504 research outputs found
Optimizing hardware function evaluation
Published versio
Multi-Band Covariance Interpolation with Applications in Massive MIMO
In this paper, we study the problem of multi-band (frequency-variant)
covariance interpolation with a particular emphasis towards massive MIMO
applications. In a massive MIMO system, the communication between each BS with
antennas and each single-antenna user occurs through a collection of
scatterers in the environment, where the channel vector of each user at BS
antennas consists in a weighted linear combination of the array responses of
the scatterers, where each scatterer has its own angle of arrival (AoA) and
complex channel gain. The array response at a given AoA depends on the
wavelength of the incoming planar wave and is naturally frequency dependent.
This results in a frequency-dependent distortion where the second order
statistics, i.e., the covariance matrix, of the channel vectors varies with
frequency. In this paper, we show that although this effect is generally
negligible for a small number of antennas , it results in a considerable
distortion of the covariance matrix and especially its dominant signal subspace
in the massive MIMO regime where , and can generally incur a
serious degradation of the performance especially in frequency division
duplexing (FDD) massive MIMO systems where the uplink (UL) and the downlink
(DL) communication occur over different frequency bands. We propose a novel
UL-DL covariance interpolation technique that is able to recover the covariance
matrix in the DL from an estimate of the covariance matrix in the UL under a
mild reciprocity condition on the angular power spread function (PSF) of the
users. We analyze the performance of our proposed scheme mathematically and
prove its robustness under a sufficiently large spatial oversampling of the
array. We also propose several simple off-the-shelf algorithms for UL-DL
covariance interpolation and evaluate their performance via numerical
simulations.Comment: A short version of this paper was submitted to IEEE International
Symposium on Information Theory (ISIT), 201
Survey of Floating-Point Software Arithmetics and Basic Library Mathematical Functions
Abstract Not Provided
Numerical methods for solving ordinary and partial differential equations
The numerical solution of ordinary differential equations will be the
main topics discussed in the first half of this thesis. In Chapter 2 initial value problems are examined and the resulting differential equations are solved
by using extrapolation techniques. Computer trials of the algorithm are
completed by a special ordinary differential equation tester program and the
statistics of its performance are compared with other established methods.
In the following Chapter the relevant theory and properties, associated
with Chebyshev polynomials, is presented. Then boundary value problems are
solved by representing the ordinary differential equations as a Chebyshev
series. Finally, similar methods are developed for the solution of partial
differential equations
A comparison of computational methods and algorithms for the complex gamma function
A survey and comparison of some computational methods and algorithms for gamma and log-gamma functions of complex arguments are presented. Methods and algorithms reported include Chebyshev approximations, Pade expansion and Stirling's asymptotic series. The comparison leads to the conclusion that Algorithm 421 published in the Communications of ACM by H. Kuki is the best program either for individual application or for the inclusion in subroutine libraries
- …