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22
Multiuser MIMOOFDM for NextGeneration Wireless Systems
, 2007
"... This overview portrays the 40year evolution of orthogonal frequency division multiplexing (OFDM) research. The amelioration of powerful multicarrier OFDM arrangements with multipleinput multipleoutput (MIMO) systems has numerous benefits, which are detailed in this treatise. We continue by highl ..."
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Cited by 17 (4 self)
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This overview portrays the 40year evolution of orthogonal frequency division multiplexing (OFDM) research. The amelioration of powerful multicarrier OFDM arrangements with multipleinput multipleoutput (MIMO) systems has numerous benefits, which are detailed in this treatise. We continue by highlighting the limitations of conventional detection and channel estimation techniques designed for multiuser MIMO OFDM systems in the socalled rankdeficient scenarios, where the number of users supported or the number of transmit antennas employed exceeds the number of receiver antennas. This is often encountered in practice, unless we limit the number of users granted access in the base station’s or radio port’s coverage area. Following a historical perspective on the associated design problems and their stateoftheart solutions, the second half of this treatise details a range of classic multiuser detectors (MUDs) designed for MIMOOFDM systems and characterizes their achievable performance. A further section aims for identifying novel cuttingedge genetic algorithm (GA)aided detector solutions, which have found numerous applications in wireless communications in recent years. In an effort to stimulate the cross pollination of ideas across the machine learning, optimization, signal processing, and wireless communications research communities, we will review the broadly applicable principles of various GAassisted optimization techniques, which were recently proposed also
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
A framework for designing MIMO systems with decision feedback equalization or TomlinsonHarashima precoding
 Proc. of the ICASSP
, 2007
"... We consider joint transceiver design for general MultipleInput MultipleOutput communication systems that implement interference (pre)subtraction, such as those based on Decision Feedback Equalization (DFE) or TomlinsonHarashima precoding (THP). We develop a unified framework for joint transceive ..."
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Cited by 13 (1 self)
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We consider joint transceiver design for general MultipleInput MultipleOutput communication systems that implement interference (pre)subtraction, such as those based on Decision Feedback Equalization (DFE) or TomlinsonHarashima precoding (THP). We develop a unified framework for joint transceiver design by considering design criteria that are expressed as functions of the Mean Square Error (MSE) of the individual data streams. By deriving two inequalities that involve the logarithms of the individual MSEs, we obtain optimal designs for two classes of communication objectives, namely those that are Schurconvex and Schurconcave functions of these logarithms. For Schurconvex objectives, the optimal design results in data streams with equal MSEs. This design simultaneously minimizes the total MSE and maximizes the mutual information for the DFEbased model. For Schurconcave objectives, the optimal DFE design results in linear equalization and the optimal THP design results in linear precoding. The proposed framework embraces a wide range of design objectives and can be regarded as a counterpart of the existing framework of linear transceiver design.
Design of block transceivers with decision feedback detection
 in IEEE Trans. Signal Process
, 2006
"... Abstract—This paper presents a method for jointly designing the transmitter–receiver pair in a blockbyblock communication system that employs (intrablock) decision feedback detection. We provide closedform expressions for transmitter–receiver pairs that simultaneously minimize the arithmetic mean ..."
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Cited by 10 (4 self)
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Abstract—This paper presents a method for jointly designing the transmitter–receiver pair in a blockbyblock communication system that employs (intrablock) decision feedback detection. We provide closedform expressions for transmitter–receiver pairs that simultaneously minimize the arithmetic mean squared error (MSE) at the decision point (assuming perfect feedback), the geometric MSE, and the bit error rate of a uniformly bitloaded system at moderatetohigh signaltonoise ratios. Separate expressions apply for the “zeroforcing ” and “minimum MSE” (MMSE) decision feedback structures. In the MMSE case, the proposed design also maximizes the Gaussian mutual information and suggests that one can approach the capacity of the block transmission system using (independent instances of) the same (Gaussian) code for each element of the block. Our simulation studies indicate that the proposed transceivers perform significantly better than standard transceivers and that they retain their performance advantages in the presence of error propagation. Index Terms—Bit error rate, block precoding, channel capacity, decision feedback detection, minimum meansquare error, mutual information, zeroforcing. I.
On the Proximity Factors of Lattice ReductionAided Decoding
"... Lattice reductionaided decoding enables significant complexity saving and nearoptimum performance in multiinput multioutput (MIMO) communications. However, its remarkable performance largely remains a mystery to date. In this paper, a first step is taken towards a quantitative understanding of ..."
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Cited by 10 (3 self)
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Lattice reductionaided decoding enables significant complexity saving and nearoptimum performance in multiinput multioutput (MIMO) communications. However, its remarkable performance largely remains a mystery to date. In this paper, a first step is taken towards a quantitative understanding of its performance limit. To this aim, the proximity factors are defined to measure the worstcase gap to maximumlikelihood (ML) decoding in terms of the signaltonoise ratio (SNR) for given error rate. The proximity factors are derived analytically and found to be bounded above by a function of the dimension of the lattice alone. As a direct consequence, it follows that lattice reductionaided decoding can always achieve full receive diversity of MIMO fading channels. The study is then extended to the dualbasis reduction. It is found that in some cases reducing the dual can result in smaller proximity factors than reducing the primal basis. The theoretic bounds on the proximity factors are further compared with numerical results.
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
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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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