Low-Complexity Methodology for Complex Square-Root Computation

Mopuri, Suresh; Acharyya, Amit

doi:10.1109/tvlsi.2017.2740343

Cited by 19 publications

(4 citation statements)

References 15 publications

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“…In this context, ϕ ∈ C m×1 , Θ ∈ C n×m and Φ ∈ C m×p are arbitrary matrices, while Ω ∈ C m×m is a diagonal matrix and Λ ∈ C m×m is a positive definite matrix. For the HQR, we consider Γ ∈ C m×n with m ≥ n. The FLOP account for the complex float-point operations (CFLOPs) in (Hunger, 2007) considers that a complex summation consists of only 2 FLOPs (2 real summations), a complex multiplication requires 6 FLOPs (4 real multiplications and 2 real summations), a complex square takes 3 FLOPs (2 real multiplications and 1 real summation), a complex square root (Mopuri and Acharyya, 2017) demands 10 FLOPs (2 real multiplications, 2 real divisions, 3 real summations and 3 real square roots) and a complex division takes 11 FLOPs (6 real multiplications, 2 real divisions and 3 real summations).…”

Section: Definitions On Complexity Evaluationmentioning

confidence: 99%

A review on principles, performance and complexity of linear estimation and detection techniques for MIMO systems

Gaspar¹,

Mendes

Pimenta

2023

Front. Comms. Net.

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The advent of the fifth generation (5G) of mobile networks has introduced several new use cases that are pushing mobile networks in environments that are typically supported by wired technologies. The initial discussions around the sixth generation (6G) of mobile networks signalizes that different approaches are needed to address all contrasting requirements, where multiple-input multiple-output (MIMO) technique stands as a key technology for most future wireless systems. In this review, we present an introduction on classical linear estimators and coherent detectors along with an innovative and accurate complexity formulation within a common framework, allowing a fair comparison and providing an initial guideline for researchers that are looking for a general view of the main techniques available for spatial multiplexing (SM)-MIMO detection and estimation.

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Section: Definitions On Complexity Evaluationmentioning

confidence: 99%

A review on principles, performance and complexity of linear estimation and detection techniques for MIMO systems

Gaspar¹,

Mendes

Pimenta

2023

Front. Comms. Net.

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show abstract

“…When implemented in software, the complex square root operation requires a long execution time, leading to difficulty in meeting requirements for high speed and low latency. Therefore, various kinds of hardware implementations have been proposed for computing complex square roots, such as the digit-recurrence algorithm [5][6][7], 2D cubic convolution [8], and the coordinate rotation digital computer (CORDIC) method [9][10][11].…”

Section: Introductionmentioning

confidence: 99%

“…Later, Ref. [9] reused circular CORDIC to reduce the area occupied and adopted a double pipeline concept to reduce latency. Similar to the architectures of the digit-recurrence algorithm and the interpolation method, such circuit reuse necessitates multiple clock cycles to obtain a valid output.…”

Section: Introductionmentioning

confidence: 99%

An Efficient Hardware Implementation for Complex Square Root Calculation Using a PWL Method

Wang

Liang

et al. 2023

Electronics

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In this paper, we propose a methodology for computing the square root of a complex number based on a piecewise linear (PWL) approximation method. The proposed method relies on a software-based segmentor that automatically divides the three real square root functions used in complex square root computation into the fewest segments with a predefined fractional bit width and maximum absolute error (MAE). The coefficients, including the start point, end point, slope and y-intercept of each segment, are stored for use in the implementation of the hardware design. The proposed fully pipelined circuit is coded in the Verilog hardware description language (HDL). The results of synthesis in TSMC (Taiwan Semiconductor Manufacturing Company) 65-nm CMOS technology show that our design achieves savings of 64.21% in area, 16.67% in delay and 65.08% in power compared to the existing methods. Moreover, implementation results on an FPGA (Field-Programmable Gate Array) platform (XC7Z020-CLG400) show that the proposed design reduces the number of LUTs by 29.38%, delay by 28.57% and power consumption by 53.47%.

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“…The CORDIC algorithm was first proposed in 1959 by E. Volder for computing trigonometric functions, multiplication and division [11,12]. To expand the usage areas, the CORDIC algorithm is applied in the computation of logarithms, exponentials, square roots, arbitrary Nth root, complex operations [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29]. In the implementation of the CORDIC algorithm, the type of computation (addition or subtraction) in the iteration is determined by the rotation direction.…”

Section: Introductionmentioning

confidence: 99%

An optimized hardware implementation of the CORDIC algorithm

Lyu

Wang

et al. 2022

IEICE Electron. Express

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In this paper, we propose a software-based simulator and an optimized hardware implementation of the CORDIC algorithm. The number of iterations and the bit width are selected by their relationship calculated by the simulator to satisfy precision requirement. In the proposed hardware implementation, the addition and subtraction operations share the hardware resources. The two's complement is calculated in two steps: inverting and adding one. The adding one operation is integrated in the addition component of the iteration. In addition, a 3:2 compressor is used to reduce the number of adders, and a carry look-ahead adder is used to reduce the critical path. The synthesized results show that when compared with state-of-the-art designs, our method reduces the area by 53.79% and the delay by 58.97% while maintaining the same precision.

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Low-Complexity Methodology for Complex Square-Root Computation

Cited by 19 publications

References 15 publications

A review on principles, performance and complexity of linear estimation and detection techniques for MIMO systems

A review on principles, performance and complexity of linear estimation and detection techniques for MIMO systems

An Efficient Hardware Implementation for Complex Square Root Calculation Using a PWL Method

An optimized hardware implementation of the CORDIC algorithm

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