20,937 research outputs found
Paperfolding morphisms, planefilling curves, and fractal tiles
An interesting class of automatic sequences emerges from iterated
paperfolding. The sequences generate curves in the plane with an almost
periodic structure. We generalize the results obtained by Davis and Knuth on
the self-avoiding and planefilling properties of these curves, giving simple
geometric criteria for a complete classification. Finally, we show how the
automatic structure of the sequences leads to self-similarity of the curves,
which turns the planefilling curves in a scaling limit into fractal tiles. For
some of these tiles we give a particularly simple formula for the Hausdorff
dimension of their boundary.Comment: 32 pages, 23 figure
Limit shape and height fluctuations of random perfect matchings on square-hexagon lattices
We study asymptotics of perfect matchings on a large class of graphs called
the contracting square-hexagon lattice, which is constructed row by row from
either a row of a square grid or a row of a hexagonal lattice. We assign the
graph periodic edge weights with period , and consider the
probability measure of perfect matchings in which the probability of each
configuration is proportional to the product of edge weights. We show that the
partition function of perfect matchings on such a graph can be computed
explicitly by a Schur function depending on the edge weights. By analyzing the
asymptotics of the Schur function, we then prove the Law of Large Numbers
(limit shape) and the Central Limit Theorem (convergence to the Gaussian free
field) for the corresponding height functions. We also show that the
distribution of certain type of dimers near the turning corner is the same as
the eigenvalues of Gaussian Unitary Ensemble, and that in the scaling limit
under the boundary condition that each segment of the bottom boundary grows
linearly with respect the dimension of the graph, the frozen boundary is a
cloud curve whose number of tangent points to the bottom boundary of the domain
depends on the size of the period, as well as the number of segments along the
bottom boundary
MIMO Transceivers With Decision Feedback and Bit Loading: Theory and Optimization
This paper considers MIMO transceivers with linear precoders and decision feedback equalizers (DFEs), with bit allocation at the transmitter. Zero-forcing (ZF) is assumed. Considered first is the minimization of transmitted power, for a given total bit rate and a specified set of error probabilities for the symbol streams. The precoder and DFE matrices are optimized jointly with bit allocation. It is shown that the generalized triangular decomposition (GTD) introduced by Jiang, Li, and Hager offers an optimal family of solutions. The optimal linear transceiver (which has a linear equalizer rather than a DFE) with optimal bit allocation is a member of this family. This shows formally that, under optimal bit allocation, linear and DFE transceivers achieve the same minimum power. The DFE transceiver using the geometric mean decomposition (GMD) is another member of this optimal family, and is such that optimal bit allocation yields identical bits for all symbol streams—no bit allocation is necessary—when the specified error probabilities are identical for all streams. The QR-based system used in VBLAST is yet another member of the optimal family and is particularly well-suited when limited feedback is allowed from receiver to transmitter. Two other optimization problems are then considered: a) minimization of power for specified set of bit rates and error probabilities (the QoS problem), and b) maximization of bit rate for fixed set of error probabilities and power. It is shown in both cases that the GTD yields an optimal family of solutions
Weyl-Heisenberg Spaces for Robust Orthogonal Frequency Division Multiplexing
Design of Weyl-Heisenberg sets of waveforms for robust orthogonal frequency
division multiplex- ing (OFDM) has been the subject of a considerable volume of
work. In this paper, a complete parameterization of orthogonal Weyl-Heisenberg
sets and their corresponding biorthogonal sets is given. Several examples of
Weyl-Heisenberg sets designed using this parameterization are pre- sented,
which in simulations show a high potential for enabling OFDM robust to
frequency offset, timing mismatch, and narrow-band interference
Analysis and optimization of pilot symbol-assisted Rake receivers for DS-CDMA systems
The effect of imperfect channel estimation (CE) on the performance of pilot-symbol-assisted modulation (PSAM) and MRC Rake reception over time- or frequency-selective fading channels with either a uniform power delay profile (UPDP) or a nonuniform power delay profile (NPDP) is investigated. For time-selective channels, a Wiener filter or linear minimum mean square error (LMMSE) filter for CE is considered, and a closed-form asymptotic expression for the mean square error (MSE) when the number of pilots used for CE approaches infinity is derived. In high signal-to-noise ratio (SNR), the MSE becomes independent of the channel Doppler spectrum. A characteristic function method is used to derive new closed-form expressions for the bit error rate (BER) of Rake receivers in UPDP and NPDP channels. The results are extended to two-dimensional (2-D) Rake receivers. The pilot-symbol spacing and pilot-to-data power ratio are optimized by minimizing the BER. For UPDP channels, elegant results are obtained in the asymptotic case. Furthermore, robust spacing design criteria are derived for the maximum Doppler frequency
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