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We investigate how well future large-scale radio surveys could measuredifferent shapes of primordial non-Gaussianity; in particular we focus onangle-dependent non-Gaussianity arising from primordial anisotropic sources,whose bispectrum has an angle dependence between the three wavevectors that ischaracterized by Legendre polynomials $\mathcal{P}_L$ and expansioncoefficients $c_L$. We provide forecasts for measurements of galaxy powerspectrum, finding that Large-Scale Structure (LSS) data could allowmeasurements of primordial non-Gaussianity competitive or improving uponcurrent constraints set by CMB experiments, for all the shapes considered. Weargue that the best constraints will come from the possibility to assignredshift information to radio galaxy surveys, and investigate a few possiblescenarios for the EMU and SKA surveys. A realistic (futuristic) modeling couldprovide constraints of $f_{\rm NL}^{\rm loc} \approx 1 (0.5)$ for the localshape, $f_{\rm NL}$ of $\mathcal{O}(10) (\mathcal{O}(1))$ for the orthogonal,equilateral and folded shapes, and $c_{L=1} \approx 80 (2)$, $c_{L=2} \approx400 (10)$ for angle-dependent non-Gaussianity. The more futuristic forecastsshow the potential of LSS analyses to considerably improve current constraintson non-Gaussianity, and so on models of the primordial Universe. Finally, wefind the minimum requirements that would be needed to reach$\sigma(c_{L=1})=10$, which can be considered as a typical (lower) valuepredicted by some (inflationary) models.

Future Constraints on Angle-Dependent Non-Gaussianity from Large Radio Surveys