The performance of the least mean squares algorithm combined with spatial smoothing

Many practical signal environments involve correlation between desired and undesired signals, causing narrowband adaptive array beamformers to exhibit signal cancellation. Spatial smoothing is a technique that can perform beamforming in such environments. This method can be incorporated into an adaptive algorithm, such as least mean squares (LMS), possibly altering the well-known performance characteristics of the algorithm. We discuss methods for combining spatial smoothing with the LMS algorithm in an array with a generalized side-lobe canceler (GSC) structure. The first of these methods is an electronic version of mechanically dithering the array. We show that this well-known method obeys a set of nonhomogeneous dynamical equations, resulting in a limit cycle that increases the misadjustment of the algorithm. The previously reported parallel spatial processing algorithm is also shown to have this increased misadjustment. We then introduce two methods that do not suffer from this misadjustment increase. We compare the methods´ computational complexity and performance, in terms of stability and steady-state behavior, including weight misadjustment, GSC output power, and signal-to-noise ratio (SNR). In conclusion, we find that the limit cycle of the first method can be avoided without any increase in complexity by using one of the new methods.