  In this paper, two Intelligent reflecting surfaces (double IRS) assisted
single-user single input single output (SISO) communication system is
considered. The cascaded channels (mobile user
(MU)$\rightarrow$IRS-1$\rightarrow$base station (BS),
MU$\rightarrow$IRS-2$\rightarrow$BS and
MU$\rightarrow$IRS-1$\rightarrow$IRS-2$\rightarrow$BS channels) are estimated
under Bayesian setting. Here, the goal is to evaluate the performance of the
estimator in case of MU$\rightarrow$IRS-1$\rightarrow$BS and
MU$\rightarrow$IRS-2$\rightarrow$BS channel links using Bayesian Cramer-Rao
lower bound (CRLB). Without the knowledge of closed form pdf of inner product
of circularly symmetric complex Gaussian (CSCG) random vectors, we cannot
obtain the fisher information. Hence, by numerical computation we obtain the
Bayesian CRLB. In the simulation results, we show that we can approximate the
pdf of the inner product of CSCG random vectors by a Rayleigh distribution by
increasing the number of elements on the IRS, which is analogous to Central
Limit Theorem (CLT). Also, the results convey that the mean squared error (MSE)
almost matches with the Bayesian CRLB.
