An Accurate and Very Low Complexity LMMSE Channel Estimation Technique for OFDM Systems

In this paper, we propose a very low linear minimum mean square error (LMMSE) channel estimation technique for orthogonal frequency division multiplexing (OFDM) systems. The conventional LMMSE, based on the autocorrelation channel matrix, requires \(O(N_P^3)\) operations (\(N_P\) represents the total number pilot in one OFDM symbol). By exploiting the structure of the channel autocorrelation matrix, we propose a very low complexity LMMSE channel estimator which requires only \(O(N_PlogN_P)\) operations. Simulation results show that the proposed technique yields the same performances as well as the classical LMMSE in terms of bit error rate and mean square error.     

On the blind estimation of the parameters of continuous phase modulated signals

In this paper, a blind estimator of the technical parameters of continuous phase modulated (CPM) signals is proposed. It consists in estimating jointly the modulation index, the symbol period and the frequency offset. It is based on the following observations. First, the inverse of the index is the smallest positive real number a CPM signal should be raised to in order to generate a deterministic harmonic signal; second, the frequencies of the harmonic signal are simply related to the symbol period and the carrier frequency. The practical implementation of this joint estimator is described and the asymptotic behavior of the estimation error is studied. If N is the number of signaling intervals, the estimate of the modulation index is shown to converge to a non-Gaussian distribution at rate 1/N, while the estimate of the frequency offset and the estimate of the symbol period converge at rate 1/N/sup 3/2/. We also investigate the case where the modulation index and the symbol period are available at the receiver side. An estimator of the frequency offset is proposed by adapting the above joint estimator to the latter case. The asymptotic behavior of this estimator is studied and compared with the case where all of the parameters are unknown, so as to evaluate the possible degradation of the performance due to the ignorance of certain technical parameters. Simulations results sustain our theoretical claims.     

一种α稳定分布噪声下OFDM信号调制识别与参数估计算法

正交频分复用（OFDM,Orthogonal Frequency Division Multiple）信号的调制识别与参数估计是非协作通信领域的重要研究内容.为了解决α稳定分布噪声下OFDM信号调制识别与参数估计困难的问题,提出一种广义循环平稳的盲处理算法.该算法首先对接收信号进行非线性变换,推导出接收信号的广义循环自相关函数表达式,分析了单载波调制信号与OFDM信号的广义循环自相关函数特性,并给出了OFDM信号的广义循环自相关函数与待估参数之间的关系.然后,基于分析结论,利用广义循环自相关函数构造调制识别特征完成OFDM信号与单载波信号的调制方式自动分类;最后,针对OFDM信号的调制参数估计问题,提出了一种基于广义循环自相关函数的调制参数估计算法.理论分析与仿真结果表明,在α稳定分布噪声环境下,该算法可以有效实现OFDM信号调制识别与参数估计,且算法不依赖接收信号的先验信息,可以直接对中频接收信号进行处理.     

Estimation of the symbol rate of linearly modulated sequences of symbols

The blind estimation of the symbol rate is one of the main issues for blind characterization of linearly modulated sequences. The estimator proposed in this article is based on the autocorrelation function of this kind of signal and exploits its limited frequency support.We prove theoretically that taking into account this property to modify some classical algorithms allows improving significantly their performances. We illustrate this result by numerical simulations, and we show that our estimator correctly detect the symbol rate in nearly 100% of the cases in many contexts as long as the signal to noise ratio is higher than 5 dB.     

Blind estimation of symbol timing and carrier frequency offset inwireless OFDM systems

Orthogonal frequency-division multiplexing (OFDM) systems are highly sensitive to synchronization errors. We introduce an algorithm for the blind estimation of symbol timing and carrier frequency offset in wireless OFDM systems. The proposed estimator is an extension of the Gini-Giannakis (see IEEE Trans. Commun., vol.46, p.400-411, 1998) estimator for single-carrier systems. It exploits the cyclostationarity of OFDM signals and relies on second-order statistics only. Our method can be applied to pulse shaping OFDM systems with arbitrary time-frequency guard regions, OFDM based on offset quadrature amplitude modulation, and biorthogonal frequency-division multiplexing systems. We furthermore propose the use of different subcarrier transmit powers (subcarrier weighting) and periodic transmitter precoding to achieve a carrier frequency acquisition range of the entire bandwidth of the OFDM signal, and a symbol timing acquisition range of arbitrary length. Finally, we provide simulation results demonstrating the performance of the new estimator     

Stochastic MV-PURE Estimator— Robust Reduced-Rank Estimator for Stochastic Linear Model

This paper proposes a novel linear estimator named stochastic MV-PURE estimator, developed for the stochastic linear model, and designed to provide improved performance over the linear minimum mean square error (MMSE) Wiener estimator in cases prevailing in practical, real-world settings, where at least some of the second-order statistics of the random vectors under consideration are only imperfectly known. The proposed estimator shares its main mathematical idea and terminology with the recently introduced minimum-variance pseudo-unbiased reduced-rank estimator (MV-PURE), developed for the linear regression model. The proposed stochastic MV-PURE estimator minimizes the mean square error (MSE) of its estimates subject to rank constraint and inducing minimium distortion to the target random vector. Therefore, the stochastic MV-PURE combines the techniques of the reduced rank Wiener filter (named in this paper RR-MMSE) and the distortionless-constrained estimator (named in this paper C-MMSE), in order to achieve greater robustness against noise or model errors than RR-MMSE and C-MMSE. Furthermore, to ensure that the stochastic MV-PURE estimator combines the reduced-rank and minimum-distortion approaches in the MSE-optimal way, we propose a rank selection criterion which minimizes the MSE of the estimates obtained by the stochastic MV-PURE. As a numerical example, we employ the stochastic MV-PURE, RR-MMSE, C-MMSE, and MMSE estimators as linear receivers in a MIMO wireless communication system. This example is chosen as a typical signal processing scenario, where the statistical information on the data, on which the estimates are built, is only imperfectly known. We verify that the stochastic MV-PURE achieves the lowest MSE and symbol error rate (SER) in such settings by employing the proposed rank selection criterion.      

一种适合软件无线电的符号定时估计算法

研究了一种适合软件无线电的符号定时估计算法,该算法通过并行方法估计线性和非线性调制方式的符号定时。计算机仿真结果表明,通过设置观测时间间隔数和并行估计样本值的个数,算法可以满足多种调制方式对符号定时估计指标的要求,在误比特率为10-5时,相对于理想的相干解调性能,信噪比最大损失0. 5dB。算法全数字实现,复杂度适中,适合于软件无线电系统中对多种调制方式条件下符号定时估计的需要。     

Periodic variation method for blind symbol rate estimation

In order to obtain unknown symbol rate of incoming signal at a receiver, in this paper, cyclostationary features of linear digitally modulated signals are exploited by proposed periodic variation method. A low complexity but highly accurate symbol rate estimation technique is obtained. The proposed method is based on a superposed epoch analysis over autocorrelations obtained blindly in different sampling frequencies. The obtained autocorrelations are analyzed in the frequency domain, and it is seen that there are large oscillations when the autocorrelation is obtained around the symbol rate. Then, a superposed epoch analysis is developed in order to estimate symbol rate based of the periodic variations on the frequency responses of autocorrelations. The proposed algorithm is quite accurate in the noisy environment because the noise is having no frequency component after taking Fourier transform of autocorrelations in all sampling rates, and this feature is also valid for the offset frequency that the purposed estimation is not affected by offset frequency. Thus, a successful blind symbol rate estimation algorithm is obtained, and it performs much better error performance than those using the well‐known cyclic correlation based symbol rate estimations, as it is proven by the obtained performances presented in the paper. Copyright © 2013 John Wiley & Sons, Ltd.     

An Unbiased Signal‐to‐Interference Ratio Estimator for the High Speed Downlink Packet Access System

We propose an unbiased signal‐to‐interference ratio (SIR) estimator for the high speed downlink packet access (HSDPA) system. The proposed SIR estimator solves the problem of underestimation present in conventional SIR estimators and is suitable for channel quality measurement in the adaptive modulation and coding scheme of HSDPA, which requires accurate SIR estimation for optimum adaptive modulation and coding selection. Our analysis and simulation results demonstrate the improved estimation performance of the proposed SIR estimator.     

Error probability minimizing pilots for OFDM with M-PSK modulation over Rayleigh-fading channels

Orthogonal frequency division multiplexing (OFDM) with pilot symbol assisted channel estimation is a promising technique for high rate transmissions over wireless frequency-selective fading channels. In this paper, we analyze the symbol error rate (SER) performance of OFDM with M-ary phase-shift keying (M-PSK) modulation over Rayleigh-fading channels, in the presence of channel estimation errors. Both least-squares error (LSE) and minimum mean-square error (MMSE) channel estimators are considered. For prescribed power, our analysis not only yields exact SER formulas, but also quantifies the performance loss due to channel estimation errors. We also optimize the number of pilot symbols, the placement of pilot symbols, and the power allocation between pilot and information symbols, to minimize this loss, and thereby minimize SER. Simulations corroborate our SER performance analysis, and numerical results are presented to illustrate our optimal claims.     

Underlay认知网络中时频重叠OFDM信号的信噪比盲估计

针对underlay认知无线电中时频重叠正交频分复用（Orthogonal Frequency Division Multiplexing,OFDM）信号的信噪比（Signal to Noise Ratio,SNR）难以估计的问题,提出了一种基于循环自相关特性的时频重叠OFDM信噪比盲估计方法.该方法提取接收信号的循环自相关函数截面中的离散谱线估计出分量信号的总功率,并结合时延和循环频率均为零时的离散谱线估计出时频重叠OFDM信号的信噪比.仿真结果表明,在无需先验信息的情况下,当SNR大于-7dB时,所提方法估计的均方误差小于0.1,并且对分量信号的功率比和频谱重叠率具有稳健性.     

A Full Rate Quasi‐orthogonal STF‐OFDM with DAC‐ZF Decoder over Wireless Fading Channels

In this letter, we propose a quasi‐orthogonal space‐time‐frequency (QOSTF) block coded orthogonal frequency division multiplexing (OFDM) that can achieve full symbol rate with four transmit antennas. Since the proposed QOSTF‐OFDM cannot achieve full diversity, we use a diversity advantage collection with zero forcing (DAC‐ZF) decoder to compensate the diversity loss at the receiving side. Due to modulation advantage and collected diversity advantage, the proposed scheme exhibits a better bit‐error rate performance than other orthogonal schemes.     

A Linear Prediction Based Estimation of Signal‐to‐Noise Ratio in AWGN Channel

Most signal‐to‐noise ratio (SNR) estimation techniques in digital communication channels derive the SNR estimates solely from samples of the received signal after the matched filter. They are based on symbol SNR and assume perfect synchronization and intersymbol interference (ISI)‐free symbols. In severe channel distortion where ISI is significant, the performance of these estimators badly deteriorates. We propose an SNR estimator which can operate on data samples collected at the front‐end of a receiver or at the input to the decision device. This will relax the restrictions over channel distortions and help extend the application of SNR estimators beyond system monitoring. The proposed estimator uses the characteristics of the second order moments of the additive white Gaussian noise digital communication channel and a linear predictor based on the modified‐covariance algorithm in estimating the SNR value. The performance of the proposed technique is investigated and compared with other in‐service SNR estimators in digital communication channels. The simulated performance is also compared to the Cramér‐Rao bound as derived at the input of the decision circuit.     

High accuracy frequency offset correction with adjustable acquisition range in OFDM systems

A new carrier frequency offset estimation scheme in orthogonal frequency-division multiplexing (OFDM) systems is proposed in this paper. Both the carrier frequency offset acquisition and tracking are based on a fixed-length training-symbol-block, which consists of multiple small identical training symbols. When each training symbol is shortened, the number of training symbols in the training-symbol-block should be increased accordingly to keep the total training-symbol-block length fixed. The proposed scheme extends Moose's estimator, where the estimation error is only dependent on total training symbol energy and cannot be reduced any more, once the total training symbol energy is determined. The proposed scheme can shorten each training symbol in a training-symbol block and select an appropriate estimator simultaneously, which can lead to further reduction of estimation error and increase of acquisition range, even with the total training-symbol-block energy being fixed. Performance analyzes for the proposed scheme in both the additive white Gaussian noise channel (AWGN) and the multipath channel are also presented in this paper. All estimators in the proposed scheme are conditionally unbiased, and simulation results demonstrate that they can work well both in the multipath channel and in the AWGN channel.     

Low-complexity equalization of OFDM in doubly selective channels

Orthogonal frequency division multiplexing (OFDM) systems may experience significant inter-carrier interference (ICI) when used in time- and frequency-selective, or doubly selective, channels. In such cases, the classical symbol estimation schemes, e.g., minimum mean-squared error (MMSE) and zero-forcing (ZF) estimation, require matrix inversion that is prohibitively complex for large symbol lengths. An analysis of the ICI generation mechanism leads us to propose a novel two-stage equalizer whose complexity (apart from the FFT) is linear in the OFDM symbol length. The first stage applies optimal linear preprocessing to restrict ICI support, and the second stage uses iterative MMSE estimation to estimate finite-alphabet frequency-domain symbols. Simulation results indicate that our equalizer has significant performance and complexity advantages over the classical linear MMSE estimator in doubly selective channels.     

An iterative algorithm for single-frequency estimation

An algorithm for the estimation of the frequency of a complex sinusoid in noise is proposed. The estimator consists of multiple applications of lowpass filtering and decimation, frequency estimation by linear prediction, and digital heterodyning. The estimator has a significantly reduced threshold relative to existing phase-based algorithms and performance close to that of maximum likelihood estimation. In addition, the mean-squared error performance is within 0.7 dB of the Cramer-Rao bound (CRB) at signal-to-noise ratios (SNRs) above threshold. Unlike many autocorrelation and phase-based methods, the proposed algorithm's performance is uniform across a frequency range of -/spl pi/ to /spl pi/. The computational complexity of the algorithm is shown to be favorable compared with maximum likelihood estimation via the fast Fourier transform (FFT) algorithm when significant zero-padding is required.     

Design of optimal interpolation filter for symbol timing recovery

We propose an optimal interpolation filter for symbol timing recovery in a digital receiver where the input analog-to-digital (A-D) conversion sampling clock is not synchronized to the transmitter symbol clock. The optimal filter is designed by minimizing the mean-square error (MSE) at the output of the receiver, assuming that the correct timing difference between the nonsynchronized input samples and the correct strobe synchronized to the symbol is given. The MSE minimization procedure results in a system of linear equations which can easily be solved to yield the optimal filter coefficients. We also analyze the symbol tracking performance of a symbol synchronizer that employs the proposed optimal interpolation filter. Although the proposed optimal filter is designed assuming the availability of the correct timing difference, we show that it minimizes the timing estimation error variance even when the computed timing difference values deviate from the ideal, we also show that the timing estimation is virtually unbiased if the length of the interpolation filter is greater than or equal to 4. Simulation results are included to show the performance improvement realizable by employing the optimal interpolation filter     

一种新的每符号两个样点的前向定时估计算法

针对线性调制信号,提出一种新的每符号两个样点的非数据辅助的前向符号定时估计算法。算法的基本思想是：首先,将两倍符号速率的样点信号通过一个特定的抗混叠滤波器,使得输出信号经非线性变换后,在符号速率处不再混叠;然后,利用传统的平方律非线性等算法估计定时相位偏差。文中详细描述了算法的推导过程。最后的仿真数据表明,在计算复杂度相当的情况下,新算法的估计性能优于其他两种算法,并且对于信号及应用环境的适应性更强。     

Low-complexity iterative channel estimation for serially concatenated systems over frequency-nonselective Rayleigh fading channels

A low-complexity iterative maximum a posteriori (MAP) channel estimator is proposed whose complexity increases linearly with the symbol alphabet size 'M. Prediction-based MAP channel estimation is not appropriate with a high-order prediction filter or a large modulation alphabet size, since the computational complexity increases with M^L , where L is the predictor order. In contrast, the proposed channel estimator has a constant number of trellis states regardless of the prediction filter order, and is shown to provide comparable error performance to the prediction-based MAP estimator     

Pilot symbol-assisted detection of CPM schemes operating in fastfading channels

We present a coherent detection technique for continuous phase modulation (CPM) operating in the Rayleigh flat fading channel. The technique is based on the idea of inserting periodically data dependent pilot symbols that force the CPM signal to pass through known phase states. This transmission format enables the receiver to extract from the received signal the channel fading gains at regularly spaced instants. When coupled with proper channel estimation filters, very accurate channel state information (CSI) can be estimated at the receiver for fading compensation. Moreover, the accuracy of the CSI can be further refined by adopting a multiple-pass decoding approach. The paper discusses (a) the pilot symbol encoding technique required to force a M-level CPM scheme with a modulation index of p/M, p is an integer, to return periodically to a set of known phase states, (b) the optimal channel estimation filters, (c) a trellis-based precoding technique that can reduce the bit error rate in M-level CPM systems by close to 50%, and (d) a multiple-pass channel estimator/demodulator. Analytical and simulation results are presented for minimum shift keying (MSK), Gaussian MSK, and four-level continuous phase frequency shift keying with a modulation index of 1/4. It is observed that our pilot symbol-assisted CPM schemes exhibit no irreducible error floor even at a channel fade rate of three percent the symbol rate. The implicit phase coding in CPM and the accurate CSI provided by the pilot symbols lead to a diversity effect in the bit error rate curves of these modulation schemes