Kon Max Wong

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.

Equal-diagonal QR decomposition and its application to precoder design for successive-cancellation detection

In multiple-input multiple-output (MIMO) multiuser detection theory, the QR decomposition of the channel matrix H can be used to form the back-cancellation detector. In this paper, we propose an optimal QR decomposition, which we call the equal-diagonal QR decomposition, or briefly the QRS decomposition. We apply the decomposition to precoded successive-cancellation detection, where we assume that both the transmitter and the receiver have perfect channel knowledge. We show that, for any channel matrix H, there exists a unitary precoder matrix S, such that HS=QR, where the nonzero diagonal entries of the upper triangular matrix R in the QR decomposition of HS are all equal to each other. The precoder and the resulting successive-cancellation detector have the following properties. a) The minimum Euclidean distance between two signal points at the channel output is equal to the minimum Euclidean distance between two constellation points at the precoder input up to a multiplicative factor that equals the diagonal entry in the R-factor. b) The superchannel HS naturally exhibits an optimally ordered column permutation, i.e., the optimal detection order for the vertical Bell Labs layered space-time (V-BLAST) detector is the natural order. c) The precoder S minimizes the block error probability of the QR successive cancellation detector. d) A lower and an upper bound for the free distance at the channel output is expressible in terms of the diagonal entries of the R-factor in the QR decomposition of a channel matrix. e) The precoder S maximizes the lower bound of the channels free distance subject to a power constraint. f) For the optimal precoder S, the performance of the QR detector is asymptotically (at large signal-to-noise ratios (SNRs)) equivalent to that of the maximum-likelihood detector (MLD) that uses the same precoder. Further, We consider two multiplexing schemes: time-division multiple access (TDMA) and orthogonal frequency-division multiplexing (OFDM). We d

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.

A fast method for real-time median filtering

A fast real-time algorithm is presented for median filtering of signals and images. The algorithm determines the kth bit of the median by inspecting the k most significant bits of the samples. The total number of full-word comparison steps is equal to the wordlength of the samples. Speed and hardware complexity of the algorithm is compared with two other fast methods for median filtering.

On information theoretic criteria for determining the number of signals in high resolution array processing

An important problem in high-resolution array processing is the determination of the number of signals arriving at the array. Information theoretic criteria provide a means to achieve this. Two commonly used criteria are the Akaike information criterion (AIC) and minimum descriptive length (MDL) criterion. While the AIC tends to overestimate even at a high signal-to-noise ratio (SNR), the MDL criterion tends to underestimate at low or moderate SNR. By excluding irrelevant parameters, a new log likelihood function has been chosen. Utilizing this new log likelihood function gives a set of more accurate estimates of the eigenvalues and in the establishment of modified information theoretic criteria which moderate the performance of the AIC and the MDL criterion. Computer simulations confirm that the modified criteria have superior performance. >

Direction finding in partly calibrated sensor arrays composed of multiple subarrays

We consider the direction-finding problem in partly calibrated arrays composed of several calibrated and identically oriented (but possibly nonidentical) subarrays that are displaced by unknown (and possibly time-varying) vector translations. A new search-free eigenstructure-based direction-finding approach is proposed for such class of sensor arrays. It is referred to as the rank-reduction (RARE) estimator and enjoys simple implementation that entails computing the eigendecomposition of the sample array covariance matrix and polynomial rooting. Closed-form expressions for the deterministic Cramer-Rao bounds (CRBs) on direction-of-arrival (DOA) estimation for the considered class of sensor arrays are derived. Comparison of these expressions with simulation results show that the finite-sample performance of RARE algorithms in both time-invariant and time-varying array cases is close to the corresponding bounds. Moreover, comparisons of the derived CRBs with the well-known bounds for the fully calibrated time-invariant array case help to discover several interesting properties of DOA estimation in partly calibrated and time-varying arrays.

Statistical analysis of the performance of information theoretic criteria in the detection of the number of signals in array processing

The performances of the Akaike (1974) information criterion and the minimum descriptive length criterion methods are examined. The events which lead to erroneous decisions are considered, and, on the basis of these events, the probabilities of error for the two criteria are derived. The probabilities of the first two events are derived based on the asymptotic distribution of the sample eigenvalues of an estimated Hermitian matrix. It is further shown that the probabilities of missing and false alarm for these two criteria can be evaluated to a close approximation. Although the derivation of the probabilities of error is based on an asymptotic analysis, the results are confirmed to be in very close agreement with computer simulation results. >

Detection of the number of signals: a predicted eigen-threshold approach

A novel method for detecting the number of signals incident upon an array of sensors is described. The method is based on finding upper thresholds for the observed eigenvalues of the correlation matrix of the array output. The asymptotic normality of the multifold eigenvalue estimate is used to derive a prediction formula for the thresholds. Due to the fact that the detection error of the method can be controlled by a parameter t, the performance of the method is superior to the MDL (minimum description length) under low SNR (signal-to-noise ratio) and superior to an AIC (Akaike information criterion) under high SNR. The distribution functions of both missing and false alarm errors are evaluated so that the performance of the method can be analyzed and so that t can be chosen. Simulation results are presented to confirm the analysis. >

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.

Soft quasi-maximum-likelihood detection for multiple-antenna wireless channels

The paper addresses soft maximum-likelihood (ML) detection for multiple-antenna wireless communication channels. We propose a soft quasi-ML detector that maximizes the log-likelihood function by deploying a semi-definite relaxation (SDR). Given perfect channel state information at the receiver, the quasi-ML SDR detector closely approximates the performance of the optimal ML detector in both coded and uncoded multiple-input, multiple-output (MIMO) channels with quadrature phase-shift keying (QPSK) modulation and frequency-flat Rayleigh fading. The complexity of the quasi-ML SDR detector is much less than that of the optimal ML detector, thus offering more favorable performance/complexity characteristics. In contrast to the existing sphere decoder, the new quasi-ML detector enjoys guaranteed polynomial worst-case complexity. The two detectors exhibit quite comparable performance in a variety of ergodic QPSK MIMO channels, but the complexity of the quasi-ML detector scales better with increasing number of transmit and receive antennas, especially in the region of low signal-to-noise ratio (SNR).