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generalized triangular decomposition in Transform Coding

IEEE TRANSACTIONS ON SIGNAL PROCESSING 2010年第2期58卷 566-574页

作者： Weng, Ching-Chih Chen, Chun-Yang Vaidyanathan, P. P. CALTECH Pasadena CA 91125 USA

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 prediction-based 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 GTD-based family includes members that are natural extensions of the PLT, and therefore also enjoy the so-called MINLAB structure of the PLT, which has the unit noise-gain property. Other special cases of the GTD-TC are the geometric mean decomposition (GMD) and the bidiagonal decomposition (BID) transform coders. The GMD-TC 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.

关键词： Bit allocation generalized triangular decomposition geometric mean decomposition linear prediction majorization Schur convexity

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Simultaneous Wireless Information and Power Transfer Based on generalized triangular decomposition

IEEE TRANSACTIONS ON GREEN COMMUNICATIONS AND NETWORKING

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IEEE TRANSACTIONS ON GREEN COMMUNICATIONS AND NETWORKING 2019年第3期3卷 751-764页

作者： Al-Baidhani, Ahmed Vehkapera, Mikko Benaissa, Mohammed Univ Sheffield Dept Elect & Elect Engn Sheffield S1 3JD S Yorkshire England Aalto Univ Sch Elect Engn Espoo 00076 Finland

In this paper, a new approach, based on the generalized triangular decomposition (GTD), is proposed for simultaneous wireless information and power transfer (SWIPT) in the spatial domain for a point-to-point multiple-input multiple-output (MIMO) system. The proposed approach takes advantage of the GTD structure to allow the transmitter to use the strongest eigen-channel jointly for energy harvesting and information exchange while these transmissions can be separated at the receiver. The optimal structure of the GTD that maximizes the total information rate constrained by a given power allocation and a required amount of energy harvesting is derived. An algorithm is developed that minimizes the total transmitted power for given information rate and energy harvesting constraints with a limited total power at the transmitter. Both theoretical and simulation results show that our proposed GTD based SWIPT outperforms singular value decomposition (SVD) based SWIPT. This is due to the flexibility introduced by the GTD to increase the energy harvested via interstream interference.

关键词： Energy harvesting SWIPT MIMO channel singular value decomposition generalized triangular decomposition optimization

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ZF-DFE TRANSCEIVER DESIGN FOR TIME-VARYING MIMO CHANNELS USING SPACE-TIME generalized triangular decomposition

ZF-DFE TRANSCEIVER DESIGN FOR TIME-VARYING MIMO CHANNELS USI...

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2010 IEEE International Conference on Acoustics, Speech, and Signal Processing

作者： Liu, Chih-Hao Vaidyanathan, P. P. CALTECH Dept Elect Engn Pasadena CA 91125 USA

ISBN: (纸本)9781424442966

We consider the design of MIMO transceivers with zero-forcing (ZF) decision feedback detection over time-varying MIMO channels. The data vectors are grouped into space-time blocks (ST-blocks) for the spatial and temporal precoding to take advantage of the diversity offered by time-varying channels. We extend the generalized triangular decomposition (GTD) for the case of time-varying channels by introducing the space-time GTD (ST-GTD). Based on ST-GTD and the channel prediction, we propose the space-time geometric mean decomposition (ST-GMD) based system which minimizes the arithmetic mean square error (MSE) for every ST-block. We also present the causal ST-GTD based system which does not require channel prediction. The simulations show that this system achieves the same BER performance asymptotically as the ST-GMD based system. In moderate high SNR, the proposed systems have superior BER performance over the conventional GMD-based systems.

关键词： generalized triangular decomposition Transceivers Time-Varying Channels Space-time GTD

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Hybrid Precoding for mm Wave Massive MIMO Systems with generalized triangular decomposition 19

Hybrid Precoding for mm Wave Massive MIMO Systems with Gener...

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IEEE 19th Wireless and Microwave Technology Conference (WAMICON)

作者： Kabalci, Yasin Arslan, Huseyin Nigde Omer Halisdemir Univ Dept Elect & Elect Engn TR-51240 Nigde Turkey Istanbul Medipol Univ Sch Engn & Nat Sci TR-34810 Istanbul Beykoz Turkey Univ S Florida Dept Elect Engn Tampa FL 33620 USA

ISBN: (纸本)9781538612675

Hybrid precoding schemes have recently gained a great attention for millimeter wave (mmWave) massive multiple input-multiple-output (massive MIMO) communication systems because of offered cost and low-power consumption advantages. The singular value decomposition (SVD) method which is exploited in the design of hybrid precoding causes several problems on system design, especially on bit allocation, precoding and equalizing processes. On the other hand, the previous works show that generalized triangular decomposition (GTD) method can present asymptotically optimal performance in conventional MIMO systems. In the light of this, we propose the use of GTD method for designing hybrid precoding operating in mmWave massive MIMO systems. The proposed design is analyzed via performed simulation studies including different system configurations. Moreover, the archived results are compared with the standard orthogonal matching pursuit (OMP) algorithm based hybrid precoding scheme. The simulation results show that the proposed hybrid precoding scheme can reach up to the performance of optimal precoding scheme.

关键词： hybrid precoding millimeter wave massive MIMO generalized triangular decomposition

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The generalized triangular decomposition

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MATHEMATICS OF COMPUTATION 2008年第262期77卷 1037-1056页

作者： Jiang, Yi Hager, William W. Li, Jian Univ Florida Dept Elect & Comp Engn Gainesville FL 32611 USA Univ Florida Dept Math Gainesville FL 32611 USA

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 the singular value decomposition (SVD) and the Schur decomposition where R is an upper triangular matrix with the eigenvalues of H on the diagonal. We show that any diagonal for R can be achieved that satisfies Weyl's multiplicative majorization conditions: (k)Pi(i =1) |r(i)| <= (k)Pi(i =1) sigma(i), 1 <= k < K, (k)Pi(i =1) |r(i)| = (k)Pi(i =1) sigma(i), where K is the rank of H, sigma(i) is the i-th largest singular value of H, and r(i) is the i-th largest (in magnitude) diagonal element of R. Given a vector r which satisfies Weyl's conditions, we call the decomposition H = QRP*, where R is upper triangular with prescribed diagonal r, the generalized triangular decomposition (GTD). A direct (nonrecursive) algorithm is developed for computing the GTD. This algorithm starts with the SVD and applies a series of permutations and Givens rotations to obtain the GTD. The numerical stability of the GTD update step is established. The GTD can be used to optimize the power utilization of a communication channel, while taking into account 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.

关键词： generalized triangular decomposition geometric mean decomposition matrix factorization unitary factorization singular value decomposition Schur decomposition MIMO systems inverse eigenvalue problems

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ZF-DFE TRANSCEIVER DESIGN FOR TIME-VARYING MIMO CHANNELS USING SPACE-TIME generalized triangular decomposition

ZF-DFE TRANSCEIVER DESIGN FOR TIME-VARYING MIMO CHANNELS USI...

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IEEE International Conference on Acoustics, Speech, and Signal Processing

作者： Chih-Hao Liu P. P. Vaidyanathan Dept. of Electrical Engineering MC 136-93 California Institute of Technology Pasadena CA 91125 USA

ISBN: (纸本)9781424442959

关键词： generalized triangular decomposition Transceivers Time-Varying Channels Space-time GTD time-varying channels Transceivers Spacetime bit error rate performance multiple input multiple output systems Mean square error decomposition geometrical theory of diffraction

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Tunable channel decomposition for MIMO communications using channel state information

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2006年第11期54卷 4405-4418页

作者： Jiang, Yi Hager, William W. Li, Jian Univ Florida Dept Elect & Comp Engn Gainesville FL 32611 USA Univ Florida Dept Math Gainesville FL 32611 USA

We consider jointly designing transceivers for multiple-input multiple-output (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 MEMO channel, in a capacity lossless manner, into multiple subchannels with prescribed capacities, or equivalently, signal-to-interference-and-noise 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 closed-form representation of minimum mean-squared-error VBLAST (MMSE-VBLAST) equalizer. The TCD scheme is particularly relevant to the applications where independent data streams with different qualities-of-service (QoS) share the same MIMO channel. The TCD scheme has two implementation forms. One is the combination of a linear precoder and a minimum mean-squared-error VBLAST (MMSE-VBLAST) equalizer, which is referred to as TCD-VBLAST, and the other includes a dirty paper (DP) precoder and a linear equalizer followed by a DP decoder, which we refer to as TCD-DP. We also include the optimal code-division multiple-access (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.

关键词： channel capacity channel decomposition dirty paper (DP) precoding generalized triangular decomposition joint transceiver design multiple-input multiple-output (MIMO) optimal CDMA sequences quality-of-service VBLAST

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MMSE DFE Transceiver Design Over Slowly Time-Varying MIMO Channels Using ST-GTD

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2011年第1期59卷 277-289页

作者： Liu, Chih-Hao Vaidyanathan, P. P. CALTECH Pasadena CA 91125 USA

In a companion paper, we have studied the zero-forcing (ZF) transceiver with decision feedback equalizer (DFE) over slowly time-varying narrowband multiinput multioutput (MIMO) channels. The space-time generalized triangular decomposition (ST-GTD) was used for the design of ZF-DFE transceivers. The space-time geometric mean decomposition (ST-GMD) ZF transceiver minimizes both the arithmetic mean square error (MSE) at the feedback detector and the average uncoded bit error rate (BER) in moderate high signal-to-noise ratio (SNR). This paper addresses the design problem of DFE transceiver without zero-forcing constraint. In the first part, a channel independent temporal precoder is superimposed on the conventional block-wise GMD-based minimum mean square error (MMSE) DFE transceiver to take advantage of the temporal diversity. In the second part, ST-GTD is applied for the design of MMSE DFE transceivers. With accurate channel prediction and space-time powerloading, the proposed ST-GMD MMSE transceiver minimizes the arithmetic MSE at the feedack detector, and maximizes Gaussian mutual information. For practical applications, the ST-GTD MMSE transceiver which does not require channel prediction but shares the same asymptotic BER performance with the ST-GMD MMSE system is also developed. In the convex region, our analysis shows that the proposed MMSE transceivers has better BER performance than the conventional GMD-based MMSE transceiver;the average BERs of the proposed systems are nonincreasing functions of the ST-block size. The superior performance of ST-GMD MMSE transceiver over the ST-GMD ZF transceiver is also verified analytically.

关键词： generalized triangular decomposition geometric mean decomposition (GMD) transceivers space-time GTD time-varying channels

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The Role of GTD in Optimizing Perfect Reconstruction Filter Banks

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2012年第1期60卷 112-128页

作者： Weng, Ching-Chih Vaidyanathan, P. P. CALTECH Pasadena CA 91125 USA

Filter bank optimization for specific input statistics has been of great interest in both theory and practice in many signal processing applications. In this paper we propose GTD (generalized triangular decomposition) filter banks as a subband coder for optimizing the theoretical coding gain. We focus on perfect reconstruction orthonormal GTD filter banks and biorthogonal GTD filter banks. We show that in both cases there are two fundamental properties in the optimal solutions, namely, total decorrelation and spectrum equalization. The optimal solutions can be obtained by performing the frequency dependent GTD on the Cholesky factor of the input power spectrum density matrices. We also show that in both theory and numerical simulations, the optimal GTD subband coders have superior performance than optimal traditional subband coders. In addition, the uniform bit loading scheme can, with no loss of optimality, be used in the optimal biorthogonal GTD coders, which solves the granularity problem in the conventional optimum bit loading formula. We then extend the use of GTD filter banks to wireless communication systems, where linear precoding and zero-forcing decision feedback equalization is used in frequency selective channels. We consider the quality of service (QoS) problem of minimizing the transmitted power subject to the bit error rate and total bit rate constraints. Optimal systems with orthonormal precoder and unconstrained precoder are both derived and shown to be related to the frequency dependent GTD of the channel frequency response.

关键词： Filter banks generalized triangular decomposition linear prediction subband coders transceivers

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MIMO Transceivers With Decision Feedback and Bit Loading: Theory and Optimization

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2010年第3期58卷 1334-1346页

作者： Weng, Ching-Chih Chen, Chun-Yang Vaidyanathan, P. P. CALTECH Pasadena CA 91125 USA

This paper considers MIMO transceivers with linear precoders and decision feedback equalizers (DFEs), with bit allocation at the transmitter. Zero-forcing (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 QR-based system used in VBLAST is yet another member of the optimal family and is particularly well-suited 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.

关键词： BER optimization bit allocation decision feed-back equalizers generalized triangular decomposition limited feedback MIMO transceivers

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