Voice over Adaptive Multi-user Channels on One Slot (VAMOS) is an extension of the Global System for Mobile Communications (GSM) standard, where two overlaid Gaussian minimum-shift keying (GMSK) signals are transmitted in the same time slot and on the same frequency. The overlaid signals are usually assigned different powers to combat slow fading and propagation loss. For channel estimation, specific training sequences are used for both signals. In the downlink, at each mobile station the channel coefficients and the sub-channel power imbalance ratio (SCPIR) have to be estimated. In this paper, the Cramer-Rao lower bound (CRB) for the training sequence based joint estimation of the SCPIR and the channel coefficients at the mobile station is derived and compared with the CRB for a conventional GSM transmission. The results are compared with the performance of channel estimation algorithms designed for VAMOS. It turns out that these algorithms perform very close to the CRB.