Methods and apparatus for designing spherical lattice codebooks for use in data transmission systems are provided. A spherical lattice codebook is constructed by determining the channel statistics of one or more channels, which can be accomplished by observing a sufficiently large set of channel realizations. After determining the channel statistics, an expression for the error probability of the decoder or expressions for bounds on the error probability and expressions for the corresponding gradients are determined. The gradient is then used in an optimization technique to produce a spherical lattice codebook which is subsequently used for transmission.