Minimum BER diagonal precoder for MIMO systems

Military Technical Academy Review, 2011

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IEEE Transactions on Wireless Communications, 2000

We study unitary precoding for multistream MIMO systems with partial channel state information at the transmitter. We introduce a quantization scheme in which the full space of non-equivalent precoding matrices is partitioned into Grassmannian and orthogonalization parts. The Grassmannian part is used for maximizing the power after precoding and the orthogonalization part is used for removing cross talk between the data streams. We show that orthogonalization improves the attainable capacity when the receiver is linear. We give a parametrization for the non-equivalent orhogonalization matrices and a metric which measures the orthogonality of the transmission. Optimal orthogonalization codebooks for two-stream transmission are presented. When feedback is limited, the optimal partitioning of feedback bits between Grassmannian and orthogonalization parts becomes an issue. In correlated scenarios, the number of feedback bits may be significantly reduced by investing bits into the orthogonalization part.

IEEE Transactions on Signal Processing, 2012

tively). This corresponds to the sudden reduction in K D and 0 R [1] R [0] (Figs. 4 and 6), and the increase in Var(n ! ) (Fig. 5). For a given receives signal strength and noise floor, a designer can manipulate SNR c by varying TI, as shown in (5). The value of TI, therefore, should be chosen to provide a sufficiently large SNRc (greater than 13 dB, for example) to sustain high receiver performance. From a dynamic performance perspective, of course, a lower value of TI is attractive as it provides superior tracking capabilities and facilitates higher tracking bandwidth loops. Perhaps, then, T I may be chosen to situate SNR c at the knee of the variance curve of .

IEEE Transactions on Signal Processing, 2012

This correspondence deals with the construction of minimum Euclidean distance precoders for multiple-input multiple-output (MIMO) systems with up to four transmit antennas. By making use of a state-ofthe-art technique for optimization over the unitary group, we can numerically optimize the MIMO precoders. The correspondence then proceeds by identifying the obtained precoders as well-known lattices (square , Schläfli , , Gosset). With three transmit antennas, the results are slightly different compared with other numbers of transmit antennas since the obtained precoder is not an instance of the densest 6-dimensional lattice. The overall conclusions of the correspondence are that the found precoders for MIMO transmission are highly structured and that, even with small constellations, lattice theory can be used for the design of MIMO precoders.

IEEE Transactions on Signal Processing, 2009

MIMO systems with perfect channel state information at both sides of the link can adapt to the instantaneous channel conditions to optimize the spectral efficiency and/or the reliability of the communication. A low-complexity approach is the use of linear MIMO transceivers which are composed of a linear precoder at the transmitter and a linear equalizer at the receiver. The design of linear transceivers has been extensively studied in the literature with a variety of cost functions. In this paper, we focus on the minimum BER design, and show that the common practice of fixing a priori the number of data symbols to be transmitted per channel use inherently limits the diversity gain of the system. By introducing the number of symbols in the optimization process, we propose a minimum BER linear precoding scheme that achieves the full diversity of the MIMO channel. For the cases of uncorrelated/semicorrelated Rayleigh and uncorrelated Rician fading, the average BER performance of both schemes is analytically analyzed and characterized in terms of two key parameters: the array gain and the diversity gain.

In multiple-input multiple-output (MIMO) systems, pre-coders design pose significant implementation challenges due to the high computational complexity of the singular value decomposition (SVD) of the channel matrix. In this pa-per, we use the iterative COordinate Rotation DIgital Com-puter (CORDIC) algorithm to compute the SVD for dif-ferent configurations of multi-antenna systems. The com-plexity/performance trade-offs involved in the design of the max −d min precoder are also considered.

2006 Fortieth Asilomar Conference on Signals, Systems and Computers, 2006

In spatial multiplexing systems, transmission reliability is enhanced by the full channel state information (CSI) used to design optimum linear precoders, but in practice a full CSI is often unrealistic. Indeed, a higher number of transmitters and/or receivers elevates the coefficient numbers of the estimated channel, and the precision on coefficients depends on the rate of the feedback stream. An interesting alternative is to return a limited amount of information to the transmitter; this led us to design a dmin precoder based on the use of i) a finite codebook known by the receiver and the transmitter and ii) feedback of only one quantized real-valued parameter. The selection criteria employed to find the optimal precoding matrix are presented. Then, the performances about BER are compared under different criteria and amounts of feedback and confronted to Alamouti code.

IEEE Transactions on Signal Processing, 2004

We describe a new precoder based on optimization of the minimum Euclidean distance d min between signal points at the receiver side and for use in multiple-input multiple-output (MIMO) spatial multiplexing systems. Assuming that channel state information (CSI) can be made available at the transmitter, the three steps noise whitening, channel diagonalization and dimension reduction, currently used in investigations on MIMO systems, are performed. Thanks to this representation, an optimal d min precoder is derived in the case of two different transmitted data streams. For QPSK modulation, a numerical approach shows that the precoder design depends on the channel characteristics. Comparisons with maximum SNR strategy and other precoders based on criteria such as water-filling (WF), minimum mean square error (MMSE) and maximization of the minimum singular value of the global channel matrix are performed to illustrate the significant bit-error-rate (BER) improvement of the proposed precoder.

In Iterative Detection and Decoding, the accuracy and computational complexity of the calculation of the a posteriori probability(APP) of each coded bit play a crucial role in the applicability of the method. It is known that the method of Maximum A Posteriori(MAP) probability provides the optimum Bit-Error Rate performance, but holds an excessive computational complexity for practical implementation. Meanwhile, numerous sub-optimal methods are proposed to reduce the complexity while trying to retain as much as possible of the optimal BER performance.

2015 Wireless Telecommunications Symposium (WTS), 2015

In this paper, the problem of designing a linear precoder for Multiple-Input Multiple-Output (MIMO) systems employing Low-Density Parity-Check (LDPC) codes is addressed under the constraint of independent receiving virtual antenna output groups, thus reducing the relevant transmitter and receiver complexities. Our approach constitutes an interesting generalization of Bit-Interleaved Coded Multiple Beamforming (BICMB) which has shown many benefits in MIMO systems. After examining the properties associated with independent output grouping, we proceed to propose an alternative, practical technique, called Per-Group Precoding (PGP), which groups together multiple input symbol streams and corresponding receiving branches in the "virtual" channel domain (after singular value decomposition of the original MIMO channel), and thus results in independent transmitting/receiving streams between groups. We show with numerical results that PGP offers almost optimal performance, albeit with significant reduction both in the precoder optimization and LDPC EXIT chart based decoding complexities.