  In this paper, we propose a feedback reduction scheme for full-duplex
relay-aided multiuser networks. The proposed scheme permits the base station
(BS) to obtain channel state information (CSI) from a subset of strong users
under substantially reduced feedback overhead. More specifically, we cast the
problem of user identification and CSI estimation as a block sparse signal
recovery problem in compressive sensing (CS). Using existing CS block recovery
algorithms, we first obtain the identity of the strong users and then estimate
their CSI using the best linear unbiased estimator (BLUE). To minimize the
effect of noise on the estimated CSI, we introduce a back-off strategy that
optimally backs-off on the noisy estimated CSI and derive the error covariance
matrix of the post-detection noise. In addition to this, we provide exact
closed form expressions for the average maximum equivalent SNR at the
destination user. Numerical results show that the proposed algorithm
drastically reduces the feedback air-time and achieves a rate close to that
obtained by scheduling schemes that require dedicated error-free feedback from
all the network users.
