Stabilisation of adaptive array patterns using signal space projection

One approach is to use all the array elements but combine them into a number of beams (essentially pointing at the signals) which become the inputs to an adaptive system with the number of degrees of freedom (one per beam) matched to the number of signals. This is the approach taken by Gabriel (1986) and is the starting point for the paper. The authors show that any basis for the signal space (i.e. not just that given by the principal eigenvectors) can be used and that suitable bases can be found by much simpler processing of the covariance matrix than by eigenanalysis. They also show that the procedure of forming the signal space beams first and then using these as inputs to the adaptive processing need not be carried out explicitly. The cases of the sidelobe canceller (SLC), the adaptive array with a set of hard linear constraints and the adaptive array with soft linear constraints are treated and it is shown in each case that the result is equivalent to applying signal space projection (SSP) to the standard optimum weight. In effect the projection ensures that the weight applied is solely in the signal space and all the components in the noise space (which provide the pattern contributions fluctuating between data sets) are eliminated