Approximate lattice detection in MIMO communications using Jacobi theta functions

We consider a multiple-input, multiple-output (MIMO) communication system in which data streams are independently transmitted over a number of antennas and collectively decoded from a number of receiving antennas. The maximum-likelihood (ML) or sphere decoder is known to yield the lowest symbol error rate (SER). However, in the worst case, complexity is exponential in the number of antennas. Seeking to reduce complexity without greatly increasing the SER, we propose an approximate lattice decoder with polynomial arithmetic complexity. The decoder performs unconstrained nonlinear optimisation of a Jacobi theta function that approximates the log-likelihood function. Simulations demonstrate that this decoder performs nearly as well as the sphere decoder in terms of bit error rate (BER) and shows a significant performance enhancement compared to linear and lattice-reduced cancellers.