Performance of adaptive MC-CDMA detectors in rapidly fading Rayleigh channels

Multicarrier code-division multiple access (MC-CDMA) combines multicarrier transmission with direct sequence spread spectrum. Different approaches have been adopted which do not assume a perfectly known channel. We examine the forward-link performance of decision-directed adaptive detection schemes, with and without explicit channel estimation, for MC-CDMA systems operating in fast fading channels. We analyze theoretically the impact of channel estimation errors by first considering a simpler system employing a threshold orthogonality restoring combining (TORC) detector with a Kalman channel estimator. We show that the performance deteriorates significantly as the channel fading rate increases and that the fading rate affects the selection of system parameters. We examine the performance of more realistic schemes based on the minimum mean square error (MMSE) criterion using least mean square (LMS) and recursive least square (RLS) adaptation. We present a discussion which compares the decision-directed and pilot-aided approaches and explores the tradeoffs between channel estimation overhead and performance. We find that there is a fading rate range where each method provides a good tradeoff between performance and overhead. We conclude that the MMSE per carrier decision-directed detector with RLS estimation combines good performance in low to moderate fading rates, robustness in parameter variations, and relatively low complexity and overhead. For higher fading rates, however, only pilot-symbol-aided detectors are appropriate.     

A new combination of adaptive channel estimation methods and TORC equalizer in MC‐CDMA systems

Adaptive systems identification has been widely studied, but most studies have focused on the convergence of these methods. Applications of equalization systems have also received much attention. This paper presents a new combination of adaptive Broadband Radio Access Networks (BRAN) channel identification algorithms for multicarrier code division multiple access (MC‐CDMA) systems downlink equalization. In fifth‐generation (5G) wireless communications, MC‐CDMA is expected to support the associated networks. The BRAN E channel parameters, representing an outdoor scenario normalized for MC‐CDMA systems, are identified using a recursive least mean pth power algorithm with logarithmic transformation (RlogLMP). For validity and test aim, this algorithm is compared with the existing recursive least square (RLS) and least mean square (LMS) algorithms. Moreover, we use the estimated coefficients in the adaptive equalization problem. We give a review of the threshold orthogonality restoring combining (TORC) equalizer, which is coupled with the presented algorithms to counteract channel fading, as evaluated by the bit error rate (BER). Our performance results show that the RlogLMP algorithm can estimate the measured BRAN E channel with good efficiency for various values of the signal‐to‐noise ratio (SNR), as compared with the classical algorithms RLS and LMS. In adaptive equalization problems, the achieved results demonstrate that two thresholds ρ_TH in the TORC equalizer minimize the performance degradation, in terms of the BER, of the MC‐CDMA system under multipath channel fading with very good accuracy, especially if the coefficients are estimated with the specific case of the power p in the RlogLMP algorithm.     

Adaptive joint beamforming and B‐MMSE detection for CDMA signal reception under multipath interference

The combination of antenna array beamforming with multiuser detection can effectively improve the detection efficiency of a wireless system under multipath interference, especially in a fast‐fading channel. This paper studies the performance of an adaptive beamformer incorporated with a block‐wise minimum mean square error(B‐MMSE) detector, which works on a unique signal frame characterized by training sequence preamble and data blocks segmented by zero‐bits. Both beam‐former weights updating and B‐MMSE detection are carried out by either least mean square (LMS) or recursive least square (RLS) algorithm. The comparison of the two adaptive algorithms applied to both beamformer and B‐MMSE detector will be made in terms of convergence behaviour and estimation mean square error. Various multipath patterns are considered to test the receiver's responding rapidity to changing multipath interference. The performance of the adaptive B‐MMSE detector is also compared with that of non‐adaptive version (i.e. through direct matrix inversion). The final performance in error probability simulation reveals that the RLS/B‐MMSE scheme outperforms non‐adaptive B‐MMSE by 1–5 dB, depending on the multipath channel delay profiles of concern. The obtained results also suggest that adaptive beamformer should use RLS algorithm for its fast and robust convergence property; while the B‐MMSE filter can choose either LMS or RLS algorithm depending on antenna array size, multipath severity and implementation complexity. Copyright © 2004 John Wiley & Sons, Ltd.     

The multi-user detection under fading channel

This paper proposes a method of blind multi-user detection algorithm based on signal sub-space estimation under the fading channels in the present of impulse noise. This algorithm adapts recursive least square (RLS) filter that can estimate the coefficients using only the signature waveform. In addition, to strengthen the ability of resisting the impulse noise, a new suppressive factor is induced, which can suppress the amplitude of the impulse, and improve the ability of convergence speed. Simulation results show that new RLS algorithm is more robust against consecutive impulse noise and have better convergence ability than conventional RLS. In addition, Compared to the least mean square (LMS) detector, the new robust RLS sub-space based method has better multi-address-inference (MAI) suppressing performance, especially, when channel degrades.     

Low Complexity Linear Channel Estimation for MIMO Communication Systems

Channel estimation is employed to get the current knowledge of channel states for an optimum detection in fading environments. In this paper, a new recursive multiple input multiple output (MIMO) channel estimation is proposed which is based on the recursive least square solution. The proposed recursive algorithm utilizes short training sequence on one hand and requires low computational complexity on the other hand. The algorithm is evaluated on a MIMO communication system through simulations. It is realized that the proposed algorithm provides fast convergence as compared to recursive least square (RLS) and robust variable forgetting factor RLS (RVFF-RLS) adaptive algorithms while utilizing lesser computational cost and provides independency on forgetting factor.     

Adaptive frequency-domain equalization and diversity combining forbroadband wireless communications

We introduce a new kind of adaptive equalizer that operates in the spatial-frequency domain and uses either least mean square (LMS) or recursive least squares (RLS) adaptive processing. We simulate the equalizer's performance in an 8-Mb/s quaternary phase-shift keying (QPSK) link over a frequency-selective Rayleigh fading multipath channel with ~3 μs RMS delay spread, corresponding to 60 symbols of dispersion. With the RLS algorithm and two diversity branches, our results show rapid convergence and channel tracking for a range of mobile speeds (up to ~100 mi/h). With a mobile speed of 40 mi/h, for example, the equalizer achieves an average bit error rate (BER) of 10 ^-4 at a signal-to-noise ratio (SNR) of 15 dB, falling short of optimum linear receiver performance by about 4 dB. Moreover, it requires only ~50 complex operations per detected bit, i.e., ~400 M operations per second, which is close to achievable with state-of-the-art digital signal processing technology. An equivalent time-domain equalizer, if it converged at all, would require orders-of-magnitude more processing     

基于压缩感知的分布式协同估计算法

为了降低分布式协同估计算法的计算量并改善其收敛性能,提出了基于压缩感知(CS)和递归最小二乘(RLS)的分布式协同估计算法.该算法在传统RLS分布式协同估计算法的基础上引入压缩感知技术,首先在压缩域中进行递归最小二乘运算,然后利用压缩感知重构算法得到未知参数向量的估计值.提出的算法能够在增量式策略和两种模式的扩散式策略下实现对未知向量的有效估计.理论分析和仿真结果表明,该算法一方面降低了RLS分布式协同估计算法的计算量,另一方面保持较快的收敛速度与良好的均方误差性能.     

Decision-feedback differential detection based on linear predictionfor MDPSK signals transmitted over Ricean fading channels

In this paper, linear prediction-based decision-feedback differential detection (DF-DD) for M-ary differential phase-shift keying (MDPSK) signals transmitted over Ricean fading channels is proposed. This scheme can improve conventional DD significantly for a multitude of frequency-nonselective channels, as shown analytically and by computer simulations. Prediction-based DF-DD is particularly well suited for application in mobile communications since the predictor coefficients may be updated regularly using the recursive least squares (RLS) algorithm. Here, adaptation can start blind, i.e., no training sequence and no a prior knowledge about the channel statistics are required. A further important characteristic of the proposed detection scheme is that no degradation occurs under frequency offset. The bit error rate (BER) performance of QDPSK with genie-aided prediction-based DF-DD is analyzed, and it is shown under which conditions the irreducible error floor of conventional DD can be removed entirely. In addition, the influence of Doppler shift is discussed. Last, the proposed scheme is compared with a second DF-DD scheme, which is based on multiple-symbol detection     

Super-orthogonal differential space-time trellis coding and decoding

In this paper, a differential space-time trellis-coded scheme based on super-orthogonal space-time trellis codes (SOSTTCs) is proposed. It achieves full diversity and provides an improved coding gain. Based on the per-survivor processing (PSP) technique, a low-complexity suboptimal differential decoder is developed. In slow fading channels, it can approach the performance of SOSTTC with coherent decoding. Furthermore, in time-varying channels, a bank of recursive least square (RLS) type channel predictors are incorporated into the Viterbi decoder to track the channel variance and the RLS predictors do not need training data and channel statistics. The performance analysis is given. Simulation results are presented to illustrate our analytical results and they show that our scheme can achieve a good performance in both slow fading and time-varying fading channels with modest complexity.     

Adaptive Equalization Techniques for HF Channels

Data transmission at rates of 1.2 kbits/s or higher through voiceband ionospheric channels is subject to impairment from severe linear distortion, fast channel time variations, and severe fading. In this paper, we have focused on the performance of DFE (decision feedback equalization) receivers for communication over 3 kHz bandwidth HF channels. We describe the results of simulations for a wide range of fading rates on simulated and real recorded HF channels, using fractionally spaced DFE receivers. Both LMS (least mean square) and FRLS (fast recursive least squares) adaptation algorithms with periodic restart were evaluated, and both ideal-reference and decision-directed operation was observed. The results indicate that FRLS adaptation yields superior performance to LMS in rapid fading conditions, but that this performance advantage diminishes at low signal-to-noise ratios. Also, fade rates greater than about 1 Hz produced relatively high error rates, irrespective of which adaptation method was employed. Finally, a novel modification of the simple LMS algorithm which improves its tracking ability was evaluated. This involved preceding the LMS DFE receiver with an adaptive lattice whitening filter.     

Tracking performance of the RLS algorithm applied to an antennaarray in a realistic fading environment

In this paper, frequency domain techniques are used to derive the tracking properties of the recursive least squares (RLS) algorithm applied to an adaptive antenna array in a mobile fading environment, expanding the use of such frequency domain approaches for nonstationary RLS tracking to the interference canceling problem that characterizes the use of antenna arrays in mobile wireless communications. The analysis focuses on the effect of the exponential weighting of the correlation estimation filter and its effect on the estimations of the time variant autocorrelation matrix and cross-correlation vector. Specifically, the case of a flat Rayleigh fading desired signal applied to an array in the presence of static interferers is considered with an AR2 fading process approximating the Jakes' fading model. The result is a mean square error (MSE) performance metric parameterized by the fading bandwidth and the RLS exponential weighting factor, allowing optimal parameter selection. The analytic results are verified and demonstrated with a simulation example     

Adaptive feedforward/feedback architectures for multiuser detectionin high data rate wireless CDMA networks

We consider the design and performance of nonlinear minimum mean-square-error multiuser detectors for direct sequence code-division multiple-access (CDMA) networks. With multiple users transmitting asynchronously at high data rates over multipath fading channels, the detectors contend with both multiple-access interference (MAI) and intersymbol interference (ISI). The cyclostationarity of the MAI and ISI is exploited through a feedforward filter (FFF), which processes samples at the output of parallel chip-matched filters, and a feedback filter (FBF), which processes detected symbols. By altering the connectivity of the FFF and FBF, we define four architectures based on fully connected (FC) and nonconnected (NC) filters. Increased connectivity of the FFF gives each user access to more samples of the received signal, while increased connectivity of the FBF provides each user access to previous decisions of other users. We consider three methods for specifying the FFF sampling and propose a nonuniform FFF sampling scheme based on multipath ray tracking that can offer improved performance relative to uniform FFF sampling. For the FC architecture, we capitalize on the sharing of filter contents among users by deriving a multiuser recursive least squares (RLS) algorithm and direct matrix inversion approach, which determine the coefficients more efficiently than single-user algorithms. We estimate the uncoded bit-error rate (BER) of the feedforward/feedback detectors for CDMA systems with varying levels of power control and timing control for multipath channels with quasi-static Rayleigh fading. Simulations of packet-based QPSK transmission validate the theoretical BER analysis and demonstrate that the multiuser RLS adapted detectors train in several hundred symbols and avoid severe error propagation during data transmission mode     

A Radon-Multiwavelet Based OFDM System Design and Simulation Under Different Channel Conditions

Finite Radon transform (FRAT) mapper has the ability to increase orthogonality of sub-carriers, it is non sensitive to channel parameters variations, and has a small constellation energy compared with conventional fast Fourier transform (FFT) based orthogonal frequency division multiplexing (OFDM). It is also able to work as a good interleaver which significantly reduces the bit error rate (BER). Due to its good orthogonality, discrete Multiwavelet transform (DMWT) is attractive for implementation in OFDM systems which reduces inter-symbol interference (ISI) and inter-carrier interference (ICI) and eliminates the need for cyclic prefix and increases the spectral efficiency of the design. In this paper both FRAT and DMWT are implemented in a new design for OFDM. The new structure was tested and compared with conventional FFT-based OFDM, Radon-based OFDM, and DMWT-based OFDM for additive white Gaussian noise channel, flat fading channel, and multi-path selective fading channel. Simulation tests were generated for different channels parameters values. The obtained results showed that proposed system has increased spectral efficiency, reduced ISI and ICI, and improved BER performance compared with other systems.     

Adaptive Filtering Techniques using Cyclic Prefix in OFDM Systems for Multipath Fading Channel Prediction

This paper presents adaptive channel prediction techniques for wireless orthogonal frequency division multiplexing (OFDM) systems using cyclic prefix (CP). The CP not only combats intersymbol interference, but also precludes requirement of additional training symbols. The proposed adaptive algorithms exploit the channel state information contained in CP of received OFDM symbol, under the time-invariant and time-variant wireless multipath Rayleigh fading channels. For channel prediction, the convergence and tracking characteristics of conventional recursive least squares (RLS) algorithm, numeric variable forgetting factor RLS (NVFF-RLS) algorithm, Kalman filtering (KF) algorithm and reduced Kalman least mean squares (RK-LMS) algorithm are compared. The simulation results are presented to demonstrate that KF algorithm is the best available technique as compared to RK-LMS, RLS and NVFF-RLS algorithms by providing low mean square channel prediction error. But RK-LMS and NVFF-RLS algorithms exhibit lower computational complexity than KF algorithm. Under typical conditions, the tracking performance of RK-LMS is comparable to RLS algorithm. However, RK-LMS algorithm fails to perform well in convergence mode. For time-variant multipath fading channel prediction, the presented NVFF-RLS algorithm supersedes RLS algorithm in the channel tracking mode under moderately high fade rate conditions. However, under appropriate parameter setting in \(2\times 1\) space–time block-coded OFDM system, NVFF-RLS algorithm bestows enhanced channel tracking performance than RLS algorithm under static as well as dynamic environment, which leads to significant reduction in symbol error rate.     

Channel‐estimate‐based frequency‐domain equalization (CE‐FDE) for broadband single‐carrier transmission

A channel‐estimate‐based frequency‐domain equalization (CE‐FDE) scheme for wireless broadband single‐carrier communications over time‐varying frequency‐selective fading channels is proposed. Adaptive updating of the FDE coefficients are based on the timely estimate of channel impulse response (CIR) to avoid error propagation that is a major source of performance degradation in adaptive equalizers using least mean square (LMS) or recursive least square (RLS) algorithms. Various time‐domain and frequency‐domain techniques for initial channel estimation and adaptive updating are discussed and evaluated in terms of performance and complexity. Performance of uncoded and coded systems using the proposed CE‐FDE with diversity combining in different time‐varying, multi‐path fading channels is evaluated. Analytical and simulation results show the good performance of the proposed scheme suitable for broadband wireless communications. For channels with high‐Doppler frequency, diversity combining substantially improves the system performance. For channels with sparse multi‐path propagation, a tap‐selection strategy used with the CE‐FDE systems can significantly reduce the complexity without sacrificing the performance. Copyright © 2004 John Wiley & Sons, Ltd.     

Chip‐interleaving direct sequence spread spectrum system over Rician multipath fading channels

Chip interleaving (CI) is a unique technique to exploit time diversity in direct sequence spread spectrum (DS/SS)‐based systems operating in fading environments. In order to facilitate design of CI systems in various fading situations, we present a performance analysis for CI DS/SS system over Rician multipath time‐varying fading channels. We derive the analytical bit error rate (BER) expression for CI DS/SS to allow fast and accurate evaluation of BER performance based on the interleaving depth selected, spreading codes employed, and the time correlation function of the channel. We then discuss some ideal cases by using the analytical results to reveal some of the insights presented in the performance analysis. For the purpose of comparison, we also obtain the BER expression for conventional DS/SS system as a special case of CI system with an interleaving depth of one. Using numerical examples, we verify the analytical results with computer simulations and illustrate the BER performance behavior of CI DS/SS system with varying interleaving depth for all possible combinations of two sets of spreading codes of different type and two different time correlation functions of the channel. Copyright © 2011 John Wiley & Sons, Ltd.     

DS-CDMA RAKE receiver with time-window control loop (TWCL) inmultipath fading environment

This paper presents a code synchronization scheme-the time-window control loop (TWCL)-for postdetection RAKE receiver systems that offers the path-diversity effect. Laboratory test results from a postdetection RAKE receiver system with TWCL under a frequency-selective fading environment are introduced. RAKE combining methods, a simple integral demodulation method within a time window, and a recursive least squares (RLS) demodulation method within the time window that uses the RLS algorithm to realize maximal ratio combining, are investigated. It is found that TWCL performance with delay paths (double-spike frequency-selective Rayleigh-fading model) surpasses the performance of both acquisition and tracking without delay paths (nonfrequency-selective Rayleigh-fading model) because of the path-diversity effect. The laboratory results show that TWCL provides good acquisition and tracking performance under the fading conditions experienced with maximum Doppler frequencies of 5 or 80 Hz. It is also shown that the signal energy per bit to noise-power spectral-density ratio (E_b/N₀) required to achieve the bit error rate (BER) of 10^-3 under the double-spike frequency-selective Rayleigh-fading model is reduced by 10 dB compared to the nonfrequency-selective Rayleigh-fading model. The difference in path-diversity effect between the two RAKE combining methods is only 1 dB. From a structural viewpoint, the simple integral demodulation method supports miniaturization and high-speed data-transmission     

Partially blind adaptive MMSE interference rejection inasynchronous DS/CDMA networks over frequency-selective fading channels

In this work, the problem of joint suppression of multiple-access and narrow-band interference (NBI) for an asynchronous direct-sequence code-division multiple-access (CDMA) system operating on a frequency-selective fading channel is addressed. The receiver structure we consider can be deemed as a two-stage one: the first stage consists of a bank of minimum mean-square-error (MMSE) filters, each keyed to a given replica of the useful signal, and aimed at suppressing the overall interference; the second stage, assuming knowledge of the fading channel coefficients realizations, combines the MMSE filters outputs according to a maximal-ratio combining rule. Due to the presence of the NBI, the resulting structure is in general time-varying, and becomes periodically time-varying if the NBI bit-rate has a rational ratio to that of the CDMA system. Moreover, enlarging the observation window beyond the signaling interval and oversampling the signal space may yield a noticeable performance improvement. For the relevant case that the said ratio is rational, a new cyclic blind recursive least squares (RLS)-based algorithm is introduced, capable of tracking the periodically time-varying receiver structure, and allowing adaptive interference cancellation with a moderate complexity increase. We also come up with a closed-form expression for the conditional bit-error rate (BER), which is useful both to evaluate semi-analytical methods to assess the unconditional BER and to derive bounds on the system near-far resistance. The results indicate that the receiver achieves very satisfactory performance in comparison to previously known structures. Computer simulations also demonstrate that the cyclic blind RLS algorithm exhibits quite fast convergence dynamics     

Low-complexity equalization for π/4 DQPSK signals based on themethod of projection onto convex sets

An equalizer adaptation technique for compensation of degradations caused by multipath Rayleigh fading channels to π/4 differential quadrature phase shift keying (DQPSK)-modulated signals is presented. The technique is applied to linear and nonlinear transversal-filter-type equalizers. It is based on the method of projection onto convex sets (POCS), realized in a particular form of the iterative least mean squares (LMS) procedure. The convergence speed of the proposed equalizer coefficient adaptation technique and its computational complexity depend on the newly introduced look-back parameter. Both can be tailored to the characteristics of the channel. For achieving convergence speeds comparable to speeds of recursive least squares (RLS) techniques, the computational load of the presented equalization is of the order of the load required of RLS techniques. However, its algorithmic implementation is notably simpler and its code and storage size requirements are smaller. The technique is numerically stable, and it is suitable for low-power implementations in digital signal processors or custom very large-scale integration (VLSI) circuits. Performed simulations verify good performance of the technique in various channel conditions for 900-MHz multipath fading radio channels     

Stochastic gradient optimization of importance sampling for theefficient simulation of digital communication systems

Importance sampling (IS) techniques offer the potential for large speed-up factors for bit error rate (BER) estimation using Monte Carlo (MC) simulation. To obtain these speed-up factors, the IS parameters specifying the simulation probability density function (PDF) must be carefully chosen. With the increased complexity in communication systems, analytical optimization of the IS parameters can be virtually impossible. We present a new IS optimization algorithm based on stochastic gradient techniques. The formulation of the stochastic gradient descent (SGD) algorithm is more general and system-independent than other existing IS methodologies, and its applicability is not restricted to a specific PDF or biasing scheme. The effectiveness of the SGD algorithm is demonstrated by two examples of communication systems where the IS techniques have not been applied before. The first example is a communication system with diversity combining, slow nonselective Rayleigh fading channel, and noncoherent envelope detection. The second example is a binary baseband communication system with a static linear channel and a recursive least square (RLS) linear equalizer in the presence of additive white Gaussian noise (AWGN)