*2.3.4. Sphere decoding MIMO receiver*

Sphere Decoding (SD) families are the new decoding techniques that aim to reduce the computational complexity of the ML decoding technique. In the sphere decoder, the received signal is compared to the closest lattice point, since each codeword is represented by a lattice point. The number of lattice points scanned in a sphere decoder depends on the initial radius of the sphere. The correctness of the codeword is in turn dependent on the SNR of the system. The search in Sphere decoding is restricted by drawing a circle around the received signal in a way to encompass a small number of lattice points. This entails a search within sub-set of the codes-words in the constellation and allows only those code-words to be checked. All codewords outside the sphere are not taken into consideration for the decoding operation [8].
