Adaptive algorithms in the space and time domains

The basic similarities and essential differences between adaptive processing structures in the space and time domains are considered. Attention is focused on the fact that a cascade structure is required to decorrelate the signals received from different elements of an antenna array, while a very different and more efficient lattice filter structure may be used to decorrelate successive samples of a time series. The difference is explained by examining the Levinson-Durbin recursion algorithm, which essentially gives rise to the lattice filter structure. The algorithm is presented in a generalised form which takes into account the effect of non-stationary statistics and shows clearly how the use of recursion in time is fundamentally responsible for its efficiency. The algorithm is clearly not appropriate for antenna array decorrelation or in the spatial domain generally.