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.

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.

• 14 lectures, each consisting of ~45 min video content to watch in advance, and ~90 min of interactive examples and discussions in class.
• 8 seminar sessions, where solutions to tutorial problems are presented and discussed. Some sessions are dedicated to paper presentations.
• 2 lab exercise, each expected to take at least 5 hours to solve.

Active attendance are expected from the students in all activities.

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.

Compendium “Introduction to Multiple Antenna Communications” written by E. Björnson. Provided in digital form to the course attendees.

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

The lab exercises are carried out in MATLAB.

Students at KTH with a permanent disability can get support during studies from Funka:

Funka - compensatory support for students with disabilities

Please inform the course coordinator if you need compensatory support during the course. Present a certificate from Funka.

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.

The examination consists of three parts:

1. A written exam (5 hours at a given time)
2. Two laboratory exercises, each expected to take at least 5 hours to solve. One of them is examined orally and the other one is examined with a written report.
3. Four homework sets with around 5 challenging exercises, which are solved individually and then actively discussed in the seminar sessions.

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.

• 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.