Block-Circulant Inverse Orthogonal Jacket Matrices and Its Applications to the Kronecker MIMO Channel
- 14 Downloads
This paper presents a note on the block-circulant generalized Hadamard matrices, which is called inverse orthogonal Jacket matrices of orders \(N=2p, 4p, 4^kp, np\), where k is a positive integer for the Kronecker MIMO channel. The class of block Toeplitz circulant Jacket matrices not only have many properties of the circulant Hadamard conjecture but also have the construction of block-circulant, which can be easily applied to fast algorithms for decomposition. The matrix decomposition is with the form of the products of block identity \(I_2\) matrix and block Hadamard \(H_2\) matrix. In this paper, a block fading channel model is used, where the channel is constant during a transmission block and varies independently between transmission blocks. The proposed block-circulant Jacket matrices can also achieve about 3db gain in high SNR regime with MIMO channel. This algorithm for realizing these transforms can be applied to the Kronecker MIMO channel.
KeywordsCirculant Hadamard conjecture Center-weighted Hadamard matrix Reciprocal transpose Block-circulant Jacket transform DFT matrix Toeplitz matrix Kronecker MIMO channel
The second author visited Concordia University from July 4 to July 25, 2008, in Canada, and talked about Jacket Matrix many times, thanks to Professor M. Omair Ahmad and Professor M.N.S. Swamy.
- 2.S. Bouguezel, M.O. Ahmad, M.N.S. Swamy, An efficient algorithm for the computation of the reverse Jacket transform, in 2006 IEEE International Symposium on Circuits and Systems, ISCAS 2006, Proceedings, 21–24 May 2006, Island of Kos, pp. 1–4. (2008). https://doi.org/10.1109/ISCAS.2006.1692780
- 6.J.J. Ding, S.C. Pei, P.H. Wu, Jacket Haar transform, in ISCAS (Rio de Janeiro, Brazil, 2011), pp. 1520–1523. https://doi.org/10.1109/ISCAS.2011.5937864
- 7.J.J. Ding, S.C. Pei, P.H. Wu, Arbitrary-length Walsh-Jacket transforms, in APSIPA Annual Summit and Conference (Xi’an, China, 2011). https://doi.org/10.1007/978-3-319-27122-4_23
- 14.J. Gutierrez-Gutierrez, P.M. Crespo, Asymptotically equivalent sequences of matrices and Hermitian block Toeplitz matrices with continuous symbols: applications to MIMO systems. IEEE Trans. Inf. Theory 54(12), 5671–5680 (2008). https://doi.org/10.1109/TIT.2008.2006401 MathSciNetCrossRefzbMATHGoogle Scholar
- 20.M.H. Lee, Jacket Matrices: Constructions and Its Applications for Fast Cooperative Wireless Signal Processing (LAP LAMBERT Publishing, Saarbrücken, 2012)Google Scholar
- 23.M.H. Lee, H. Hai, X.-D. Zhang, MIMO Communication Method and System using the Block Circulant Jacket Matrix, USA Patent. no. 9,356,671, 05/31/2016Google Scholar
- 34.S.C. Pei, J.J. Ding, Generalizing the Jacket transform by sub orthogonality extension, in EUSIOCO (European Signal Processing Conference), pp. 408–412 (2009)Google Scholar
- 42.R.K. Yarlagadda, J.E. Hershey, Hadamard Matrix Analysis and Synthesis With Applications to Communications Signal/Image Processing (Kluwer Academic Publishers, Norwell, 1997)Google Scholar