Showing papers in "IEEE Transactions on Communications in 2006"

Dual methods for nonconvex spectrum optimization of multicarrier systems

Abstract: The design and optimization of multicarrier communications systems often involve a maximization of the total throughput subject to system resource constraints. The optimization problem is numerically difficult to solve when the problem does not have a convexity structure. This paper makes progress toward solving optimization problems of this type by showing that under a certain condition called the time-sharing condition, the duality gap of the optimization problem is always zero, regardless of the convexity of the objective function. Further, we show that the time-sharing condition is satisfied for practical multiuser spectrum optimization problems in multicarrier systems in the limit as the number of carriers goes to infinity. This result leads to efficient numerical algorithms that solve the nonconvex problem in the dual domain. We show that the recently proposed optimal spectrum balancing algorithm for digital subscriber lines can be interpreted as a dual algorithm. This new interpretation gives rise to more efficient dual update methods. It also suggests ways in which the dual objective may be evaluated approximately, further improving the numerical efficiency of the algorithm. We propose a low-complexity iterative spectrum balancing algorithm based on these ideas, and show that the new algorithm achieves near-optimal performance in many practical situations

Optimal multiuser spectrum balancing for digital subscriber lines

Abstract: Crosstalk is a major issue in modern digital subscriber line (DSL) systems such as ADSL and VDSL. Static spectrum management, which is the traditional way of ensuring spectral compatibility, employs spectral masks that can be overly conservative and lead to poor performance. This paper presents a centralized algorithm for optimal spectrum balancing in DSL. The algorithm uses the dual decomposition method to optimize spectra in an efficient and computationally tractable way. The algorithm shows significant performance gains over existing dynamics spectrum management (DSM) techniques, e.g., in one of the cases studied, the proposed centralized algorithm leads to a factor-of-four increase in data rate over the distributed DSM algorithm iterative waterfilling.

Bounds for multihop relayed communications in nakagami-m fading

Abstract: We present closed-form lower bounds for the performance of multihop transmissions with nonregenerative relays over not necessarily identically distributed Nakagami-m fading channels. The end-to-end signal-to-noise ratio is formulated and upper bounded by using an inequality between harmonic and geometric means of positive random variables (RVs). Novel closed-form expressions are derived for the moment generating function, the probability density function, and the cumulative distribution function of the product of rational powers of statistically independent Gamma RVs. These statistical results are then applied to studying the outage probability and the average bit-error probability for phase- and frequency-modulated signaling. Numerical examples compare analytical and simulation results, verifying the tightness of the proposed bounds.

Maximum-likelihood synchronization and channel estimation for OFDMA uplink transmissions

Abstract: Maximum-likelihood estimation of the carrier frequency offset (CFO), timing error, and channel response of each active user in the uplink of an orthogonal frequency-division multiple-access system is investigated in this study, assuming that a training sequence is available. The exact solution to this problem turns out to be too complex for practical purposes as it involves a search over a multidimensional domain. However, making use of the alternating projection method, we replace the above search with a sequence of mono-dimensional searches. This results in an estimation algorithm of a reasonable complexity which is suitable for practical applications. As compared with other existing semi-blind methods, the proposed algorithm requires increased overhead but has more flexibility as it can be used with any subcarrier assignment scheme. Simulations indicate that the accuracy of the CFO estimates asymptotically achieves the Cramer-Rao bound.

Distributed space-time block coding

Abstract: In this paper, a new class of distributed space-time block codes (DSTBCs) is introduced. These DSTBCs are designed for wireless networks which have a large set of single-antenna relay nodes Nscr, but at any given time only a small, a priori unknown subset of nodes SsubeNscr can be active. In the proposed scheme, the signal transmitted by an active relay node is the product of an information-carrying code matrix and a unique node signature vector of length Nc. It is shown that existing STBCs designed for Nc2 co-located antennas are favorable choices for the code matrix, guaranteeing a diversity order of d=min{NS,Nc} if NS nodes are active. For the most interesting case, NSgesNc, the performance loss entailed by the distributed implementation is analytically characterized. Furthermore, efficient methods for the optimization of the set of signature vectors are provided. Depending on the chosen design, the proposed DSTBCs allow for low-complexity coherent, differential, and noncoherent detection, respectively. Possible applications include ad hoc and sensor networks employing decode-and-forward relaying

Closed-form statistics for the sum of squared Nakagami-m variates and its applications

Abstract: We present closed-form expressions for the probability density function (PDF) and the cumulative distribution function (CDF) of the sum of non-identical squared Nakagami-m random variables (RVs) with integer-order fading parameters. As it is shown, they can be written as a weighted sum of Erlang PDFs and CDFs, respectively, while the analysis includes both independent and correlated sums of RVs. The proposed formulation significantly improves previously published results, which are either in the form of infinite sums or higher order derivatives of the fading parameter m. The obtained formulas can be applied to the performance analysis of diversity combining receivers operating over Nakagami-m fading channels

Coding performance of hybrid ARQ schemes

Abstract: We develop a unified performance metric and detailed analysis for hybrid automatic repeat request (HARQ) schemes based on incremental redundancy (IR) and Chase combining (CC). The general result is applicable to both symbol-based and bit-interleaved coded modulations, to HARQ processes based on rateless and fixed-rate mother codes, and IR schemes with and without a self-decodability restriction. The analysis shows that IR over CC coding gains tend to increase with the initial coding rate, but decrease with the signal-to-noise (SNR) variation between retransmissions. The gains can also be diminished when a fixed-rate mother code is used or when the self-decodability criterion is imposed. The theoretical prediction is compared with observed gains at 10% codeword error rates based on turbo-coding simulations. For scenarios with moderately varying SNR between retransmissions, the analytical model tracks actual simulation results very well. However, when the SNR varies widely and the systematic part of the turbo codeword is effectively erased, the CC scheme could, in fact, outperform some IR schemes. For these scenarios, which can be induced by fast time-varying fading or long retransmission delays, the self-decodable IR and the CC schemes prove to be more robust without much performance comprise. Finally, we discuss adaptive improvement to the conventional IR schemes based on the analytical result

Mathematical analysis of the impact of timing synchronization errors on the performance of an OFDM system

Abstract: This letter addresses the effect of timing synchronization errors that are introduced by an erroneous detection of the start of an orthogonal frequency-division multiplexing (OFDM) symbol. Throughout this letter, the term "timing error" would refer to this type of error. Such errors degrade the performance of an OFDM receiver by introducing intercarrier interference (ICI) and intersymbol interference (ISI). They can occur due to either an erroneous initial frame synchronization or a change in the power delay profile of the channel. In this letter, we provide a mathematical analysis of the effect of timing errors on the performance of an OFDM receiver in a frequency-selective fading environment. The analysis presented in this letter is for the case that no equalization technique has been used to mitigate the introduced ICI and ISI. We find exact formulas for the power of interference terms and the resulting average signal-to-interference ratio. We further extend the analysis to the subsample level. Our results show the nonsymmetric effect of timing errors on the performance of an OFDM system. Finally, simulation results confirm the analysis. The results of this letter can be easily extended to address the effect of such errors on DMT modems.

Cooperative Regions and Partner Choice in Coded Cooperative Systems

Abstract: User cooperation is an efficient approach to obtain diversity in both centralized and distributed wireless networks. In this paper, we consider a coded cooperative system under quasi-static Rayleigh fading and investigate the partner-choice problem. We find conditions on the interuser and user-to-destination channel qualities for cooperation to be beneficial. Using frame-error rate (FER) as a metric, we define the user cooperation gain (G) for evaluating the relative performance improvement of cooperative over direct transmissions when a particular channel code is used. We introduce the cooperation decision parameter (CDP), which is a function of user-to-destination average received signal-to-noise ratios (SNRs), and demonstrate that whether cooperation is useful or not ( $G≫1$ or $G≪1$ ) depends only on the CDP, not the interuser link quality. We use an analytical formulation of the CDP to investigate user cooperation gain and provide insights on how a user can choose among possible partners to maximize cooperation gain. We first consider the asymptotic performance when one or both partners have high average received SNR at the destination. We then provide conditions on user and destination locations for cooperation to be beneficial for arbitrary SNRs. We illustrate these cooperative regions and study geometric conditions for the best partner choice. We also define the system cooperation gain and illustrate cooperation benefit for both users. All of our theoretical results are verified through numerical examples.

A Comparison of DCT-Based OFDM and DFT-Based OFDM in Frequency Offset and Fading Channels

Abstract: A precise method for calculating the bit-error probability (BEP) of a discrete cosine transform (DCT)-based orthogonal frequency-division multiplexing (OFDM) system on additive white Gaussian noise (AWGN) channels in the presence of frequency offset is derived. These accurate results are used to examine and compare the BEP performance of a DCT-OFDM system and the conventional discrete Fourier transform (DFT)-based OFDM system in an AWGN environment. Several signaling formats, such as binary phase-shift keying, quaternary phase-shift keying, and 16-ary quadrature amplitude modulation are considered. The performance of a DCT-OFDM with a zero-padding guard-interval scheme is then compared with a zero-padded DFT-OFDM with the employment of minimum mean-square error (MMSE) detection and MMSE decision-feedback detection with ordering scheme over frequency-selective fast Rayleigh fading channels. Analysis and simulation results show that the DCT-OFDM system outperforms the DFT-OFDM system in the presence of frequency offset, and in frequency-selective fast-fading environments

Performance of coherent DPSK free-space optical communication systems in K-distributed turbulence

Abstract: Closed-form solutions for the bit-error rate of a freespace, heterodyne optical communication system is derived when the optical beam is subjected to K-distributed optical turbulence. It is assumed that the scintillation index is confined to the range (2,3) or that the number of scatterers in the propagation path is a random variable.

Outage minimization with limited feedback for the fading relay channel

Abstract: In this paper, we consider practical methods to approach the theoretical performance limits in the fading relay channel under different assumptions of transmitter channel knowledge. Specifically, we consider two degrees of transmitter channel knowledge: 1) perfect feedback is available and power control is employed and 2) no channel state knowledge is available at the transmitters and only spatial power allocation is possible. First, when perfect feedback is available, the optimal power control policy determines the ultimate limits of performance for constant rate transmission in the slow fading environment. However, in practice, perfect channel knowledge is not possible at the transmitters due to the finite capacity of the feedback links. We find practical methods to approach this performance limit through the use of power control with finite rate feedback. The finite-rate feedback results are shown for the low-complexity, full-diversity amplify-and-forward (AF) protocol. Interestingly, we see that only a few feedback bits are needed to achieve most of the gains of the optimal perfect feedback power control algorithm. Second, we consider the performance limit when the transmitters have no channel state knowledge and derive the optimal spatial power allocation between the source and relay for a given sum power constraint for the AF protocol. For most practical cases of interest, equal power allocation between the source and relay is shown to be nearly optimal. Our work suggests that there is minimal power savings from using spatial power allocation at the transmitters. To obtain large performance improvements over constant power transmission, it is imperative to have feedback for each realization of the channel state to allow for temporal power control.

Benefit of pattern diversity via two-element array of circular patch antennas in indoor clustered MIMO channels

Abstract: In this paper, we analyze a multiple-input multiple-output (MIMO) array consisting of two circular microstrip antennas, designed to exploit pattern diversity. We analytically derive the spatial correlation coefficients of this array as a function of the mode excited, for realistic clustered MIMO channel models. We compare the performance of the circular patch array (CPA) against an array of two spaced dipoles. In particular, we compute a theoretical tradeoff to predict when the pattern diversity provided by the CPA is more effective than space diversity from the uniform linear array (ULA), based on the eigenvalues of the spatial correlation matrix. Through simulations, we show that CPAs yield better performance or satisfy more restrictive size constraints than ULAs in clustered MIMO channels, depending on the element spacing of the ULA. These results make the CPA an attractive solution for miniaturized MIMO arrays for portable devices or access points.

A unified capacity analysis for wireless systems with joint multiuser scheduling and antenna diversity in Nakagami fading channels

Abstract: In this paper, we present a cross-layer analytical framework to jointly investigate antenna diversity and multiuser scheduling under the generalized Nakagami fading channels. We derive a unified capacity formula for the multiuser scheduling system with different multiple-input multiple-output antenna schemes, including: 1) selective transmission/selective combining (ST/SC); 2) maximum ratio transmission/maximum ratio combining (MRT/MRC); 3) ST/MRC; and 4) space-time block codes (STBC). Our analytical results lead to the following four observations regarding the interplay of multiuser scheduling and antenna diversity. First, the higher the Nakagami fading parameter, the lower the multiuser diversity gain for all the considered antenna schemes. Second, from the standpoint of multiuser scheduling, the multiple antennas with the ST/SC method can be viewed as virtual users to amplify multiuser diversity order. Third, the boosted array gain of the MRT/MRC scheme can compensate the detrimental impact of the reduced amount of fading gain on multiuser scheduling, thereby resulting in greater capacity than the ST/SC method. Last, employing the STBC scheme together with multiuser diversity may cause capacity loss due to the reduced amount of fading gain, but without the supplement of array gain.

Constant-power waterfilling: performance bound and low-complexity implementation

Abstract: In this letter, we investigate the performance of constant-power waterfilling algorithms for the intersymbol interference channel and for the independent identically distributed fading channel where a constant power level is used across a properly chosen subset of subchannels. A rigorous performance analysis that upper bounds the maximum difference between the achievable rate under constant-power waterfilling and that under true waterfilling is given. In particular, it is shown that for the Rayleigh fading channel, the spectral efficiency loss due to constant-power waterfilling is at most 0.266 b/s/Hz. Furthermore, the performance bound allows a very-low-complexity, logarithm-free, power-adaptation algorithm to be developed. Theoretical worst-case analysis and simulation show that the approximate waterfilling scheme is very close to the optimum.

Throughput and delay analysis for the IEEE 802.11e enhanced distributed channel access

Abstract: In this letter, we propose a three-dimensional Markov chain model for the 802.11e enhanced distributed channel access (EDCA) mode. This model can be used to compute the maximum sustainable throughput and service delay distribution for each priority class when under saturation load. The new framework models the performance impact of major quality-of-service (QoS)-specific features (e.g., CWMin, CWMax, AIFS, internal collision resolution) of the 802.11e EDCA mode, and hence can provide an analytical approach to pick the parameter values associated with EDCA to meet the QoS requirements of each priority.

Asymptotic Throughput Analysis for Channel-Aware Scheduling

Abstract: In this paper, we provide an asymptotic performance analysis of channel-aware packet scheduling based on the extreme value theory. We first address the average throughput of systems with a homogeneous average signal-to-noise ratio (SNR), and obtain its asymptotic expression. Compared with the exact throughput expression, the asymptotic one, which is applicable to a broader range of fading channels, is more concise and easier from which to get insights. Furthermore, we confirm the accuracy of the asymptotic results by theoretical analysis and numerical simulation. For a system with heterogeneous SNRs, normalized-SNR-based scheduling needs to be used for fairness. We also investigate the asymptotic average throughput of the normalized-SNR-based scheduling, and prove that the average throughput in this case is less than that in the homogeneous case with a power constraint

A useful integral for wireless communication theory and its application to rectangular signaling constellation error rates

Abstract: A useful integral, representing the average over Rayleigh fading of the product of two Gaussian Q-functions, is solved in closed-form. A closed-form solution for the symbol-error probability of general rectangular quadrature amplitude modulation in Rayleigh fading is derived.

Carrier frequency offset estimation for OFDM systems using null subcarriers

Abstract: Carrier frequency offset (CFO) in orthogonal frequency-division multiplexing(OFDM) systems, which can induce the loss of orthogonality among subcarriersand result in significant performance degradation, is critical to be estimatedand compensated for. In this paper, a suboptimal scheme is proposed to estimatethe CFO using null subcarriers. In the proposed scheme, the CFO is dividedinto the fractional part and the integer part, with the fractional CFO estimatedfollowed by the integer CFO estimation. Compared with previous work usingnull subcarriers and exhaustive search, the implementation complexity of theproposed scheme is significantly lower due to the fact that the main componentrequired is a simple correlator. Furthermore, with only one trainingOFDM symbol and proper null subcarrier allocation, the estimation range ofthe proposed scheme can be the inverse of the sampling duration. In contrast,conventional schemes with the same estimation range and complexity require two OFDM symbols. To achieve good performance,it will be shown that the null subcarrier allocation should be based uponsome specific binary sequences such as the proposed extended m-sequences. It willalso be shown by simulations that the same null subcarrier allocation criterionshould be employed for optimal maximum-likelihood CFO estimation.

Synchronization algorithms for UWB signals

Abstract: This paper is concerned with timing recovery for ultra-wideband communication systems operating in a dense multipath environment. Two timing algorithms are proposed that exploit the samples of the received signal to estimate the start of the individual frames with respect to the receiver's clock (frame timing) and the location of the first frame in each symbol (symbol timing). Channel estimation comes out as a by-product and can be used for coherent matched filter detection. The proposed algorithms require sampling rates on the order of the inverse of the pulse duration. Their performance is assessed by simulating the operation of coherent and differential detectors. Their sensitivity to the sampling rate is discussed, and the effects of the multiple access interference are evaluated.

SNR estimation in time-varying fading channels

Abstract: Signal-to-noise ratio (SNR) estimation is considered for phase-shift keying communication systems in time-varying fading channels. Both data-aided (DA) estimation and nondata-aided (NDA) estimation are addressed. The time-varying fading channel is modeled as a polynomial-in-time. Inherent estimation accuracy limitations are examined via the Cramer-Rao lower bound, where it is shown that the effect of the channel's time variation on SNR estimation is negligible. A novel maximum-likelihood (ML) SNR estimator is derived for the time-varying channel model. In DA scenarios, where the estimator has a simple closed-form solution, the exact performance is evaluated both with correct and incorrect (i.e., mismatched) polynomial order. In NDA estimation, the unknown data symbols are modeled as random, and the marginal likelihood is used. The expectation-maximization algorithm is proposed to iteratively maximize this likelihood function. Simulation results show that the resulting estimator offers statistical efficiency over a wider range of scenarios than previously published methods.

Approaching MIMO channel capacity with soft detection based on hard sphere decoding

Abstract: Hard sphere decoding (HSD) has well-appreciated merits for near-optimal demodulation of multiuser, block single-antenna or multi-antenna transmissions over multi-input multi-output (MIMO) channels. At increased complexity, a soft version of sphere decoding (SD), so-termed list SD (LSD), has been recently applied to coded layered space-time (LST) systems enabling them to approach the capacity of MIMO channels. By introducing a novel bit-level multi-stream coded LST transmitter along with a soft-to-hard conversion at the decoder, we show how to achieve the near-capacity performance of LSD, and even outperform it as the size of the block to be decoded (M) increases. Specifically, for binary real LST codes, we develop exact max-log-based SD schemes with M + 1 HSD steps, and an approximate alternative with only one HSD step to trade off performance for average complexity. These schemes apply directly to the real and imaginary parts of quaternary phase-shift keying signaling, and also to quadrature amplitude modulation signaling after incorporating an appropriate interference estimation and cancellation module. We corroborate our near-optimal soft detection (SoD) algorithms based on HSD (SoD-HSD) with simulations.

Diversity analysis of single and multiple beamforming

Abstract: In this letter, we study two techniques, known as single and multiple beamforming, to exploit the perfect channel state information (CSI) available both at the transmitter and the receiver of a multiantenna wireless system. Assuming N and M are the number of antennas at the transmitter and the receiver, respectively, we show that single beamforming (transmission of a single symbol from all transmit antennas at the same time, employing the best subchannel) can achieve the maximum spatial diversity order in the channel (NM). We extend our analytical results to multiple beamforming (transmission of S symbols simultaneously, S>1) and calculate that the diversity order achievable for this system is (N-S+1)(M-S+1)

Code-division multiple-access techniques in optical fiber networks - part III: optical AND logic gate receiver structure with generalized optical orthogonal codes

Abstract: In this paper, we present a deep insight into the behavior of optical code-division multiple-access (CDMA) systems based on an incoherent, intensity encoding/decoding technique using a well-known class of codes, namely, optical orthogonal codes (OOCs). As opposed to parts I and II of this paper, where OOCs with cross-correlation $lambda = 1$ were considered, we consider generalized OOCs with $1 leq lambda leq w$ , where $w$ is the weight of the corresponding codes. To enhance the performance of such systems, we propose that use of optical AND gate receiver, which, in an ideal case, e.g., in the absence of any noise source except the optical multiple-access noise, is optimum. Using some basic laws on probability, we present direct and exact solutions for OOCs with $lambda = 1,2,3,ldots,w$ , with optical AND gate as receiver. Using the exact solution, we obtain empirical solutions that can be easily used in optimizing the design criteria of such systems. From our optimization scheme, we obtain some fresh insight into the performance of OOCs with $lambdageq 1$ . In particular, we can obtain some simple relations between $ P_ e min$ (minimum error rate), $L_min$ (minimum required OOC length), and $N_max$ (maximum number of interfering users to be supported), which are the most desired parameters for any optical CDMA system design. Furthermore, we show that in most practical cases, OOCs with $lambda = 2$ or $3$ perform better than OOCs with $lambda = 1$ , while having a much bigger cardinality. Finally, we show that an upper bound on the maximum weight of OOCs are on the order of $sqrt2lambda L$ where L is the length of the OOCs used in systems.

Algebraic construction of quasi-cyclic LDPC codes for the AWGN and erasure channels

Abstract: This paper is concerned with construction of quasi-cyclic (QC) low-density parity-check (LDPC) codes for three different types of channels: the additive white Gaussian noise, the binary random erasure, and the binary burst erasure channels. Two algebraic methods for systematic construction of QC-LDPC codes are presented. Codes constructed perform well over all three types of channels

Optimum DCT-Based Multicarrier Transceivers for Frequency-Selective Channels

Abstract: We derive conditions on the impulse response and input signal of a frequency-selective finite-impulse response channel to be diagonalized by the discrete cosine transform (DCT) into parallel, decoupled, and memoryless subchannels. We show how these conditions can be satisfied in a practical multicarrier transceiver through a novel design of the guard sequence and the front-end prefilter. This DCT-based design results in complete elimination of interblock and intercarrier interference without channel knowledge at the transmitter and at the same guard sequence overhead, compared with DFT-based multicarrier transceivers. Extensions to multiinput multioutput frequency-selective channels are also described. Finally, we present numerical examples from wireline and wireless communications scenarios to illustrate the viability and practicality of the DCT as a modulation/demodulation basis for baseband and passband signaling over frequency-selective channels.

Efficient Computation of EXIT Functions for Nonbinary Iterative Decoding

Abstract: The calculation of nonbinary extrinsic information transfer charts for the iterative decoding of concatenated index-based codes is addressed We show that the extrinsic information at the output of a constituent a posteriori probability decoder can be calculated with very low complexity, where expensive histogram measurements are not required any more An example for turbo trellis-coded modulation demonstrates the capabilities of the proposed approach

Multirate crosstalk identification in xDSL systems

Abstract: Crosstalk between multiple services transmitting through the same telephone cable is the primary limitation to digital subscriber line (DSL) services. From a spectrum management point of view, it is important to have an accurate map of all the services that generate crosstalk into a given pair. This paper on crosstalk identification is motivated by an important practical consideration: the signals constituting the crosstalk are transmitted at different rates in xDSL systems. Therefore, we here propose to use the "blocking technique," we derive blocked state-space models for multirate xDSL networks, and we set up the mapping relationship between available input and output data. Further, we use the least-squares principle to identify the crosstalk functions, and study the convergence rate and upper bound of the parameter-estimation error. Finally, we illustrate and verify the theoretical findings with simulation examples

Achieving Full Frequency and Space Diversity in Wireless Systems via BICM, OFDM, STBC, and Viterbi Decoding

Abstract: Orthogonal frequency-division multiplexing (OFDM) is known as an efficient technique to combat frequency-selective channels. In this paper, we show that the combination of bit-interleaved coded modulation (BICM) and OFDM achieves the full frequency diversity offered by a frequency-selective channel with any kind of power delay profile (PDP), conditioned on the minimum Hamming distance dfree of the convolutional code. This system has a simple Viterbi decoder with a modified metric. We then show that by combining such a system with space-time block coding (STBC), one can achieve the full space and frequency diversity of a frequency-selective channel with N transmit and M receive antennas. BICM-STBC-OFDM achieves the maximum diversity order of NML over L-tap frequency-selective channels regardless of the PDP of the channel. This latter system also has a simple Viterbi decoder with a properly modified metric. We verify our analytical results via simulations, including channels employed in the IEEE 802.11 standards

A combined timing and frequency synchronization and channel estimation for OFDM

Abstract: This letter addresses training-signal-based combined timing and frequency synchronization and channel estimation for orthogonal frequency-division multiplexing systems. The proposed scheme consists of two stages. At the first stage, coarse timing and frequency-offset estimates are obtained. Based on these estimates, a (coarse) channel response estimate is obtained. The timing and frequency-offset estimates at the second stage are obtained by maximum-likelihood (ML) realization based on a sliding observation vector. Then ML channel estimation is performed. A means of complexity reduction by an adaptive scheme is also presented. The simulation results show that the proposed combined approach performs quite well, and circumvents the problem of mismatch among individual synchronization tasks.