Radio observations being insensitive to the dust-obscuration, have been exploited to unveil the population of active galactic nuclei residing in galaxies with large dust content. In this paper, we investigate the radio characteristics of 321 dust-obscured galaxies (DOGs; $S_{24 \ \mu{\rm m}}/S_{r\mbox{−}{\rm band}} \geq 1000$) by using mainly deep band-3 (250–550 MHz) observations from the upgraded giant metrewave radio telescope (uGMRT) and 1.5 GHz Jansky very large array (JVLA) observations. We find that for our sample of DOGs, deep (median noise-rms $=$ 30 $\mu$Jy beam$^{-1}$) 400 MHz band-3 uGMRT observations yield the highest detection rate (28%) among those obtained with the JVLA, and low frequency array (LOFAR) radio observations and XMM-N X-ray observations. The radio characteristics of our sample sources, i.e., linear extent (<40 kpc at $z$ < 1.2), bimodal spectral index ($\alpha^{1.5 \ {\rm GHz}}_{400 \ {\rm MHz}}$) distribution and the radio luminosities ($L_{1.5 \ {\rm GHz}}$ > $5.0 \times 10^{23}$ W Hz$^{-1}$), suggestthem to be mainly consist of compact-steep-spectrum (CSS) or peaked-spectrum (PS) sources representing an early phase of the AGN-jet activity in dust-obscured environments. With stacking, we find the existence of faint radio emission ($S_{400 \ {\rm MHz}} = 72.9$ $\mu$Jy beam$^{-1}$ and $S_{1.5 \ {\rm GHz}} = 29$ $\mu$Jy beam$^{-1}$ with signal-to-noise ratio $\sim$20) in otherwise radio-undetected DOGs. Our study reveals the faint emission at a few tens of $\mu$Jy level in high-$z$ DOGs, which can be used as a test-bed for the deeper radio continuum surveys planned with the square-kilometer array (SKA) and its pathfinders.

The cessation of AGN activity in radio galaxies leads to a remnant phase during which jets are no longer sustained, but lobes can be detected for a period of time before they fade away due to radiative and dynamical energy losses. The time-scale of the remnant phase and AGN duty cycle are vital to understand the evolution of radio galaxies. In this paper, we report newband-3 observations with the upgraded Giant Meterwave Radio Telescope (uGMRT) for five remnant radio galaxies. Our uGMRT observations reveal emission of low-surface-brightness in all five remnants with 400 MHz surface brightness in the range of 36–201 mJy arcmin$^{-2}$. With band-3 uGMRT observations, we discover wing-shaped radio morphology in one of our sample sources. Using radio observations at 150, 325, 400 MHz and 1.5 GHz, we model the radio spectral energy distributions (SEDs) of our sample sources with the continuous injection-off (CI$_{\rm OFF}$) model, that assumes an active phase with continuous injection followed by a remnant phase. We obtain total source ages ($t_{\rm s}$) in the range of 20.3–41.4 Myr with $t_{\rm OFF}/t_{\rm s}$ distributed in the range of 0.16–0.63, which in turn suggests that they belong to different evolutionary phases. We note that when compared to the remnants reported in the literature, our sample sources tend to show lower spectral ages that can be explained by the combined effects of more dominant inverse Compton losses for our sources present at the relatively higher redshifts and possible rapid expansion of lobesin their less dense environments.