Capacity and performance of lattice reduction aided linear processing with lattice encoding and decoding in limited feedback systems

Linear processing for multi-input multi-output (MIMO) antenna systems is preferred to non-linear ones for computational efficiency. Using channel state information (CSI) at the receiver, channel matrix can be decomposed via singular value decomposition (SVD), and if the transmitter can be fed back with the right-unitary-matrix of the SVD from the receiver, the maximum channel-capacity can be achieved with linear processing in point-to-point wireless MIMO communications. However, if the transmitter receives no-feedback, the optimal linear detector at the receiver is the minimum-mean-squareerror- estimator, of which capacity is far below the channelcapacity. In practice, reducing the amount of feedback information to achieve a "reasonably close channel-capacity" is an important issue in point-to-point wireless communications. In this paper, we propose a limited feedback system employing linear processing, which achieves near-channel-capacity. The feedback information is only an integer matrix, which is much less than that of the right-unitary-matrix of the SVD. Key ideas of the proposed scheme are the lattice reduction and modulo operation. Moreover, the amount of feedback information can be further reduced to a binary matrix using multi-level/multi-stage encode and decode. Under the turbo channel code the proposed scheme shows excellent performance at high data rates. We compare our simulation results with Shannon capacity limits for ergodic MIMO channels.