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31
Joint TxRx beamforming design for multicarrier MIMO channels: a unified framework for convex optimization
 IEEE TRANS. SIGNAL PROCESSING
, 2003
"... This paper addresses the joint design of transmit and receive beamforming or linear processing (commonly termed linear precoding at the transmitter and equalization at the receiver) for multicarrier multipleinput multipleoutput (MIMO) channels under a variety of design criteria. Instead of consid ..."
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Cited by 127 (12 self)
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This paper addresses the joint design of transmit and receive beamforming or linear processing (commonly termed linear precoding at the transmitter and equalization at the receiver) for multicarrier multipleinput multipleoutput (MIMO) channels under a variety of design criteria. Instead of considering each design criterion in a separate way, we generalize the existing results by developing a unified framework based on considering two families of objective functions that embrace most reasonable criteria to design a communication system: Schurconcave and Schurconvex functions. Once the optimal structure of the transmitreceive processing is known, the design problem simplifies and can be formulated within the powerful framework of convex optimization theory, in which a great number of interesting design criteria can be easily accommodated and efficiently solved, even though closedform expressions may not exist. From this perspective, we analyze a variety of design criteria, and in particular, we derive optimal beamvectors in the sense of having minimum average bit error rate (BER). Additional constraints on the peaktoaverage ratio (PAR) or on the signal dynamic range are easily included in the design. We propose two multilevel waterfilling practical solutions that perform very close to the optimal in terms of average BER with a low implementation complexity. If cooperation among the processing operating at different carriers is allowed, the performance improves significantly. Interestingly, with carrier cooperation, it turns out that the exact optimal solution in terms of average BER can be obtained in closed form.
On the construction of some capacityapproaching coding schemes
, 2000
"... This thesis proposes two constructive methods of approaching the Shannon limit very closely. Interestingly, these two methods operate in opposite regions, one has a block length of one and the other has a block length approaching infinity. The first approach is based on novel memoryless joint source ..."
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Cited by 56 (2 self)
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This thesis proposes two constructive methods of approaching the Shannon limit very closely. Interestingly, these two methods operate in opposite regions, one has a block length of one and the other has a block length approaching infinity. The first approach is based on novel memoryless joint sourcechannel coding schemes. We first show some examples of sources and channels where no coding is optimal for all values of the signaltonoise ratio (SNR). When the source bandwidth is greater than the channel bandwidth, joint coding schemes based on spacefilling curves and other families of curves are proposed. For uniform sources and modulo channels, our coding scheme based on spacefilling curves operates within 1.1 dB of Shannon’s ratedistortion bound. For Gaussian sources and additive white Gaussian noise (AWGN) channels, we can achieve within 0.9 dB of the ratedistortion bound. The second scheme is based on lowdensity paritycheck (LDPC) codes. We first demonstrate that we can translate threshold values of an LDPC code between channels accurately using a simple mapping. We develop some models for density evolution
Stochastic Linear Control over a Communication Channel
, 2003
"... We examine linear stochastic control systems when there is a communication channel connecting the sensor to the controller. The problem consists of designing the channel encoder and decoder as well as the controller to satisfy some given control objectives. In particular we examine the role communic ..."
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Cited by 52 (8 self)
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We examine linear stochastic control systems when there is a communication channel connecting the sensor to the controller. The problem consists of designing the channel encoder and decoder as well as the controller to satisfy some given control objectives. In particular we examine the role communication has on the classical LQG problem. We give conditions under which the classical separation property between estimation and control holds and the certainty equivalent control law is optimal. We then present the sequential rate distortion framework. We present bounds on the achievable performance and show the inherent tradeo#s between control and communication costs. In particular we show that optimal quadratic cost decomposes into two terms: a full knowledge cost and a sequential rate distortion cost.
Gradient of mutual information in linear vector Gaussian channels
 IEEE Trans. Inf. Theory
, 2006
"... Abstract — This paper considers a general linear vector Gaussian channel with arbitrary signaling and pursues two closely related goals: i) closedform expressions for the gradient of the mutual information with respect to arbitrary parameters of the system, and ii) fundamental connections between i ..."
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Cited by 46 (11 self)
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Abstract — This paper considers a general linear vector Gaussian channel with arbitrary signaling and pursues two closely related goals: i) closedform expressions for the gradient of the mutual information with respect to arbitrary parameters of the system, and ii) fundamental connections between information theory and estimation theory. Generalizing the fundamental relationship recently unveiled by Guo, Shamai, and Verdú [1], we show that the gradient of the mutual information with respect to the channel matrix is equal to the product of the channel matrix and the error covariance matrix of the estimate of the input given the output. I.
Optimum power allocation for parallel Gaussian channels with arbitrary input distributions
 IEEE TRANS. INF. THEORY
, 2006
"... The mutual information of independent parallel Gaussiannoise channels is maximized, under an average power constraint, by independent Gaussian inputs whose power is allocated according to the waterfilling policy. In practice, discrete signaling constellations with limited peaktoaverage ratios (m ..."
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Cited by 35 (9 self)
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The mutual information of independent parallel Gaussiannoise channels is maximized, under an average power constraint, by independent Gaussian inputs whose power is allocated according to the waterfilling policy. In practice, discrete signaling constellations with limited peaktoaverage ratios (mPSK, mQAM, etc.) are used in lieu of the ideal Gaussian signals. This paper gives the power allocation policy that maximizes the mutual information over parallel channels with arbitrary input distributions. Such policy admits a graphical interpretation, referred to as mercury/waterfilling, which generalizes the waterfilling solution and allows retaining some of its intuition. The relationship between mutual information of Gaussian channels and nonlinear minimum meansquare error (MMSE) proves key to solving the power allocation problem.
Optimum linear joint transmitreceive processing for MIMO channels with QoS constraints
 IEEE Transactions on Signal Processing
, 2004
"... Abstract—This paper considers vector communications through multipleinput multipleoutput (MIMO) channels with a set of quality of service (QoS) requirements for the simultaneously established substreams. Linear transmitreceive processing (also termed linear precoder at the transmitter and linear ..."
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Cited by 23 (3 self)
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Abstract—This paper considers vector communications through multipleinput multipleoutput (MIMO) channels with a set of quality of service (QoS) requirements for the simultaneously established substreams. Linear transmitreceive processing (also termed linear precoder at the transmitter and linear equalizer at the receiver) is designed to satisfy the QoS constraints with minimum transmitted power (the exact conditions under which the problem becomes unfeasible are given). Although the original problem is a complicated nonconvex problem with matrixvalued variables, with the aid of majorization theory, we reformulate it as a simple convex optimization problem with scalar variables. We then propose a practical and efficient multilevel waterfilling algorithm to optimally solve the problem for the general case of different QoS requirements. The optimal transmitreceive processing is shown to diagonalize the channel matrix only after a very specific prerotation of the data symbols. For situations in which the resulting transmit power is too large, we give the precise way to relax the QoS constraints in order to reduce the required power based on a perturbation analysis. We also propose a robust design under channel estimation errors that has an important interest for practical systems. Numerical results from simulations are given to support the mathematical development of the problem. Index Terms—Array signal processing, beamforming, joint transmitreceive equalization, linear precoding, MIMO channels, spacetime filtering, waterfilling. I.
Suppression of near and farend crosstalk by linear pre and postfiltering
 IEEE J. Select. Areas Commun
, 1992
"... AbstractFullduplex data communications over a multiinput/multioutput linear timeinvariant channel is considered. The minimum mean square error (MMSE) linear equalizer is derived in the presence of both near and farend crosstalk and independent additive noise, assuming correlated data, and co ..."
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Cited by 21 (1 self)
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AbstractFullduplex data communications over a multiinput/multioutput linear timeinvariant channel is considered. The minimum mean square error (MMSE) linear equalizer is derived in the presence of both near and farend crosstalk and independent additive noise, assuming correlated data, and colored noise. The MMSE equalizer is completely specified in terms of the channel and crosstalk transfer functions by using a generalization of previous work due to Salz. Conditions are given under which the equalizer can completely eliminate both near and farend crosstalk and intersymbol interference. The MMSE transmitter filter, subject to a transmitted power constraint, is specified when the channel and crosstalk transfer functions are bandlimited to the Nyquist frequency. Also considered is the design of MMSE transmitter and receiver filters when the data signals are arbitrary widesense stationary continuous or discretetime signals, corresponding to the situation where the crosstalk is not phasesynchronous with the desired signal. For a particular twoinput/twooutput discretetime channel model, we study the behavior of the MMSE, assuming FIR transmitter and receiver filters, as a function of how the matrix taps are allocated between these filters, and on timing phase. In this case, the jointly optimal transmitter and receiver filters are obtained numerically using an iterative technique. For the channel model considered, the MSE is a very sensitive function of timing phase, but is nearly independent of how taps are allocated between the transmitter and receiver filters. I.
Multichannel signal processing for data communications in the presence of crosstalk
 IEEE Trans. Commun
, 1990
"... Abstruct We consider transmission of data over multiple coupled channels, such as bundles of twistedpair copper wires in the local subscriber loop, and between central offices in the public switched telephone network. Transceiver designs for such channels typically treat the crosstalk between ad ..."
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Cited by 14 (0 self)
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Abstruct We consider transmission of data over multiple coupled channels, such as bundles of twistedpair copper wires in the local subscriber loop, and between central offices in the public switched telephone network. Transceiver designs for such channels typically treat the crosstalk between adjacent twisted pairs as random noise uncorrelated with the transmitted signal. We propose a transmitterheceiver pair that compensates for crosstalk by treating an entire bundle of twisted pairs as a single multiinput~ultioutput channel with a (slowly varying) matrix transfer function. The proposed transceiver uses multichannel adaptive FIR filters to cancel near and farend crosstalk, and to pre and postprocess the input/output of the channel. The linear pre and postprocessors that minimize mean squared error between the received and transmitted signal in the presence of both near and farend crosstalk are derived. The performance of an adaptive nearend crosstalk canceller using the stochastic gradient (LMS) transversal algorithm is illustrated via numerical simulation. Plots of mean squared error versus time and eye diagrams are presented assuming a standard transmission line model for the channel. A signal design algorithm that maps a vector input bit stream to a stream of channel symbol vectors is also presented. This algorithm is illustrated explicitly for a simple model of two coupled channels. It is shown that the achievable rate using the proposed signaling scheme is very close to the rate attainable in the absence of farend crosstalk, and is significantly greater than the achievable rate assuming that farend crosstalk is treated as additive noise with unknown statistics. 0 I.
Bandwidth Compression For Continuous Amplitude Channels Based On Vector Approximation To A Continuous Subset Of The Source Signal Space
 in Proc. Int. Conf. on Acoustics, Speech, and Signal Proc. (ICASSP
, 1997
"... Two methods for transmission of a continuous amplitude source signal over a continuous amplitude channel with a power constraint are proposed. For both methods, bandwidth reduction is achieved by mapping from a higher dimensional source space to a lower dimensional channel space. In the first system ..."
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Cited by 13 (6 self)
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Two methods for transmission of a continuous amplitude source signal over a continuous amplitude channel with a power constraint are proposed. For both methods, bandwidth reduction is achieved by mapping from a higher dimensional source space to a lower dimensional channel space. In the first system, a source vector is quantized and mapped to a discrete set of points in a multidimensional PAM signal constellation. In the second system the source vector is approximated with a point in a continuous subset of the source space. This operation is followed by mapping the resulting vector to the channel space by a onetoone continuous mapping resulting in continuous amplitude channel symbols. The proposed methods are evaluated for a memoryless Gaussian source with an additive white Gaussian noise channel, and offer significant gains over previously reported methods. Specifically, in the case of twodimensional source vectors, and onedimensional channel vectors, the gap to the optimum perfor...
Joint TransmitReceive SpaceTime Equalization in Spatially Correlated MIMO Channels: A Beamforming Approach
, 2003
"... Multiinput multioutput (MIMe) channels have been shown in the literature to present a significant capacity increase over singleinput singleoutput ones in some situations. To achieve this theoretical capacity, the constituent parallel subchannels arising from the MIMe channel have to be proper ..."
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Cited by 8 (1 self)
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Multiinput multioutput (MIMe) channels have been shown in the literature to present a significant capacity increase over singleinput singleoutput ones in some situations. To achieve this theoretical capacity, the constituent parallel subchannels arising from the MIMe channel have to be properly used. Many practical schemes are being currently developed to achieve this goal. In this paper, we first show that, from an informationtheoretic point of view, beamforming becomes asymptotically optimal as the spatial correlation of the channel fading increases. In light of this result, wideband beamvectors are jointly derived for both transmission and reception. We allow a controlled partial response and design zero forcing (ZF) and minimum mean squared error (MMSE) transmitreceive filters. Concep tually, the beamforming scheme is shown to decompose into two stages: the first one corresponds to a spatial flattening of the MIMe channel, i.e., choosing the subchannel with the highest gain at each frequency; the second stage depends on the particular design criterion and performs a power distribution at the transmitter and defines the equalizer at the receiver. These methods are further extended to the general case of multiple beamforming, i.e., when more than one subchannel are used. An exact and practical implementation of a modified "waterfilling" solution required for the filter design is proposed.