Systematic Optimization of Programmable QRD Implementation for Multiple Application Scenarios

Abstract

Orthogonal-Triangular Decomposition (QRD) is one of the most fundamental signal processing primitives based on complex matrix operations [1]. It forms the core of many advanced multi-dimension and statistical signal processing algorithms that utilize orthogonalization, projection, and rank-revealing principles. Especially in the domain of wireless signal processing, many emerging algorithms in MIMO and OFDM systems have explicit or implicit connections to QRD [2]. This paper is about the systematic optimization of QRD implementation on programmable architectures. Based on the analysis of existing works, we introduce the following higher level components to the new optimization methodology: (1) Exploring high level algorithmic alternatives. (2) Categorizing different application scenarios. (3) Merging cascaded matrix operations. The systematic optimization brings significant improvements for programmable QRD implementations. Comparing to the widely accepted implementation in Numerical Receipts [3], our work achieves up to 79.76% cycle count reduction on TI TMS320C6713, a typical VLIW DSP. Moreover, our work achieves remarkable improvement on the memory subsystem, which is very critical for the power consumption and performance of modern DSP. Specifically, when QRD is used to solve least-square linear equations, our work reduces 99.55% LIP misses and 96.52% LID misses for 32×32 equations.