A plurality of communication bursts are used to communicate data in a shared spectrum in a time slot of a time division duplex communication system. Each burst has an associated midamble sequence of a set of known sequences. A wireless communication apparatus has a receiver component configured to receive the plurality of communication bursts and to define a received vector corresponding to the received bursts. A channel estimator is provided that is configured to estimate channel information of the plurality of communication bursts by constructing a block matrix having a plurality of identical right circulant matrix blocks using the known midamble sequences and the received vector. A data detector then recovers data from the received communication bursts using the estimated wireless channel information.