Timothy N. Davidson

Quasi-maximum-likelihood multiuser detection using semi-definite relaxation with application to synchronous CDMA

The maximum-likelihood (ML) multiuser detector is well known to exhibit better bit-error-rate (BER) performance than many other multiuser detectors. Unfortunately,ML detection (MLD) is a nondeterministic polynomial-time hard (NP-hard) problem, for which there is no known algorithm that can find the optimal solution with polynomial-time complexity (in the number of users). In this paper, a polynomial-time approximation method called semi-definite (SD) relaxation is applied to the MLD problem with antipodal data transmission. SD relaxation is an accurate approximation method for certain NP-hard problems. The SD relaxation ML (SDR-ML) detector is efficient in that its complexity is of the order of K3.5, where K is the number of users. We illustrate the potential of the SDR-ML detector by showing that some existing detectors, such as the decorrelator and the linear-minimum-mean-square-error detector, can be interpreted as degenerate forms of the SDR-ML detector. Simulation results indicate that the BER performance of the SDR-ML detector is better than that of these existing detectors and is close to that of the true ML detector, even when the cross-correlations between users are strong or the near-far effect is significant.

Minimum BER block precoders for zero-forcing equalization

In this paper we derive an analytic expression for the linear precoder which minimizes the bit error rate (BER) for block transmission systems with zero-forcing equalization and threshold detection. The design is developed for the two standard schemes for eliminating inter-block interference; viz, zero padding (ZP) and cyclic prefix (CP). The CP minimum BER precoder has a structure similar to that of the conventional water-filling discrete multitone (DMT) modulation scheme, but the diagonal water-filling power loading matrix is replaced by a full matrix consisting of a diagonal minimum mean square error (MMSE) power loading matrix post-multiplied by a Discrete Fourier Transform (DFT) matrix. The ZP minimum BER precoder has a corresponding structure. Performance evaluations indicate that the signal-to-noise ratio (SNR) gain of the ZP and CP minimum BER precoders over conventional water-filling DMT, MMSE, and orthogonal frequency division multiplexing (OFDM) schemes can be as much as several decibels.

Transceiver optimization for block-based multiple access through ISI channels

In this paper, we describe a formulation of the minimum mean square error (MMSE) joint transmitter-receiver design problem for block-based multiple access communication over intersymbol interference (ISI) channels. Since the direct formulation of this problem turns out to be nonconvex, we develop various alternative convex formulations using techniques of linear matrix inequalities (LMIs) and second-order cone programming (SOCP). In particular, we show that the optimal MMSE transceiver design problem can be reformulated as a semidefinite program (SDP), which can be solved using highly efficient interior point methods. When the channel matrices are diagonal (as in cyclic prefixed multicarrier systems), we show that the optimal MMSE transceivers can be obtained by subcarrier allocation and optimal power loading to each subcarrier for all the users. Moreover, the optimal subcarrier allocation and power-loading can be computed fairly simply (in polynomial time) by the relative ratios of the magnitudes of the subchannel gains corresponding to all subcarriers. We also prove that any two users can share no more than one subcarrier in the optimal MMSE transceivers. By exploiting this property, we design an efficient strongly polynomial time algorithm for the determination of optimal powerloading and subcarrier allocation in the two-user case.

Blind ML detection of orthogonal space-time block codes: efficient high-performance implementations

Orthogonal space-time block codes (OSTBCs) have attracted much attention owing to their simple code construction, maximal diversity gain, and low maximum-likelihood (ML) detection complexity when channel state information (CSI) is available at the receiver. This paper addresses the problem of ML OSTBC detection with unknown CSI. Focusing on the binary and quaternary PSK constellations, we show that blind ML OSTBC detection can be simplified to a Boolean quadratic program (BQP). From an optimization viewpoint the BQP is still a computationally hard problem, and we propose two alternatives for dealing with this inherent complexity. First, we consider the semidefinite relaxation (SDR) approach, which leads to a suboptimal, but accurate, blind ML detection algorithm with an affordable worst-case computational cost. We also consider the sphere decoding approach, which leads to an exact blind ML detection algorithm that remains computationally expensive in the worst case, but generally incurs a reasonable average computational cost. For the two algorithms, we study implementation methods that can significantly reduce the computational complexity. Simulation results indicate that the two blind ML detection algorithms are competitive, in that the bit error performance of the two algorithms is almost the same and is noticeably better than that of some other existing blind detectors. Moreover, numerical studies show that the SDR algorithm provides better complexity performance than the sphere decoder in the worst-case sense, and vice versa in the average sense.

Wavelet packet division multiplexing and wavelet packet design under timing error effects

Wavelet packet division multiplexing (WPDM) is a multiple signal transmission technique in which the message signals are waveform coded onto wavelet packet basis functions for transmission. The overlapping nature of such waveforms in time and frequency provides a capacity improvement over the commonly used frequency division multiplexing (FDM) and time division multiplexing (TDM) schemes while their orthogonality properties ensure that the overlapping message signals can be separated by a simple correlator receiver. The interference caused by timing offset in transmission is examined. A design procedure that exploits the inherent degrees of freedom in the WPDM structure to mitigate the effects of timing error is introduced, and a waveform that minimizes the energy of the timing error interference is designed. An expression for the probability of error due to the presence of Gaussian noise and timing error for the transmission of binary data is derived. The performance advantages of the designed waveform over standard wavelet packet basis functions are demonstrated by both analytical and simulation methods. The capacity improvement of WPDM, its simple implementation, and the possibility of having optimum waveform designs indicate that WPDM holds considerable promise as a multiple signal transmission technique.

Optimal waveform design for UWB radios

With transmit power spectra strictly limited by regulatory spectral masks, the emerging ultra-wideband (UWB) communication systems call for judicious pulse shape design in order to achieve optimal spectrum utilization, spectral mask compatibility, and coexistence with other wireless services. Meanwhile, orthogonal pulse sets are often desired in order to apply high-rate multidimensional modulation and (carrier-free) orthogonal frequency-division multiple access. Motivated by these considerations, we suggest a digital finite impulse response (FIR) filter approach to synthesizing UWB pulses and propose filter design techniques by which optimal waveforms that satisfy the spectral mask can be efficiently obtained. For single pulse design, we develop a convex formulation for the design of the FIR filter coefficients that maximize the spectrum utilization efficiency in terms of both the bandwidth and power allowed by the spectral mask. For orthogonal pulse design, a sequential strategy is derived to formulate the overall pulse design problem as a set of convex subproblems, which are then solved in a sequential manner to yield a set of mutually orthogonal pulses. Our design techniques not only provide waveforms with high spectrum utilization and guaranteed spectral mask compliance but also permit simple modifications that can accommodate several other system objectives.

A framework for designing mimo systems with decision feedback equalization or tomlinson-harashima precoding

We consider joint transceiver design for point-to-point Multiple-Input Multiple-Output communication systems that implement interference (pre-)subtraction; i.e., Decision Feedback Equalization (DFE) or Tomlinson-Harashima precoding (THP). We develop a unified framework for joint transceiver design of these two dual systems by considering design criteria that are expressed as functions of the (logarithm of the) Mean Square Error (MSE) of the individual data streams. By deriving two inequalities that involve the logarithms of the individual MSEs, we obtain optimal designs for two broad classes of communication objectives, namely those that are Schur-convex and Schur-concave functions of these logarithms. These two classes embrace several design criteria for which the optimal transceiver design has remained an open problem. For Schur-convex objectives, the optimal design results in data streams with equal MSEs. In addition to other desirable properties, this design simultaneously minimizes the total MSE and the average bit error rate, and maximizes the Gaussian mutual information; a property that is not achieved by a linear transceiver. Moreover, we show that the optimal design yields objective values that are superior to the corresponding optimal objective value for a linear transceiver. For Schur-concave objectives, the optimal DFE design results in linear equalization and the optimal THP design results in linear precoding. The proposed design framework can be regarded as a counterpart of the existing framework for linear transceiver design.

Robust transmit eigen beamforming based on imperfect channel state information

Transmit beamforming is a powerful technique for enhancing the performance and increasing the throughput of wireless communication systems that employ multiple antennas at the transmitter. A major drawback of most existing transmit beamforming techniques is that they require nearly perfect knowledge of the channel at the transmitter, which is typically not available in practice. Transmitter designs that address the imperfect channel state information (CSI) problem commonly use statistical models for the channel and/or mismatch between the presumed and actual transmitter CSI. Since these approaches are model based, they can suffer from mismodeling. In this paper, a more robust framework is proposed in which no statistical assumptions are made about the CSI mismatch or the channel. The goal is to design a transmitter that has the best performance under the worst-case CSI mismatch. The transmitter designed herein achieves this goal for all CSI mismatches below a certain threshold level. The proposed design combines beamforming along the eigenvectors of the (deterministic) autocorrelation of the channel matrix perceived by the transmitter and power loading across those beams. While the power-loading algorithm resembles conventional water-filling to some degree, it explicitly incorporates robustness to the CSI mismatch, and the water level can be determined in a simple systematic way.

Optimal waveform design for cognitive radar

A key component of a cognitive radar system is the method by which the transmitted waveform is adapted in response to information regarding the radar environment. The goal of such adaptation methods is to provide a flexible framework that can synthesize waveforms that provide different tradeoffs between a variety of performance objectives, and can do so efficiently. In this paper, we propose a waveform design method that efficiently synthesizes waveforms that provide a trade-off between estimation performance for a Gaussian ensemble of targets and detection performance for a specific target. In particular, the method synthesizes (finite length) waveforms that achieve an inherent trade-off between the (Gaussian) mutual information and the signal-to-noise ratio (SNR) for a particular target. In addition, the method can accommodate a variety of constraints on the transmitted spectrum. We show that the waveform design problem can be formulated as a convex optimization problem in the autocorrelation of the waveform, and we develop a customized interior point method for efficiently obtaining a globally optimal waveform.

Noncoherent MIMO Communication: Grassmannian Constellations and Efficient Detection

This paper considers the design of both a transmitter and a receiver for noncoherent communication over a frequency-flat, richly scattered multiple-input multiple-output (MIMO) channel. The design is guided by the fact that at high signal-to-noise ratios (SNRs), the ergodic capacity of the channel can be achieved by input signals that are isotropically distributed on the (compact) Grassmann manifold. The first part of the paper considers the design of Grassmannian constellations that MIMIC the isotropic distribution. A subspace perturbation analysis is used to determine an appropriate metric for the distance between Grassmannian constellation points, and using this metric, greedy, direct and rotation-based techniques for designing constellations are proposed. These techniques offer different tradeoffs between the minimum distance of the constellation and the design complexity. In addition, the rotation-based technique results in constellations that have lower storage requirements and admit a natural ldquoquasi-set-partitioningrdquo binary labeling.