This course is discontinued

INF9960 – Phase mode array processing

Course content

Array processing is a central component in important industrial and medical applications such as seismic imaging, sonar, and medical ultrasound imaging, but also in everyday applications like WiFi and cell-phone base stations, hands-free telephony and video conferencing systems. It consists of using an array of sensors to receive or transmit signals in the form of acoustic or electromagnetic waves. The actual research being done in array technology often consists of finding various optimal ways of combining the sensors.

Phase mode array processing has become increasingly popular over the last decade, following a massive amount of research on the advantages of spherical and circular antenna arrays. The concept of phase mode processing can most easily be explained as transforming array data from the spatio-temporal domain to the so-called phase mode domain, where a lot of signal and array properties become apparent, such as:

  • diffraction effects around solid objects like spheres and cylinders, which yield larger apertures and therefore higher resolution.
  • superdirective beamformers for spatially oversampled arrays only have closed-form solutions in the phase mode domain.
  • frequency invariant array characteristics become easily realizable (unfortunately at the cost of decreased robustness)
  • a regular, virtual uniform linear representation of a circular aperture/array, which has traditionally been viewed as difficult to work with due to its non-regular geometry (in cartesian coordinates)

However, the transition from spatio-temporal data to phase mode data is not trivial, and there are a lot of challenges associated with designing arrays that are meant to work in the phase mode domain, and performing the actual phase mode domain processing. Specifically, there are a lot of mathematical details and physical interpretations involved in deriving the transformations, the associated constraints, and evaluating the reliability of the results. This course will cover all the basics required for understanding and performing phase mode processing, covering most of the recent publications on the subject.

Learning outcome

After finishing this course, the students should:
• be able to choose spatial sampling constellations on circles and spheres that minimize spatial aliasing of signals under practical constraints.
• describe the transformations to and from the phase mode domain, and the restrictions set by the physical properties of the array.

  • be able to perform array weight design in the phase mode domain and draw parallels to the spatio-temporal domain.
  • be able to realize super-directive beamformers while knowing their restrictions.
  • be able to implement a complete phase mode array processor for spherical and circular arrays using a high level programming language such as MATLAB.


PhD candidates from the University of Oslo should apply for classes and register for examinations through Studentweb.

If a course has limited intake capacity, priority will be given to PhD candidates who follow an individual education plan where this particular course is included. Some national researchers’ schools may have specific rules for ranking applicants for courses with limited intake capacity.

PhD candidates who have been admitted to another higher education institution must apply for a position as a visiting student within a given deadline.


Recommended previous knowledge

Basic knowledge of signal processing in both space and time. A suitable basis is the combination INF3470 – Digital signalbehandling (continued) or FYS3220 – Linear Circuit Electronics and INF5410 – Signal processing in space and time (continued)


3 hours of lectures evey week


Written project report.

Grading scale

Grades are awarded on a pass/fail scale. Read more about the grading system.

Explanations and appeals

Resit an examination

This subject does not offer new examination in the beginning of the subsequent term for candidates who withdraw during an ordinary examination or fail an ordinary examination. For general information about new examination, see /studier/admin/eksamen/sykdom-utsatt/mn/index.html and

Facts about this course






Every autumn


Every autumn

Teaching language