Linear expansions for frequency selective channels in OFDM

Modeling the frequency selective fading channels as random processes, we employ a linear expansion based on the Karhunen–Loeve (KL) series representation involving a complete set of orthogonal deterministic vectors with a corresponding uncorrelated random coefficients. Focusing on OFDM transmissions through frequency selective fading, this paper pursues a computationally efficient, pilot-aided linear minimum mean square error (MMSE) uncorrelated KL series expansion coefficients estimation algorithm. Based on such an expansion, no matrix inversion is required in the proposed MMSE estimator. Moreover, truncation in the linear expansion of channel is achieved by exploiting the optimal truncation property of the KL expansion resulting in a smaller computational load on the estimation algorithm. The performance of the proposed approach is studied through analytical and experimental results. We first exploit the performance of the MMSE channel estimator based on the evaluation of minimum Bayesian MSE. We also provide performance analysis results studying the influence of the effect of SNR and correlation mismatch on the estimator performance. Simulation results confirm our theoretical results and illustrate that the proposed algorithm is capable of tracking fast fading and improving performance.     

BEM-based SISO detection of orthogonal space-time block codes over frequency flat-fading channels

The expectation-maximization algorithm for maximum a posteriori (MAP) estimation of a random vector is applied to the problem of detection of orthogonal space-time block codes over time-selective Rayleigh fading channels. This results in a soft-in soft-out detection algorithm suitable for iterative detection/decoding schemes. Simulation results show that the error performance of the proposed detection algorithm is very close to that of a MAP detector endowed with an ideal knowledge of the channel state if the fading rate is not too fast.     

Adaptive MAP receiver via the EM algorithm and message passings for MIMO-OFDM mobile communications

This paper proposes two new types of maximum a posteriori probability (MAP) receivers for multiple-input-multiple-output and orthogonal frequency-division multiplexing mobile communications with a channel coding such as the low-density parity-check code. One proposed receiver employs the expectation-maximization algorithm so as to improve performance of approximated MAP detection. Differently from a conventional receiver employing the minimum mean-square estimation (MMSE) algorithm, it applies the recursive least squares (RLS) algorithm to the channel estimation in order to track a fast fading channel. For the purpose of further improvement, the other proposed receiver applies a new adaptive algorithm that can be derived from the message passing on factor graphs. The algorithm exploits all detected signals but one of targeted time, and can gain a considerable advantage over the MMSE and RLS. Computer simulations show that the first proposed receiver is superior in channel-tracking ability to the conventional receiver employing the MMSE. Furthermore, it is demonstrated that the second proposed receiver remarkably outperforms both the conventional and the first proposed ones.     

A space-time block-coded OFDM scheme for unknownfrequency-selective fading channels

We introduce a space-time block-coded orthogonal frequency-division multiplexing (STBC-OFDM) selective fading channels which does not require channel knowledge either at the transmitter or at the receiver. The decoding algorithm is based on generalized maximum-likelihood sequence estimation. We investigate the performance of the proposed scheme over two-tap Rayleigh fading channels. Simulation results show the performance to be near optimum     

Receive antenna subset selection based on orthogonal components

A new receive antenna subset selection algorithm with low complexity for wireless Multipie-Input Multiple-Output （MIMO） systems is proposed, which is based on the orthogonal components of the channel matrix. Larger capacity is achieved compared with the existing antenna selection methods. Simulation results of quasi-static fiat fading channel demonstrate the significant performance of the proposed selection algorithm.     

一种改进的MIMO-OFDM的信道估计算法

针对频率选择性衰落信道下MIMO—OFDM的系统,基于瑞利衰落信道的模型,利用m序列的自相关性,提出了一种基于m序列做梳状导频的多输入多输出正交频分复用最小二乘算法,该算法可以避免对大矩阵求伪逆,以减少计算复杂度,从而提高了信道估计的计算性能。通过对该算法的误码率性能分析和计算复杂度分析,结果表明,相比传统经典最小二乘算法,所提出信道估计算法在中低信噪比下,有效提高了信道估计性能,适合于在实际应用中实现。     

Low complexity joint estimation of synchronization impairments in sparse channel for MIMO–OFDM system

Low complexity joint estimation of synchronization impairments and channel in a single-user MIMO–OFDM system is presented in this paper. Based on a system model that takes into account the effects of synchronization impairments such as carrier frequency offset, sampling frequency offset, and symbol timing error, and channel, a Maximum Likelihood (ML) algorithm for the joint estimation is proposed. To reduce the complexity of ML grid search, the number of received signal samples used for estimation need to be reduced. The conventional channel estimation techniques using Least-Squares (LS) or Maximum a posteriori (MAP) methods fail for the reduced sample under-determined system, which results in poor performance of the joint estimator. The proposed ML algorithm uses Compressed Sensing (CS) based channel estimation method in a sparse fading scenario, where the received samples used for estimation are less than that required for an LS or MAP based estimation. The performance of the estimation method is studied through numerical simulations, and it is observed that CS based joint estimator performs better than LS and MAP based joint estimator.     

Joint MAP channel estimation and data detection for OFDM in presence of phase noise from free running and phase locked loop oscillator

This paper addresses a computationally compact and statistically optimal joint Maximum a Posteriori (MAP) algorithm for channel estimation and data detection in the presence of Phase Noise (PHN) in iterative Orthogonal Frequency Division Multiplexing (OFDM) receivers used for high speed and high spectral efficient wireless communication systems. The MAP cost function for joint estimation and detection is derived and optimized further with the proposed cyclic gradient descent optimization algorithm. The proposed joint estimation and detection algorithm relaxes the restriction of small PHN assumptions and utilizes the prior statistical knowledge of PHN spectral components to produce a statistically optimal solution. The frequency-domain estimation of Channel Transfer Function (CTF) in frequency selective fading makes the method simpler, compared with the estimation of Channel Impulse Response (CIR) in the time domain. Two different time-varying PHN models, produced by Free Running Oscillator (FRO) and Phase-Locked Loop (PLL) oscillator, are presented and compared for performance difference with proposed OFDM receiver. Simulation results for joint MAP channel estimation are compared with Cramer-Rao Lower Bound (CRLB), and the simulation results for joint MAP data detection are compared with “NO PHN” performance to demonstrate that the proposed joint MAP estimation and detection algorithm achieve near-optimum performance even under multipath channel fading.     

基于多中继导频频分复用的协同通信系统信道估计算法

本文针对频率选择性衰落环境下结合正交频分复用技术的放大转发多中继协同通信系统,提出了基于导频频分复用的频域信道估计算法,包括最小二乘（LS）估计算法和线性最小均方误差（LMMSE）估计算法。理论分析和仿真结果表明,该算法不仅成功分辨了多中继协同通信系统的所有频域信道衰落系数,避免了各中继节点转发的导频符号在目的节点上的混叠干扰,而且减少了频域信道估计所需的导频符号数量和时隙周期长度,提高了协同通信系统的传输效率和频谱利用率,同时显著提高了信道估计的精度,降低了算法的复杂度,具有较高的实用价值。      

On the Performance of FFT/DWT/DCT-based OFDM Systems with Chaotic Interleaving and Channel Estimation Algorithms

The efficiency of data transmission over fading channels in orthogonal frequency division multiplexing (OFDM) systems depends on the employed interleaving method. In this study, we propose an improved chaotic interleaving scheme which aims to improve the performance of OFDM system under fading channel. In the proposed scheme, the binary data is interleaved with chaotic Baker map prior to the modulation process. In the sequel, significant degree of encryption is being added during data transmission. The performance of the proposed approach is tested on the conventional fast Fourier transform OFDM, discrete wavelet transform OFDM, and discrete cosine transform OFDM with and without chaotic interleaving. Furthermore, an expectation–maximization (EM) algorithm is proposed for improving channel impulse response (CIR) estimation based on a maximum likelihood principle. The proposed scheme makes use of EM algorithm to update the channel estimates until convergence is reached. The simulation results show the efficiency of the proposed algorithms under Rayleigh fading environments where the symbol error rate essentially coincides with that of the perfect channel case after the fifth EM iteration.     

Performance of parallel and serial concatenated codes on fading channels

The performance of parallel and serial concatenated codes on frequency-nonselective fading channels is considered. The analytical average upper bounds of the code performance over Rician channels with independent fading are derived. Furthermore, the log-likelihood ratios and extrinsic information for maximum a posteriori (MAP) probability and soft-output Viterbi algorithm (SOVA) decoding methods on fading channels are developed. The derived upper bounds are evaluated and compared to the simulated bit-error rates over independent fading channels. The performance of parallel and serial codes with MAP and SOVA iterative decoding methods, with and without channel state information, is evaluated by simulation over independent and correlated fading channels. It is shown that, on correlated fading channels, the serial concatenated codes perform better than parallel concatenated codes. Furthermore, it has been demonstrated that the SOVA decoder has almost the same performance as the MAP decoder if ideal channel state information is used on correlated Rayleigh fading channels.     

A systematic approach to detecting OFDM signals in a fading channel

We derive the maximum a posteriori probability (MAP) receiver for orthogonal frequency-division multiplexed signals in a fading channel. As the complexity of the MAP receiver is high, we obtain a low-complexity, suboptimal receiver and evaluate its performance     

基于奇异值分解的MIMO-OFDM系统角域MAP信道估计算法

最大后验概率信道估计算法应用于多输入多输出-正交频分复用(MIMOOFDM)系统时需要大规模的矩阵求逆和乘积运算,且系统数据传输效率随发送天线数的增加明显降低.为克服这些问题,提出了一种基于奇异值分解的角域最大后验概率信道估计算法.该算法通过期望最大化把(MIMO)信道估计问题简化为一系列独立的单输入单输出(SISO)问题,并使用奇异值分解避免了大规模矩阵求逆和乘积运算;通过多个OFDM符号联合估计信道提高了系统数据传输效率及算法的估计性能.仿真实验验证了此算法的有效性.     

基于正交多相序列的OFDM信道估计算法

提出了一种基于正交多相序列的OFDM信道估计算法。该算法采用相关性能良好的正交多相序列作为发送信号的循环前缀,在接收端,提取循环前缀,进行相关计算,最终得到系统频域响应的估计值。通过仿真,验证了在多径衰落信道中,提出的算法比频域梳状导频插入的时域滤波算法及采用小m序列作为循环前缀的信道估计算法具有更高的信道估计精度。     

Iterative receivers for space-time block-coded OFDM systems indispersive fading channels

We consider the design of iterative receivers for space-time block-coded orthogonal frequency-division multiplexing (STBC-OFDM) systems in unknown wireless dispersive fading channels, with or without outer channel coding. First, we propose a maximum-likelihood (ML) receiver for STBC-OFDM systems based on the expectation-maximization (EM) algorithm. By assuming that the fading processes remain constant over the duration of one STBC code word and by exploiting the orthogonality property of the STBC as well as the OFDM modulation, we show that the EM-based receiver has a very low computational complexity and that the initialization of the EM receiver is based on the linear minimum mean square error (MMSE) channel estimate for both the pilot and the data transmission. Since the actual fading processes may vary within one STBC code word, we also analyze the effect of a modeling mismatch on the receiver performance and show both analytically and through simulations that the performance degradation due to such a mismatch is negligible for practical Doppler frequencies. We further propose a turbo receiver based on the maximum a posteriori-EM algorithm for STBC-OFDM systems with outer channel coding. Compared with the previous noniterative receiver employing a decision-directed linear channel estimator, the iterative receivers proposed here significantly improve the receiver performance and can approach the ML performance in typical wireless channels with very fast fading, at a reasonable computational complexity well suited for real-time implementations     

Joint MAP equalization and channel estimation forfrequency-selective and frequency-flat fast-fading channels

This paper presents a new fractionally-spaced maximum a posteriori (MAP) equalizer for data transmission over frequency-selective fading channels. The technique is applicable to any standard modulation technique. The MAP equalizer uses an expanded hypothesis trellis for the purpose of joint channel estimation and equalization. The fading channel is estimated by coupling minimum mean square error techniques with the (fixed size) expanded trellis. The new MAP equalizer is also presented in an iterative (turbo) receiver structure. Both uncoded and conventionally coded systems (including iterative processing) are studied. Even on frequency-flat fading channels, the proposed receiver outperforms conventional techniques. Simulations demonstrate the performance of the proposed equalizer     

Bayesian blind turbo receiver for coded OFDM systems with frequencyoffset and frequency-selective fading

The design of a blind receiver for coded orthogonal frequency-division multiplexing communication systems in the presence of frequency offset and frequency-selective fading is investigated. The proposed blind receiver iterates between a Bayesian demodulation stage and a maximum a posteriori channel decoding stage. The extrinsic a posteriori probabilities of data symbols are iteratively exchanged between these two stages to achieve successively improved performance. The Bayesian demodulator computes the a posteriori data symbol probabilities, based on the received signals (without knowing or explicitly estimating the frequency offset and the fading channel states), by using Markov chain Monte Carlo (MCMC) techniques. In particular, two MCMC methods-the Metropolis-Hastings algorithm and the Gibbs sampler-are studied for this purpose. Computer simulation results show that the proposed Bayesian blind turbo receiver can achieve good performance and is robust against modeling mismatch     

Channel estimation for OFDM systems using adaptive radial basis function networks

We propose a new scheme for pilot-symbol-aided channel estimation in orthogonal frequency-division multiplexing (OFDM) systems in multipath fading channels, that does not require knowledge of the channel statistics (e.g., Doppler or power spectrum). It is based on using the radial basis function (RBF) network to model the dynamics of the fading process. Both one-dimensional and two-dimensional RBF networks are proposed to exploit the channel correlation in the time domain and in the time-frequency domain. The proposed RBF networks are essentially nonlinear interpolators of the pilot channels. Compared with the existing OFDM channel estimation methods based on linear filtering, the proposed new techniques offer both robustness to fading rate, and a better performance especially in relatively fast fading channels.     

A sequential Monte Carlo blind receiver for OFDM systems infrequency-selective fading channels

We consider the application of the sequential Monte Carlo (SMC) methodology to the problem of blind symbol detection in a wireless orthogonal frequency-division multiplexing (OFDM) system over a frequency-selective fading channel. Bayesian inference of the unknown data symbols in the presence of an unknown multipath fading channel is made only from the observations over one OFDM symbol duration. A novel blind SMC detector built on the techniques of importance sampling and resampling is developed for differentially encoded OFDM systems. The performance of different schemes of delayed-weight estimation methods is studied. Furthermore, being soft-input and soft-output in nature, the proposed SMC detector is employed as the first-stage demodulator in a turbo receiver for a coded OFDM system. Such a turbo receiver successively improves the receiver performance by iteratively exchanging the so-called extrinsic information with the maximum a posteriori (MAP) outer channel decoder. Finally, the performance of the proposed sequential Monte Carlo receiver is demonstrated through computer simulations     

Iterative Channel Estimators in V-BLAST OFDM Systems

An iterative pilot-symbol aided modulation (PSAM) channel estimation approach is proposed for vertical Bell Laboratories layered space-time (V-BLAST) orthogonal frequency division multiplexing systems operating on frequency-selective fading channels. Since the signals at the receive antennas are the superposition of signals from multiple transmit antennas, accurate channel estimates are crucial for good error performance. Furthermore, the time selectivity of the fading channels leads to inter-carrier interference (ICI). While ICI can be ignored for slow fading channels, it should be mitigated for fast fading channels. This paper proposes an ICI mitigation scheme for time-varying channels. We also propose an iterative channel estimator with low-complexity. Simulation results demonstrate the usefulness of the proposed algorithm on frequency-selective fading channels.