On the efficiency of sphere decoding for linearly precoded MIMO systems

To reduce the decoding complexity of linearly precoded MIMO systems, the sphere decoder is applied instead of maximum likelihood and the performance complexity trade-off is investigated. The max-d_min precoding criterion allows to enhance dramatically the Bit-Error-Rate (BER) of MIMO systems by maximizing the minimum Euclidean distance between the lattice points of received constellation. The maximum likelihood (ML) decoder, therefore, is the optimal solution for the receiver, but its computational complexity is exponential in function of the number of antennas and constellation size. The sphere decoding (SD) algorithm, proposed as a sub-optimal ML-decoding, just considers a subset of lattice points that drop into the sphere centered by the received point to obtain the decoded solution, thus reducing significantly the complexity. In this paper, two structures of SD will be investigated: general SD with its adaptive covering radius and real-valued fixed complexity sphere decoder (RFSD). Because the structure of max-d_min is complicated and strongly depends on the channel, it exists the case when all power is poured only on the best sub-channel. Some adjustments, therefore, of traditional sphere decoding algorithm will be made to adapt to the precoded MIMO systems.