Unlike the channel matrix in the spatial division multiplexing (SDM) multiple-input multiple-output (MIMO) communication system, the equivalent channel matrix in the layered Alamouti space-time block coding (STBC) MIMO system comprised 2-by-2 Alamouti sub-blocks. One novel property, found by Sayed et al. about the QR-decomposition (QRD) of this equivalent channel matrix is that the produced -and -matrices are also matrices with Alamouti sub-blocks. Taking advantage of this property, we propose a new block-wise complex Givens rotation (BCGR) based algorithm and a triangular systolic array (TSA) to compute the QRD of the equivalent channel matrix in an Alamouti block by block manner. Implementation results reveal that our new TSA can compute QRDs of 4-by-4 equivalent channel matrices faster than any architecture that has been developed for the SDM MIMO system. This property of fast QRD makes our TSA very attractive for the layered Alamouti STBC MIMO system combined with the orthogonal frequency division multiplexing. Our new BCGR based approach can also be applied to the hybrid Alamouti STBC MIMO system, which is also a system with equivalent channel matrix consisting of Alamouti sub-blocks.Index Terms-Alamouti space-time block coding, CORDIC module, Givens rotation, multiple input multiple output system, QR-decomposition, triangular systolic array.
Codebooks with constant modulus entries are being considered for the limited feedback beamforming multiple-inputmultiple-output (MIMO) system to improve the power amplifier efficiency at the transmitter. Assume that one such codebook is known to both the transmitter and receiver. The receiver must determine a target codeword from this codebook and send its index back to the transmitter. A receiver can be implemented with low cost if fast codeword selection algorithm is executed. In this study, the authors utilise the properties possessed by three such codebooks and propose a novel tree search algorithm for fast codeword selection. Compared with two previously reported codeword selection algorithms, our algorithm is of fixed complexity and does find the target codeword. Furthermore, our algorithm for codeword selection is similar to the tree search for MIMO detection. These two similar tree search algorithms for both codeword selection and MIMO detection can be implemented by the same hardware architecture. A baseband receiver with small chip area for the dual-mode (the spatial multiplexing and beamforming transmission modes) MIMO system is possible.
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