Partial regularisation approach for detection problems in underdetermined linear systems

The maximum likelihood detection problem in many underdetermined linear communications systems can be described as an underdetermined integer least squares (ILS) problem. To solve it efficiently, a partial regularisation approach is proposed. The original underdetermined ILS problem is first transformed to an equivalent overdetermined ILS problem by using part of the transmit vector to do the regularisation. Then the overdetermined ILS problem is solved by conventional sphere decoding algorithms. Simulation results indicate that this approach can be much more efficient than other approaches for any square constellation higher than 4QAM.