Distance measures for near-maximum-likelihood detection processes

In maximum-or near-maximum-likelihood detection processes of the type frequently considered for use in applications where the digital data signal is received in the presence of both additive noise and severe intersymbol interference, the detector computes, for each of a number of possible sequences of received data symbols, the Euclidean or unitary distance between the corresponding received sequence, for the given signal distortion but in the absence of noise, and the sequence actually received. Such computations involve numerous operations of squaring or multiplication. The paper studies a general class of piecewise linear distance measures that involve no operations of squaring or multiplication, other than multiplication by the integer 2, leading to a useful simplification in the implementation of the detection process. The departure of each distance measure from the ideal is analysed theoretically for the simplest case of just one complex-valued received sample, and the results obtained are then extended to the general case of a message involving several received samples. Finally, results are presented of computer simulation tests assessing the effect of each distance measure on the tolerance of the detector to additive white Gaussian noise.