Partial feedback based orthogonal block coding

Orthogonal space-time block codes (OSTBC) from orthogonal designs have both advantages of complex symbol-wise maximum-likelihood (ML) decoding and full diversity. However, their symbol rates are upper bounded by 3/4 for more than 2 antennas for complex symbols. To increase the symbol rates, they have been generalized to quasi-orthogonal space-time block codes (QOSTBC) in the literature but the diversity order is reduced by half and the complex symbol-wise ML decoding is significantly increased to complex symbol pair-wise (pair of complex symbols) ML decoding. The QOSTBC has been modified by rotating half of the complex symbols for achieving the full diversity while maintaining the complex symbol pair-wise ML decoding. The optimal rotation angles for any signal constellation of any finite symbols located on both square lattices and equal-literal triangular lattices have been found by Su-Xia, where the optimality means the optimal diversity product (or product distance). QOSTBC has also been modified by Yuen-Guan-Tjhung by rotating information symbols in another way such that it has full diversity and in the meantime it has real symbol pair-wise ML decoding (the same complexity as complex symbol-wise decoding) and the optimal rotation angle for square and rectangular QAM constellations has been found.In this paper, we systematically study general linear transformations of information symbols for QOSTBC to have both full diversity and real symbol pair-wise ML decoding. We present the optimal transformation matrices (among all possible linear transformations not necessarily symbol rotations) of information symbols for QOSTBC with real symbol pair-wise ML decoding such that the optimal diversity product is achieved for both general square QAM and general rectangular QAM signal constellations. Furthermore, our newly proposed optimal linear transformations for QOSTBC also work for general QAM constellations in the sense that QOSTBC have full diversity with good diversity product property and real symbol pair-wise ML decoding. Interestingly, the optimal diversity products for square QAM constellations from the optimal linear transformations of information symbols found in this paper coincide with the ones presented by Yuen-Guan-Tjhung by using their optimal rotations. However, the optimal diversity products for (non-square) rectangular QAM constellations from the optimal linear transformations of information symbols found in this paper are better than the ones presented by Yuen-Guan-Tjhung by using their optimal rotations. In this paper, we also present the optimal transformations for the co-ordinate interleaved orthogonal designs (CIOD) proposed by Khan-Rajan for rectangular QAM constellations. Index TermsComplex symbol-wise decoding, Hurwitz-Radon family, linear transformations of information symbols, optimal product diversity, quasi-orthogonal space-time block codes, real symbol pair-wise decoding.

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“…When a limited feedback is available, studies on OSTBC and QOSTBC can be found in, for example, [48]- [52].…”

Section: Discussionmentioning

confidence: 99%

On optimal quasi-orthogonal space-time block codes with minimum decoding complexity

Wang

Xia

2005

Proceedings. International Symposium on Information Theory, 2005. ISIT 2005.

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“…Unfortunately, both virtual channel matrices H (4) v and H (8) v are no more orthogonal. However, in the following it will be shown that H (4) v and H (8) v are "nearly orthogonal".…”

Section: A Extended Alamouti Scheme For Four Transmit Antennasmentioning

confidence: 99%

“…v is the (4 × 1) noise vector with complex Gaussian components with zero mean and variance σ 2 v . S (4) 1 and S (4) 2 are defined as:…”

Section: A Caeacs Using One Feedback Bit Per Code Blockmentioning

confidence: 99%

“…As it is assumed that the receiver has full information of the channel state knowing h 1 to h 4 , the receiver can compute X 1 and X 2 . With this information the receiver returns the feedback bit b informing the transmitter to select that code block S (4) i (i = 1, 2) which leads to the smaller value of X i . With this information the transmitter switches between the EACs S (4) 1 and S (4) 2 such that the resulting X i will correspond to min(|X 1 |, |X 2 |).…”

Section: ) Imentioning

confidence: 99%

“…In some schemes, low decoding complexity, high diversity and a higher code rate can be obtained even if only partial channel information is sent back to the transmitter. An example of this is given in [4] where the the space time block code is combined with limited feedback to take advantages of it.…”

Section: Introductionmentioning

confidence: 99%

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Extended Alamouti codes in correlated channels using partial feedback

Badic

Rupp

Weinrichter

2004

2004 IEEE International Conference on Communications (IEEE Cat. No.04CH37577)

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Abstract-In this paper we present a family of quasiorthogonal space-time codes for correlated MIMO (multiinput/multi-output) channels using four and eight transmit antennas when only partial channel state information is sent back to the transmitter. Transmit diversity is improved up to nearly the optimum diversity value. This high diversity can be exploited with zero forcing receivers as well as with maximum-likelihood receivers.

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