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The cross-correlation of the Ly-alpha forest and redshifted 21-cm emissionhas recently been proposed as an observational tool for mapping out thelarge-scale structures in the post-reionization era z < 6. This has asignificant advantage as the problems of continuum subtraction and foregroundremoval are expected to be considerably less severe in comparison to therespective auto-correlation signals. Further, the effect of discrete quasarsampling is less severe for the cross-correlation in comparison to the Ly-alphaforest auto-correlation signal. In this paper we explore the possibility ofusing the cross-correlation signal to detect the baryon acoustic oscillation(BAO). To this end, we have developed a theoretical formalism to calculate theexpected cross-correlation signal and its variance. We have used this topredict the expected signal, and estimate the range of observational parameterswhere a detection is possible.  For the Ly-$\alpha$ forest, we have considered BOSS and BIGBOSS which areexpected have a quasar density of 16 deg^{-2} and 64 deg^{-2} respectively. Aradio interferometric array that covers the redshift range z=2 to 3 usingantennas of size 2 m * 2 m, is well suited for the 21-cm observations. It isrequired to observe 25 independent fields of view, which corresponds to theentire angular extent of BOSS. We find that it is necessary to achieve a noiselevel of 1.1 * 10^{-5} K^2 and 6.25 * 10^{-6} mK^2 per field of view in the21-cm observations to detect the angular and radial BAO respectively with BOSS.The corresponding figures are 3.3 * 10^{-5} mK^2 and 1.7 * 10^{-5} mK^2 forBIGBOSS. Four to five independent radio interferometric arrays, each containing400 antennas uniformly sampling all the baselines within 50 m will be able tocarry out these observations in the span of a few years.

The Imprint of the Baryon Acoustic Oscillations (BAO) in the Cross-correlation of the Redshifted HI 21-cm Signal and the Ly-alpha Forest