Triangular systolic array with reduced latency for QR-decomposition of complex matrices

Maltsev, Alexander; Pestretsov, Vladimir; Maslennikov, Roman; Khoryaev, Alexey

doi:10.1109/iscas.2006.1692603

Cited by 66 publications

(40 citation statements)

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“…Our proposed QR decomposition hardware was implemented using TSMC 0.25 µm technology and the experimental results are compared with the TACR/TSA based hardware [9] and low complexity QR decomposition architecture [12]. Table 1 with a 3-iteration step lookahead unit, the proposed SSL-CORDIC based architecture needs 3 cycles with 19.60 nsec clock (total 58.80 nsec) to finish QR decomposition, however, 3 cycles with 27.10 nsec clock (total 81.30 nsec) is spent in the Compact CORDIC based one [12].…”

Section: Numerical Resultsmentioning

confidence: 99%

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Sign-Select Lookahead CORDIC based High-Speed QR Decomposition Architecture for MIMO Receiver Applications

Lee¹

2011

JSTS:Journal of Semiconductor Technology and Science

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Abstract-This paper presents a high-speed QR decomposition architecture for the multi-input-multioutput (MIMO) receiver based on Givens rotation. Under fast-varying channel, since the inverse matrix calculation has to be performed frequently in MIMO receiver, a high performance and low latency QR decomposition module is highly required. The proposed QR decomposition architecture is composed of Sign-Select Lookahead (SSL) coordinate rotation digital computer (CORDIC). In the SSL-CORDIC, the sign bits, which are computed ahead to select which direction to rotate, are used to select one of the last iteration results, therefore, the data dependencies on the previous iterations are efficiently removed. Our proposed QR decomposition module is implemented using TSMC 0.25 µm CMOS process. Experimental results show that the proposed QR architecture achieves 34.83% speed-up over the Compact CORDIC based architecture for the 4 × 4 matrix decomposition.

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Section: Numerical Resultsmentioning

confidence: 99%

“…Triangular systolic arrays (TSA) [9] are frequently used for matrix inversion with the properties Manuscript received Nov. 30, 2010; revised Feb. 28, 2011. School of Electrical Engineering, Korea University, Korea E-mail : jongsun@korea.ac.kr of inherent parallelism and pipelining.…”

Section: Introductionmentioning

confidence: 99%

Sign-Select Lookahead CORDIC based High-Speed QR Decomposition Architecture for MIMO Receiver Applications

Lee¹

2011

JSTS:Journal of Semiconductor Technology and Science

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“…In [9], triangular systolic array (TSA) and three angle complex rotation (TACR) algorithm are used together to implement QR decomposition hardware. The TACR-based approach significantly reduces the QR decomposition time compared to the conventional Givens rotation-based architecture, however, it still needs large number of clock cycles to fill up the TSAbased architecture with inputs.…”

Section: Introductionmentioning

confidence: 99%

“…A low complexity complex Givens rotation approach, which we will refer to LC-CGR in the following [10], is also proposed by separating complex elements into real and imaginary parts. As a result, the delay can be reduced to almost half in case of 2 × 2 matrix compared to TSA/TACR approach [9]. However, as the matrix size increases, the latency will become much larger than TSA/TACR.…”

Section: Introductionmentioning

confidence: 99%

High-speed tournament givens rotation-based QR Decomposition Architecture for MIMO Receiver

Lee

Yoon

2012

2012 IEEE International Symposium on Circuits and Systems

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This paper presents a high-speed hardware architecture of an improved Givens rotation-based QR decomposition, named tournament-based complex Givens rotation (T-CGR). In the proposed approach, more than one pivots are selected and zero-insertion processes of Givens-rotations are performed in parallel like tournament in order to increase the throughput. As a result, the QR decomposition performance significantly increases compared to the triangular systolic array (TSA) approach. Moreover, the circuit area was reduced due to the smaller number of flip-flops for holding the computed results during the decomposition process. The proposed QR decomposition hardware was implemented using TSMC 0.25 um technology. The experimental results show that the proposed architecture achieves 73.00% speed-up over the TACR/TSA-based architecture for the 8 × 8 matrix decomposition.

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“…Architectures which employ the Gram-Schmidt [5] and conventional Givens rotations (CGR) [6] algorithms are disadvantaged as they require high-complexity squareroot operations. Whilst the shift-and-add processing nature of CORDIC-based matrix inversion [7] offers lowcomplexity hardware implementation, its inherent latency can preclude it from high-performance applications [8]. Squared Givens rotations (SGR) [9] offer square-root free processing and a number of SGR-based matrix inversion architectures have been proposed [10], [11].…”

Section: Introductionmentioning

confidence: 99%

MSGR-based low latency complex matrix inversion architecture

Dickson

McAllister

et al. 2008

2008 9th International Conference on Signal Processing

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This paper presents a matrix inversion architecture based on the novel Modified Squared Givens Rotations (MSGR) algorithm, which extends the original SGR method to complex valued data, and also corrects erroneous results in the original SGR method when zeros occur on the diagonal of the matrix either initially or during processing. The MSGR algorithm also avoids complex dividers in the matrix inversion, thus minimising the complexity of potential real-time implementations. A systolic array architecture is implemented and FPGA synthesis results indicate a high-throughput low-latency complex matrix inversion solution.

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Triangular systolic array with reduced latency for QR-decomposition of complex matrices

Cited by 66 publications

References 1 publication

Sign-Select Lookahead CORDIC based High-Speed QR Decomposition Architecture for MIMO Receiver Applications

Sign-Select Lookahead CORDIC based High-Speed QR Decomposition Architecture for MIMO Receiver Applications

High-speed tournament givens rotation-based QR Decomposition Architecture for MIMO Receiver

MSGR-based low latency complex matrix inversion architecture

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