Results 1  10
of
29
MIMO broadcast channels with finite rate feedback
 IEEE Trans. on Inform. Theory
, 2006
"... Multiple transmit antennas in a downlink channel can provide tremendous capacity (i.e. multiplexing) gains, even when receivers have only single antennas. However, receiver and transmitter channel state information is generally required. In this paper, a system where each receiver has perfect channe ..."
Abstract

Cited by 95 (9 self)
 Add to MetaCart
Multiple transmit antennas in a downlink channel can provide tremendous capacity (i.e. multiplexing) gains, even when receivers have only single antennas. However, receiver and transmitter channel state information is generally required. In this paper, a system where each receiver has perfect channel knowledge, but the transmitter only receives quantized information regarding the channel instantiation is analyzed. The well known zero forcing transmission technique is considered, and simple expressions for the throughput degradation due to finite rate feedback are derived. A key finding is that the feedback rate per mobile must be increased linearly with the SNR (in dB) in order to achieve the full multiplexing gain, which is in sharp contrast to pointtopoint MIMO systems in which it is not necessary to increase the feedback rate as a function of the SNR. I.
MIMO Broadcast Channels With FiniteRate Feedback
, 2006
"... Multiple transmit antennas in a downlink channel can provide tremendous capacity (i.e., multiplexing) gains, even when receivers have only single antennas. However, receiver and transmitter channel state information is generally required. In this correspondence, a system where each receiver has per ..."
Abstract

Cited by 50 (1 self)
 Add to MetaCart
Multiple transmit antennas in a downlink channel can provide tremendous capacity (i.e., multiplexing) gains, even when receivers have only single antennas. However, receiver and transmitter channel state information is generally required. In this correspondence, a system where each receiver has perfect channel knowledge, but the transmitter only receives quantized information regarding the channel instantiation is analyzed. The wellknown zeroforcing transmission technique is considered, and simple expressions for the throughput degradation due to finiterate feedback are derived. A key finding is that the feedback rate per mobile must be increased linearly with the signaltonoise ratio (SNR) (in decibels) in order to achieve the full multiplexing gain. This is in sharp contrast to pointtopoint multipleinput multipleoutput (MIMO) systems, in which it is not necessary to increase the feedback rate as a function of the SNR.
On some inequalities for the gamma and psi functions
 MATH. COMP
, 1997
"... We present new inequalities for the gamma and psi functions, and we provide new classes of completely monotonic, starshaped, and superadditive functions which are related to Γ and ψ. Euler’s gamma function Γ(x) = ..."
Abstract

Cited by 38 (1 self)
 Add to MetaCart
We present new inequalities for the gamma and psi functions, and we provide new classes of completely monotonic, starshaped, and superadditive functions which are related to Γ and ψ. Euler’s gamma function Γ(x) =
A completely monotonic function involving divided differences of psi and polygamma functions and an application
 RGMIA Res. Rep. Coll
"... Abstract. A class of functions involving the divided differences of the psi function and the polygamma functions and originating from Kershaw’s double inequality are proved to be completely monotonic. As applications of these results, the monotonicity and convexity of a function involving ratio of t ..."
Abstract

Cited by 17 (13 self)
 Add to MetaCart
Abstract. A class of functions involving the divided differences of the psi function and the polygamma functions and originating from Kershaw’s double inequality are proved to be completely monotonic. As applications of these results, the monotonicity and convexity of a function involving ratio of two gamma functions and originating from establishment of the best upper and lower bounds in Kershaw’s double inequality are derived, two sharp double inequalities involving ratios of double factorials are recovered, the probability integral or error function is estimated, a double inequality for ratio of the volumes of the unit balls in R n−1 and R n respectively is deduced, and a symmetrical upper and lower bounds for the gamma function in terms of the psi function is generalized. 1.
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 ..."
Abstract

Cited by 16 (1 self)
 Add to MetaCart
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.
Capacity of Beamforming with Limited Training and Feedback
"... We examine the capacity of beamforming over a MultiInput/SingleOutput block Rayleigh fading channel with finite training for channel estimation and limited feedback. A fixedlength packet is assumed, which is spanned by ¢ training symbols, £ feedback bits, and the data symbols. The training symb ..."
Abstract

Cited by 10 (5 self)
 Add to MetaCart
We examine the capacity of beamforming over a MultiInput/SingleOutput block Rayleigh fading channel with finite training for channel estimation and limited feedback. A fixedlength packet is assumed, which is spanned by ¢ training symbols, £ feedback bits, and the data symbols. The training symbols are used to obtain a Minimum Mean Squared Error (MMSE) estimate of the channel vector. Given this estimate, the receiver selects a transmit beamforming vector from a codebook containing ¤¦ ¥ i.i.d. random vectors, and relays the corresponding £ bits back to the transmitter. We derive bounds on the capacity and show that for a large number of transmit antennas §© ¨ , the optimal ¢ and £ , which maximize the bounds, are approximately equal and both increase as §�¨������¦��§© ¨. We conclude that with limited training and feedback, the optimal number of antennas to activate also increases as § ¨ �����¦�� § ¨.
Monotonicity and convexity for the gamma function
 J. Inequal. Pure Appl. Math
"... ABSTRACT. Let a and b be given real numbers with 0 ≤ a < b < a + 1. Then the function θa,b(x) = [Γ(x + b)/Γ(x + a)] 1/(b−a) − x is strictly convex and decreasing on (−a, ∞) with θa,b(∞) = a+b−1 2 and θa,b(−a) = a, where Γ denotes the Euler’s gamma function. Key words and phrases: Gamma fun ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
ABSTRACT. Let a and b be given real numbers with 0 ≤ a < b < a + 1. Then the function θa,b(x) = [Γ(x + b)/Γ(x + a)] 1/(b−a) − x is strictly convex and decreasing on (−a, ∞) with θa,b(∞) = a+b−1 2 and θa,b(−a) = a, where Γ denotes the Euler’s gamma function. Key words and phrases: Gamma function; monotonicity; convexity.
Bounds for the ratio of two gamma functions—From Wendel’s and related inequalities to logarithmically completely monotonic functions, submitted
"... Abstract. In the survey paper, along one of main lines of bounding the ratio of two gamma functions, we look back and analyse some known results, including Wendel’s, Gurland’s, Kazarinoff’s, Gautschi’s, Watson’s, Chu’s, LazarevićLupa¸s’s, Kershaw’s and ElezovićGiordanoPečarić’s inequalities, clai ..."
Abstract

Cited by 5 (5 self)
 Add to MetaCart
Abstract. In the survey paper, along one of main lines of bounding the ratio of two gamma functions, we look back and analyse some known results, including Wendel’s, Gurland’s, Kazarinoff’s, Gautschi’s, Watson’s, Chu’s, LazarevićLupa¸s’s, Kershaw’s and ElezovićGiordanoPečarić’s inequalities, claim, monotonic and convex properties. On the other hand, we introduce some related advances on the topic of bounding the ratio of two gamma functions in recent years. Contents
SOME PROPERTIES OF THE GAMMA AND PSI FUNCTIONS, WITH APPLICATIONS
"... Abstract. In this paper, some monotoneity and concavity properties of the gamma, beta and psi functions are obtained, from which several asymptotically sharp inequalities follow. Applying these properties, the authors improve some wellknown results for the volume Ωn of the unit ball B n ⊂ R n,thesu ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
Abstract. In this paper, some monotoneity and concavity properties of the gamma, beta and psi functions are obtained, from which several asymptotically sharp inequalities follow. Applying these properties, the authors improve some wellknown results for the volume Ωn of the unit ball B n ⊂ R n,thesurface area ωn−1 of the unit sphere S n−1, and some related constants. 1.