Generic SoC QR Array Processor for Adaptive Beamforming

A generic architecture for implementing a QR array processor in silicon is presented. This improves on previous research by considerably simplifying the derivation of timing schedules for a QR system implemented as a folded linear array, where account has to be taken of processor cell latency and timing at the detailed circuit level. The architecture and scheduling derived have been used to create a generator for the rapid design of System-on-a-Chip (SoC) cores for QR decomposition. This is demonstrated through the design of a single-chip architecture for implementing an adaptive beamformer for radar applications. Published as IEEE Trans Circuits and Systems Part II, Analog and Digital Signal Processing, April 2003 NOT Express Briefs. Parts 1 and II of Journal reorganised since then into Regular Papers and Express briefs

Online CORDIC algorithm and VLSI architecture for implementing QR-array processors

A novel most significant digit first CORDIC architecture is presented that is suitable for the VLSI design of systolic array processor cells for performing QR decomposition. This is based on an on-line CORDIC algorithm with a constant scale factor and a latency independent of the wordlength. This has been derived through the extension of previously published CORDIC algorithms. It is shown that simplifying the calculation of convergence bounds also greatly simplifies the derivation of suitable VLSI architectures. Design studies, based on a 0.35-µ CMOS standard cell process, indicate that 20 such QR processor cells operating at rates suitable for radar beamfoming can be readily accommodated on a single chip.

Linear QR architecture for a single chip adaptive beamformer

This paper presents the design of a novel single chip adaptive beamformer capable of performing 50 Gflops, (Giga-floating-point operations/second). The core processor is a QR array implemented on a fully efficient linear systolic architecture, derived using a mapping that allows individual processors for boundary and internal cell operations. In addition, the paper highlights a number of rapid design techniques that have been used to realise this system. These include an architecture synthesis tool for quickly developing the circuit architecture and the utilisation of a library of parameterisable silicon intellectual property (IP) cores, to rapidly develop detailed silicon designs.

QR decomposition-based matrix inversion for high performance embedded MIMO receivers

Real-time matrix inversion is a key enabling technology in multiple-input multiple-output (MIMO) communications systems, such as 802.11n. To date, however, no matrix inversion implementation has been devised which supports real-time operation for these standards. In this paper, we overcome this barrier by presenting a novel matrix inversion algorithm which is ideally suited to high performance floating-point implementation. We show how the resulting architecture offers fundamentally higher performance than currently published matrix inversion approaches and we use it to create the first reported architecture capable of supporting real-time 802.11n operation. Specifically, we present a matrix inversion approach based on modified squared Givens rotations (MSGR). This is a new QR decomposition algorithm which overcomes critical limitations in other QR algorithms that prohibits their application to MIMO systems. In addition, we present a novel modification that further reduces the complexity of MSGR by almost 20%. This enables real-time implementation with negligible reduction in the accuracy of the inversion operation, or the BER of a MIMO receiver based on this.

Generic scheduling methods for a linear QR array SoC processor

A scheduling method for implementing a generic linear QR array processor architecture is presented. This improves on previous work. It also considerably simplifies the derivation of schedules for a folded linear system, where detailed account has to be taken of processor cell latency. The architecture and scheduling derived provide the basis of a generator for the rapid design of System-on-a-Chip (SoC) cores for QR decomposition.

Parameterizable QR core

The design of a generic QR core for adaptive beamforming is presented. The work relies on an existing mapping technique that can be applied to a triangular QR array in such a way to allow the generation of a range of QR architectures. All scheduling of data inputs and retiming to include processor latency has been included within the generic representation.

Fast Moving Window Algorithm for QR and Cholesky Decompositions

This paper proposes a fast moving window algorithm for QR and Cholesky decompositions by simultaneously applying data updating and downdating. The developed procedure is based on inner products and entails a similar downdating to that of the Chambers’ approach. For adding and deleting one row of data from the original matrix, a detailed analysis shows that the proposed algorithm outperforms existing ones in terms or computational efficiency, if the number of columns exceeds 7. For a large number of columns, the proposed algorithm is numerically superior compared to the traditional sequential technique.

Application-Specific Instruction Set Processor for SoC implementation of Modern Signal Processing Algorithms

A novel application-specific instruction set processor (ASIP) for use in the construction of modern signal processing systems is presented. This is a flexible device that can be used in the construction of array processor systems for the real-time implementation of functions such as singular-value decomposition (SVD) and QR decomposition (QRD), as well as other important matrix computations. It uses a coordinate rotation digital computer (CORDIC) module to perform arithmetic operations and several approaches are adopted to achieve high performance including pipelining of the micro-rotations, the use of parallel instructions and a dual-bus architecture. In addition, a novel method for scale factor correction is presented which only needs to be applied once at the end of the computation. This also reduces computation time and enhances performance. Methods are described which allow this processor to be used in reduced dimension (i.e., folded) array processor structures that allow tradeoffs between hardware and performance. The net result is a flexible matrix computational processing element (PE) whose functionality can be changed under program control for use in a wider range of scenarios than previous work. Details are presented of the results of a design study, which considers the application of this decomposition PE architecture in a combined SVD/QRD system and demonstrates that a combination of high performance and efficient silicon implementation are achievable. © 2005 IEEE.

CORDIC based application-specific instruction set processor for QRD/SVD

An application specific programmable processor (ASIP) suitable for the real-time implementation of matrix computations such as Singular Value and QR Decomposition is presented. The processor incorporates facilities for the issue of parallel instructions and a dual-bus architecture that are designed to achieve high performance. Internally, it uses a CORDIC module to perform arithmetic operations, with pipelining of the internal recursive loop exploited to multiplex the two independent micro-rotations onto a single piece of hardware. The net result is a flexible processing element whose functionality can be changed under program control, which combines high performance with efficient silicon implementation. This is illustrated through the results of a detailed silicon design study and the applications of the techniques to a combined SVD/QRD system.