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FIK3510 Multiple Antenna Communications 9.0 credits

The course covers the fundamental theory for how antenna arrays can be utilized to achieve more efficient wireless communication systems, for example, in 5G cellular networks. The focus is on physical layer aspects, including channel estimation, spectral efficiency computation, spatial signal processing, and power optimization. The course covers the fundamentals of “Massive MIMO (multiple input multiple output), point-to-point MIMO, as well as modeling of line-of-sight and fading multi-antenna channels. The course is recommended for doctoral students with an interest in wireless communications and its applications, and no previous third-cycle courses on topic are required.

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Headings with content from the Course syllabus FIK3510 (Spring 2021–) are denoted with an asterisk ( )

Content and learning outcomes

Course contents

Fundamental limits: Capacity behavior as power or bandwidth increases. Examples of practical systems that are power and bandwidth limited. Orthogonal versus non-orthogonal transmission in scenarios with multiple users.

Basic multiple antenna channels: Array gain, capacity of channels with multiple antennas at one side. Modeling of multi‐antenna channel responses.

Fading channels: Rayleigh fading channels, outage capacity, diversity, channel coherence, ergodic capacity.

Point‐to‐point MIMO: Capacity of channels with multiple antennas at both sides, multiplexing gain, spatial degrees of freedom.

Uplink multi‐user MIMO: Uplink capacity, non‐linear and linear detection, channel estimation, capacity bounds in systems with many antennas.

Downlink multi‐user MIMO: Linear precoding, capacity bounds in systems with many antennas, differences and similarities between uplink and downlink.
Power control: Rate region, typical operating points, basic power allocation formulations.

Cellular networks: Engineering aspects of applying multiple antenna techniques in cellular networks, including reuse strategies, pilot contamination, and interference management.

Intended learning outcomes

After passing the course, the student should

  1. be able to describe, apply, and analyze the fundamental limitations when using the wireless medium for communications; in particular, the relations between channel capacity, channel coherence, spatial degrees of freedom, transmission power, pilot contamination, and bandwidth.
  2. be able to apply multiple antenna techniques to achieve high capacity in point‐to‐point as well as multi‐user communications, as well as being able to examine and interpret the results.
  3. with high precision be able to formulate and solve engineering oriented problems regarding the achievable performance and limits of multiple antenna communications.
  4. be able to utilize power control and other resource management parameters to design communication systems that meet given service requirements on spectral efficiency and energy efficiency.
  5. be able to implement, validate and compare the main theoretic multiple antenna concepts via computer simulations.

Course disposition

14 lectures, each consisting of around 45 min video to watch in advance and 90 min of examples and discussions in class.

8 tutorial sessions that require preparations and active attendance.

2 lab exercises that each is expected to take around 5 hours to solve.

4 homework sets with around 5 exercises each.

Literature and preparations

Specific prerequisites

Enrolled as doctoral student.

Recommended prerequisites

From linear algebra and calculus: Computations with matrices and vectors, determinant, eigenvalues. Computations with complex numbers.

From mathematical statistics: Stochastic variables, estimation of realizations of stochastic variables.

From elementary communication theory: Channel models, channel capacity, the entropy concept.


Lab exercises are carried out in MATLAB.


Compendium “Introduction to Multiple Antenna Communications” written by E. Björnson

T. L. Marzetta, E. G. Larsson, H. Yang, and H. Q. Ngo, Fundamentals of Massive MIMO. Cambridge University Press, 2016.

Examination and completion

If the course is discontinued, students may request to be examined during the following two academic years.

Grading scale

P, F


  • EXA1 - Written examination, 9.0 credits, grading scale: P, F

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

The examination consists of three parts: A written exam, laboratory exercises carried out in MATLAB, and a set of homework problems that are solved individually and then actively discussed in joint tutorial sessions.

Other requirements for final grade

The grade on the course is Pass/fail. The requirements for passing the course is at least 2/3 correct answers on the written exam and on the homework problems, correct solutions to the laboratory exercises and a lab report of sufficient quality. Moreover, 90% attendance on the scheduled laboratory exercises and tutorials is required.

Opportunity to complete the requirements via supplementary examination

No information inserted

Opportunity to raise an approved grade via renewed examination

No information inserted


Profile picture Emil Björnson

Ethical approach

  • All members of a group are responsible for the group's work.
  • In any assessment, every student shall honestly disclose any help received and sources used.
  • In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.

Further information

Course web

Further information about the course can be found on the Course web at the link below. Information on the Course web will later be moved to this site.

Course web FIK3510

Offered by

EECS/Communication Systems

Main field of study

No information inserted

Education cycle

Third cycle

Add-on studies

No information inserted


Emil Björnson (

Supplementary information

Parts of the lecture material consists of videos.

Postgraduate course

Postgraduate courses at EECS/Communication Systems