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- Mohammed, Saif Khan, 1977-, et al.
(author)
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MIMO Precoding with X- and Y- Codes
- 2011
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In: IEEE Transactions on Information Theory. - New Jersey, USA : IEEE. - 0018-9448 .- 1557-9654. ; 57:6, s. 3542-3566
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Journal article (peer-reviewed)abstract
- We consider a slow fading nt x nr multiple-input multiple-output (MIMO) system with channel state information (CSI) at both the transmitter and receiver. Since communication in such scenarios is subject to block fading, reception reliability, quantified in terms of the achievable diversity gain, is of importance. A simple and well known precoding scheme is based upon the singular value decomposition (SVD) of the channel matrix, which transforms the MIMO channel into parallel subchannels. Despite having low maximum likelihood decoding (MLD) complexity, this SVD based precoding scheme provides a diversity gain which is limited by the diversity gain of the weakest subchannel. We therefore propose X- and YCodes, which improve the diversity gain of the SVD precoding scheme, by jointly coding information across a pair of subchannels (i.e., pairing subchannels). In particular, subchannels with high diversity gain are paired with those having low diversitygain. A pair of subchannels is jointly encoded using a 2 x 2 real matrix, which is fixed a priori and does not change with each channel realization. For X-Codes, these matrices are 2-dimensional rotation matrices parameterized by a single angle, while for Y-Codes, these matrices are 2-dimensional upper left triangular matrices. Also, since joint coding is performed only across a pair of subchannels, the joint MLD complexity remains low. In particular, the MLD complexity of Y-Codes is even lower than that of X-Codes, and is equivalent to symbol by symbol detection. Moreover, we propose X-, Y-Precoders with the same structure as X-, Y-Codes, but with encoding matrices adapted to each channel realization. With respect to the error probability performance, the optimal encoding matrices for X-, YCodes/ Precoders are derived analytically and numerically. Whencompared to other precoding schemes reported in the literature, it is observed that X-Codes/Precoders perform better in wellconditioned channels, while Y-Codes/Precoders perform better in ill-conditioned channels.
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| 3. |
- Mohammed, Saif Khan, 1977-, et al.
(author)
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Precoding by Pairing Subchannels to Increase MIMO Capacity with Discrete Input Alphabets
- 2011
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In: IEEE Transactions on Information Theory. - New Jersey, USA : IEEE. - 0018-9448 .- 1557-9654. ; 57:7, s. 4156-4169
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Journal article (peer-reviewed)abstract
- We consider Gaussian multiple-input multiple-output (MIMO) channels with discrete input alphabets. We propose a non-diagonal precoder based on the X-Codes in \cite{Xcodes_paper} to increase the mutual information. The MIMO channel is transformed into a set of parallel subchannels using Singular Value Decomposition (SVD) and X-Codes are then used to pair the subchannels. X-Codes are fully characterized by the pairings and a $2\times 2$ real rotation matrix for each pair (parameterized with a single angle). This precoding structure enables us to express the total mutual information as a sum of the mutual information of all the pairs. The problem of finding the optimal precoder with the above structure, which maximizes the total mutual information, is solved by {\em i}) optimizing the rotation angle and the power allocation within each pair and {\em ii}) finding the optimal pairing and power allocation among the pairs. It is shown that the mutual information achieved with the proposed pairing scheme is very close to that achieved with the optimal precoder by Cruz {\em et al.}, and is significantly better than Mercury/waterfilling strategy by Lozano {\em et al.}. Our approach greatly simplifies both the precoder optimization and the detection complexity, making it suitable for practical applications.
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