PU2RC: Wikis


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Per-User Unitary Rate Control (PU2RC) is the advanced multi-user MIMO technique which utilizes the concept of both pre-coding matrices and scheduling to enhance the system performance of multiple antenna wireless networks.

  • Background technologies
A single-user MIMO is initially developed to improve the spectral efficiency of point-to-point wireless transmission link. A multi-user MIMO was developed for cellular systems where the base station simultaneously communicates with multiple users.
  • Principle
The concept of Per-User Unitary Rate Control (PU2RC) was proposed in US Patent No. 7,324,480, Mobile communication apparatus and method including base station and mobile station having multi-antenna by James S. Kim, Kwangbok Lee, Kiho Kim and Changsoon Park.

Recently, PU2RC has been adopted to the IEEE 802.16m system description documentation (SDD) and the concept of this scheme was included in 3GPP LTE standard.



Per-User Unitary Rate Control (PU2RC) is the first practical multi-user MIMO scheme. In this scheme different data may simultaneously be transmitted to multiple users from the base station.

Users to be served are selected from the set of service-requesting users by the base station using the information provided by users.

Data transmitted to mobile users are multiplied by a pre-coding matrix selected from the set of predefined matrices before transmission. The selection of a pre-coding matrix is made based on the information provided by users.

The selection of users and a pre-coding matrix using the information provided by mobiles enables the utilization of multi-user diversity and reduces feedback overhead from users to the base station.

Pre-coding matrices used in this scheme is unitary. The use of unitary pre-coding matrices facilitates the estimation of interference from other users’ data to the unintended user.

Mathematical description

Throughput performance of PU2RC over the single-user & no scheduling scheme

The operation is described mathematically below for the transmitter and receiver side.


Transmitter Side

The transmitter antenna array has Nt elements. The transmit signal vector is modeled as follows:

 \mathbf{x} = \sum_{i=1}^K \mathbf{w}_i P_i s_i

where \mathbf{x} is the N_t \times 1 vector of transmitted symbols and \mathbf{w}_i is the N_t \times 1 linear precoding vector. PU2RC generates {\mathbf{w}_i} based on the received finite channel status information, which is delivered to the base station by the user equipment (UE) using a coded look-up table index.

Receiver Side

Every receiver has a receive antenna array with Nr elements. The receive signal vector at user k (=1,2,\ldots,K) is modeled as follows:

\mathbf{y}_k = \mathbf{H}_k\mathbf{x}+\mathbf{n}_k

where \mathbf{y}_k and \mathbf{n}_k are the N_r \times 1 received symbol and noise, respectively, and \mathbf{H}_k is the N_t \times N_r matrix with the channel coefficients.

Throughput performance

The figure illustrates the throughput advantage of PU2RC over the conventional single-user and no scheduling scheme, assuming that the codebook size is one, i.e., (G = 1). For larger codebook sizes the performance can be better than the performance of the unit-size codebook. Because of codebook-based multi-user scheduling, PU2RC outperforms the conventional single-user and no scheduling scheme when the number of users is larger than one. Note that the performance plotted in the figure for the two systems were obtained assuming linear receiver.

PU2RC Source and Background Materials

Source Materials

Enhanced Methods

  • Multiuser MIMO Scheme for Enhanced 3GPP HSDPA
  • Kim, J.S., Hojin Kim, Yongxing Zhou, Jianjun Li, ``Multi-Mode Multi-User MIMO System with Finite Rate Feedback, IEEE Wireless Communication Systems, 2006. ISWCS '06. 3rd International Symposium on, 6-8 Sept. 2006

Background References

  • R. W. Heath, Jr., M. Airy, and A. J. Paulraj, "Multiuser Diversity for MIMO Wireless Systems with Linear Receivers," Proc. of the IEEE Asilomar Conf. on Signals, Systems, and Computers, pp. 1194 -1199, vol.2, Pacific Grove, California, Nov. 4 - 7, 2001.
  • A. Kogiantis and L. Ozarow, "Downlink best-effort packet data with multiple antennas," ICC’03, Volume 1, 11-15 May 2003 Page(s):715 - 719.
  • K.K. Wong, R.D. Murch and K.B. Letaief, "Performance Enhancement of Multiuser MIMO Wireless Communication Systems," IEEE Transactions on Communications, Vol 50 No 12 , Dec. 2002, pp 1960 –1970
  • Further benefits of the revised definition of CQI for TxAA, 3GPP TSG-R1-030130, San Diego, Jan. 7-10, 2003.

PU2RC Citations


[1] Borko Furht, Syed A. Ahson, Long Term Evolution: 3GPP LTE Radio and Cellular Technology

  • Page 169: In 3GPP LTE MU-MIMO is still a topic in discussion. Per-user unitary and rate control (PU2RC) is a typical proposed MU-MIMO scheme.
  • Page 170: In fact, because a single user's multiple code words can also be scheduled even in the same time-frequency resource, PU2RC realizes SDM

[2] George V. Tsoulos, MIMO system technology for wireless communications

  • Page 237, Per-User Unitary Rate Control (PU2RC). This algorithm is based on the singular value decomposition of the MIMO channels.

[3] Radio Network Planning and Optimisation for UMTS by Jaana Laiho, Achim Wacker, and Tomá Novosad (Hardcover - Feb 10, 2006)

  • Page 366: "... backward incompatibility with previous standard releases. Per-User Unitary Rate Control (PU2RC) is based on the singular value decomposition of MIMO .

[4] MIMO System Technology for Wireless Communications (Electrical Engineering and Applied Signal Processing) by George Tsoulos (Hardcover - Mar 28, 2006)

  • Page 237: "... I due to additional transmit antennas. Per-User Unitary Rate Control (PU2RC). This algorithm is based on the singular value decomposition of ..."

[5] Marcos Katz,Frank H. P. Fitzek, WiMAX Evolution: Emerging Technologies and Applications

  • Page 327, A similar design has also been developed in the industry and is called Per-User Unitary and Rate Control (PU2RC)

Journal and Conference Papers

[1] Jianhong Zheng, Zongzhi Huang, Jianrong Wei, ""A Novel Multi-User MIMO Scheme in OFDM Systems," Circuits, Communications and Systems, Pacific-Asia Conference on, pp. 43-46, 2009 Pacific-Asia Conference on Circuits, Communications and Systems, 2009.

  • Page 4, [6] Samsung, SNU, “Downlink MIMO for EUTRA,” in 3GPP TSG-RAN WG1, 44 R1-060335, February 2006.

[2] D. J. Love, R. W. Heath, Jr., V. K. N. Lau, D. Gesbert, B. D. Rao, and M. Andrews, “An overview of limited feedback in wireless communication systems ,” IEEE J. Select. Areas Commun., vol. 26, no. 8, pp. 1341–1365, Oct. 2008

  • Page 21: [148] J. S. Kim, H. Kim, and K. B. Lee, “Limited feedback signaling for MIMO broadcast channels,” in Proc. IEEE Int. Workshop on Signal Proc. Adv. Wireless Commun., June 2005, pp. 855–859.
  • Page 21: [149] J. S. Kim, H. Kim, C. S. Park, and K. B. Lee, “Adaptive precoding for wireless MIMO broadcast channels with limited feedback,” IEICE Transactions, vol. 88-B, no. 11, pp. 4237–4245, Nov. 2005.

[3] M. Cho, Y. Kim, D. Hong, Feedback Reduction of Channel Quality Information for Multiuser MIMO Systems, pp. 798~803 (6 pages), UCI : G300-j12264717.v31n8Ap798

[4] Tae Hyun Kim, Robert W. Heath Jr., Sunghyun Choi, "Multiuser MIMO Downlink with Limited Feedback using Transmit-Beam Matching,", IEEE ICC2008

  • Page 5, [10] Samsung, SNU, Downlink MIMO for EUTRA, 3GPP TSG RAN WG1 44/R1-060335.

[5] M. Trivellato, F. Boccardi, and H. Huang, "Zero-Forcing vs Unitary Beamforming in Multiuser MIMO Systems with Limited Feedback," in Proc. PIMRC 2008, Cannes, France, Sept. 2008.

  • Page 6: [9] Samsung, SNU, “Downlink MIMO for EUTRA,” 3GPP TGS RAN WG1,R1-060335, Feb. 2006.

[6] K. Huang, J. G. Andrews, and Jr R. W. Heath, “Performance of Orthogonal Beamforming for SDMA with Limited Feedabck,” accepted for publication in IEEE Trans. Vehic. Tech., May 2008.

  • Page 22, [5] Samsung, SNU, “Downlink MIMO for EUTRA,” in 3GPP TSG RAN WG1#44/R1-060335.

[7] N. Ravindran, N. Jindal, and H. Huang, Beamforming with Finite Rate Feedback for LOS MIMO Downlink Channels, IEEE Globecom, Nov. 2007.

  • Page 5, [5] Samsung, SNU, “Downlink MIMO for EUTRA,” 3GPP TSG RAN WG1 #44, no. R1-060335, Feb. 2006.

[8] Kaibin Huang, MIMO Networking with Imperfect Channel State Information, Ph.D. Thesis, UTexas, Supervisor: Jafferey G. Andrews, May 2008

  • Page 224, [16] Samsung, SNU, "Downlink MIMO for EUTRA," in 3GPP TSG RAN WG1 #44/R1-060335, Feb. 2006.

[9] Love, D.J., Heath, R.W.' Lau, V.K.N. Gesbert, D., Rao, B.D., Andrews, M., An overview of limited feedback in wireless communication systems, JSAC 2008

[10] W Choi, A Forenza, JG Andrews, RW Heath Jr , "Opportunistic space-division multiple access with beam selection", IEEE Transactions on Communications, 2007

  • Page 16, [25] S. J. Kim, H. Kim, C. S. Park, and K. B. Lee, “Space-time technique for wireless multiuser MIMO systems with SIC receivers,” Proc. IEEE Int. Symp. on Pers., Indoor and Mobile Radio Comm., vol. 3, pp. 2013–2017, Sep. 2004.
  • Page 16, [26] S. J. Kim, H. Kim, M. Kountouris, A. Forenza, C. S. Park, and K. B. Lee, “Efficient feedback signaling using multi-channel selection diversity for multi-user MIMO systems,” Proc. of Wireless World Research Forum, Mar. 2005.
  • Page 16, [27] S. J. Kim, A. Forenza, M. Kountouris, H. Kim, C. S. Park, A. Pandharipande, and K. B. Lee, “On the performance of multiuser MIMO systems in beyond 3G: beamforming, feedback and scheduling,” Proc. of Wireless World Research Forum, Mar. 2005.

[11] Seong-Bo Shim, Sung Kyo Kang, and Yun Hee Kim°, Capacity Comparison of Multiuser MIMO-OFDM Transmission with Limited Feedback

[12] N. Ravindran, and N. Jindal, Multi-User Diversity vs. Accurate Channel State Information in MIMO Downlink Channels, Submitted to IEEE Trans. Communications, July 2009.], [http://www.ece.umn.edu/~nihar/mud_csi_code.html (Matlab Code)

  • Page 20, [15] J. Kim, H. Kim, C. Park, and K. Lee, “On the performance of multiuser MIMO systems in WCDMA/HSDPA: Beamforming, feedback and user diversity,” IEICE Trans. on Commun., vol. 89, no. 8, pp. 2161–2169, 2006.

[13] Bartosz Mielczarek and Witold A. Krzymien, “Vector Quantization of Channel Information in Linear Multi-User MIMO Systems”, 2006 IEEE 9th International Symposium on Spread Spectrum Techniques and Applications

[14] Mohammad Ali Khojastepour, Xiaodong Wang, and Mohammad Madihian, “Quantized Linear MIMO Precoding for Multiuser Downlink Systems”, CISS 2008

  • Page 306, J.S. Kim, H. Kim, and K.B. Lee, “Limited feedback signaling for MIMO broadcast channels,” in 2005 IEEE 6th Workshop on Signal Processing Advances in Wireless Communications, New York,USA, June 2005.

[15] Peilu Ding, Member, IEEE, David J. Love, Member, IEEE, and Michael D. Zoltowski, Fellow, IEEE, "Multiple Antenna Broadcast Channels With Shape Feedback and Limited Feedback", IEEE Transactions on Signal Processing, 2007, http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=04244670

  • Page 3427, [36] J. S. Kim, H. Kim, and K. B. Lee, “Limited feedback precoding for wireless MIMO broadcast channels,” in Proc. IST Mobile Wireless Commun. Summit, Jun. 2005.

[16] Peilu Ding, Love, D.J., Zoltowski, M.D.,WLC26-2: Limited Feedback in Multiple Antenna Broadcast Channels, Global Telecommunications Conference, 2006. GLOBECOM '06. IEEE

  • Page 5, [14] J. S. Kim, H. Kim, and K. B. Lee, “Limited feedback precoding for wireless MIMO broadcast channels,” in Proc. IST: Mobile and Wireless Commun. Summit, June 2005.

[17] H Chae, Y Kim, JH Yang, BC Ihm, DK Kim, "Multimode Random Beamforming for Multiuser Downlink MIMO System with Limited Feedback", Proc. IEEE Veh. Technol. Conf, 2008 - mnet.skku.ac.kr

  • Page 5, [5] J. Kim, H. Kim, C. S. Park, and K. B. Lee, “On the Performance of Multiuser MIMO Systems in WCDMA/HSDPA: Beamforming, Feedback and User Diversity”, IEICE Trans. Comm. Vol. E89-B, pp.2161 - 2169, Aug. 2006

Slide and Documentations

  1. Forschungszentrum Telekommunikation, Wien LVA 389.089, Lecture January 15, 2004., High Speed Downlink Packet Access (HSDPA)
  2. http://ettrends.etri.re.kr/PDFData/21-3_048_058.pdf
  3. http://onyx.yonsei.ac.kr/~tta2007/files/5_WiBro.pdf
  4. 802.11vht (Motorola), July 2007, Another resource to exploit: multi-user diversity
  5. Christoph Mecklenbräuker, MU-MIMO schemes in current standards for 3GPP Long Term Evolution, Wireless LAN, and WiMax, November 16, 2007.
  6. Douglas S. Chan, Technologies Delivering Multiuser Transmission for Next-Generation IEEE 802.11 Wireless Networks, November 5, 2007
  7. Lucent Technologies, “Link-level results for nonunitary precoding using zero-forcing in LOS channels,” 3GPP TSG-RAN WG1#46-bis, no. R1-062925, Oct. 2006.
  8. Smart Antennas, MIMO systems and Related Technologies, WWRF
  9. F. Boccardi (joint work with H. Huang) MIMO MULTIUSER schemes for downlink transmissions: theoretic bounds and practical techniques
  10. “Link-level results for nonunitary precoding using zero-forcing in LOS channels,” 3GPP TSG-RAN WG1#46-bis, no. R1-062925, Oct. 2006.
  11. M. Khojastepour, X. Wang, M. Madihian, Structured codebook and successive beamforming for multiple-antenna systems
  12. MU-MIMO Comparison(C80216m-08_406.doc), May 3, 2008,Intel

MU-MIMO Standard Contributions

The following documents are standard contributions about both PU2RC related and general MU-MIMO issues.

General MU-MIMO issues

  1. 3GPP, R1-072464, MU-MIMO for E-UTRA DL, Ericsson
  2. 3GPP, R1-072513, Details on MU-MIMO, Freescale Semiconductor
  3. 3GPP, R1-072514, Codebook design for MU-MIMO, Freescale Semiconductor
  4. 3GPP, R1-072515, Reference Signalling for MU-MIMO, Freescale Semiconductor

PU2RC related issues

  1. 3GPP TSG RAN WG1#31, R1-030354, Per unitary basis stream user and rate Control (PU2RC), 3GPP TSG-R1-030354, Tokyo, Fed 18-21, 2003. (See also R1-030130)
  2. 3GPP, TSG RAN WG1#44/R1-060335 “Downlink MIMO for EUTRA,” Samsung and SNU
  3. 3GPP, R1-072401, User Grouping Method for PU2RC Downlink MU-MIMO, Alcatel-Lucent

See also

Codebook and Signal Processing

  • Quantized Principal Component Selection Precoding for Limited Feedback Spatial Multiplexing, 2006 ICC
  • System level performance evaluation of spatial multiplexing with per common basis rate control, 2005-fall VTC
  • Multimode basis selection for spatial multiplexing with limited feedback, 2005 Electronics Letters

Wikipedia Articles

MU-MIMO papers

KNOL Article



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