# Basics of Sphere Decoding for MIMO

I am working on a project that involves Spatial Modulation for MIMO channels. This uses a ML (Maximum Likelihood) detector which is computationally intensive. Sphere Decoders are developed to reduce this computations by limiting the search spaces. I understand that it uses a radius (can be soft or hard) to determine this and that it uses QR decomposition where R is triangular and uses this to create a tree structure. This is where I'm lost as to how this tree is created. If any can explain this or provide a link which explains this I would be very grateful.

I am trying to learn the basics of sphere decoding so as to be able to implement the algorithm in this paper: http://arxiv.org/abs/1305.1478

• Depending on the dimensions of the problem, what is meant by sphere and its radius can be quite counterintuitive. See this answer on stats.SE to understand why extrapolation from our understanding of three-dimensional Euclidean space to $n$-dimensional spaces and spheres in such spaces can lead to very puzzling phenomena. – Dilip Sarwate Jun 30 '15 at 13:13
• @DilipSarwate I understand that higher dimensions can lead to such counter intuitive ideas and that link was quite interesting thank you. But my question is about how do they arrive at this multi-dimensions (if they even are). From what I understand in the paper since R which is factored is a triangular matrix it arranges the different computational paths as a tree and then uses the radius to decide how far into the tree is required. But i am not clear on how the tree is created. – PSK Jul 1 '15 at 4:00