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Ph.D. Level Courses

Multiuser MIMO and Spatial Resource Allocation


This course will teach the fundamentals of multiuser MIMO communications, with depth in system modeling, beamforming/precoding optimization, spatial channel correlation, spatial resource allocation, and tradeoffs between data rates, energy efficiency and hardware.


Associate Professor Emil Björnson, ISY/Communication Systems.


The course is open to students enrolled in a Ph.D. program at Linköping University/ISY. External participants are welcome upon request, but must attend 80% of the lectures and 100% of the homework sessions.

If you have interest to participate, please register by doing the following by February 8:

  • Send an email to the instructor
  • Mark your availability for the first lecture on a Doodle-link provided by the instructor.

The remaining schedule will be set during the first lecture.


Good knowledge of wireless and digital communications, information theory, linear algebra, matrix analysis, and probability theory. General mathematical maturity.

Course outline and organization (tentative)

  1. Principles for designing cellular networks with high spectral efficiency
    February 20, 2017, 10-12. Room: Algoritmen.
    (Reading: Section 1.1-1.3.4 in [R2])
  2. Basic modeling of multiuser MIMO systems and their performance
    February 28, 2017, 13-15. Room: Transformen.
    (Reading: Section 1, Section 4.7 in [R1])
  3. Rate region and problem classification
    March 10, 2017, 10-12. Room: Transformen.
    (Reading: Section 2.1 in [R1])
  4. Homework session 1
    March 13, 2017, 13-15. Room: Nollstället.
  5. Basic optimization theory and convex beamforming optimization
    March 23, 2017, 10-12. Room: Transformen.
    (Reading: Section 2.2 in [R1])
  6. Convex and Monotonic optimization for beamforming optimization
    March 28, 2017, 13-15. Room: Transformen.
    (Reading: Section 2.3 in [R1], Sections 1-3 in [R3])
  7. Parameterization of optimal beamforming and heuristic schemes
    March 29, 2017, 10-12. Room: Transformen.
    (Reading: Section 3 in [R1] and [R4])
  8. Homework session 2
    April 19, 2017, 10-12. Room: Nollstället.
  9. Distributed implementation of optimization, Introduction to Massive MIMO
    April 20, 2017, 13-15. Room: Transformen.
    (Reading: Section 4.2 in [R1], Section 1.3.5-1.4 in [R2])
  10. Massive MIMO for correlated fading channels: Channel estimation
    April 24, 2017, 13-15. Room: Transformen.
    (Reading: Section 2.1 in [R2])
  11. Massive MIMO for correlated fading channels: Uplink detection
    May 9, 2017, 13-15. Room: Transformen.
    (Reading: Section 2.2 in [R2])
  12. Massive MIMO for correlated fading channels: Downlink precoding and asymptotics
    May 11, 2017, 13-15. Room: Transformen.
    (Reading: Section 2.3-2.4 in [R2])
  13. Practical deployment considerations: Spatial resource allocation in Massive MIMO
    May 15, 2017, 10-12. Room: Transformen.
    (Reading: Section 5.1-5.2 in [R2])
  14. Homework session 3
    June 7, 2017, 10-12. Room: Nollstället.

The examination consists of 4 homework assignments. The lectures provide an overview of the content in the course literature, but you need to read it in detail to solve the homework assignments.


You can obtain the password from the lecturer

Homework 1 (updated)

Homework 2

Homework 3

Slide set 1: Section 1 in [R2] (updated)

Slide set 2: All parts of [R1] (updated)

Slide set 1: Section 2 in [R2] (updated)

Proofs in Section 2 from [R2]

Reference list from [R2]

Course literature

[R1] E. Björnson, E. Jorswieck, "Optimal Resource Allocation in Coordinated Multi-Cell Systems," Foundations and Trends in Communications and Information Theory, vol. 9, no. 2-3, pp. 113-381, 2013.
Download e-book: //kth.diva-portal.org/smash/get/diva2:608533/FULLTEXT01

[R2] Selected material from the manuscript "Massive MIMO Networks: Spectral, Energy, and Hardware Efficiency" by E. Björnson, L. Sanguinetti, and J. Hoydis. It will be distributed in printed form to those who follow the course.

[R3] Y. J. Zhang, L. Qian, J. Huang, "Monotonic Optimization in Communication and Networking Systems," vol. 7, no. 1, pp 1-75, Foundations and Trends in Networking, 2012.
Download e-book: https://staff.ie.cuhk.edu.hk/~yjzhang/1300000038-Zhang-Vol7-NET-028.pdf

[R4] E. Björnson, Mats Bengtsson, Björn Ottersten, "Optimal Multiuser Transmit Beamforming: A Difficult Problem with a Simple Solution Structure," IEEE Signal Processing Magazine, vol. 31, no. 4, pp. 142-148, July 2014.
Download article: https://arxiv.org/pdf/1404.0408.pdf

Page responsible: Emil Björnson
Last updated: 2017 05 15   16:28