Accurate error-rate performance analysis of OFDM on frequency-selective Nakagami-m fading channels

Error rates of orthogonal frequency-division multiplexing (OFDM) signals in multipath slow fading Nakagami-m fading channels are considered. The exact probability density function of a sum of Nakagami-m random phase vectors is used to derive a closed-form expression for the error rates of OFDM signals. The precise error-rate analysis is extended to a system using multichannel reception with maximal ratio combining. An asymptotic error-rate analysis is also provided. For a two-tap channel with finite values of Nakagami-m fading parameters, our analysis and numerical results show that the asymptotic error-rate performance of an OFDM signal is similar to that of a single carrier signal transmitted over a Rayleigh fading channel. On the other hand, our analysis further shows that a frequency-selective channel that can be represented by two constant taps has similar asymptotic error-rate performance to that of a one-sided Gaussian fading channel. It is observed that, depending on the number of channel taps, the error-rate performance does not necessarily improve with increasing Nakagami-m fading parameters.     

Performance of binary FSK communications over frequency-selectiveRayleigh fading channels

The performance of binary frequency-shift-keyed communications over frequency-selective wide-sense-stationary uncorrelated-scattering Rayleigh fading channels is discussed. Previous analyses of FSK communications over frequency-selective channels have considered the average probability of error for specific models for the fading channel and typically assume that the two FSK signals are orthogonal. A technique for obtaining bounds on the average error probability for FSK in terms of one or two parameters obtainable from multipath spread or frequency correlation functions channel measurements is described     

Iterative EM receiver for space-time coded systems in MIMO frequency-selective fading channels with channel gain and order estimation

An iterative receiver for a space-time trellis coded system in frequency-selective fading channel is proposed. It performs channel gain estimation and sequence detection by using the expectation-maximization (EM) algorithm. Channel order estimation is included in the receiver to avoid unnecessary trellis computations by using the conditional model order estimator (CME). In addition, three modifications to the original CME criterion are proposed to improve the estimation accuracy. Simulation results show that the proposed receiver has a slight degradation in frame error rate performance to the known channel maximum likelihood receiver. Moreover, it outperforms the conventional fixed long-tap length EM receiver with a lesser complexity. Furthermore, the proposed modifications to the CME criterion improve the channel order estimation accuracy, thus minimizing unnecessary computations.     

Modulation diversity for frequency-selective fading channels

In this article, 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.     

An adaptive CMMSE receiver for space-time block-coded CDMA systems in frequency-selective fading channels

A technique that can suppress multiple-access interference (MAI) in space-time block-coded (STBC) multiple-input-multiple-output (MIMO) code-division multiple-access (CDMA) systems is developed. The proposed scheme, called a constrained minimum mean square error (CMMSE) receiver, is an extension of the CMMSE receiver for a single-input-single-output system to MIMO systems. It is shown that the complexity of the proposed CMMSE receiver is almost independent of the number of transmitter antennas. The advantage of the proposed receiver over the existing receivers for STBC CDMA systems is demonstrated by comparing the closed-form expressions of the signal-to-interference plus noise ratio and simulated bit error rates. The results indicate that the proposed CMMSE receiver can provide a significant performance improvement over the conventional receivers and that the gain achieved by suppressing the MAI can be larger than that from increasing the transmitter or receiver diversity.     

Universal decoding for frequency-selective fading channels

We address the problem of universal decoding in unknown frequency-selective fading channels, using an orthogonal frequency-division multiplexing (OFDM) signaling scheme. A block-fading model is adopted, where the bands' fading coefficients are unknown yet assumed constant throughout the block. Given a codebook, we seek a decoder independent of the channel parameters whose worst case performance relative to a maximum-likelihood (ML) decoder that knows the channel is optimal. Specifically, the decoder is selected from a family of quadratic decoders, and the optimal decoder is referred to as a quadratic minimax (QMM) decoder for that family. As the QMM decoder is generally difficult to find, a suboptimal QMM decoder is derived instead. Despite its suboptimality, the proposed decoder is shown to outperform the generalized likelihood ratio test (GLRT), which is commonly used when the channel is unknown, while maintaining a comparable complexity. The QMM decoder is also derived for the practical case where the fading coefficients are not entirely independent but rather satisfy some general constraints. Simulations verify the superiority of the proposed QMM decoder over the GLRT and over the practically used training sequence approach.     

Concatenated coding performance for FSK modulation ontime-correlated Rician fading channels

We present an analytical method for evaluating the performance of noninterleaved concatenated codes over channels modeled as a nonfrequency selective correlated Rician fading channel with a known power spectral density. The main idea is to model the communication system from the modulator input to the demodulator output as a finite state channel (FSC) model, and apply powerful enumeration techniques to such a discrete channel in order to gain useful information on the system performance. The concatenated scheme makes use of two codes; Reed-Solomon codes are employed for the outer code, and binary block codes are used as the inner code. Next, the method is extended to study the effect on the performance when an interleaving with finite depth is incorporated into the communication system. A comparison between symbol and bit interleaving is made. Finally, we study the potential gain produced when channel information is passed on to the outer decoder in the form of an erasure symbol. In all cases, analytical expressions for the probability of the number of error symbols produced by the FSC model were obtained in terms of a coefficient in a formal power series. This is an interesting alternative approach with respect to computer simulations     

一种频率选择性衰落信道下的盲自适应去相关Rake接收机

多用户检测是DS－CDMA系统中的一项关键技术,而Rake接收是解决多径效应的一种有效方法,本文将基于Kalman滤波的多用户检测器与Rake接收相结合,提出了一种频率选择性衰落信道下的盲自适应去相关Rake接收机,研究结果表明,这种接收机具有较强的抑制多址干扰和克服“远－近”效应能力,并且能快速收敛。     

Performance analysis and design of STBCs for frequency-selective fading channels

In this paper, space-time block-coded transmission over frequency-selective fading channels is investigated. A lower bound for the pairwise error probability for optimum detection is given. Also, an approximation for the bit-error rate is derived and compared with simulation results for maximum-likelihood sequence estimation (MLSE) for the GSM/EDGE (Enhanced Data Rates for GSM Evolution) system. Furthermore, a novel design rule for space-time block codes (STBCs) for frequency-selective fading channels is provided. A corresponding code is designed and shown to yield higher performance than Alamouti's code. It is demonstrated that for fading channels with L independent impulse response coefficients, STBCs designed for the flat fading channel can achieve at most a diversity order of (N/sub T/+L-1)N/sub R/ if N/sub T/ transmit antennas and N/sub R/ receive antennas are used. On the other hand, the maximum diversity order employing the proposed code design rule is LN/sub T/N/sub R/.     

Optimal periodic training signal for frequency offset estimation in frequency-selective fading channels

This paper addresses an optimal periodic training signal design for frequency offset estimation in frequency-selective multipath Rayleigh fading channels. For a fixed transmitted training signal energy within a fixed-length block, the optimal periodic training signal structure (the optimal locations of identical training subblocks) and the optimal training subblock signal are presented. The optimality is based on the minimum Cramer-Rao bound (CRB) criterion. Based on the CRB for joint estimation of frequency offset and channel, the optimal periodic training structure (optimality only in frequency offset estimation, not necessarily in joint frequency offset and channel estimation) is derived. The optimal training subblock signal is obtained by using the average CRB (averaged over the channel fading) and the received training signal statistics. A robust training structure design is also presented in order to reduce the occurrence of outliers at low signal-to-noise ratio values. The proposed training structures and subblock signals achieve substantial performance improvement.     

频率选择性信道下多节点放大转发协作通信中的信道估计方法

针对频率选择性信道下基于正交频分复用(OFDM,orthogonal frequency division multiplexing)技术的多节点放大转发(AF,amplify-and-forward)协作通信,提出了一种基于训练序列的最小二乘信道估计方法,推导出其均方误差性能的下界并给出了相应的最优训练序列方案.同时,该方法选取经功率分配优化后具有恒幅特性的Chu序列作为训练序列,实现了多节点AF协作通信中信道估计的最小均方误差.仿真结果证实了该信道估计方法在多节点AF协作通信环境下的有效性以及所提最优训练序列方案在系统性能上的优越性.     

Optimal training for MIMO frequency-selective fading channels

High data rates give rise to frequency-selective propagation effects. Space-time multiplexing and/or coding offer attractive means of combating fading and boosting capacity of multi-antenna communications. As the number of antennas increases, channel estimation becomes challenging because the number of unknowns increases, and the power is split at the transmitter. Optimal training sequences have been designed for flat-fading multi-antenna systems or for frequency-selective single transmit antenna systems. We design a low-complexity optimal training scheme for block transmissions over frequency-selective channels with multiple antennas. The optimality in designing our training schemes consists of maximizing a lower bound on the ergodic (average) capacity that is shown to be equivalent to minimizing the mean square error of the linear channel estimator. Simulation results confirm our theoretical analysis that applies to both single- and multicarrier transmissions.     

Equalization of linearly frequency-selective fading channels

A simple technique for removing intersymbol interference (ISI) introduced by “linearly frequency-selective” fading channels is presented. The technique involves the optimization of the overall impulse response of the transmit and receive filters and effectively reduces the channel to one which is flat fading. Computer simulation results show that this equalization method works for channels with small delay spreads     

Performance analysis of MMSE receivers for DS-CDMA in frequency-selective fading channels

The performance of the minimum mean-squared error (MMSE) receiver for the detection of direct sequence code division multiple access is considered in various fading channel models. Several modifications to the basic MMSE receiver structure which have been previously proposed for use on nonselective fading channels are reviewed and shown to represent different approximations to a single common form. The performance of this general structure is analyzed as well as various extensions suitable for frequency-selective fading channels. Particular attention is given to the performance advantage gained through knowledge of the fading parameters of the various transmission paths of each user's signal. It is shown that having this knowledge is not particularly useful on a flat fading channel unless the loading is very heavy and even then the difference in performance is only minimal. On the other hand, having this knowledge is crucial in a multipath fading channel and the inability to learn the fading channel parameters will lead to substantial degradation in capacity. A heuristic explanation to support this result based on a dimensionality argument is also presented.     

Unified analysis of error performance for binary signalling over Rayleigh fading channels

Using the unified expression as devised by Wojner, an analytical framework is presented to determine error performance of all binary modulation schemes employing coherent or non-coherent detection and operating over a slow flat Rayleigh fading channel with different diversity combining. A class of generalised expressions for the bit error probability has been obtained following the probability density function or the cumulative distribution function approach.     

Effective capacity channel model for frequency-selective fading channels

To efficiently support quality of service (QoS) in future wireless networks, it is important to model a wireless channel in terms of connection-level QoS metrics such as data rate, delay and delay-violation probability. To achieve this, in [7], we proposed and developed a link-layer channel model termed effective capacity (EC) for flat fading channels. In this paper, we apply the effective capacity technique to modeling frequency selective fading channels. Specifically, we utilize the duality between the distribution of a queue with superposition of N i.i.d. sources, and the distribution of a queue with a frequency-selective fading channel that consists of N i.i.d. sub-channels, to model a frequency selective fading channel. In the proposed model, a frequency selective fading channel is modeled by three EC functions; we also propose a simple and efficient algorithm to estimate these EC functions. Simulation results show that the actual QoS metric is closely approximated by the QoS metric predicted by the proposed EC channel model. The accuracy of the prediction using our model can translate into efficiency in admission control and resource reservation. Dapeng Wu received B.E. in Electrical Engineering from Huazhong University of Science and Technology, Wuhan, China, in 1990, M.E. in Electrical Engineering from Beijing University of Posts and Telecommunications, Beijing, China, in 1997, and Ph.D. in Electrical and Computer Engineering from Carnegie Mellon University, Pittsburgh, PA, in 2003. From July 1997 to December 1999, he conducted graduate research at Polytechnic University, Brooklyn, New York. During the summers of 1998, 1999 and 2000, he conducted research at Fujitsu Laboratories of America, Sunnyvale, California, on architectures and traffic management algorithms in the Internet and wireless networks for multimedia applications. Since August 2003, he has been with Electrical and Computer Engineering Department at University of Florida, Gainesville, FL, as an Assistant Professor. His research interests are in the areas of networking, communications, multimedia, signal processing, and information and network security. He received the IEEE Circuits and Systems for Video Technology (CSVT) Transactions Best Paper Award for Year 2001. Currently, he is an Associate Editor for the IEEE Transactions on Vehicular Technology and Associate Editor for International Journal of Ad Hoc and Ubiquitous Computing. He served as Program Chair for IEEE/ACM First International Workshop on Broadband Wireless Services and Applications (BroadWISE 2004); and as TPC member of over 30 conferences. He is Vice Chair of Mobile and wireless multimedia Interest Group (MobIG), Technical Committee on Multimedia Communications, IEEE Communications Society. He is a member of the Best Paper Award Committee, Technical Committee on Multimedia Communications, IEEE Communications Society. He is also Director of Communications, IEEE Gainesville Section. Rohit Negi received the B.Tech. degree in Electrical Engineering from the Indian Institute of Technology, Bombay, India in 1995. He received the M.S. and Ph.D. degrees from Stanford University, CA, USA, in 1996 and 2000 respectively, both in Electrical Engineering. He has received the President of India Gold medal in 1995. Since 2000, he has been with the Electrical and Computer Engineering department at Carnegie Mellon University, Pittsburgh, PA, USA, where he is an Associate Professor. His research interests include signal processing, coding for communications systems, information theory, networking, cross-layer optimization and sensor networks.     

Bit-error probability analysis of linear receivers for CDMA systemsin frequency-selective fading channels

The bit-error probability of a linear receiver for code-division multiple-access communications is analyzed. The analysis is presented for the additive white Gaussian noise and fading multipath channels also with data-aided channel estimation. Two ways to approximate the averaging over the interfering data symbol combinations are considered and compared. Numerical examples are presented to demonstrate the usefulness of the analysis methods     

Performance analysis of a predetection EGC receiver in exponentially correlated nakagami-m fading channels for noncoherent binary modulations

Average symbol error rate (ASER) of an equal gain combining (EGC) receiver with an arbitrary number of branches in exponentially correlated, Nakagami-m fading channels has been derived for binary, differential phase-shift keying (DPSK) and noncoherent frequency-shift keying (NCFSK) modulations. A Parseval's theorem based approach has been used. Numerical and simulation results have been found to be in close agreement. Results show that for a given ASER, as expected, exponentially correlated fading requires a higher SNR with respect to independent fading. For a given number of branches L, increase in SNR required (SNR penalty) with respect to independent fading is less for higher values of fading parameter m while for a given m, SNR penalty is more for higher L     

Adaptive Bayesian and EM-based detectors for frequency-selective fading channels

The problems of adaptive maximum a posteriori (MAP) symbol detection for uncoded transmission and of adaptive soft-input soft-output (SISO) demodulation for coded transmission of data symbols over time-varying frequency-selective channels 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 earlier developments of the BW and BEM algorithms, these formulations 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 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.     

Sequential sequence estimation for trellis-coded modulation onmultipath fading ISI channels

A new receiver structure is proposed for trellis-coded modulation on multipath fading intersymbol interference (ISI) channels that permits the use of large-state trellis codes. The receiver uses a sequential sequence estimator with the Fano algorithm, and a channel estimator consisting of a fast nonrecursive start-up algorithm for training and the LMS algorithm for tracking. During the tracking mode, the channel estimates are updated dynamically by using recent tentative decisions produced by the sequential sequence estimator. This approach results in good tracking even on rapidly varying channels, and reduces the degradation in performance of the sequential sequence estimator due to channel estimation error. The effect of fading is mitigated using both implicit time diversity in the form of interleaved trellis-coded modulation and explicit antenna diversity