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Optimal linear nonregenerative multihop MIMO relays with MMSEDFE receiver at the destination
 IEEE Trans. Wireless Commun
, 2010
"... Abstract—In this paper, we study multihop nonregenerative multipleinput multipleoutput (MIMO) relay communications with any number of hops. We design the optimal source precoding matrix and the optimal relay amplifying matrices for such relay network where a nonlinear minimal meansquared error ..."
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Abstract—In this paper, we study multihop nonregenerative multipleinput multipleoutput (MIMO) relay communications with any number of hops. We design the optimal source precoding matrix and the optimal relay amplifying matrices for such relay network where a nonlinear minimal meansquared error (MMSE)decision feedback equalizer (DFE) is used at the destination node. We first derive the structure of the optimal source and relay matrices. Then based on the link between most commonly used MIMO system design objectives and the diagonal elements of the MSE matrix, we classify the objective functions into two categories: Schurconvex and Schurconcave composite objective functions. We show that when the composite objective function is Schurconvex, the MMSEDFE receiver together with the optimal source and relay matrices enable an arbitrary number of source symbols to be transmitted at one time, and yield a significantly improved BER performance compared with nonregenerative MIMO relay systems using linear receivers at the destination. We also show that for Schurconcave composite objective functions, the optimal source and relay matrices, and the optimal feedforward matrix at the destination node jointly diagonalize the multihop MIMO relay channel, and thus in such case, the nonlinear MMSEDFE receiver is essentially equivalent to a linear MMSE receiver. Index Terms—MIMO relay network, multihop relay, MMSE, DFE, nonregenerative relay, majorization.
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 16 (6 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.
Multihop nonregenerative MIMO relays: QoS considerations
 IEEE Trans. Signal Process
, 2011
"... tipleoutput (MIMO) relay communication systems, the optimal source precoding matrix and the optimal relay amplifying matrices have been recently established for a broad class of objective functions subjecting to the transmission power constraint at each node. However, existing works do not conside ..."
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Cited by 9 (6 self)
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tipleoutput (MIMO) relay communication systems, the optimal source precoding matrix and the optimal relay amplifying matrices have been recently established for a broad class of objective functions subjecting to the transmission power constraint at each node. However, existing works do not consider any qualityofservice (QoS) constraints, which are important in practical communication systems. In this paper, we derive the optimal source and relay matrices of a multihop MIMO relay system that guarantee the predetermined QoS criteria be attained with the minimal total transmission power. In particular, we consider two types of receivers at the destination node: the linear minimal meansquared error (MMSE) receiver and the nonlinear decision feedback equalizer (DFE) based on the MMSE criterion. We show that for both types of receivers, the solution to the original optimization problem can be upperbounded by using a successive geometric programming (GP) approach and lowerbounded by utilizing a dual decomposition technique. Simulation results show that both bounds are tight, and to obtain the same QoS, the MIMO relay system using the nonlinear MMSEDFE receiver requires substantially less total transmission power than the linear MMSE receiverbased system. Index Terms—Linear nonregenerative relay, majorization, minimal meansquared error (MMSE), multihop relay, multipleinput multipleoutput (MIMO) relay, QoS. I.
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 3 (3 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
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 2 (2 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
HIGH PERFORMANCE ORDERING SCHEME FOR MIMO TRANSMISSION
"... The QROSIC receiver design for the transmitterside power allocated MIMO system. Based on the properties of the function and ordering results, we develop the efficient ordering algorithms in combination with the PA scheme. From the convexity of thefunction, we derive the ordering strategy that mak ..."
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The QROSIC receiver design for the transmitterside power allocated MIMO system. Based on the properties of the function and ordering results, we develop the efficient ordering algorithms in combination with the PA scheme. From the convexity of thefunction, we derive the ordering strategy that makes the channel gains converge to their geometric mean. Based on this approach, the fixed ordering algorithm is first designed, for which the geometric mean is used for a constant threshold. To further improve the performance, the modified scheme employing adaptive thresholds is developed using the correlation among ordering results. Theoretical analysis and simulation results show that proposed ordering schemes using QRdecomposition not only require a reduced computational complexity compared to the conventional scheme, but result in improved error performance. Keywords — Detection ordering, MIMO, OSIC, power allocation, QRdecomposition. I.
A Systolic Array Based GTD Processor With a Parallel Algorithm
"... Abstract—Generalized triangular decomposition (GTD) has been found to be useful in the field of signal processing, but the feasibility of the related hardware has not yet been established. This paper presents (for the first time) a GTD processor architecture with a parallel algorithm. The proposed ..."
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Abstract—Generalized triangular decomposition (GTD) has been found to be useful in the field of signal processing, but the feasibility of the related hardware has not yet been established. This paper presents (for the first time) a GTD processor architecture with a parallel algorithm. The proposed parallel GTD algorithm achieves an increase in speed of up to 1.66 times, compared to the speed of its conventional sequential counterpart for an 8 8 matrix. For hardware implementation, the proposed reconfigurable architecture is capable of computing singular value decomposition (SVD), geometric mean decomposition (GMD), and GTD for matrix sizes from 1 1 to 8 8. The proposed GTD processor is composed of 16 processing cores in a heterogeneous systolic array. Computations are distributed over areaefficient coordinate rotation digital computers (CORDICs) to achieve a high throughput. To establish the validity of the concept, a GTD processor was designed and implemented. The latency constraint of 16 specified in the 802.11ac standard is adopted for the hardware realization. The proposed design achieves a maximum throughput of 83.3k matrices/s for an 8 8 matrix at 112.4 MHz. The estimated power and core area are 172.7 mW and 1.96 mm, respectively, based on standard 90 nm CMOS technology. Index Terms—Generalized triangular decomposition (GTD), geometric mean decomposition (GMD), multipleinput multipleoutput (MIMO), reconfigurable architecture. I.
The DiversityMultiplexing Tradeoff of RF Chain Limited MIMO System with Antenna Selection: Part I Theoretical Framework
"... The large gain promised by the multiinput multioutput (MIMO) technology comes with a cost. In particular multiple analog radio frequency (RF) chains, which are expensive and power consuming, are required at both the transmitter and receiver sides. On the other hand, the antennas connecting to the ..."
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The large gain promised by the multiinput multioutput (MIMO) technology comes with a cost. In particular multiple analog radio frequency (RF) chains, which are expensive and power consuming, are required at both the transmitter and receiver sides. On the other hand, the antennas connecting to the RF chains are less expensive. Hence one engineering compromise is to implement more antennas than RF chains and to use only a subset of them based on some antenna selection (AS) algorithm. An interesting question therefore arises: given a RF chain limited MIMO system, what is the fundamental performance gain by adding more antennas. In this twopart paper, we answer this question by using the diversitymultiplexing (DM) gain tradeoff metric. Consider a Rayleigh fading channel with Mt antennas and Lt (Lt ≤ Mt) RF chains at the transmitter while Mr antennas and Lr (Lr ≤ Mr) RF chains at the receiver. We obtain the fundamental DM tradeoff as a function of Mt, Mr, and min(Lr, Lt). Referring to the special case where Lt = Mt and Lr = Mr as the RF unlimited system (or full system) and RF limited system (or pruned system) otherwise, we prove that the pruned system with optimal channeldependent AS has the same DM tradeoff as the full system if the multiplexing gain is less than some integer threshold P, while it suffers from some diversity gain loss for multiplexing gains larger than P. In particular, if min(Lr, Lt) = K, min(Mr,Mt), then P = K, i.e. the DM tradeoffs of the pruned system and the full system are the same. Moreover, this result
Precoder Optimization for Nonlinear MIMO Transceiver Based on Arbitrary Cost Function
"... Abstract — Assuming full channel state information (CSI) at both transmitter (CSIT) and receiver (CSIR), we consider optimizing a nonlinear MIMO transceiver with (nonlinear) decision feedback equalizer (DFE) with respect to some global cost function f0. Setting the receiver to be a minimum meansquar ..."
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Abstract — Assuming full channel state information (CSI) at both transmitter (CSIT) and receiver (CSIR), we consider optimizing a nonlinear MIMO transceiver with (nonlinear) decision feedback equalizer (DFE) with respect to some global cost function f0. Setting the receiver to be a minimum meansquared error (MMSE) DFE, the MIMO transceiver optimization problem reduces to optimizing a linear precoder. Based on the generalized triangular decomposition (GTD) and majorization theory, we prove that for any cost function f0 the optimum precoder is of the same special structure and hence the original complicated matrix optimization problem can be significantly simplified to an optimization problem with scalarvalued variables. Furthermore, if the cost function is specialized to the cases where the composite function f0 ◦ exp is either Schurconvex or Schurconcave, then the nonlinear transceiver design becomes exceedingly simple. In particular, when f0 ◦ exp is Schurconvex, the optimum nonlinear transceiver design turns out to be the uniform channel decomposition (UCD) scheme; when f0 ◦ exp is Schurconcave, the optimum nonlinear design degenerates to linear diagonal transmission. Index Terms — MIMO transceiver optimization, generalized triangular decomposition, majorization theory, Schurconvex. I.
THE ROLES OF MAJORIZATION AND GENERALIZED TRIANGULAR DECOMPOSITION IN COMMUNICATION AND SIGNAL PROCESSING
, 2011
"... I still remember the day I first met my advisor, Professor P. P. Vaidyanathan, during an admission interview back in February of 2006. I was nervous, but hopeful at the same time, for the potential to study under such an esteemed scholar. When he told me that he would gladly take me under his wing, ..."
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I still remember the day I first met my advisor, Professor P. P. Vaidyanathan, during an admission interview back in February of 2006. I was nervous, but hopeful at the same time, for the potential to study under such an esteemed scholar. When he told me that he would gladly take me under his wing, I was ecstatic—my parents thought I won a secret lottery of some sort because I was overfilled with joy. It is therefore now, five years later, that I express my most sincere gratitude to Prof. Vaidyanathan. He is a true gentleman, whose considerate guidance and careful nurturing led me to complete one of the most important milestones in my life. Without his advice and inspiration, my academic career would not have been the same. In every respect, he is the perfect teacher and a role model and I know all of his students will continue to learn from as we journey through our lives. I would also like to thank members of my defense and candidacy examining committee: Professor Yaser AbuMostafa, Professor Babak Hassibi, Dr. Andre Tkacenko, and Dr. Kevin Quirk. Their knowledge and expertise have been instrumental to my study at Caltech. I studied information theory from Yaser, and stochastic signal processing from Babak; I learned communication theory with Kevin, and Andre’s excellent papers on filter bank theory built a solid basis for my own academic research. In regard to providing me with the financial resources to pursue this degree, I would like to thank the Office of Naval Research (ONR) and Taiwan’s TMS scholarship from the National Science Council. Because of their generous support, I was able to join Caltech’s excellent academic environment. This is a unique place on Earth because of all the researchers and scholars that have contributed their knowledge to better human lives, and continue to do so with uncompromising dedication. It has been an honor to be a part of their extraordinary community. Speaking of scholars, my personal appreciations go to my current and former labmates, Professor