Reduced complexity sphere decoding using forcing rules

We improve the conventional sphere decoder (SD), which is widely used for lattice codes and multiple antenna space-time communications, by showing that some of the variables can be predetermined by using bounds on partial derivatives of the cost function. This reduces the number of variables to be estimated by the SD. Moreover, we combine the forcing rules combined with the conventional SD provide several hybrid algorithms, which are found to be computationally more efficient. Forcing rules reduces complexity significantly when the dimension of the lattice is less than 12.