Low-Power Approximate Logarithmic Squaring Circuit Design for DSP Applications

The squaring function is widely used in Digital Signal Processing (DSP). There are many DSP applications with noisy inputs for which simplifying approximations of the squaring function implementation have a minor impact on the output quality, while permitting significant reductions in the hardware cost. This article proposes a Low-Error Squaring Function (LESF) and its low-power hardware implementation. Unlike the existing logarithmic squaring functions, LESF benefits from a double-sided error distribution and, consequently, error cancellation in larger calculations. LESF approximates a base-2 logarithmic function with a linear polynomial, i.e.,
$\mathrm{log_2}\;f(x) \approx ax+b$
. Since input
$b$
in this sum is a constant, LESF replaces the conventional full-adder with a compact specialized adder for hardware efficiency. Our simulation results show that the 16-bit LESF is 23.23 percent more accurate (in the mean relative error distance) than the baseline Mitchell approximate logarithmic squaring function while being 1.8× faster and 39 percent more energy-efficient. LESF and other logarithmic squaring functions are evaluated for the square-law detector application. LESF is shown to be more than 3× more accurate in this application (with respect to the Euclidean distance) than the next most accurate design in the literature, which uses an iterative error compensation technique.