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Zhi Ding

University of California, Davis, Electrical and Computer Engineering, Faculty Member

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Address: Davis, CA, USA

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Papers by Zhi Ding

Energy-Efficient Processing and Robust Wireless Cooperative Transmission for Edge Inference

IEEE Internet of Things Journal

Edge machine learning can deliver low-latency and private artificial intelligent (AI) services fo... more Edge machine learning can deliver low-latency and private artificial intelligent (AI) services for mobile devices by leveraging computation and storage resources at the network edge. This paper presents an energy-efficient edge processing framework to execute deep learning inference tasks at the edge computing nodes whose wireless connections to mobile devices are prone to channel uncertainties. Aimed at minimizing the sum of computation and transmission power consumption with probabilistic quality-of-service (QoS) constraints, we formulate a joint inference tasking and downlink beamforming problem that is characterized by a group sparse objective function. We provide a statistical learning based robust optimization approach to approximate the highly intractable probabilistic-QoS constraints by nonconvex quadratic constraints, which are further reformulated as matrix inequalities with a rank-one constraint via matrix lifting. We design a reweighted power minimization approach by iteratively reweighted 1 minimization with difference-of-convexfunctions (DC) regularization and updating weights, where the reweighted approach is adopted for enhancing group sparsity whereas the DC regularization is designed for inducing rankone solutions. Numerical results demonstrate that the proposed approach outperforms other state-of-the-art approaches.

A New Algorithm for Improved Blind Detection of Polar Coded PDCCH in 5G New Radio

In recent release of the new cellular standard known as 5G New Radio (5G-NR), the physical downli... more In recent release of the new cellular standard known as 5G New Radio (5G-NR), the physical downlink control channel (PDCCH) has adopted polar codes for error protection. Similar to 4G-LTE, each active user equipment (UE) must blindly detect its own PDCCH in the downlink search space. This work investigates new ways to improve the accuracy of PDCCH blind detection in 5G-NR. We develop a novel design of joint detection and decoding receiver for 5G multiple-input multiple-output (MIMO) transceivers. We aim to achieve robustness against practical obstacles including channel state information (CSI) errors, noise, co-channel interferences, and pilot contamination. To optimize the overall receiver performance in PDCCH blind detection, we incorporate the polar code information during the signal detection stage by relaxing and transforming the Galois field code constraints into the complex signal field. Specifically, we develop a novel joint linear programming (LP) formulation that takes int...

OTFS Signaling for Uplink NOMA of Heterogeneous Mobility Users

IEEE Transactions on Communications

We investigate a coded uplink non-orthogonal multiple access (NOMA) configuration in which groups... more We investigate a coded uplink non-orthogonal multiple access (NOMA) configuration in which groups of co-channel users are modulated in accordance with orthogonal time frequency space (OTFS). We take advantage of OTFS characteristics to achieve NOMA spectrum sharing in the delay-Doppler domain between stationary and mobile users. We develop an efficient iterative turbo receiver based on the principle of successive interference cancellation (SIC) to overcome the co-channel interference (CCI). We propose two turbo detector algorithms: orthogonal approximate message passing with linear minimum mean squared error (OAMP-LMMSE) and Gaussian approximate message passing with expectation propagation (GAMP-EP). The interactive OAMP-LMMSE detector and GAMP-EP detector are respectively assigned for the reception of the stationary and mobile users. We analyze the convergence performance of our proposed iterative SIC turbo receiver by utilizing a customized extrinsic information transfer (EXIT) chart and simplify the corresponding detector algorithms to further reduce receiver complexity. Our proposed iterative SIC turbo receiver demonstrates performance improvement over existing receivers and robustness against imperfect SIC process and channel state information uncertainty.

Receiver Design for OTFS with a Fractionally Spaced Sampling Approach

IEEE Transactions on Wireless Communications

The recent emergence of orthogonal time frequency space (OTFS) modulation as a novel PHYlayer mec... more The recent emergence of orthogonal time frequency space (OTFS) modulation as a novel PHYlayer mechanism is more suitable in high-mobility wireless communication scenarios than traditional orthogonal frequency division multiplexing (OFDM). Although multiple studies have analyzed OTFS performance using theoretical and ideal baseband pulseshapes, a challenging and open problem is the development of effective receivers for practical OTFS systems that must rely on non-ideal pulseshapes for transmission. This work focuses on the design of practical receivers for OTFS. We consider a fractionally spaced sampling (FSS) receiver in which the sampling rate is an integer multiple of the symbol rate. For rectangular pulses used in OTFS transmission, we derive a general channel inputoutput relationship of OTFS in delay-Doppler domain without the common reliance on impractical assumptions such as ideal bi-orthogonal pulses and on-the-grid delay/Doppler shifts. We propose two equalization algorithms: iterative combining message passing (ICMP) and turbo message passing (TMP) for symbol detection by exploiting delay-Doppler channel sparsity and the channel diversity gain via FSS. We analyze the convergence performance of TMP receiver and propose simplified message passing (MP) receivers to further reduce complexity. Our FSS receivers demonstrate stronger performance than traditional receivers and robustness to the imperfect channel state information knowledge.

Blind Over-the-Air Computation and Data Fusion via Provable Wirtinger Flow

IEEE Transactions on Signal Processing

Over-the-air computation (AirComp) shows great promise to support fast data fusion in Internet-of... more Over-the-air computation (AirComp) shows great promise to support fast data fusion in Internet-of-Things (IoT) networks. AirComp typically computes desired functions of distributed sensing data by exploiting superposed data transmission in multiple access channels. To overcome its reliance on channel station information (CSI), this work proposes a novel blind overthe-air computation (BlairComp) without requiring CSI access, particularly for low complexity and low latency IoT networks. To solve the resulting non-convex optimization problem without the initialization dependency exhibited by the solutions of a number of recently proposed efficient algorithms, we develop a Wirtinger flow solution to the BlairComp problem based on random initialization. To analyze the resulting efficiency, we prove its statistical optimality and global convergence guarantee. Specifically, in the first stage of the algorithm, the iteration of randomly initialized Wirtinger flow given sufficient data samples can enter a local region that enjoys strong convexity and strong smoothness within a few iterations. We also prove the estimation error of BlairComp in the local region to be sufficiently small. We show that, at the second stage of the algorithm, its estimation error decays exponentially at a linear convergence rate.

Data Shuffling in Wireless Distributed Computing via Low-Rank Optimization

IEEE Transactions on Signal Processing

Intelligent mobile platforms such as smart vehicles and drones have recently become the focus of ... more Intelligent mobile platforms such as smart vehicles and drones have recently become the focus of attention for onboard deployment of machine learning mechanisms to enable low latency decisions with low risk of privacy breach. However, most such machine learning algorithms are both computationand-memory intensive, which makes it highly difficult to implement the requisite computations on a single device of limited computation, memory, and energy resources. Wireless distributed computing presents new opportunities by pooling the computation and storage resources among devices. For low-latency applications, the key bottleneck lies in the exchange of intermediate results among mobile devices for data shuffling. To improve communication efficiency, we propose a co-channel communication model and design transceivers by exploiting the locally computed intermediate values as side information. A low-rank optimization model is proposed to maximize the achieved degrees-of-freedom (DoF) by establishing the interference alignment condition for data shuffling. Unfortunately, existing approaches to approximate the rank function fail to yield satisfactory performance due to the poor structure in the formulated low-rank optimization problem. In this paper, we develop an efficient DC algorithm to solve the presented low-rank optimization problem by proposing a novel DC representation for the rank function. Numerical experiments demonstrate that the proposed DC approach can significantly improve the communication efficiency whereas the achievable DoF almost remains unchanged when the number of mobile devices grows.

Cumulant matrix subspace algorithms for blind single FIR channel identification

Blind identification of discrete non-minimum phase FIR channels is studied here. Exploiting highe... more Blind identification of discrete non-minimum phase FIR channels is studied here. Exploiting higher order statistics of the unknown channel output, a closed-form solution to the FIR channel impulse response is presented. The algorithm is simple and relies only on nullspace decomposition. It does not involve global minimization of non-unimodal cost functions nor does it use overparametrization. Its application is broad. It can be used either as the final channel estimate or as a good initial point in nonlinear cumulant matching techniques

Column-anchored zeroforcing blind equalization for multiuser wireless FIR channels

We propose a direct blind zeroforcing approach to cancel intersymbol interference (ISI) in multip... more We propose a direct blind zeroforcing approach to cancel intersymbol interference (ISI) in multiple user finite impulse response (FIR) channels. By selectively anchoring columns of the channel convolution matrix, we present two columnanchored zeroforcing equalizers (CAZE), one without output delay and one with a chosen delay. Unlike many known blind identification algorithms, these equalizers do not need an accurate estimate of the channel orders. Exploiting second-order statistics (SOS) of the received signals, they can retain preselected d d d columns in the channel convolution matrix (d d d is the number of users) and force the remaining columns to zero. CAZE can effectively equalize single-input-multiple-output (SIMO) systems and can reduce dynamic multiple-input-multiple-output (MIMO) systems into a memoryless signal mixing system for source separation. Simulation results show that the CAZE is not only effective for blind equalization of linear quadrature amplitude modulation (QAM) systems, but it is also applicable to the nonlinear GMSK modulation in the popular wireless GSM systems when computational cost severely limits the use of nonlinear methods such as the Viterbi algorithm.

Joint transmitter-receiver optimization for partial response channels based on nonmaximally decimated filterbank precoding technique

Transmitter and receiver filter design plays a key role in communication systems with partial res... more Transmitter and receiver filter design plays a key role in communication systems with partial response channels. For a partial response system, a nonmaximally decimated multirate filter bank can be used as a precoder. Based on MMSE criterion, a closed-form solution to the joint transmitter-receiver optimization problem for noisy partial response channels is presented in this paper. It is found that the redundancy introduced by the nonmaximally decimated filter bank precoder can compensate for spectral nulls in partial response channels that can impair several known joint optimization methods. Simulation results corroborate the analysis that joint transmitter-receiver optimization can achieve significant performance improvement over inverse filter receiver and receiver optimization schemes.

A matrix-pencil approach to blind separation of colored nonstationary signals

For many signal sources such as speech with distinct, nonwhite power spectral densities, second-o... more For many signal sources such as speech with distinct, nonwhite power spectral densities, second-order statistics of the received signal mixture can be exploited for signal separation. Without knowledge on noise correlation matrix, we propose a simple and yet effective signal extraction method for signal source separation under unknown temporally white noise. This new and unbiased signal extractor is derived from the matrix pencil formed between output autocorrelation matrices at different delays. Based on the matrix pencil, an ESPRIT-type algorithm is derived to get an optimal solution in least square sense. Our method is well suited for systems with colored sensor noises and for nonstationary signals.

Matrix outer-product decomposition method for blind multiple channel identification

Blind channel identification and equalization have recently attracted a great deal of attention d... more Blind channel identification and equalization have recently attracted a great deal of attention due to their potential application in mobile communications and digital TV systems. In this paper, we present a new algorithm that utilizes second-order statistics for multichannel parameter estimation. The algorithm is simple and relies on an outer-product decomposition. Its implementation requires no adjustment for single-or multiple-user systems. This new algorithm can be viewed as a generalization of a recently proposed linear prediction algorithm. It is capable of generating more accurate channel estimates and is more robust to overmodeling errors in channel order estimate. The superior performance of this new algorithm is demonstrated through simulation examples.

$Historically, there has been a belief that a noninteger oversampling factor may be more beneficial. In fact, it is heuristically plausible that an oversampling period of A = qI/p in which g is an integer will yield fewer nonzero channel samples than using A = T/p, Hence, argument persists that a rational oversampling factor may help reduce the dimensionality of channel identification and simplify the problem. Here, we show that, in fact, a noninteger fractional sampling generates an equivalent multiuser system whose dimensionality is not reduced and may be more difficult to identify. Clearly, mo is the order of the N dynamic FIR channels. There are a total of (mo +1)NpJ unknown parameters to identify in the blind identification of FIR channels. With these notations, a sampled channel output signal vector of length Mp can be written as$

$Now, form an MpJ x (mo +M \N block Toeplitz matrix with (M -1)N trailing zeros in the first pJ rows$

$Hence, matrix AD forms the outer-product of the channel parameter matrix 7, The singular value decomposition of this outer-product matrix can be used to generate an estimate where @ is an N x N unitary matrix. Recall from [13] and [17] that this memoryless ambiguity is intrinsic to the multiuser blind identification problem and cannot be resolved unless additional information is available. For signal recovery, if a perfect multichannel equalizer is designed according to the channel estimate 7(Q, then the N receiver outputs will be memoryless combinations of the N channel inputs and will need to be separated, as discussed in works such as [17]. This ambiguity would also add to the cost of channel identification using noninteger fractional sampling.$

Sampling and prefiltering effects on blind equalizer design

In the development of equalization algorithms for unknown channels, the effects of the sampling r... more In the development of equalization algorithms for unknown channels, the effects of the sampling rate and the analog receive prefilter prior to discretization of the received signal are often overlooked. In this paper, these effects are investigated. The relationship between the fractionally spaced output samples of a noise-limiting prefilter and the symbol spaced output samples of a matched filter is studied for both the time-invariant and the timevarying channels. It is shown that the prefilter and the sampling rate can have significant effects on blind equalization algorithms. Thus, this paper provides a common framework for comparing different blind algorithms that are studied in the literature with different sampling rates. A case study of the well-known subspace method for blind channel identification is presented. The effects of the noise color due to the prefilter on equalizers is investigated, and the sensitivity of the truncation of the overall channel impulse response in terms of the mean squared error (MSE) performance criterion is investigated through numerical examples.

Blind adaptive equalizers for quadrature amplitude modulated communication systems based on convex cost functions

Local convergence of the Sato blind equalizer and generalizations under practical constraints

An early use of recursive identification in blind adaptive channel equalization is an algorithm d... more An early use of recursive identification in blind adaptive channel equalization is an algorithm developed by Sato. An important generalization of the Sat0 algorithm with extensive analysis appears in the work of Benveniste, Goursat, and Ruget. These generalized algorithms have been shown to possess a desirable global convergence property under two idealized conditions. The convergence properties of this class of blind algorithms under practical constraints common to a variety of channel equalization applications that violate these idealized conditions are studied. Results show that, in practice, when either the equalizer is finite-dimensional and/or the input is discrete (as in digital communications) the equalizer parameters may converge to parameter settings that fail to achieve the objective of approximating the channel inverse. It is also shown, that a center spike initialization is insufficient to guarantee avoiding such ill-convergence. Simulations verify the analytical results.

Semi-blind channel identification for individual data bursts in GSM wireless systems

... These semiblind methods can overcome some serious limitations of SOS blind algorithms. We als... more

Characteristics of band-limited channels unidentifiable from second-order cyclostationary statistics

IEEE Signal Processing Letters, 1996

Several works on blind channel identification and equalization rely on a system model with multip... more Several works on blind channel identification and equalization rely on a system model with multiple sub-channels driven by a single input. These methods depend on a critical condition that no common zero exists among the sub-channels. We aimed at establishing the physical significance of this critical zero condition and understanding the limitation of methods based on second-order statistics, By deriving a number of sufficient conditions, we characterize several classes of band-limited channels that are not identifiable from only the second-order statistics of the channel output.

$Research paper thumbnail of Global convergence of fractionally spaced Godard (CMA) adaptive equalizers$

Global convergence of fractionally spaced Godard (CMA) adaptive equalizers

IEEE Transactions on Signal Processing, 1996

The Godard or constant modulus algorithm (CMA) equalizer is perhaps the best known and the most p... more The Godard or constant modulus algorithm (CMA) equalizer is perhaps the best known and the most popular scheme for blind adaptive channel equalization. Most published works on blind equalization convergence analysis are confined to T-spaced equalizers with real-valued inputs. The common belief is that analysis of fractionally spaced equalizers (FSE's) with complex inputs is a straightforward extension with similar results. This belief is, in fact, untrue. In this paper, we present a convergence analysis of GodardCMA FSE's that proves the important advantages provided by the FSE structure. We show that an FSE allows the exploitation of the channel diversity that supports two important conclusions of great practical significance: 1) A finite-length channel satisfying a length-and-zero condition allows Godard/CMA FSE to be globally convergent, and 2) the linear FSE filter length need not be longer than the channel delay spread. Computer simulation demonstrates the performance improvement provided by the adaptive Godard FSE.

$Research paper thumbnail of On convergence analysis of fractionally spaced adaptive blind equalizers$

On convergence analysis of fractionally spaced adaptive blind equalizers

IEEE Transactions on Signal Processing, 1997

Blind channel identification based on second order cyclostationary statistics

In this communication, necessary and sufficient conditions are presented for the unique blind ide... more In this communication, necessary and sufficient conditions are presented for the unique blind identification of possibly nonminimum phase channels driven by cyclostationary processes. Using a frequencydomain formulation, it is first shown that a channel can be identified by the second-order statistics of the observation if and only if the channel transfer function does not have special uniformly spaced zeros. This condition leads to several necessary and sufficient conditions on the observation spectra and the channel impulse response. Based on the frequency-domain formulation, a new identification algorithm is proposed.

On the (non)existence of undesirable equilibria of Godard blind equalizers

IEEE Transactions on Signal Processing, 1992

Energy-Efficient Processing and Robust Wireless Cooperative Transmission for Edge Inference

IEEE Internet of Things Journal

Edge machine learning can deliver low-latency and private artificial intelligent (AI) services fo... more Edge machine learning can deliver low-latency and private artificial intelligent (AI) services for mobile devices by leveraging computation and storage resources at the network edge. This paper presents an energy-efficient edge processing framework to execute deep learning inference tasks at the edge computing nodes whose wireless connections to mobile devices are prone to channel uncertainties. Aimed at minimizing the sum of computation and transmission power consumption with probabilistic quality-of-service (QoS) constraints, we formulate a joint inference tasking and downlink beamforming problem that is characterized by a group sparse objective function. We provide a statistical learning based robust optimization approach to approximate the highly intractable probabilistic-QoS constraints by nonconvex quadratic constraints, which are further reformulated as matrix inequalities with a rank-one constraint via matrix lifting. We design a reweighted power minimization approach by iteratively reweighted 1 minimization with difference-of-convexfunctions (DC) regularization and updating weights, where the reweighted approach is adopted for enhancing group sparsity whereas the DC regularization is designed for inducing rankone solutions. Numerical results demonstrate that the proposed approach outperforms other state-of-the-art approaches.

A New Algorithm for Improved Blind Detection of Polar Coded PDCCH in 5G New Radio

In recent release of the new cellular standard known as 5G New Radio (5G-NR), the physical downli... more In recent release of the new cellular standard known as 5G New Radio (5G-NR), the physical downlink control channel (PDCCH) has adopted polar codes for error protection. Similar to 4G-LTE, each active user equipment (UE) must blindly detect its own PDCCH in the downlink search space. This work investigates new ways to improve the accuracy of PDCCH blind detection in 5G-NR. We develop a novel design of joint detection and decoding receiver for 5G multiple-input multiple-output (MIMO) transceivers. We aim to achieve robustness against practical obstacles including channel state information (CSI) errors, noise, co-channel interferences, and pilot contamination. To optimize the overall receiver performance in PDCCH blind detection, we incorporate the polar code information during the signal detection stage by relaxing and transforming the Galois field code constraints into the complex signal field. Specifically, we develop a novel joint linear programming (LP) formulation that takes int...

OTFS Signaling for Uplink NOMA of Heterogeneous Mobility Users

IEEE Transactions on Communications

We investigate a coded uplink non-orthogonal multiple access (NOMA) configuration in which groups... more We investigate a coded uplink non-orthogonal multiple access (NOMA) configuration in which groups of co-channel users are modulated in accordance with orthogonal time frequency space (OTFS). We take advantage of OTFS characteristics to achieve NOMA spectrum sharing in the delay-Doppler domain between stationary and mobile users. We develop an efficient iterative turbo receiver based on the principle of successive interference cancellation (SIC) to overcome the co-channel interference (CCI). We propose two turbo detector algorithms: orthogonal approximate message passing with linear minimum mean squared error (OAMP-LMMSE) and Gaussian approximate message passing with expectation propagation (GAMP-EP). The interactive OAMP-LMMSE detector and GAMP-EP detector are respectively assigned for the reception of the stationary and mobile users. We analyze the convergence performance of our proposed iterative SIC turbo receiver by utilizing a customized extrinsic information transfer (EXIT) chart and simplify the corresponding detector algorithms to further reduce receiver complexity. Our proposed iterative SIC turbo receiver demonstrates performance improvement over existing receivers and robustness against imperfect SIC process and channel state information uncertainty.

Receiver Design for OTFS with a Fractionally Spaced Sampling Approach

IEEE Transactions on Wireless Communications

The recent emergence of orthogonal time frequency space (OTFS) modulation as a novel PHYlayer mec... more The recent emergence of orthogonal time frequency space (OTFS) modulation as a novel PHYlayer mechanism is more suitable in high-mobility wireless communication scenarios than traditional orthogonal frequency division multiplexing (OFDM). Although multiple studies have analyzed OTFS performance using theoretical and ideal baseband pulseshapes, a challenging and open problem is the development of effective receivers for practical OTFS systems that must rely on non-ideal pulseshapes for transmission. This work focuses on the design of practical receivers for OTFS. We consider a fractionally spaced sampling (FSS) receiver in which the sampling rate is an integer multiple of the symbol rate. For rectangular pulses used in OTFS transmission, we derive a general channel inputoutput relationship of OTFS in delay-Doppler domain without the common reliance on impractical assumptions such as ideal bi-orthogonal pulses and on-the-grid delay/Doppler shifts. We propose two equalization algorithms: iterative combining message passing (ICMP) and turbo message passing (TMP) for symbol detection by exploiting delay-Doppler channel sparsity and the channel diversity gain via FSS. We analyze the convergence performance of TMP receiver and propose simplified message passing (MP) receivers to further reduce complexity. Our FSS receivers demonstrate stronger performance than traditional receivers and robustness to the imperfect channel state information knowledge.

Blind Over-the-Air Computation and Data Fusion via Provable Wirtinger Flow

IEEE Transactions on Signal Processing

Over-the-air computation (AirComp) shows great promise to support fast data fusion in Internet-of... more Over-the-air computation (AirComp) shows great promise to support fast data fusion in Internet-of-Things (IoT) networks. AirComp typically computes desired functions of distributed sensing data by exploiting superposed data transmission in multiple access channels. To overcome its reliance on channel station information (CSI), this work proposes a novel blind overthe-air computation (BlairComp) without requiring CSI access, particularly for low complexity and low latency IoT networks. To solve the resulting non-convex optimization problem without the initialization dependency exhibited by the solutions of a number of recently proposed efficient algorithms, we develop a Wirtinger flow solution to the BlairComp problem based on random initialization. To analyze the resulting efficiency, we prove its statistical optimality and global convergence guarantee. Specifically, in the first stage of the algorithm, the iteration of randomly initialized Wirtinger flow given sufficient data samples can enter a local region that enjoys strong convexity and strong smoothness within a few iterations. We also prove the estimation error of BlairComp in the local region to be sufficiently small. We show that, at the second stage of the algorithm, its estimation error decays exponentially at a linear convergence rate.

Data Shuffling in Wireless Distributed Computing via Low-Rank Optimization

IEEE Transactions on Signal Processing

Intelligent mobile platforms such as smart vehicles and drones have recently become the focus of ... more Intelligent mobile platforms such as smart vehicles and drones have recently become the focus of attention for onboard deployment of machine learning mechanisms to enable low latency decisions with low risk of privacy breach. However, most such machine learning algorithms are both computationand-memory intensive, which makes it highly difficult to implement the requisite computations on a single device of limited computation, memory, and energy resources. Wireless distributed computing presents new opportunities by pooling the computation and storage resources among devices. For low-latency applications, the key bottleneck lies in the exchange of intermediate results among mobile devices for data shuffling. To improve communication efficiency, we propose a co-channel communication model and design transceivers by exploiting the locally computed intermediate values as side information. A low-rank optimization model is proposed to maximize the achieved degrees-of-freedom (DoF) by establishing the interference alignment condition for data shuffling. Unfortunately, existing approaches to approximate the rank function fail to yield satisfactory performance due to the poor structure in the formulated low-rank optimization problem. In this paper, we develop an efficient DC algorithm to solve the presented low-rank optimization problem by proposing a novel DC representation for the rank function. Numerical experiments demonstrate that the proposed DC approach can significantly improve the communication efficiency whereas the achievable DoF almost remains unchanged when the number of mobile devices grows.

Cumulant matrix subspace algorithms for blind single FIR channel identification

Blind identification of discrete non-minimum phase FIR channels is studied here. Exploiting highe... more Blind identification of discrete non-minimum phase FIR channels is studied here. Exploiting higher order statistics of the unknown channel output, a closed-form solution to the FIR channel impulse response is presented. The algorithm is simple and relies only on nullspace decomposition. It does not involve global minimization of non-unimodal cost functions nor does it use overparametrization. Its application is broad. It can be used either as the final channel estimate or as a good initial point in nonlinear cumulant matching techniques

Column-anchored zeroforcing blind equalization for multiuser wireless FIR channels

We propose a direct blind zeroforcing approach to cancel intersymbol interference (ISI) in multip... more We propose a direct blind zeroforcing approach to cancel intersymbol interference (ISI) in multiple user finite impulse response (FIR) channels. By selectively anchoring columns of the channel convolution matrix, we present two columnanchored zeroforcing equalizers (CAZE), one without output delay and one with a chosen delay. Unlike many known blind identification algorithms, these equalizers do not need an accurate estimate of the channel orders. Exploiting second-order statistics (SOS) of the received signals, they can retain preselected d d d columns in the channel convolution matrix (d d d is the number of users) and force the remaining columns to zero. CAZE can effectively equalize single-input-multiple-output (SIMO) systems and can reduce dynamic multiple-input-multiple-output (MIMO) systems into a memoryless signal mixing system for source separation. Simulation results show that the CAZE is not only effective for blind equalization of linear quadrature amplitude modulation (QAM) systems, but it is also applicable to the nonlinear GMSK modulation in the popular wireless GSM systems when computational cost severely limits the use of nonlinear methods such as the Viterbi algorithm.

Joint transmitter-receiver optimization for partial response channels based on nonmaximally decimated filterbank precoding technique

Transmitter and receiver filter design plays a key role in communication systems with partial res... more Transmitter and receiver filter design plays a key role in communication systems with partial response channels. For a partial response system, a nonmaximally decimated multirate filter bank can be used as a precoder. Based on MMSE criterion, a closed-form solution to the joint transmitter-receiver optimization problem for noisy partial response channels is presented in this paper. It is found that the redundancy introduced by the nonmaximally decimated filter bank precoder can compensate for spectral nulls in partial response channels that can impair several known joint optimization methods. Simulation results corroborate the analysis that joint transmitter-receiver optimization can achieve significant performance improvement over inverse filter receiver and receiver optimization schemes.

A matrix-pencil approach to blind separation of colored nonstationary signals

For many signal sources such as speech with distinct, nonwhite power spectral densities, second-o... more For many signal sources such as speech with distinct, nonwhite power spectral densities, second-order statistics of the received signal mixture can be exploited for signal separation. Without knowledge on noise correlation matrix, we propose a simple and yet effective signal extraction method for signal source separation under unknown temporally white noise. This new and unbiased signal extractor is derived from the matrix pencil formed between output autocorrelation matrices at different delays. Based on the matrix pencil, an ESPRIT-type algorithm is derived to get an optimal solution in least square sense. Our method is well suited for systems with colored sensor noises and for nonstationary signals.

Matrix outer-product decomposition method for blind multiple channel identification

Blind channel identification and equalization have recently attracted a great deal of attention d... more Blind channel identification and equalization have recently attracted a great deal of attention due to their potential application in mobile communications and digital TV systems. In this paper, we present a new algorithm that utilizes second-order statistics for multichannel parameter estimation. The algorithm is simple and relies on an outer-product decomposition. Its implementation requires no adjustment for single-or multiple-user systems. This new algorithm can be viewed as a generalization of a recently proposed linear prediction algorithm. It is capable of generating more accurate channel estimates and is more robust to overmodeling errors in channel order estimate. The superior performance of this new algorithm is demonstrated through simulation examples.

$Historically, there has been a belief that a noninteger oversampling factor may be more beneficial. In fact, it is heuristically plausible that an oversampling period of A = qI/p in which g is an integer will yield fewer nonzero channel samples than using A = T/p, Hence, argument persists that a rational oversampling factor may help reduce the dimensionality of channel identification and simplify the problem. Here, we show that, in fact, a noninteger fractional sampling generates an equivalent multiuser system whose dimensionality is not reduced and may be more difficult to identify. Clearly, mo is the order of the N dynamic FIR channels. There are a total of (mo +1)NpJ unknown parameters to identify in the blind identification of FIR channels. With these notations, a sampled channel output signal vector of length Mp can be written as$

$Now, form an MpJ x (mo +M \N block Toeplitz matrix with (M -1)N trailing zeros in the first pJ rows$

$Hence, matrix AD forms the outer-product of the channel parameter matrix 7, The singular value decomposition of this outer-product matrix can be used to generate an estimate where @ is an N x N unitary matrix. Recall from [13] and [17] that this memoryless ambiguity is intrinsic to the multiuser blind identification problem and cannot be resolved unless additional information is available. For signal recovery, if a perfect multichannel equalizer is designed according to the channel estimate 7(Q, then the N receiver outputs will be memoryless combinations of the N channel inputs and will need to be separated, as discussed in works such as [17]. This ambiguity would also add to the cost of channel identification using noninteger fractional sampling.$

Sampling and prefiltering effects on blind equalizer design

In the development of equalization algorithms for unknown channels, the effects of the sampling r... more In the development of equalization algorithms for unknown channels, the effects of the sampling rate and the analog receive prefilter prior to discretization of the received signal are often overlooked. In this paper, these effects are investigated. The relationship between the fractionally spaced output samples of a noise-limiting prefilter and the symbol spaced output samples of a matched filter is studied for both the time-invariant and the timevarying channels. It is shown that the prefilter and the sampling rate can have significant effects on blind equalization algorithms. Thus, this paper provides a common framework for comparing different blind algorithms that are studied in the literature with different sampling rates. A case study of the well-known subspace method for blind channel identification is presented. The effects of the noise color due to the prefilter on equalizers is investigated, and the sensitivity of the truncation of the overall channel impulse response in terms of the mean squared error (MSE) performance criterion is investigated through numerical examples.

Blind adaptive equalizers for quadrature amplitude modulated communication systems based on convex cost functions

Local convergence of the Sato blind equalizer and generalizations under practical constraints

An early use of recursive identification in blind adaptive channel equalization is an algorithm d... more An early use of recursive identification in blind adaptive channel equalization is an algorithm developed by Sato. An important generalization of the Sat0 algorithm with extensive analysis appears in the work of Benveniste, Goursat, and Ruget. These generalized algorithms have been shown to possess a desirable global convergence property under two idealized conditions. The convergence properties of this class of blind algorithms under practical constraints common to a variety of channel equalization applications that violate these idealized conditions are studied. Results show that, in practice, when either the equalizer is finite-dimensional and/or the input is discrete (as in digital communications) the equalizer parameters may converge to parameter settings that fail to achieve the objective of approximating the channel inverse. It is also shown, that a center spike initialization is insufficient to guarantee avoiding such ill-convergence. Simulations verify the analytical results.

Semi-blind channel identification for individual data bursts in GSM wireless systems

... These semiblind methods can overcome some serious limitations of SOS blind algorithms. We als... more

Characteristics of band-limited channels unidentifiable from second-order cyclostationary statistics

IEEE Signal Processing Letters, 1996

Several works on blind channel identification and equalization rely on a system model with multip... more Several works on blind channel identification and equalization rely on a system model with multiple sub-channels driven by a single input. These methods depend on a critical condition that no common zero exists among the sub-channels. We aimed at establishing the physical significance of this critical zero condition and understanding the limitation of methods based on second-order statistics, By deriving a number of sufficient conditions, we characterize several classes of band-limited channels that are not identifiable from only the second-order statistics of the channel output.

$Research paper thumbnail of Global convergence of fractionally spaced Godard (CMA) adaptive equalizers$

Global convergence of fractionally spaced Godard (CMA) adaptive equalizers

IEEE Transactions on Signal Processing, 1996

The Godard or constant modulus algorithm (CMA) equalizer is perhaps the best known and the most p... more The Godard or constant modulus algorithm (CMA) equalizer is perhaps the best known and the most popular scheme for blind adaptive channel equalization. Most published works on blind equalization convergence analysis are confined to T-spaced equalizers with real-valued inputs. The common belief is that analysis of fractionally spaced equalizers (FSE's) with complex inputs is a straightforward extension with similar results. This belief is, in fact, untrue. In this paper, we present a convergence analysis of GodardCMA FSE's that proves the important advantages provided by the FSE structure. We show that an FSE allows the exploitation of the channel diversity that supports two important conclusions of great practical significance: 1) A finite-length channel satisfying a length-and-zero condition allows Godard/CMA FSE to be globally convergent, and 2) the linear FSE filter length need not be longer than the channel delay spread. Computer simulation demonstrates the performance improvement provided by the adaptive Godard FSE.

$Research paper thumbnail of On convergence analysis of fractionally spaced adaptive blind equalizers$

On convergence analysis of fractionally spaced adaptive blind equalizers

IEEE Transactions on Signal Processing, 1997

Blind channel identification based on second order cyclostationary statistics

In this communication, necessary and sufficient conditions are presented for the unique blind ide... more In this communication, necessary and sufficient conditions are presented for the unique blind identification of possibly nonminimum phase channels driven by cyclostationary processes. Using a frequencydomain formulation, it is first shown that a channel can be identified by the second-order statistics of the observation if and only if the channel transfer function does not have special uniformly spaced zeros. This condition leads to several necessary and sufficient conditions on the observation spectra and the channel impulse response. Based on the frequency-domain formulation, a new identification algorithm is proposed.

On the (non)existence of undesirable equilibria of Godard blind equalizers

IEEE Transactions on Signal Processing, 1992