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The problem of iterative detection/decoding of data symbols transmitted over an additive white Gaussian noise (AWGN) channel in the presence of phase uncertainty is addressed in this paper. By modelling the phase uncertainty either as an unknown deterministic variable/process or random variable/process with a known a priori probability density function, a number of non-Bayesian and Bayesian detection algorithms with various amount of suboptimality have been proposed in the literature to solve the problem. In this paper, a new set of suboptimal iterative detection algorithms is obtained by utilizing the variational bounding technique. Especially, applying the generic variational Bayesian (VB) framework, efficient iterative joint estimation and detection/decoding schemes are derived for the constant phase model as well as for the dynamic phase model. In addition, the relation of the VB-based approach to the optimal noncoherent receiver as well as to the classical approach via the expectation-maximization (EM) algorithm is provided. Performance of the proposed detectors in the presence of a strong dynamic phase noise is compared to the performance of the existing detectors. Furthermore, an incremental scheduling of the VB (or EM) algorithm is shown to reduce the overall complexity of the receiver. Index Terms--Adaptive iterative detection, variational Bayesian algorithms, expectation-maximization algorithm, Bayesian estimation.

This paper presents a unifying framework for designing a joint channel-estimation-and-data-detection (CE/DD) scheme and space-time block code (STBC) that improves the performances in a multiple-input-multiple-output (MIMO) slow flat Rayleigh fading channel. Modeling the channel using the continuous-fading model, a matrix state-space model, which naturally represents the temporal and spatial dimensions of a MIMO system, is introduced. A consistent and novel matrix CE/DD scheme is developed using a matrix Kalman filter and a matrix normalized-innovations-based maximum-likelihood detector. In MIMO CE/DD in multiplicative fading, symmetric STBCs (S-STBCs) cause isometric data sequences, which lead to a detection error floor. Motivated by the minimization of the probability of error, two asymmetric STBCs are introduced to be used with these S-STBCs to mitigate isometry. To further improve detection performance, a self-matching STBC (SM-STBC), which mitigates isometry using asymmetry, improves estimation performance using training, and improves detection performance by adapting its code properties, is introduced. This SM-STBC generalizes a limited version that was previously proposed. A comprehensive analysis, which is supported by some simulation studies, indicates that the proposed framework of transceiver and STBC designs offers excellent detection performance. Index Terms--Asymmetric space-time block code (STBC), continuous-fading model (CFM), innovations, matrix Kalman filtering, self-matching STBC (SM-STBC).

Many algorithms in signal processing and digital communications must deal with the problem of computing the probabilities of the hidden state variables given the observations, i.e., the inference problem, as well as with the problem of estimating the model parameters. Such an inference and estimation problem is encountered, for e.g., in adaptive turbo equalization/demodulation where soft information about the transmitted data symbols has to be inferred in the presence of the channel uncertainty, given the received signal samples and a priori information provided by the decoder. An exact inference algorithm computes the a posteriori probability (APP) values for all transmitted symbols, but the computation of APPs is known to be an NP-hard problem, thus, rendering this approach computationally prohibitive in most cases. In this paper, we show how many of the well-known low-complexity soft-input soft-output (SISO) equalizers, including the channel-matched filter-based linear SISO equalizers and minimum mean square error (MMSE) SISO equalizers, as well as the expectation-maximization (EM) algorithm-based SISO demodulators in the presence of the Rayleigh fading channel, can be formulated as solutions to a variational optimization problem. The variational optimization is a well-established methodology for low-complexity inference and estimation, originating from statistical physics. Importantly, the imposed variational optimization framework provides an interesting link between the APP demodulators and the linear SISO equalizers. Moreover, it provides a new set of insights into the structure and performance of these widely celebrated linear SISO equalizers while suggesting their fine tuning as well. Index Terms--Linear equalizers, mean field inference, turbo receivers, variational optimization.

A partial ordering on general finite-state Markov channels is given, which orders the channels in terms of probability of symbol error under iterative estimation decoding of a low-density parity-check (LDPC) code. This result is intended to mitigate the complexity of characterizing the performance of general finite-state Markov channels, which is difficult due to the large parameter space of this class of channel. An analysis tool, originally developed for the Gilbert-Elliott channel, is extended and generalized to general finite-state Markov channels. In doing so, an operator is introduced for combining finite-state Markov channels to create channels with larger state alphabets, which are then subject to the partial ordering. As a result, the probability of symbol error performance of finite-state Markov channels with different numbers of states and wide ranges of parameters can be directly compared. Several examples illustrating the use of the techniques are provided, focusing on binary finite-state Markov channels and Gaussian finite-state Markov channels. Furthermore, this result is used to order Gilbert-Elliott channels with different marginal state probabilities, which was left as an open problem by previous work. Index Terms--Estimation-decoding, iterative decoding, low-density parity-check (LDPC) codes, Markov channels, partial ordering.

This paper presents a reduced-complexity approximate density evolution (DE) scheme for low-density parity-check (LDPC) codes in channels with memory in the form of a hidden Markov chain. This approximation is used to design degree sequences representing some of the best known LDPC code ensembles for the Gilbert-Elliott channel, and example optimizations are also given for other Markov channels. The problem of approximating the channel estimation is addressed by obtaining a specially constructed message-passing schedule in which the channel messages all approach their stable densities. It is shown that this new schedule is much easier to approximate than the standard schedule, but has the same ultimate performance in the limits of long block length and many decoding iterations. This result is extended to show that all message-passing schedules that satisfy mild conditions will have the same threshold under density evolution. Index Terms--Code optimization, density evolution, estimation-decoding, Gaussian assumption, irregular low-density parity-check (LDPC) codes, Markov channels, message-passing schedules.

Pulse shaping is examined as a means to improve the performance of a differential offset quadrature phase-shift keying system in a bandwidth-constrained environment. Through optimization with respect to a composite Nyquist criterion, the derived pulse shapes have comparable performance to a [pi]/4-differential quadrature phase-shift keying in an additive white Gaussian noise (AWGN) channel and better performance in a hard-limited AWGN channel. Index Terms--Differential offset quadrature phase-shift keying (DOQPSK), pulse shaping.

We introduce a rate-adaptive system in which the receiver demodulates only those bits that have a high probability of being correct, treating nondemodulated bits as erasures. Several sets of decision regions, derived using composite hypothesis testing, are proposed for 16-QAM and 16-phase-shift keying, which allow for the simple implementation of this demodulation strategy. We demonstrate that pre-encoding the data with a Raptor code allows for simple reconstruction of the message, regardless of the erasure pattern introduced from the nondemodulated bits. We prove the optimality of the proposed decision regions in selecting the most likely subset of bits from any received symbol in moderate-to-high signal-to-noise ratios, and we analyze the performance of demodulating with these decision regions over an additive white Gaussian noise channel. Also demonstrated is the strong performance of 16-QAM for this application, compared with other power-efficient constellations and the near-optimality of using Gray mapping, even under the proposed alternate sets of decision regions. Index Terms--Adaptive modulation, decision regions, demodulation, Gray mapping, hierarchical modulation, phase-shift keying (PSK) constellations, quadrature amplitude modulation (QAM) constellations, Raptor code.

In this paper, we focus on the joint estimation of the carrier frequency offset and statistical parameters of the multipath mobile channel. By modeling the multipath fading channel with a complex bandpass autoregressive (AR) model, we show how the estimates for the frequency offset, Doppler spread, and power profile of the multipath channel can be extracted from the estimated complex AR coefficients obtained via the expectation-maximization algorithm. A main advantage of the proposed joint estimator is that while it has a capability of performing equally well in all scattering environments, it can provide accurate estimates even in high-mobility channel conditions. We also demonstrate how the complexity of the estimator can be significantly reduced, while only slightly trading off performance, by applying the mean field approximation technique. Moreover, we derive a fully adaptive joint synchronization and channel-estimation scheme, as well as a novel Kalman-smoother-based frequency-error detector that can be used in feedback frequency-recovery schemes and is particularly well suited for fast-fading channel conditions. Finally, we revisit the Cramer-Rao lower bound analysis, and show how the Fisher information matrix can be conveniently computed in the presence of a frequency-selective Rayleigh fading channel. Index Terms--Doppler spread, expectation-maximization (EM) algorithm, frequency offset, Kalman smoother, mean field approximation (MFA).

In this letter, we study the asymptotic performance of hybrid-selection/maximal-ratio combining (HS/MRC) and post-detection HS/equal-gain combining (HS/EGC) over generalized fading channels for large average signal-to-noise ratios (ASNRs). By evaluating the asymptotic moment generating function of the HS/MRC output SNR at high ASNR, we derive the diversity and coding gains for HS/MRC for a large class of modulation formats and versatile fading conditions, including different types of fading channels and nonidentical SNR statistics across diversity branches. Our analytical results reveal that the diversity gains of HS/MRC and HS/EGC are equivalent to that of MRC, and the difference in the coding gains for different modulation formats is manifested in terms of a modulation factor defined in this letter. Some new analytical results about effects of the number of combined branches for HS/MRC and noncoherent combining loss of HS/EGC are also provided. Index Terms--Coding gain, diversity gain, error and outage probabilities, generalized selection combining (GSC), hybrid-selection/maximal-ratio combining (HS/MRC).

This paper studies an enhanced widely linear (WL) receiver for direct-sequence code-division multiple-access (DS-CDMA) systems that employ aperiodic spreading sequences with offset quadrature phase-shift keying (OQPSK) modulation. The modulation scheme generates improper complex multiple-access interference (MAI) and necessitates the use of WL receivers. Focus is on bandlimited pulse shapes and the inherent cyciostationarity (CS) of the uncoded received signal. The enhanced WL receiver replaces the conventional chip-matched filter with new filters that exploit the CS of the received signal through frequency shifting. The proposed WL receiver is shown to outperform the classical strictly linear (SL) receiver when the interfering users are (quasi-)synchronous with respect to the user of interest. High-powered interfering users, that may exist to support high data rates, increase the performance improvement delivered by the WL receiver. Moreover, it is shown that MAI can become proper, either identically or asymptotically, when users are asynchronous and equally powered. This is despite the fact that individual interfering signals are improper. Numerical results demonstrate that the WL receiver can outperform the SL receiver by 1-3 dB under the examined scenarios with current CDMA standards settings. In asynchronous or quasi-synchronous transmission modes, performance gain of the WL receiver degrades unless the number of high-powered active users remains small. An example for implementation of the WL receiver is proposed and compared with that of the SL receiver when minimum-shift keying modulation, a special case of OQPSK, is used. The implementation is based on a fractionally spaced equalizer whose taps are updated by an adaptive algorithm. It is shown that the proposed structure is capable of delivering the maximum signal-to-noise ratio predicted by theory. Index Terms--Bandlimited pulses, code-division multiple-access (CDMA), cyciostationarity (CS), fractionally spaced equalizer (FSE), improper noise, linear/conjugate-linear (L/CL) filtering, minimum-shift keying (MSK), offset quadrature phase-shift keying (OQPSK), widely linear (WL) receiver.

In this paper, we present a unified mathematical framework to analyze the bit-error rate (BER) performance of general linear coherent multiuser receivers with diversity reception and imperfect channel estimation for doubly selective Rician-fading asynchronous code-division multiple-access channels. BERs of linear receivers with channel state information and data-aided channel estimation are analyzed, and both exact and low-complexity approximate BER evaluation formulas are presented. Furthermore, by using a Markov chain steady-state analysis, a tight BER approximation for receivers with decision-directed channel estimation is proposed. Numerical and simulation results verify the accuracy of the proposed BER evaluation methods. Index Terms--Bit-error rate (BER), data-aided channel estimation (DACE), decision-directed channel estimation (DDCE), diversity combining, doubly selective Rician-fading channels.

The Bell Labs layered space-time (BLAST) architecture is a simple and efficient multiantenna coding structure that can achieve high spectral efficiency. Many BLAST detectors require more receiver antennas than transmitter antennas. We propose two novel turbo-processing BLAST detectors that can operate in systems with fewer receiver antennas than transmitter antennas. Both detectors are based on the group-detection strategy. The first proposed detector, the reduced-dimension maximum a posteriori (RDMAP) detector uses a dynamically formed group for each bit decision, while the second proposed detector, the group maximum a posteriori (GMAP) uses a static grouping. For both detectors, a maximum a posteriori (MAP) decision is made using a group of transmitted symbols, and the remaining signal contribution is treated as interference. The interference is characterized as nonzero mean colored-noise source that is whitened before a decision is made. Both proposed detectors are generalizations of the MAP detector and the turbo-processing minimum mean-squared error (MMSE) detector in Sellathurai and Haykin, and Abe and Matsumoto. An uncoded bit-error rate analysis for an independent Rayleigh fading environment is also presented. Simulated results are presented which show that both the RDMAP and GMAP detectors have a performance improvement over the MMSE detector, especially in systems having an excess number of transmitter antennas. Index Terms--Iterative methods, multidimensional signal detection, multiple-input multiple-output (MIMO) systems, nonlinear detection.

We study the effect of imperfect channel estimation (ICE) on the performance of M-ary phase shift keying (M-PSK) with maximum ratio combining (MRC) in generalized Rician fading channels. First, we derive the error probability formulas for M-PSK with MRC and ICE in arbitrary Rician fading channels. Furthermore, we derive the effective receiver output signal-to-noise ratio (SNR) statistics and the outage probability, and analytically quantify the average SNR loss of M-PSK caused by ICE, assuming independent diversity branches. Finally, we point out a major approximation in a popular approach used in the literature to evaluate the adverse effect of ICE. Index Terms--Correlated fading, imperfect channel estimation, maximum ratio combining (MRC), Rician fading channels.

Density evolution analysis of low-density parity-check (LDPC) codes in memoryless channels is extended to the Gilbert-Elliott (GE) channel, which is a special case of a large class of channels with hidden Markov memory. In a procedure referred to as estimation decoding, the sum-product algorithm (SPA) is used to perform LDPC decoding jointly with channel-state detection. Density evolution results show (and simulation results confirm) that such decoders provide a significantly enlarged region of successful decoding within the GE parameter space, compared with decoders that do not exploit the channel memory. By considering a variety of ways in which a GE channel may be degraded, it is shown how knowledge of the decoding behavior at a single point of the GE parameter space may be extended to a larger region within the space, thereby mitigating the large complexity needed in using density evolution to explore the parameter space point-by-point. Using the GE channel as a straightforward example, we conclude that analysis of estimation decoding for LDPC codes is feasible in channels with memory, and that such analysis shows large potential gains. Index Terms--Density evolution, estimation-decoding, Gilbert-Elliott channel, low-density parity-check codes.

A new method is proposed in this paper to design the time-domain equalizer for orthogonal frequency division multiplexing systems based on maximizing signal-to-interference-plus-noise ratio (SINR) at the output of the equalizer. The method called Maximum SINR Time-domain Equalization (MSINR-TEQ) is derived based on a new formulation of SINR. Computer simulation and analytical results show the performance of the MSINR-TEQ method and its superiority in comparison with the performance of the much-used method of channel impulse response shortening. Index Terms--Channel shortening, discrete multitone, minimum intersymbol interference equalizer, orthogonal frequency-division multiplexing (OFDM) systems, time-domain equalization.

Using a moment-generating function (MGF)-based approach, we study the performance of M-ary phase-shift keying (M-PSK) with generalized selection combining (GSC) and equal gain combining (EGC) in fading channels (including Rayleigh, Rician, Nakagami-m, and Nakagami-q fading) with independent and identically distributed (i.i.d) branches. Analytical expressions for the error and outage probabilities, the signal-to-noise-ratio (SNR) statistics, and the channel capacity of M-PSK diversity receivers are derived, taking into account the effects of Gaussian weighting errors and all relevant system and channel parameters. Unlike the case of perfect channel-state information (CSI), the outage probability for the case of imperfect channel estimation (ICE) is not only a function of the normalized SNR with respect to the SNR threshold, but also a function of the operating SNR itself. The SNR loss of the M-PSK GSC and EGC receivers due to ICE and the relation between the receiver input and output SNRs for ICE are derived. Our results show that, even with ICE, GSC and EGC are effective in improving the output SNR and significantly reduce the error floor and the channel-capacity loss caused by ICE. Index Terms--Channel capacity, coherent receivers, discrete memoryless channel (DMC), equal gain combining (EGC), error and outage probabilities, fading channels, generalized selection combining (GSC), imperfect channel estimation (ICE).

Continuous phase modulation schemes, such as Gaussian minimum-shift keying (GMSK), are frequently used with limiter-discriminator (LD) detectors. This paper studies how the side information derived from the signal envelope can enhance the performance of a Viterbi algorithm (VA)-based receiver operating on the LD output of a GMSK scheme. By considering the joint probability density function of envelope and frequency, different approximations yield different novel metrics for VA, using the three-variables envelope and its derivative, and frequency error in different combinations. Simulation results confirm that such envelope-aided VA gives significant performance gains, and that envelope information complements the frequency information output by the LD detector in frequency-selective fading channels. Index Terms--Envelope information, Gaussian minimum-shift keying (GMSK), limiter discriminator (LD), maximum-likelihood sequence detector (MLSD), multipath channel.

In multiplicative fading channels, joint channel estimation and data detection (CE/DD) schemes cannot differentiate among certain sequences of amplitude-and/or phase-modulated (AM/PM) symbols drawn from rotationally invariant signal constellations. This paper identifies these so-called isometric sequences as the main source of performance degradation, and introduces a unifying framework that effectively solves the problem by using asymmetric signal constellations (ASC) and a normalized innovations-based detector. The encompassing nature of the solution is clearly demonstrated by showing that seemingly unrelated previous results, such as training-based solutions, can be viewed as special cases of the modulation-based solution discussed here. A comprehensive analysis, supported by simulation studies, of the relationships among modulation schemes, isometry, and detection performance is provided. Results indicate that the proposed ASC solution offers excellent performance without incurring significant complexity or reducing the transmission rate. Furthermore, it is shown to be robust in various fading rates, and for different signal constellations. Index Terms--Asymmetric modulation, innovations, isometry, Kalman filtering, maximum-likelihood detection.

In this correspondence, modulation diversity (MD) for frequency-selective fading channels is proposed. The achievable performance with MD is analyzed and a simple design criterion for MD codes for Rayleigh-fading channels is deduced from an upper bound on the pairwise error probability (PEP) for single-symbol transmission. This design rule is similar to the well-known design rule for MD codes for flat fading and does not depend on the power-delay profile of the fading channel. Several examples for MD codes with prescribed properties are given and compared. Besides the computationally costly optimum receiver, efficient low-complexity linear equalization (LE) and decision-feedback equalization (DFE) schemes for MD codes are also introduced. Simulations for the widely accepted COST fading models show that performance gains of several decibels can be achieved by MD combined with LE or DFE at bit-error rates (BERs) of practical interest. In addition, MD also enables the suppression of cochannel interference. Index Terms--Code design, equalization, modulation diversity, performance bounds.

In this paper, the problem of adaptive maximum a posteriori (MAP) symbol detection for the uncoded transmission as well as the problem of adaptive soft-input soft-output (SISO) demodulation for the coded transmission of data symbols over the time-varying frequency-selective channel are explored within the framework of the expectation-maximization (EM) algorithm. In particular, several recursive forms of the classical Baum-Welch (BW) algorithm and its Bayesian counterpart (often referred to a Bayesian EM algorithm) are derived in an unified way. In contrast to the earlier developments of the BW and BEM algorithms, the formulations derived in this paper lead to computationally attractive algorithms which avoid matrix inversions while using sequential processing over the time and trellis branch indices. Moreover, it is shown how these recursive versions of the BW and BEM algorithms can be integrated with the well-known forward-backward processing SISO algorithms resulting in adaptive SISOs with embedded soft decision directed (SDD) channel estimators. An application of the proposed algorithms to the iterative "turbo-processing" receivers illustrates how these SDD channel estimators can efficiently exploit the extrinsic information obtained as feedback from the SISO decoder in order to enhance their estimation accuracy. Index Terms--adaptive soft-input soft-output (A-SISOs), Baum-Welch (BW) algorithm, Bayesian expectation-maximization (EM) algorithm, soft statistics, turbo receivers.

In this letter, we design decision-feedback differential detection (DF-DD) schemes for channels with phase noise. If the DF-DD feedback filter is properly optimized, a performance similar to that of a more complex scheme, recently reported by Chiavaccini and Vitetta, based on expectation maximization, can be achieved. However, it is also shown that an error floor is unavoidable for channels with phase noise. If a constraint is introduced, the DF-DD receiver can be made robust against unknown frequency offsets. Index Terms--Decision-feedback differential detection (DF-DD), differential phase-shift keying (DPSK), error floor, frequency offset, noncoherent receivers, phase noise.

In this letter, we give a tight approximation for the bit-error rate (BER) of decision-feedback differential detection (DF-DD). The influence of error propagation is modeled by a Markov chain. A simple state reduction method is proposed to limit computational complexity. Our results show that error propagation strongly depends on the chosen feedback filter. In particular, the popular assumption that error propagation increases BER by a factor of two is not always justified. Index Terms--Bit-error rate (BER) analysis, decision-feedback differential detection (DF-DD), Markov chains.

In this correspondence, block and convolutional coding for Gaussian minimum shift keying (GMSK) in additive white Gaussian noise (AWGN) channels is investigated. The performance improvement that can be obtained without an increase in bandwidth is found for block and convolutional codes with various block lengths and constraint lengths, respectively, when a simple suboptimal demodulation scheme is used. For a fixed system transmission bandwidth, the tradeoff between the percentage of bandwidth to use for coding and the percentage to use for modulation is examined and optimized for various values of bandwidth. Index Terms--Block codes, convolutional codes, encoding, Gaussian minimum shift keying (GMSK), optimization methods.

A new double-filter receiver for spread spectrum wireless systems is presented in this paper. The receiver exploits the inherent diversity due to the small delay difference between the multipaths which may not be exploited by the conventional Rake receiver. The bit error rate performances of both the coherent and the noncoherent detectors are analyzed and compared with the ideal Rake receiver and the matched filter bound. We also examine the best and the worst cases of a three-path fading channel for the proposed receiver. Optimum pulse shapes under various channel conditions are designed. Implementation issues in code-division multiple access systems are discussed. The numerical results show that the proposed receiver achieves significant gains for a given spreading factor under a complexity constraint. Index Terms--Code-division multiple access, coherent and non-coherent detection, delay spread, diversity, double-filter.

This paper discusses the performance of communication systems using binary coherent and differential phase-shift keyed (PSK) modulation, in correlated Rician fading channels with diversity reception. The presence of multiple Rician-faded cochannel users, which may have arbitrary and nonidentical parameters, is modeled exactly. Exact bit error probability (BEP) expressions are derived via the moment generating functions (MGFs) of the relevant decision statistics, which are obtained through coherent detection with maximum ratio combining for coherent PSK modulation, and differential detection with equal gain combining (EGC) for differential modulation. Evaluating the exact expressions requires a complexity that is exponential in the number of interferers. To avoid this potentially time-consuming operation, we derive two low-complexity approximate methods each for coherent and differential modulation formats, which are more accurate than the traditional Gaussian approximation approach. Two new and interesting results of this analysis are: 1) unlike in the case of Rayleigh fading channels, increasing correlation between diversity branches may lead to better performance in Rician fading channels and 2) the phase distribution of the line-of-sight or static fading components of the desired user has a significant influence on the BEP performance in correlated diversity channels. Index Terms--Arbitrary Rician channels, bit error probability, cochannel interferers, coherent and differentially coherent modulations, equal gain combining (EGC), maximum ratio combining (MRC).

A synchronized per survivor processing (PSP) maximum likelihood sequence detection (MLSD) receiver is presented for a fast frequency-selective Rayleigh fading channel and large carrier frequency offset. It is shown that, by incorporating the syn-chronization parameters (the timing error, carrier frequency and phase offsets) into the channel-impulse response (CIR) and modifying the resulting state-space model by a differential approach, the time-varying carrier frequency offset can be effectively tracked using a simple least mean square (LMS) estimator. New criteria are proposed based on the smoothness of the estimated channel derivatives. New criteria are proposed based on this fact that, for smoothly time-varying CIR and frequency offset, the magnitude of the CIR time derivative compared with the magnitude of CIR should be very small. It is illustrated that the new criteria and the conventional mean square error (MSE) are complementary. Index Terms--Adaptive equalizers, adaptive Kalman filtering, data communication, maximum-likelihood detection, maximum-likelihood sequence estimation, phase synchronization, synchronization, time-divison multiple access, tracking.

Recursive (online) expectation-maximization (EM) algorithm along with stochastic approximation is employed in this paper to estimate unknown time-invariant/variant parameters. The impulse response of a linear system (channel) is modeled as an unknown deterministic vector/process and as a Gaussian vector/process with unknown stochastic characteristics. Using these models which are embedded in white or colored Gaussian noise, different types of recursive least squares (RLS), Kalman filtering and smoothing and combined RLS and Kalman-type algorithms are derived directly from the recursive EM algorithm. The estimation of unknown parameters also generates new recursive algorithms for situations, such as additive colored noise modeled by an autoregressive process. The recursive EM algorithm is shown as a powerful tool which unifies the derivations of many adaptive estimation methods. Index Terms - Adaptive estimation, colored noise, estimation and maximization algorithm, estimation theory, Kalman filtering, maximum-likelihood estimation, recursive estimation.

Modern data acquisition systems record large volumes of data which are often not suitable for direct computer processing - a first stage of preprocessing (or data 'editing') is usually needed. In earlier work [5] the authors have developed an algorithm for multichannel data preprocessing, based on Kalman filtering and suitable for real-time geophysical data collection applications. The present work presents results of further investigations in the area of adaptive methods for estimation of noise covariance matrices Q and R, within the time-variant, fixed-lag Kalman filtering framework of the original problem. An algorithm is developed whereby asymptotically normal, unbiased, and consistent estimates are produced based on the correlation-innovations method introduced by Mehra (1970). This provides for direct estimation of R, and leads to a set of (n, [m.sup.2]) equations, not linearly independent, from which an appropriate subset must be selected to achieve estimation of up to (n, m) unknowns in Q. For the model considered (n = m, M, with M = 4 the single-channel system order, and n and m the state and measurement vector dimensions respectively), an explicit algorithm has been developed for estimation of the (m, m) unknowns in Q, based on a least squares fit of a subset of the equations available. A new approach is also introduced to ensure positive-definiteness of the covariance matrices. Since the time variant nature of the model prevents direct application of the adaptive algorithm, a parallel implementation is proposed. A first processor implements the time variant Kalman filter, using estimates of Q and R updated every [N.sub.s] samples. A second processor computes these estimates, operating on the output of a steady state Kaiman filter based on a simplified model, in which data editing features, responsible for rendering the model time variant, have been removed. A spike/step removal filter, and a Riccati equation solver are also implemented by this second processor. Computational requirements are analyzed and compared against those of other approaches. Simulations demonstrate the performance of the method proposed, and show it to be superior to other alternatives. An example showing application to real geophysical data is also presented.

The use of head movements in control applications leaves the hands free for other tasks and utilizes the mobility of the head to acquire and track targets over a wide field of view. We present the results of applying a Kalman filter to generate prediction estimates for tracking head positions. A simple kinematics approach based on the assumption of a piecewise constant acceleration process is suggested and is shown to track head positions with an rms error under 2 [degrees] for head movements with accelerations smaller than 3000 [degrees]/s. To account for the wide range of head dynamic characteristics, an adaptive approach with input estimation is developed. The performance of the Kalman filter is compared to that based on a simple polynomial predictor.

Error performance of maximum likelihood sequence estimation (MLSE) of digital signals transmitted over Rayleigh fading channels is studied in this paper. The application of the innovations approach provides us not only with a general MLSE receiver structure, but also with a tool for analyzing the performance of the receiver. We show that the sequence pairwise error probability of the MLSE receiver is determined by the eigenvalues of a matrix generated from the autocorrelation function of the received signal. For any practical applications, the MLSE for Rayleigh fading channels exhibits an irreducible error floor that depends on the channel characteristics such as the Doppler frequency bandwidth and frequency selectivity. An upper bound on bit error probability can be calculated by using the sequence pairwise error probability. Also, it is shown that diversity reception can significantly improve the MLSE error performance.

A simple, robust processing strategy, called the Fading Magnitude-Integrate, Sample and Dump (FM-ISD) processor, is proposed for use with Limiter-Discriminator detection of CPM signals in Rayleigh, fast fading channels. The FM-ISD processor is introduced as a simplification of an optimal estimator-correlator receiver. The performance is compared to a standard integrator processor and found to provide an improvement in performance for all values of signal-to-noise ratio. The FM-ISD processor is also shown to be robust to changes in modulation format, channel fading rate and pre-detection filter type.

Noncoherent detection over Rayleigh fading diversity channels with known or perfectly estimated amplitudes is studied for binary, uniformly orthogonal signaling. The optimum receiver is well known, but is too difficult to implement. Hence, two suboptimal receivers are considered: the 'BiQuadratic' receiver, optimum at low signal-to-noise ratios (SNR's), and the 'BiLinear' receiver (optimum at high SNR's) which is also a generalized likelihood ratio test (GLRT) receiver for this case. We analyze the performances of the two suboptimal receivers over two-path channels and compare them to the basic quadratic receiver. For this purpose we present a general method for computing the error probability that can be applied to any dual-diversity binary detection problem whenever the method of characteristic functions fails. We present the exact analytical expressions for the BiQuadratic receiver, and the numerically computed results for the GLRT receiver, in terms of the conditional, average and asymptotic error probabilities. It is shown that the two receivers are rather close in performance in most of the SNR ranges of interest.

This paper deals with the use of the innovations approach for developing a general and practical MLSE algorithms for signals transmitted over Rayleigh fading channels. The proposed MLSE receiver can be implemented by a bank of FIR time-invariant filters followed by a Viterbi processor and is applicable to any practically modulated signal over either frequency-nonselective or selective, fast or slowly fading channels. Simulation results are presented that demonstrate the superiority of the innovations-based receiver over differential detection in the presence of fast fading. To further improve the error performance, the rived MLSE receiver is combined with diversity reception. The simulation also shows that the diversity technique results in a significant improvement of the error performance. A unified interpretation of MLSE of signals transmitted over both Gaussian noise channels in the presence of ISI and Rayleigh fading channels is obtained by using the innovations approach.

We consider a Code Division Multiple Access (CDMA) cellular network and propose sub-optimal multi-user detectors which exploit a type of diversity inherent in the system and are based on the processing of signals received at multiple base stations. We investigate the performance of conventional matched-filter, linear, and decision-based detection schemes, using this diversity scheme, for both synchronous and asynchronous systems. The detection of user signals is based on tracking the signals at several base stations. The optimal detector would operate on all the signals received at all the base stations but would have a high degree of complexity. We discuss the case where the detection of a given signal is based on received signals at a small subset of base stations. We show that with judicious selection of this smaller set of base stations, good performance can be obtained without much increase in complexity.

Indoor wireless communication in the 20-60 GHz band requires schemes that are biased toward power efficiency rather than bandwidth efficiency and use simple, robust detectors. Using the two-wave Rayleigh-fading channel as a model for the indoor wireless channel, the optimum detector structure is derived, and a simple suboptimum detector is developed. This suboptimum detector is a straightforward extension of the optimum detector for the single-wave Rayleigh-fading channel. The suboptimum detector is optimum for the channel when the delay of the second wave is known, and whenever the equal energy signals have a normalized complex autocorrelation of either zero or unity at that delay. The performance of this suboptimum detector on the two-wave Rayleigh-fading channel with known delay is studied. An exact expression for the probability of error is derived for uniformly orthogonal, equal energy, binary signals. This expression, which is in terms of the average signal-to-noise ratios in the waves and the complex autocorrelation of the signals, explicitly exhibits the presence of a diversity-like effect when the delay between the waves is non zero, and is an approximation for the probability of error when the complex cross-correlation is small. When the suboptimum detector is used, wideband signals, such as chirp signals and variants, perform well on this channel, enhancing the diversity-like effect. Such signals are also shown to make the suboptimum detector nearly optimal in structure.

Multidimensional constellation shaping with a family of regions called truncated polydiscs is studied. This family achieves maximum shaping gain for a given two-dimensional peak-to-average energy ratio or a given two-dimensional constellation expansion ratio. An efficient algorithm for mapping data words to constellation points is described that requires O(N log N) arithmetic operations and O([N.sup.2]) lookup table space. Truncated polydisc shaping can easily be incorporated into standard coded modulation schemes.

The optimal detector structures and error probability performances for the two-wave Rayleigh fading channel with known delay are compared for different levels of channel knowledge. A number of different detectors are examined, for equal energy signals having equal complex autocorrelation magnitudes. Envelope orthogonal frequency-shift keying and variants of chirp signals are considered, so that the complex cross correlation of the signals is unconstrained. The performance of the optimal detector, when the fading in neither wave is tracked, is obtained. Two other, suboptimal, quadratic detectors are also considered for this case. Optimal detection, when the fading in only one of the waves is tracked, while a statistical knowledge of the other wave is available, is examined. The optimal performance that can be achieved by a time-varying matched-filter detector that makes use of complete knowledge of the channel fading in both waves is also determined. These detectors, for all the different levels of channel information we consider, are studied in a unified framework, the probability of error being expressed as the probability that a quadratic form in Gaussian random variables is less than zero. It is found that the power gain that can be derived from partial or complete tracking is small. All these detectors exhibit a diversity-like effect for all nonzero values of the delay and for most values of the signal parameters. Signals with larger dispersion factors, such as chirp signals and variants, perform well on the channel, enhancing the diversity effect, even at small delays.