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11
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 27 (5 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
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 15 (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
Tunable channel decomposition for MIMO communications using channel state information
 IEEE Transactions on Signal Processing
, 2006
"... Abstract—We consider jointly designing transceivers for multipleinput multipleoutput (MIMO) communications. Assuming the availability of the channel state information (CSI) at the transmitter (CSIT) and receiver (CSIR), we propose a scheme that can decompose a MIMO channel, in a capacity lossless ..."
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Cited by 6 (0 self)
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Abstract—We consider jointly designing transceivers for multipleinput multipleoutput (MIMO) communications. Assuming the availability of the channel state information (CSI) at the transmitter (CSIT) and receiver (CSIR), we propose a scheme that can decompose a MIMO channel, in a capacity lossless manner, into multiple subchannels with prescribed capacities, or equivalently, signaltointerferenceandnoise ratios (SINRs). We refer to this scheme as the tunable channel decomposition (TCD), which is based on the recently developed generalized triangular decomposition (GTD) algorithm and the closedform representation of minimum meansquarederror VBLAST (MMSEVBLAST) equalizer. The TCD scheme is particularly relevant to the applications where independent data streams with different qualitiesofservice (QoS) share the same MIMO channel. The TCD scheme has two implementation forms. One is the combination of a linear precoder and a minimum meansquarederror VBLAST (MMSEVBLAST) equalizer, which is referred to as TCDVBLAST, and the other includes a dirty paper (DP) precoder and a linear equalizer followed by a DP decoder, which we refer to as TCDDP. We also include the optimal codedivision multipleaccess (CDMA) sequence design as a special case in the framework of MIMO transceiver designs. Hence, our scheme can be directly applied to optimal CDMA sequence design, both in the uplink and downlink scenarios. Index Terms—Channel capacity, channel decomposition, dirty paper (DP) precoding, generalized triangular decomposition, joint transceiver design, multipleinput multipleoutput (MIMO), optimal CDMA sequences, qualityofservice, VBLAST. I.
MIMO Transceivers With Decision Feedback and Bit Loading: Theory and Optimization
, 2010
"... This paper considers MIMO transceivers with linear precoders and decision feedback equalizers (DFEs), with bit allocation at the transmitter. Zeroforcing (ZF) is assumed. Considered first is the minimization of transmitted power, for a given total bit rate and a specified set of error probabilities ..."
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Cited by 5 (4 self)
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This paper considers MIMO transceivers with linear precoders and decision feedback equalizers (DFEs), with bit allocation at the transmitter. Zeroforcing (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 QRbased system used in VBLAST is yet another member of the optimal family and is particularly wellsuited 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.
Joint optimization of transceivers with decision feedback and bit loading
 in Proc. 42nd Asilomar Conf. Signals, Systems, and Computers
, 2008
"... Abstract — The transceiver optimization problem for MIMO channels has been considered in the past with linear receivers as well as with decision feedback (DFE) receivers. Joint optimization of bit allocation, precoder, and equalizer has in the past been considered only for the linear transceiver (tr ..."
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Cited by 2 (2 self)
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Abstract — The transceiver optimization problem for MIMO channels has been considered in the past with linear receivers as well as with decision feedback (DFE) receivers. Joint optimization of bit allocation, precoder, and equalizer has in the past been considered only for the linear transceiver (transceiver with linear precoder and linear equalizer). It has also been observed that the use of DFE even without bit allocation in general results in better performance that linear transceivers with bit allocation. This paper provides a general study of this for transceivers with the zeroforcing constraint. It is formally shown that when the bit allocation, precoder, and equalizer are jointly optimized, linear transceivers and transceivers with DFE have identical performance in the sense that transmitted power is identical for a given bit rate and error probability. The developments of this paper are based on the generalized triangular decomposition (GTD) recently introduced by Jiang, Li, and Hager. It will be shown that a broad class of GTDbased systems solve the optimal DFE problem with bit allocation. The special case of a linear transceiver with optimum bit allocation will emerge as one of the many solutions. 1
Block Diagonal Geometric Mean Decomposition (BDGMD) for MIMO Broadcast Channels
"... Abstract—In recent years, the research on multipleinput multipleoutput (MIMO) broadcast channels has attracted much interest, especially since the discovery of the broadcast channel capacity achievable through the use of dirty paper coding (DPC). In this paper, we propose a new matrix decompositio ..."
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Cited by 1 (1 self)
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Abstract—In recent years, the research on multipleinput multipleoutput (MIMO) broadcast channels has attracted much interest, especially since the discovery of the broadcast channel capacity achievable through the use of dirty paper coding (DPC). In this paper, we propose a new matrix decomposition, called the block diagonal geometric mean decomposition (BDGMD), and develop transceiver designs that combine DPC with BDGMD for MIMO broadcast channels. We also extend the BDGMD to the block diagonal uniform channel decomposition (BDUCD) with which the MIMO broadcast channel capacity can be achieved. Our proposed schemes decompose each user’s MIMO channel into parallel subchannels with identical SNRs/SINRs, thus equalrate coding can be applied across the subchannels of each user. Numerical simulations show that the proposed schemes demonstrate superior performance over conventional schemes. Index Terms—MIMO systems, broadcast channel (BC), uplinkdownlink duality, equalrate coding, geometric mean decomposition (GMD), block diagonal geometric mean decomposition (BDGMD), block diagonal uniform channel decomposition (BDUCD), decision feedback equalization (DFE), dirty paper coding (DPC), channel capacity. I.
Generalized Triangular Decomposition in Transform Coding
"... Abstract—A general family of optimal transform coders (TCs) is introduced here based on the generalized triangular decomposition (GTD) developed by Jiang et al. This family includes the Karhunen–Loeve transform (KLT) and the generalized version of the predictionbased lower triangular transform (PLT ..."
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Cited by 1 (1 self)
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Abstract—A general family of optimal transform coders (TCs) is introduced here based on the generalized triangular decomposition (GTD) developed by Jiang et al. This family includes the Karhunen–Loeve transform (KLT) and the generalized version of the predictionbased lower triangular transform (PLT) introduced by Phoong and Lin as special cases. The coding gain of the entire family, with optimal bit allocation, is equal to that of the KLT and the PLT. Even though the original PLT introduced by Phoong et al. is not applicable for vectors that are not blocked versions of scalar wide sense stationary processes, the GTDbased family includes members that are natural extensions of the PLT, and therefore also enjoy the socalled MINLAB structure of the PLT, which has the unit noisegain property. Other special cases of the GTDTC are the geometric mean decomposition (GMD) and the bidiagonal decomposition (BID) transform coders. The GMDTC in particular has the property that the optimum bit allocation is a uniform allocation; this is because all its transform domain coefficients have the same variance, implying thereby that the dynamic ranges of the coefficients to be quantized are identical. Index Terms—Bit allocation, generalized triangular decomposition, geometric mean decomposition, linear prediction, majorization, Schur convexity.
GTDbased transceivers for decision feedback and Bit Loading
 in Proc. IEEE Int. Conf. Acoustics
, 1981
"... Abstract — We consider new optimization problems for transceivers with DFE receivers and linear precoders, which also use bit loading at the transmitter. First, we consider the MIMO QoS (quality of service) problem, which is to minimize the total transmitted power when the bit rate and probability o ..."
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Cited by 1 (1 self)
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Abstract — We consider new optimization problems for transceivers with DFE receivers and linear precoders, which also use bit loading at the transmitter. First, we consider the MIMO QoS (quality of service) problem, which is to minimize the total transmitted power when the bit rate and probability of error of each data stream are specified. The developments of this paper are based on the generalized triangular decomposition (GTD) recently introduced by Jiang, Li, and Hager. It is shown that under some multiplicative majorization conditions there exists a custom GTDbased transceiver which achieves the minimal power. The problem of maximizing the bit rate subject to the total power constraint and given error probability is also considered in this paper. It is shown that the GTDbased systems also give the optimal solutions to the bit rate maximization problem. 1
Transceiver Design with Vector Perturbation Technique and Iterative Power Loading
"... Abstract — In this paper we consider the optimization of transceivers which use the nonlinear vector perturbation technique at the transmitter. Since the perturbation vector can be almost totally removed at the receiver, the transmitter can use this extra freedom to reduce the transmitted power whil ..."
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Abstract — In this paper we consider the optimization of transceivers which use the nonlinear vector perturbation technique at the transmitter. Since the perturbation vector can be almost totally removed at the receiver, the transmitter can use this extra freedom to reduce the transmitted power while maintaining the performance. The two cases considered in this paper are linear transceivers and transceivers with decision feedback (DFE). For both cases, efficient iterative power loading algorithms are developed to reduce the average bit error rate under the total transmitted power constraint. We present simulation results showing that the proposed technique performs better than the existing stateoftheart uniform channel decomposition (UCD) system and the vector perturbation (VP) precoder. 1
DOI 10.1155/ASP/2006/91919 Efficient ClosedLoop Schemes for MIMOOFDMBased WLANs
"... The singleinput singleoutput (SISO) orthogonal frequencydivision multiplexing (OFDM) systems for wireless local area networks (WLAN) defined by the IEEE 802.11a standard can support data rates up to 54 Mbps. In this paper, we consider deploying two transmit and two receive antennas to increase th ..."
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The singleinput singleoutput (SISO) orthogonal frequencydivision multiplexing (OFDM) systems for wireless local area networks (WLAN) defined by the IEEE 802.11a standard can support data rates up to 54 Mbps. In this paper, we consider deploying two transmit and two receive antennas to increase the data rate up to 108 Mbps. Applying our recent multipleinput multipleoutput (MIMO) transceiver designs, that is, the geometric mean decomposition (GMD) and the uniform channel decomposition (UCD) schemes, we propose simple and efficient closedloop MIMOOFDM designs for much improved performance, compared to the standard singular value decomposition (SVD) based schemes as well as the openloop VBLAST (vertical Bell Labs layered spacetime) based counterparts. In the explicit feedback mode, precoder feedback is needed for the proposed schemes. We show that the overhead of feedback can be made very moderate by using a vector quantization method. In the timedivision duplex (TDD) mode where the channel reciprocity is exploited, our schemes turn out to be robust against the mismatch between the uplink and downlink channels. The advantages of our schemes are demonstrated via extensive numerical examples. Copyright © 2006 Xiayu Zheng et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1.