Achieving the Welch Bound With Difference Sets

Xia, Pengfei; Zhou, Shengli; Giannakis, Georgios B.

doi:10.1109/tit.2005.846411

Cited by 383 publications

(326 citation statements)

References 21 publications

(28 reference statements)

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“…Another manifestation of the same problem is in communications and refers to the design of code books that minimize the maximal cross-correlation amplitude (see [13], [18] and references therein). In particular, the rows of the matrix V are codewords, which are taken to have unit norm.…”

Section: Grassmannian Spaces and Code Booksmentioning

confidence: 99%

“…Designing codes that meet the optimality bound (9) for E max with equality is a difficult problem that is still open for the case of general pairs (n, s), while it has found elegant closed form solutions for special values of (n, s) and complex valued unit norm codewords [18]. On the other hand, designing real valued codes that meet the E rms bound with equality is considered to be an easy problem.…”

Section: Grassmannian Spaces and Code Booksmentioning

confidence: 99%

“…Recall that M is the number of Chebychev polynomials in the expansion (18) and s the number of vectors employed in the diagonal estimator. Using Algorithm 2 in the diagonal estimator (Fig.…”

Section: Using Chebychev Vectorsmentioning

confidence: 99%

“…We emphasize that when calculating charge densities we employ an approximation at two levels. First, we rely on the Chebychev expansion (18) to approximate the density matrix P and then we employ the diagonal estimator in order to approximate the charge densities (diagonal of P ). In this paper we are primarily interested in studying the approximating qualities of the diagonal estimator.…”

Section: Experiments With Density Matricesmentioning

confidence: 99%

See 3 more Smart Citations

An estimator for the diagonal of a matrix

Bekas

Kokiopoulou

Saad

2007

Applied Numerical Mathematics

163

190

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A number of applications require to compute an approximation of the diagonal of a matrix when this matrix is not explicitly available but matrix-vector products with it are easy to evaluate. In some cases, it is the trace of the matrix rather than the diagonal that is needed. This paper describes methods for estimating diagonals and traces of matrices in these situations. The goal is to obtain a good estimate of the diagonal by applying only a small number of matrix-vector products, using selected vectors. We begin by considering the use of random test vectors and then explore special vectors obtained from Hadamard matrices. The methods are tested in the context of computational materials science to estimate the diagonal of the density matrix which holds the charge densities. Numerical experiments indicate that the diagonal estimator may offer an alternative method that in some cases can greatly reduce computational costs in electronic structures calculations.

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Section: Grassmannian Spaces and Code Booksmentioning

confidence: 99%

Section: Grassmannian Spaces and Code Booksmentioning

confidence: 99%

Section: Using Chebychev Vectorsmentioning

confidence: 99%

Section: Experiments With Density Matricesmentioning

confidence: 99%

See 2 more Smart Citations

An estimator for the diagonal of a matrix

Bekas

Kokiopoulou

Saad

2007

Applied Numerical Mathematics

163

190

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show abstract

“…We consider codebook construction from fast Fourier transform matrices [5], [6]. This class of codewords in the codebook can be thought of as subset of m columns of the N × N FFT matrix [21].…”

Section: A Channel Quantization and Codebook Designmentioning

confidence: 99%

Low Complexity Multiuser Scheduling in MIMO Broadcast Channel with Limited Feedback

Luo

Chen

2008

2008 4th IEEE International Conference on Circuits and Systems for Communications

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Abstract-This paper deals with the design and analysis of low complexity user scheduling algorithm in multi-antenna broadcast (downlink) systems under zero-forcing multiplexing with limited feedback. By using quantization technology, the channel matrix can be divided into serval unoverlapped channel regions. Based on the quantized channel regions, we can get semi-orthogonal region sets. Then the transmitter can carry out user scheduling by using the feedback channel direction information (CDI), channel quality information (CQI) and the quantized semi-orthogonal channel region sets. Simulation results show that the presented user scheduling algorithm can achieve a sum rate close to the full searching algorithms while with much lower complexity than those of the previous algorithms.

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Kronecker product‐based codebook design and optimisation for correlated 3D channels

Wang

Jiang

Chen

2014

Trans. Emerging Tel. Tech.

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Discrete Fourier transform (DFT) codebook has been favoured by long term evolution because of its simplicity and effectiveness for two-dimensional multi-input multi-output channels. In order to further explore vertical freedom, a Kronecker product-based codebook (KPC), which is the Kronecker product of a horizontal DFT codebook and a vertical one, has been proposed. However, how to effectively design the codebook is still a challenge, because neither its effectiveness nor optimisation has been studied. In this paper, we demonstrate that the codewords in the KPC approximately match the distribution of the optimal beamforming vectors under spatially correlated three-dimensional channels, showing the effectiveness of such codebook structure. Moreover, because the maximal cross-correlation amplitude .I max / of the original KPC is high, we investigate the structure of the codebook and then find a criterion of constructing the optimal KPC to achieve the lowest I max , namely the Welch bound. Furthermore, considering the optimal codebook only exists under certain conditions, a modified discrete stochastic approximation algorithm is used to construct a near-optimal codebook. Simulation results show that our algorithm greatly reduces I max and respectively provides 1 and 0.5 dB coding gain compared to the traditional DFT codebook and the original KPC, which confirms the efficiency of the codebook design.

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Achieving the Welch Bound With Difference Sets

Cited by 383 publications

References 21 publications

An estimator for the diagonal of a matrix

An estimator for the diagonal of a matrix

Low Complexity Multiuser Scheduling in MIMO Broadcast Channel with Limited Feedback

Kronecker product‐based codebook design and optimisation for correlated 3D channels

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