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A comparison of timesharing, DPC, and beamforming for MIMO broadcast channels with many users
 IEEE Trans. Commun
, 2007
"... In this paper, we derive the scaling laws of the sum rate for fading MIMO Gaussian broadcast channels using timesharing to the strongest user, dirty paper coding (DPC), and beamforming when the number of users (receivers) n is large. Throughout the paper, we assume a fix average transmit power and ..."
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Cited by 31 (0 self)
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In this paper, we derive the scaling laws of the sum rate for fading MIMO Gaussian broadcast channels using timesharing to the strongest user, dirty paper coding (DPC), and beamforming when the number of users (receivers) n is large. Throughout the paper, we assume a fix average transmit power and consider a block fading Rayleigh channel. First, we show that for a system with M transmit antennas and users equipped with N antennas, the sum rate scales like M log log nN for DPC and beamforming when M is fixed and for any N (either growing to infinity or not). On the other hand, when both M and N are fixed, the sum rate of timesharing to the strongest user scales like min(M, N) log log n. Therefore, the asymptotic gain of DPC over timesharing for the sum rate is M min(M,N) when M and N are fixed. It is also shown that if M grows as log n, the sum rate of DPC and beamforming will grow linearly in M, but with different constant multiplicative factors. In this region, the sum rate capacity of timesharing scales like N log log n.
The Incomplete Gamma Functions Since Tricomi
 In Tricomi's Ideas and Contemporary Applied Mathematics, Atti dei Convegni Lincei, n. 147, Accademia Nazionale dei Lincei
, 1998
"... The theory of the incomplete gamma functions, as part of the theory of conuent hypergeometric functions, has received its rst systematic exposition by Tricomi in the early 1950s. His own contributions, as well as further advances made thereafter, are surveyed here with particular emphasis on asy ..."
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Cited by 15 (1 self)
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The theory of the incomplete gamma functions, as part of the theory of conuent hypergeometric functions, has received its rst systematic exposition by Tricomi in the early 1950s. His own contributions, as well as further advances made thereafter, are surveyed here with particular emphasis on asymptotic expansions, zeros, inequalities, computational methods, and applications.
Uniform bounds for the complementary incomplete gamma function, Preprint at http://locutus.cs.dal.ca:8088/archive/00000335
"... Abstract. We prove upper and lower bounds for the complementary incomplete gamma function Γ(a, z) with complex parameters a and z. Our bounds are refined within the circular hyperboloid of one sheet {(a, z) : z > ca − 1} with a real and z complex. Our results show that within the hyperboloid, Γ ..."
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Abstract. We prove upper and lower bounds for the complementary incomplete gamma function Γ(a, z) with complex parameters a and z. Our bounds are refined within the circular hyperboloid of one sheet {(a, z) : z > ca − 1} with a real and z complex. Our results show that within the hyperboloid, Γ(a, z)  is of order z  a−1 e − Re(z) , and extends an upper estimate of Natalini and Palumbo to complex values of z.
'f ii TABLE OF CONTENTS Chapter
, 1960
"... This research was supported by the Office of Naval Research under Contract No. Nonr855(06) for resear~h in probability and statistics at Chapel Hill. Reproduction in whole or in part is permitted for any purpose ..."
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This research was supported by the Office of Naval Research under Contract No. Nonr855(06) for resear~h in probability and statistics at Chapel Hill. Reproduction in whole or in part is permitted for any purpose
SHOULD AUCTIONS BE TRANSPARENT? By
, 2010
"... We investigate the role of market transparency in repeated firstprice auctions. We consider a setting with private and independent values across bidders. The values are assumed to be perfectly persistent over time. We analyze the firstprice auction under three distinct disclosure regimes regarding ..."
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We investigate the role of market transparency in repeated firstprice auctions. We consider a setting with private and independent values across bidders. The values are assumed to be perfectly persistent over time. We analyze the firstprice auction under three distinct disclosure regimes regarding the bid and award history. Of particular interest is the minimal disclosure regime, in which each bidder only learns privately whether he won or lost the auction at the end of each round. In equilibrium, the winner of the initial auction lowers his bids over time, while losers keep their bids constant, in anticipation of the winner’s lower future bids. This equilibrium is efficient, and all information is eventually revealed. Importantly, this disclosure regime does not give rise to pooling equilibria. We contrast the minimal disclosure setting with the case in which all bids are public, and the case in which only the winner’s bids are public. In these settings, an inefficient pooling equilibrium with low revenues always exists with a sufficiently large number of bidders.
ON THE ORTHOGONAL SYMMETRY OF LFUNCTIONS OF A FAMILY OF HECKE GRÖSSENCHARACTERS
"... Abstract. The family of symmetric powers of an Lfunction associated with an elliptic curve with complex multiplication has received much attention from algebraic, automorphic and padic points of view. Here we examine this family from the perspectives of classical analytic number theory and random ..."
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Abstract. The family of symmetric powers of an Lfunction associated with an elliptic curve with complex multiplication has received much attention from algebraic, automorphic and padic points of view. Here we examine this family from the perspectives of classical analytic number theory and random matrix theory, especially focusing on evidence for the symmetry type of the family. In particular, we investigate the values at the central point and give evidence that this family can be modeled by ensembles of orthogonal matrices. We prove an asymptotic formula with power savings for the average of these Lvalues, which reproduces, by a completely different method, an asymptotic formula proven by Greenberg and Villegas–Zagier. We give an upper bound for the second moment which is conjecturally too large by just one logarithm. We also give an explicit conjecture for the second moment of this family, with power savings. Finally, we compute the one level density for this family with a test function whose Fourier transform has limited support. It is known by the work of Villegas – Zagier that the subset of these Lfunctions which have even functional equations never vanish; we show to what extent this result is reflected by our analytic results.
RESEARCH ARTICLE A note on the real zeros of the incomplete gamma function
"... Asymptotic formulae that estimate the locations of real zeros of the lower incomplete gamma function are obtained using methods based in part on the original derivations by Tricomi. It is shown that these original calculations are correct, aside from some minor typographical errors, whereas later pa ..."
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Asymptotic formulae that estimate the locations of real zeros of the lower incomplete gamma function are obtained using methods based in part on the original derivations by Tricomi. It is shown that these original calculations are correct, aside from some minor typographical errors, whereas later papers have overstated the accuracy of the approximations. For one of the zeros, a minor alteration to Tricomi’s working leads to a formula that is more accurate than those that have appeared in the literature to date. 1.