Hierarchical pipelining and folding of QRD-RLS adaptive filters and its application to digital beamforming

This paper presents a novel hierarchical approach for pipelining and folding the large CORDIC-based systolic array of a QR decomposition-based recursive least square algorithm (QRD-RLS) adaptive filter to a small fixed size array. With the annihilation-reordering look-ahead transformation, the iteration bound of a QRD-RLS adaptive filter can be reduced linearly with respect to the look-ahead factor. This paper presents, for the first time, how to pipeline and fold such a look-ahead transformed QRD-RLS adaptive filter. Unlike the previously published algorithms, this approach has low complexity and can result in a physical array of any size. In addition, a mathematical model for evaluating these transformations is developed. Using this model, it is shown how a combination of look-ahead, pipelining, and folding transformations can lead to a large increase in throughput and large reduction in area or power consumption. Therefore, the proposed approach is of great significance for application-specific IC chip design, high-level hardware synthesis, and special-purpose processor design. The optimally designed QRD-RLS adaptive filters can be used for adaptive digital beamforming applications, which play an important role in radar, sonar, and mobile/wireless communication systems