems with Limited Feedback" and "Interpolation of Beamforming Vectors with Quantization" sections):

• A. Narula, M. J. Lopez, M. D. Trott, and G. W. Wornell, “Efficient use of side information in multiple-antenna data transmission over fading channels,” IEEE J. Select. Areas Commun., vol. 16, no. 8, pp. 1423-1436, Oct. 1998.
  • Publication Date: October 1998
  • Brief Description: This paper discusses the efficient use of side information in multiple-antenna data transmission over fading channels, likely involving the use of codebooks for limited feedback in narrowband MIMO systems.
  • Potential Anticipation (35 U.S.C. § 102): This reference potentially anticipates aspects of claims related to using a codebook for quantizing beamforming vectors in a limited feedback scenario, as generally described in independent claims 1, 19, 25, 28, 40, 41, 42, and 43 where a codebook is mentioned or implied for quantization. Specifically, it could anticipate the concept of quantizing beamforming vectors using a codebook, as mentioned in claim 12 and the general description of limited feedback.
• D. J. Love and R. W. Heath, Jr., “Equal gain transmission in multi-input multi-output wireless systems,” IEEE Trans. Commun., vol. 51, no. 7, pp. 1102-1110, July 2003.
  • Publication Date: July 2003
  • Brief Description: This paper likely explores "equal gain transmission" in MIMO wireless systems, which is a beamforming technique. It could involve the design or use of beamforming vectors in a feedback system.
  • Potential Anticipation (35 U.S.C. § 102): This reference might anticipate beamforming techniques for MIMO systems, particularly those focused on maximizing gain. It could potentially anticipate aspects of claims 1, 3, 19, 25, 28, 40, 41, 42, and 43 regarding the general concept of beamforming or precoding, especially if "equal gain transmission" is implemented using beamforming vectors similar to those in the patent.
• D. J. Love, R. W. Heath, Jr., and T. Strohmer, “Grassmannian beamforming for multiple-input multiple-output wireless systems,” IEEE Trans. Inform. Theory, vol. 49, no. 10, pp. 2735-2747, Oct. 2003.
  • Publication Date: October 2003
  • Brief Description: This paper focuses on "Grassmannian beamforming," a specific method for designing beamforming vectors in MIMO systems, often in conjunction with codebooks for limited feedback.
  • Potential Anticipation (35 U.S.C. § 102): This reference directly anticipates the use of Grassmannian precoding, as mentioned in the detailed description ("In another embodiment, the precoding is Grassmannian precoding."). It could anticipate aspects of claims 1, 5, 25, 28, 38, 40, 42, and 43, particularly regarding the use of specific codebook designs or precoding strategies for MIMO systems.
• K. K. Mukkavilli, A. Sabharwal, E. Erkip, and B. Aazhang, “On beamforming with finite rate feedback in multiple-antenna systems,” IEEE Trans. Inform. Theory, vol. 49, no. 10, pp. 2562-2579, Oct. 2003.
  • Publication Date: October 2003
  • Brief Description: This paper addresses beamforming with finite rate feedback in multiple-antenna systems, directly relevant to the limited feedback aspect of US7676007.
  • Potential Anticipation (35 U.S.C. § 102): This reference is highly relevant as it discusses finite rate feedback for beamforming. It could anticipate the general concept of limited feedback for beamforming vectors in claims 1, 19, 40, and 41, and potentially the use of quantization with a codebook (claims 12, 34) to reduce feedback information.

References related to Spherical Interpolation (cited in "One Embodiment of the Spherical Interpolator 305" section):

• S. R. Buss and J. P. Fillmore, “Spherical averages and applications to spherical splines and interpolation,” ACM Trans. Graphics, vol. 20, no. 2, pp. 95-126, Apr. 2001.
  • Publication Date: April 2001
  • Brief Description: This paper discusses spherical averages and their applications to spherical splines and interpolation, providing foundational concepts for interpolation on a sphere.
  • Potential Anticipation (35 U.S.C. § 102): This reference anticipates the general concept of spherical interpolation, as mentioned in claims 15 and 38 ("interpolate on a Grassmann manifold," which can be a type of spherical interpolation). However, the patent US7676007 distinguishes itself by introducing a phase rotation parameter for distortion reduction, which is not explicitly covered by this general reference on spherical interpolation.
• K. Shoemake, “Animating rotation with quaternion curves,” in Proc. SIGGRAPH'85, ACM, San Francisco, July 1985, vol. 19, pp. 245-254.
  • Publication Date: July 1985
  • Brief Description: This paper focuses on animating rotations using quaternion curves, a mathematical technique for interpolating rotations on a sphere.
  • Potential Anticipation (35 U.S.C. § 102): Similar to Buss and Fillmore, this reference provides a method of spherical interpolation (using quaternions). It could anticipate the general concept of spherical interpolation for beamforming vectors (claims 1, 4, 15, 38, 40, 42). Again, the specific innovation of phase rotation in US7676007 would likely differentiate it.
• G. S. Watson, Statistics on spheres, Wiley, New York, 1983.
  • Publication Date: 1983
  • Brief Description: This book covers statistical methods for data on spheres, which would include interpolation and averaging techniques on spherical manifolds.
  • Potential Anticipation (35 U.S.C. § 102): This book anticipates foundational statistical and interpolation techniques on spheres, broadly covering the mathematical basis for spherical interpolators as used in US7676007. Similar to the other spherical interpolation references, the specific application of phase rotation for distortion reduction in beamforming for MIMO-OFDM is the distinguishing feature of the granted patent.

References related to MRT/MRC (cited in "MIMO-OFDM Systems with Limited Feedback" section):

• P. A. Dighe, R. K. Mallik, and S. S. Jamuar, “Analysis of transmit-receive diversity in Rayleigh fading,” IEEE Trans. Commun., vol. 51, no. 4, pp. 694-703, Apr. 2003.
  • Publication Date: April 2003
  • Brief Description: This paper analyzes transmit-receive diversity in Rayleigh fading channels, covering concepts like Maximum Ratio Transmission (MRT) and Maximum Ratio Combining (MRC).
  • Potential Anticipation (35 U.S.C. § 102): This reference anticipates the underlying principles of MRT and MRC, which are fundamental to the beamforming and combining strategies in US7676007. It could anticipate aspects of the system where MRT and MRC are used for designing w(k) and z(k), as described in claims 1, 3, 19, 40, and 41, particularly where the receiver uses MRC (claim 19).
• C.-H. Tse, K.-W. Yip, and T.-S. Ng, “Performance tradeoffs between maximum ratio transmission and switched-transmit diversity,” in Proc. IEEE PIMRC, Sept. 2000, vol. 2, pp. 1485-1489.
  • Publication Date: September 2000
  • Brief Description: This paper compares the performance tradeoffs between MRT and switched-transmit diversity.
  • Potential Anticipation (35 U.S.C. § 102): Similar to the Dighe et al. reference, this work anticipates the core concepts of MRT in communication systems, which forms the basis for transmit beamforming in US7676007. It could anticipate the general use of MRT for transmit beamforming in claims 1, 3, 19, 40, and 41.

It is important to note that while these references describe elements or concepts used in US7676007, the patent often claims a novel combination or modification of these elements, specifically the inclusion of interpolation parameters (phase values) for distortion reduction in beamforming or precoding vectors in a MIMO-OFDM system with partial feedback. Therefore, while individual components might be anticipated, the specific combination and the method of determining and using the phase rotation for interpolation are key to the patent's inventiveness.

Obviousness Analysis of US Patent 7676007 Under 35 U.S.C. § 103

This analysis identifies combinations of prior art references that would render the claims of US Patent 7676007 obvious to a person having ordinary skill in the art (POSITA) at the time of the invention (priority date July 21, 2004). The core innovation claimed by US7676007 lies in addressing the phase ambiguity inherent in optimal beamforming vectors (or the non-uniqueness of precoding matrices) when performing interpolation for limited feedback MIMO-OFDM systems.

General Motivation for Combination

A POSITA in wireless communications would be continually motivated to improve spectral efficiency and reliability while reducing feedback overhead in MIMO-OFDM systems. Given the known correlation of channel conditions across adjacent subcarriers in OFDM, using subsampling and interpolation to reduce feedback for channel state information (CSI) (such as beamforming vectors or precoding matrices) would be a natural and expected engineering approach. The challenge addressed by the patent is the effective interpolation of these vectors/matrices despite their inherent phase invariance or unitary non-uniqueness. A POSITA would recognize this challenge and seek methods to enhance interpolation accuracy by addressing this ambiguity.

Combination of Prior Art for Obviousness

The obviousness of US7676007 stems from combining the following known concepts and the explicit problem identification within the patent itself:

Combination 1: For Beamforming Claims (e.g., Claims 1, 19, 40, 41)

1. MIMO-OFDM Systems with Transmit Beamforming and Full Feedback: It was well-established in the prior art to utilize Multiple-Input Multiple-Output (MIMO) systems with Orthogonal Frequency Division Multiplexing (OFDM) to exploit diversity and array gain over frequency-selective channels. In such systems, transmit beamforming with receive combining was a known technique to maximize Signal-to-Noise Ratio (SNR) or capacity. For non-reciprocal channels (e.g., FDD systems), the receiver would estimate the channel and feed back optimal beamforming vectors for each OFDM subcarrier to the transmitter. [cite: Source: Patent Detailed Description, "Background" and "MIMO-OFDM Systems with Limited Feedback" sections] References such as Dighe (P. A. Dighe et al., 2003) and Tse (C.-H. Tse et al., 2000), cited in the patent, describe aspects of MRT/MRC which forms the basis for optimal beamforming. [cite: Source: Patent Detailed Description, "MIMO-OFDM Systems with Limited Feedback"]
2. Reducing Feedback via Subsampling and Interpolation: The significant feedback overhead associated with sending beamforming vectors for all subcarriers in MIMO-OFDM was a recognized problem. A POSITA would be motivated to reduce this overhead. Given the inherent correlation between adjacent OFDM subchannels (explicitly acknowledged in the patent as the basis for feedback reduction: "the neighboring subchannels of OFDM is substantially correlated"), it would be an obvious solution to subsample the subcarriers, send feedback only for a subset of them, and then use interpolation at the transmitter to estimate the beamforming vectors for the un-fed-back subcarriers. [cite: Source: Patent Detailed Description, "Further Description"]
3. Spherical Interpolation for Unit Vectors: Beamforming vectors are typically unit-norm complex vectors. Methods for interpolating unit vectors on a sphere, known as spherical interpolation, were established in the art. The patent itself cites references like Buss (S. R. Buss and J. P. Fillmore, 2001), Shoemake (K. Shoemake, 1985), and Watson (G. S. Watson, 1983) for spherical interpolators. [cite: Source: Patent Detailed Description, "One Embodiment of the Spherical Interpolator 305"] A POSITA would naturally consider applying these techniques to interpolate beamforming vectors.
4. Addressing Phase Invariance in Beamforming Vectors: The patent explicitly identifies a critical challenge when applying conventional spherical interpolators to beamforming vectors: "when w(k) is the optimal beamforming vector maximizing the effective channel gain, e jΦ w(k) also maximizes the effective channel gain. In other words, the optimal beamforming vector is not a unique point but a line on the unit sphere." [cite: Source: Patent Detailed Description, "One Embodiment of the Spherical Interpolator 305"] A POSITA, recognizing this fundamental property of beamforming vectors and the limitations it imposes on direct interpolation (e.g., leading to arbitrary interpolation paths and distortion if phases are not aligned), would be motivated to introduce a phase alignment mechanism. It would be obvious to incorporate a phase rotation parameter (θl) to "remove the distortion caused by the arbitrary phase rotation of the optimal beamforming vectors" [cite: Source: Patent Detailed Description, "One Embodiment of the Spherical Interpolator 305"] prior to or as part of the interpolation process. Optimizing this phase parameter at the receiver to maximize standard performance metrics, such as minimum effective channel gain or capacity (as described by equations (5), (6), (12), and (13) in the patent), would be a routine optimization task for a skilled engineer. Feeding back these phase values as "interpolation information" along with the subsampled beamforming vectors would be a logical step to enable the transmitter to perform the improved interpolation.

Therefore, the claimed features of using phase values as interpolation information for beamforming vectors to reduce distortion during interpolation, particularly in a spherical interpolation context for MIMO-OFDM with partial feedback, would be obvious.

Combination 2: For Precoding Claims (e.g., Claims 25, 28, 42, 43)

1. MIMO-OFDM Systems with Precoding and Full Feedback: Similar to beamforming, MIMO-OFDM systems employing linear precoding for spatial multiplexing were known. Precoding matrices are chosen based on channel information to improve spectral efficiency and robustness. In non-reciprocal channels, feedback of precoding matrices or related CSI from the receiver to the transmitter was necessary. [cite: Source: Patent Detailed Description, "Overall System Summary" and "FIG. 6 is a block diagram illustrating a multiple-input multiple-output—orthogonal frequency division multiplex (MIMO-OFDM) communication system 600 with precoding."]
2. Reducing Feedback via Subsampling and Interpolation for Precoding: Just as with beamforming, the overhead of feeding back precoding matrices for all subcarriers would motivate a POSITA to reduce feedback. Exploiting the correlation of precoding matrices on adjacent subcarriers by sending a subset and interpolating at the transmitter would be an obvious extension of the feedback reduction techniques known for beamforming. [cite: Source: Patent Detailed Description, "Overall System Summary"]
3. Addressing Non-Uniqueness/Derotation in Precoding Matrices: The patent explicitly points out that optimal precoding matrices exhibit a "performance invariant to the right multiplication of the orthogonal matrix" (e.g., MSE(W(k), H(k))=MSE(W(k)Q, H(k))). [cite: Source: Patent Detailed Description, "The system 600 has a tone model"] This is directly analogous to the phase invariance issue for beamforming vectors. A POSITA would recognize that such non-uniqueness would cause similar interpolation problems to phase ambiguity. Therefore, it would be obvious to introduce a unitary derotation matrix (Q) to align the precoding matrices (as described in the patent's equation (22) for "derotated interpolation" and the concept of "a unitary derotation matrix Q is associated with precoder interpolation" [cite: Source: Patent Detailed Description, "Overall System Summary"]) before or during interpolation to ensure consistent and accurate reconstruction. Optimizing this derotation matrix Q from a finite codebook (as per equations (23) and (24) in the patent) based on performance measures like MMSE or capacity maximization would be a routine optimization for a skilled artisan, and then feeding this Q as part of the limited feedback is a logical implementation.

Therefore, the claimed features of using derotation (via matrix multiplication or unitary matrices) as interpolation information for precoding vectors/matrices to reduce distortion during interpolation, particularly in a MIMO-OFDM system with partial feedback, would be obvious.

In both beamforming and precoding scenarios, the explicit recognition of the phase/unitary ambiguity problem by the patent itself, combined with the known techniques for feedback reduction, interpolation, and optimization of wireless system parameters, would have led a POSITA to the claimed solution. The various mathematical approaches to finding the optimal phase or derotation matrix (e.g., grid search or closed-form solutions as detailed in the patent) are standard optimization methodologies.

To accurately detail any patent term adjustments (PTA), patent term extensions (PTE), continuation applications, divisional applications, related family members, and the projected expiration date for US Patent 7676007, it's necessary to access the USPTO's Patent Center directly. The Google Patents record provides some, but not all, of this information.

Based on the available information from the Google Patents record and general USPTO guidelines:

US Patent 7676007 Details:

• Application Number: US11/188,233
• Filing Date: 2005-07-21
• Publication Date: 2010-03-09
• Adjusted Expiration Date: 2028-08-29

Patent Term Adjustments (PTA):
Patent Term Adjustment (PTA) can extend the term of a U.S. patent to compensate for delays caused by the USPTO during the examination process. The Google Patents record indicates an "Adjusted expiration" date of 2028-08-29. This suggests that PTA has been applied to the patent. Without direct access to the USPTO Patent Center's "Patent Term Adjustment" section for application number US11/188,233, the specific breakdown of A, B, and C delays, applicant delays, or the total number of adjusted days cannot be determined. PTA is typically calculated by adding days for USPTO delays and subtracting days for applicant delays.

Patent Term Extensions (PTE):
Patent Term Extensions (PTEs) are mechanisms to extend a patent's duration beyond its original expiration date, primarily granted to compensate for time lost during regulatory approval processes for products like human drugs, medical devices, or food additives. There is no indication in the Google Patents record or the provided search results that US Patent 7676007 is related to a product requiring regulatory approval (such as a pharmaceutical or medical device). Therefore, it is highly unlikely to have received any PTE.

Continuation Applications, Divisional Applications, and Related Family Members:
The Google Patents record lists the following priority application:

• US11/188,233 (which is the application number for US7676007B1 itself)
  And claims priority from:
• U.S. Provisional Patent Application Ser. No. 60/589,713, filed on July 21, 2004.

A "continuation" application is filed before the parent application is patented, abandoned, or its proceedings are terminated, and it discloses the same invention without new subject matter. A "divisional" application arises when the USPTO determines that a single application contains two or more independent and distinct inventions. A "continuation-in-part" (CIP) incorporates all or part of the parent disclosure and adds new subject matter.

Based on the provided information, US Patent 7676007 (Application Number US11/188,233) claims priority to a provisional application. A provisional application establishes an early filing date but is not a "continuing application" in the sense of being a continuation, divisional, or continuation-in-part of a prior non-provisional application. Therefore, as of the current analysis, there is no evidence of continuation or divisional applications for US7676007, nor other related non-provisional family members stemming from US11/188,233. The term "Family has litigation" on Google Patents refers to the overall patent family, which may include other patents, but without explicit listing in the "Applications Claiming Priority" or "Family Applications" sections, specific details of those other family members are not provided.

Projected Expiration Date:
The adjusted expiration date listed in the Google Patents record for US7676007B1 is 2028-08-29. This date already accounts for any Patent Term Adjustment (PTA). Assuming no further events (like a terminal disclaimer from a later-filed patent, which could shorten the term, or an unlikely PTE), this is the current projected expiration date. The standard patent term for applications filed on or after June 8, 1995, is 20 years from the earliest filing date (or earliest claimed priority date), plus any PTA. In this case, the earliest priority date is July 21, 2004 (from the provisional application), so 20 years from that would be July 21, 2024. The adjusted expiration date of August 29, 2028, indicates a PTA of approximately 4 years and 1 month.