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Sum capacity of the vector Gaussian broadcast channel and uplinkdownlink duality
 IEEE TRANS. ON INFORM. THEORY
, 2003
"... We characterize the sum capacity of the vector Gaussian broadcast channel by showing that the existing inner bound of Marton and the existing upper bound of Sato are tight for this channel. We exploit an intimate fourway connection between the vector broadcast channel, the corresponding pointtopo ..."
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Cited by 323 (2 self)
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We characterize the sum capacity of the vector Gaussian broadcast channel by showing that the existing inner bound of Marton and the existing upper bound of Sato are tight for this channel. We exploit an intimate fourway connection between the vector broadcast channel, the corresponding pointtopoint channel (where the receivers can cooperate), the multiple access channel (where the role of transmitters and receivers are reversed), and the corresponding pointtopoint channel (where the transmitters can cooperate).
Uplinkdownlink duality via minimax duality
 in Canadian Workshop on Info. Theory
, 2003
"... Abstract—The sum capacity of a Gaussian vector broadcast channel is the saddle point of a minimax Gaussian mutual information expression where the maximization is over the set of transmit covariance matrices subject to a power constraint and the minimization is over the set of noise covariance matri ..."
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Cited by 63 (6 self)
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Abstract—The sum capacity of a Gaussian vector broadcast channel is the saddle point of a minimax Gaussian mutual information expression where the maximization is over the set of transmit covariance matrices subject to a power constraint and the minimization is over the set of noise covariance matrices subject to a diagonal constraint. This sum capacity result has been proved using two different methods, one based on decisionfeedback equalization and the other based on a duality between uplink and downlink channels. This paper illustrates the connection between the two approaches by establishing that uplink–downlink duality is equivalent to Lagrangian duality in minimax optimization. This minimax Lagrangian duality relation allows the optimal transmit covariance and the leastfavorablenoise covariance matrices in a Gaussian vector broadcast channel to be characterized in terms of the dual variables. In particular, it reveals that the least favorable noise is not unique. Further, the new Lagrangian interpretation of uplink–downlink duality allows the duality relation to be generalized to Gaussian vector broadcast channels with arbitrary linear constraints. However, duality depends critically on the linearity of input constraints. Duality breaks down when the input constraint is an arbitrary convex constraint. This shows that the minimax representation of the broadcast channel sum capacity is more general than the uplink–downlink duality representation. Index Terms—Broadcast channel, Lagrangian duality, minimax optimization, multipleinput multipleoutput (MIMO), multipleaccess
Joint transceiver design for MIMO communications using geometric mean decomposition
 IEEE Trans. Signal Process
, 2005
"... Abstract—In recent years, considerable attention has been paid to the joint optimal transceiver design for multiinput multioutput (MIMO) communication systems. In this paper, we propose a joint transceiver design that combines the geometric mean decomposition (GMD) with either the conventional zer ..."
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Cited by 51 (7 self)
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Abstract—In recent years, considerable attention has been paid to the joint optimal transceiver design for multiinput multioutput (MIMO) communication systems. In this paper, we propose a joint transceiver design that combines the geometric mean decomposition (GMD) with either the conventional zeroforcing VBLAST decoder or the more recent zeroforcing dirty paper precoder (ZFDP). Our scheme decomposes a MIMO channel into multiple identical parallel subchannels, which can make it rather convenient to design modulation/demodulation and coding/decoding schemes. Moreover, we prove that our scheme is asymptotically optimal for (moderately) high SNR in terms of both channel throughput and bit error rate (BER) performance. This desirable property is not shared by any other conventional schemes. We also consider the subchannel selection issues when some of the subchannels are too poor to be useful. Our scheme can also be combined with orthogonal frequency division multiplexing (OFDM) for intersymbol interference (ISI) suppression. The effectiveness of our approaches has been validated by both theoretical analyses and numerical simulations. Index Terms—Channel capacity, dirty paper precoding, intersymbol interference suppression, joint transceiver design, matrix
Uniform channel decomposition for MIMO communications
 IEEE Transactions on Signal Processing
, 2005
"... Abstract—Assuming the availability of the channel state information at the transmitter (CSIT) and receiver (CSIR), we consider the joint optimal transceiver design for multiinput multioutput (MIMO) communication systems. Using the geometric mean decomposition (GMD), we propose a transceiver design ..."
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Cited by 49 (8 self)
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Abstract—Assuming the availability of the channel state information at the transmitter (CSIT) and receiver (CSIR), we consider the joint optimal transceiver design for multiinput multioutput (MIMO) communication systems. Using the geometric mean decomposition (GMD), we propose a transceiver design that can decompose, in a strictly capacity lossless manner, a MIMO channel into multiple subchannels with identical capacities. This uniform channel decomposition (UCD) scheme has two implementation forms. One is the combination of a linear precoder and a minimum meansquarederror VBLAST (MMSEVBLAST) detector, which is referred to as UCDVBLAST, and the other includes a dirty paper (DP) precoder and a linear equalizer followed by a DP decoder, which we refer to as UCDDP. The UCD scheme can provide much convenience for the modulation/demodulation and coding/decoding procedures due to obviating the need for bit allocation. We also show that UCD can achieve the maximal diversity gain. The simulation results show that the UCD scheme exhibits excellent performance, even without the use of any error correcting codes. Index Terms—Channel capacity, DBLAST, dirty paper precoder, diversity gain, geometric mean decomposition, joint transceiver
Sum Capacity of the Multiple Antenna Gaussian Broadcast Channel And UplinkDownlink Duality
 IEEE Transactions on Information Theory
, 2002
"... We characterize the sum capacity of the multiple antenna Gaussian broadcast channel by showing that the existing inner bound of Marton and the existing upper bound of Sato are tight for this channel. We exploit an intimate fourway connection between the multiple antenna broadcast channel, the corre ..."
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Cited by 48 (4 self)
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We characterize the sum capacity of the multiple antenna Gaussian broadcast channel by showing that the existing inner bound of Marton and the existing upper bound of Sato are tight for this channel. We exploit an intimate fourway connection between the multiple antenna broadcast channel, the corresponding pointtopoint channel (where the receivers can cooperate), the multiple access channel (where the role of transmitters and receivers are reversed), and the corresponding pointtopoint channel (where the transmitters can cooperate).
Great expectations: The value of spatial diversity in wireless networks
 PROCEEDINGS OF THE IEEE
, 2004
"... In this paper, the effect of spatial diversity on the throughput and reliability of wireless networks is examined. Spatial diversity is realized through multiple independently fading transmit/receive antenna paths in singleuser communication and through independently fading links in multiuser commu ..."
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Cited by 45 (8 self)
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In this paper, the effect of spatial diversity on the throughput and reliability of wireless networks is examined. Spatial diversity is realized through multiple independently fading transmit/receive antenna paths in singleuser communication and through independently fading links in multiuser communication. Adopting spatial diversity as a central theme, we start by studying its informationtheoretic foundations, then we illustrate its benefits across the physical (signal transmission/coding and receiver signal processing) and networking (resource allocation, routing, and applications) layers. Throughout the paper, we discuss engineering intuition and tradeoffs, emphasizing the strong interactions between the various network functionalities.
On the Capacity of the Multiple Antenna Broadcast Channel
 DIMACS SERIES IN DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE
"... The capacity region of the multiple antenna (transmit and receive) broadcast channel is considered. We propose an outer bound to the capacity region by converting this nondegraded broadcast channel into a degraded one with users privy to the signals of users ordered below them. We extend our proof ..."
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Cited by 37 (3 self)
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The capacity region of the multiple antenna (transmit and receive) broadcast channel is considered. We propose an outer bound to the capacity region by converting this nondegraded broadcast channel into a degraded one with users privy to the signals of users ordered below them. We extend our proof techniques in the characterization of the sum capacity of the multiple antenna broadcast channel to evaluate this outer bound with Gaussian inputs. Our main result is the observation that if Gaussian inputs are optimal to the constructed degraded channel, then the capacity region of the multiple antenna broadcast channel is characterized.
The generalized triangular decomposition
 Mathematics of Computation
, 2006
"... Abstract. Given a complex matrix H, we consider the decomposition H = QRP ∗ , where R is upper triangular and Q and P have orthonormal columns. Special instances of this decomposition include (a) the singular value decomposition (SVD) where R is a diagonal matrix containing the singular values on th ..."
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Cited by 32 (4 self)
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Abstract. Given a complex matrix H, we consider the decomposition H = QRP ∗ , where R is upper triangular and Q and P have orthonormal columns. Special instances of this decomposition include (a) the singular value decomposition (SVD) where R is a diagonal matrix containing the singular values on the diagonal, (b) the Schur decomposition where R is an upper triangular matrix with the eigenvalues of H on the diagonal, (c) the geometric mean decomposition (GMD) [The Geometric Mean Decomposition, Y. Jiang, W. W. Hager, and J. Li, December 7, 2003] where the diagonal of R is the geometric mean of the positive singular values. We show that any diagonal for R can be achieved that satisfies Weyl’s multiplicative majorization conditions: k� k� ri  ≤ σi, 1 ≤ k < K, i=1 i=1 K� K� ri  = σi, where K is the rank of H, σi is the ith largest singular value of H, and ri is the ith largest (in magnitude) diagonal element of R. We call the decomposition H = QRP ∗ , where the diagonal of R satisfies Weyl’s conditions, the generalized triangular decomposition (GTD). The existence of the GTD is established using a result of Horn [On the eigenvalues of a matrix with prescribed singular values, Proc. Amer. Math. Soc., 5 (1954), pp. 4–7]. In addition, we present a direct (nonrecursive) algorithm that starts with the SVD and applies a series of permutations and Givens rotations to obtain the GTD. The GMD has application to signal processing and the design of multipleinput multipleoutput (MIMO) systems; the lossless filters Q and P minimize the maximum error rate of the network. The GTD is more flexible than the GMD since the diagonal elements of R need not be identical. With this additional freedom, the performance of a communication channel can be optimized, while taking into account differences in priority or differences in quality of service requirements for subchannels. Another application of the GTD is to inverse eigenvalue problems where the goal is to construct matrices with prescribed eigenvalues and singular values. Key words. Generalized triangular decomposition, geometric mean decomposition, matrix factorization, unitary factorization, singular value decomposition, Schur decomposition, MIMO systems, inverse eigenvalue problems
PerTone Equalization for MIMOOFDM Systems
, 2003
"... This paper focuses on MultipleInput MultipleOutput (MIMO) Orthogonal Frequency Division Multiplexing (OFDM) systems, where the MIMO channel order is larger than the length of the Cyclic Prefix (CP). By swapping the filtering operations of the MIMO channel and the Fast Fourier Transform (FFT), it is ..."
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Cited by 13 (1 self)
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This paper focuses on MultipleInput MultipleOutput (MIMO) Orthogonal Frequency Division Multiplexing (OFDM) systems, where the MIMO channel order is larger than the length of the Cyclic Prefix (CP). By swapping the filtering operations of the MIMO channel and the Fast Fourier Transform (FFT), it is shown that each tone of a MIMO OFDM system can be viewed as a MIMO SingleCarrier (SC) system. As a result, the existing equalization approach for MIMO SC systems can be applied to each tone of a MIMO OFDM system. This socalled pertone equalization (PTEQ) approach for MIMO OFDM systems is an attractive alternative for the recently developed timedomain equalization (TEQ) approach for MIMO OFDM systems. The main difference between the PTEQ and TEQ approach is that a pertone equalizer equalizes a single tone on the symbol level (low rate), whereas a timedomain equalizer equalizes all tones together on the sample level (high rate). Next to some other advantages, this means that a pertone equalizer can much more easily be designed in practice than a timedomain equalizer. This is illustrated in the second part, where we adapt an existing semiblind equalization algorithm for a Generalized SpaceTime Block Coded (GSTBC) MIMO SC system to a semiblind pertone equalization algorithm for a GSTBC MIMO OFDM system.