Comparisons of different systolic arrays for the QR decomposition based least squares technique

Systolic arrays are very useful for implementing complex signal processing algorithms particularly for real-time and high bandwidth requirements. For example, the two systolic array implementations developed by Gentleman and Kung (1981) and McWhirter (1983) are two-dimensional arrays of processing elements. The QR decomposition-based least-squares method for linear prediction has been applied to the problem of computing the reflection coefficients of a lattice predictor, instead of using the conventional Burg algorithm. A modified one-dimensional ring architecture was proposed for implementing the QR algorithm. This means that the QR algorithm can now be implemented on a linear one-dimensional array of processors rather than a 2-dimensional array as is customary. This 1-D linear array was obtained by a mapping technique. There are other one-dimensional (linear) arrays derived algorithmically or by mapping methods for solving the same problem. In this paper, we specify the details of the cells of our new one-dimensional linear array and then compare this array with the other possible linear arrays for solving the same and QR decomposition least-squares problem