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Exploring Cosmic History and Origins (ECHO), popularly known as`CMB-Bh$\overline{a}$rat', is a space mission that has been proposed to theIndian Space Research Organisation (ISRO) for the scientific exploitation ofthe Cosmic Microwave Background (CMB) at the next level of precision andaccuracy. The quest for the CMB polarization $B$-mode signals, generated byinflationary gravitational waves in the very early universe, is one of the keyscientific goals of its experimental design. This work studies the potential ofthe proposed ECHO instrumental configuration to detect the targettensor-to-scalar ratio $r \sim 10^{-3}$ at $3\sigma$ significance level, whichcovers the predictions of a large class of inflationary models. We investigatethe performance of two different component separation pipelines, NILC andCommander, for the measurement of $r$ in presence of different physicallymotivated models of astrophysical foregrounds. For a simplistic foregroundmodel (only polarized dust and synchrotron), both component separationpipelines can achieve the desired sensitivity of ECHO, i.e. $\sigma (r =0) \sim(0.4 - 0.7)\times 10^{-3}$. NILC performs better than Commander in terms ofbias on recovered $r$ for complex spectral models (power-law and curvedpower-law) of the synchrotron emission and complex dust models (dustdecorrelation). Assuming 84 % delensing, we can achieve an improvement of$\sigma (r = 0)$ by approximately 50 % as compared to the results obtained forthe same configuration without any lensing correction.

$B$-mode forecast of CMB-Bh$\overline{a}$rat