Pipelined CORDIC-Based State-Space Orthogonal Recursive Digital Filters Using Matrix Look-Ahead

Abstract

Orthogonal recursive or infinite impulse response (IIR) digital filters can achieve a sharp transition band, have good finite word-length behavior, and are used in many modern digital signal processing (DSP) applications such as mobile communications. However, Givens rotation or coordinate rotation digital computer (CORDIC)-based fine-grain pipelined true orthogonal recursive digital filters have yet to be developed. In this paper, a state-space approach-based novel algorithm for designing fine-grain pipelined true orthogonal recursive digital filters is proposed using the matrix look-ahead technique. The algorithm is developed for designing general multi-input/multi-output (MIMO) digital filters, whereas the single-input/single-output (SISO) filters are treated as special cases. The filter synthesis procedure contains five major steps and only involves applying orthogonal transformations that are known to be numerically very reliable and, therefore, is ideal for very large scale integration (VLSI) implementations. The proposed filter architectures are pipelined at fine-grain level and, thus, can be operated at arbitrarily high sample rates. The total complexity is MN(m+p)+(m+N)p+p(p-1)/2 Givens rotations for MIMO filters, where N, m, p, and M are the filter order, number of inputs, number of outputs, and pipelining level, respectively. For the SISO case, the complexity reduces to (2M+1)N+1 Givens rotations, which is linear with respect to the filter order and pipelining level. Furthermore, the filter realizations consist of only Givens rotations, which can be mapped onto CORDIC arithmetic-based processors. Different filter design and realization approaches are explored, and the resulting topologies are compared. As an application, a pipelined intermediate frequency filter for an American mobile telephone system is designed using the proposed approach. Finally, finite word-length simulations are carried out for various orthogonal topologies. It is shown both theoretically and numerically how the proposed orthogonal filter realizations achieve low sensitivity due to finite word-length truncations.