Backbone network of the mobile networks, i.e. mobile backhaul networks, is an important part of mobile network system. With the decreasing size of mobile network system cells, it is considered next-generation mobile backhaul networks will form mesh topology. Most mobile backhaul networks are formed with microwave radios. To increase data rate, Adaptive Modulation and Coding (AMC) is used for wireless links. However, the data rate of each wireless link changes over time and leads to unexpected packet loss or traffic degradation. This paper proposes a routing scheme and methods for estimating the transmission parameters or modes of wireless links to route bandwidth guaranteed flows over mobile backhaul networks. Proposed routing scheme can reduce degradation of flows caused by unexpected changes of the data rate of wireless links. We evaluate our routing scheme when mode distribution of links follows normal, uniform and Poisson distributions. This paper shows mode estimation using mode history of link to estimate the link quality can route bandwidth guaranteed flows efficiently by choosing more stable links for the path.