Optimal power and subcarriers allocation in downlink OFDMA system with imperfect channel knowledge

Most of existing work on resource allocation in TDMA and OFDMA systems assumes the availability of perfect channel state information (CSI) at the transmitter, which is rarely possible due to feedback delay and channel estimation error. In this paper, we study the effect of feedback delay and channel estimation error on margin adaptive resource allocation in a downlink OFDMA system. By using convex optimization framework, we find an optimal solution to the problem. First, we study the individual effect of feedback delay and channel estimation error on resource allocation by considering them exclusively. Then, we consider the simultaneous presence of feedback delay and channel estimation error and study their combined effect on resource allocation. We derive an explicit close form expression for the users’ transmit power and propose an algorithm for power and subcarriers allocation for each of these three scenarios. The algorithms have polynomial complexities and solve the problem with zero optimality gaps. Simulation results show that the system performance is very sensitive to feedback delay and is affected significantly by imperfect channel estimation. Our proposed algorithms highly improve the system performance in the availability of only imperfect CSI at the transmitter.     

基于差分进化的时变信道最大似然估计算法

研究了隧道环境下的通信信道估计。针对隧道环境的地铁列车与轨旁设备之间无线通信中无线传输信道快速变化的特点,提出了一种采用元胞差分进化(DE)方法实时获取时变信道的有效信道长度的新型最大似然(ML)信道估计算法——DE-ML算法。仿真结果表明该算法在使用较少导频信息的情况下,通过差分进化方法有效估计跟踪有效信道长度,其估计性能优于最小二乘(LS)、线性最小均方误差(LMMSE)、传统ML等经典信道估计算法。该算法能在提高系统传输效率的同时显著提高算法的估计精度,尤其在高速移动情况下也具有了非常良好的性能。     

High mobility orthogonal frequency division multiple access channel estimation using basis expansion model

Owing to the loss of subcarrier orthogonalities in high-speed applications, the use of conventional frequency-domain-based channel estimation in high mobility orthogonal frequency division multiple access (OFDMA) systems such as mobile WiMax may give rise to an unacceptable high channel estimation error floor. To alleviate this problem, the authors develop some basis expansion model (BEM)-based estimation schemes for the OFDMA uplink. Specifically, the authors express the time-varying channel as a superposition of a small number of complex exponential basis functions spanning the entire Doppler range, and then formulate least square (LS) and linear minimum mean square error (LMMSE) algorithms to estimate the basis coefficients for two different types of pilot patterns. The authors also derive the respective Cramer-Rao lower bounds for these estimators. It has been shown that the time domain BEM using a pilot scheme where pilots are placed over time axis will give better performance under a high Doppler scenario. Lastly, using simulation results, the proposed algorithms have been found to have better estimation accuracy over current frequency domain estimation techniques. This is in addition to the advantage that the proposed algorithms have in general a lower computational complexity.     

Effect of error in channel state information on the channel capacity with QAM signalling and the design of robust signal constellations

The effects of channel estimation errors on the channel capacity of a discrete time, discrete input, infinite output Rayleigh fading channel are investigated. The case of conventional modulation methods such as phase shift keying (PSK) and quatrature amplitude modulation (QAM) is investigated at first where it was observed that the capacity degrades rapidly with increasing channel estimation errors. The effect of error in the channel estimation is similar to the effect of higher noise in the channel that depends on the transmitted signal. A genetic algorithm is used to optimise the signal constellation in order to maximise the capacity for a given finite number of signal points. The aim of trying to maximise the capacity is to estimate the remaining gap in performance between a traditional modulation scheme such as QAM and the best possible constellation that is optimised for the channel. The constellations obtained from the genetic algorithm are, in general, not directly implementable. A method to design practical robust signal constellations that overcome the effect of channel state information (CSI) error is presented. The robust signal constellations obtained show a performance that is very close to the optimal constellations. In this work, the probability distribution of the error in CSI is assumed to be known.     

Bit error ratio performance of a receiver diversity scheme with channel estimation

The performance of diversity combining techniques with channel estimation for the case of unequal power branches is discussed. The performance of binary phase shift keying (BPSK), pulse amplitude modulation (PAM) and quadrature amplitude modulation (QAM) formats is investigated and their performance with nonideal channel estimation is explored. The case of combining multiple branches with unequal power levels is considered and optimal weighting factors for a log likelihood ratio test (LLRT) detector for the BPSK case are presented. These weights are shown to operate in a similar manner to those obtained by the linear minimum mean squared error (LMMSE) criterion and are compared with the well known maximal ratio combining (MRC) technique. The probability of error of this receiver is derived and simplifications for high signal-to-noise ratios are presented. Finally, numerical results are presented to compare the performance of the LLRT, LMMSE and MRC based receivers     

无线城域网OFDM系统信道估计算法

OFDM技术是无线城域网IEEE802.16a标准中物理层面的主流调制技术,今建立符合IEEE802.16a标准的OFDM信道估计模型,阐述其导频基本信道估计方法的原理及特点,分析比较了LS/MMSE/LMMSE/SVD四种算法的MSE和BER性能特点.仿真结果说明,LMMSE算法的均方误差和误码率性能最好,且计算复杂度相对较低,易于物理实现.     

Sparsity constrained regularization for multiframe image restoration

In this paper we present a new algorithm for restoring an object from multiple undersampled low-resolution (LR) images that are degraded by optical blur and additive white Gaussian noise. We formulate the multiframe superresolution problem as maximum a posteriori estimation. The prior knowledge that the object is sparse in some domain is incorporated in two ways: first we use the popular l(1) norm as the regularization operator. Second, we model wavelet coefficients of natural objects using generalized Gaussian densities. The model parameters are learned from a set of training objects, and the regularization operator is derived from these parameters. We compare the results from our algorithms with an expectation-maximization (EM) algorithm for l(1) norm minimization and also with the linear minimum-mean-squared error (LMMSE) estimator. Using only eight 4 x 4 pixel downsampled LR images the reconstruction errors of object estimates obtained from our algorithm are 5.5% smaller than by the EM method and 14.3% smaller than by the LMMSE method.     

MIMO-OFDM系统中一种新的信道估计方法

提出了多输入多输出-正交频分复用(MIMO-OFDM)系统中一种新的信道估计方法.根据最小均方误差的准则,推导出了求解信道频率响应的方程,方程求解的运算量主要集中在一个矩阵的求逆上.对每一个符号,此矩阵是固定的,所以矩阵的求逆仅需计算一次,整个求解过程的运算量较低.计算机仿真给出了这种方法的归一化均方误差和误码率性能.仿真结果表明,本文方法在多普勒频移为60Hz和360Hz下,其归一化的均方误差值相当,表明本文方法可以在不同的移动环境中良好工作.在不同的数据调制方式和不同的多普勒频移下,本文方法的误码率性能优于最小平方算法,略差于线性最小均方误差算法,但复杂度大大降低.     

An efficient joint channel estimation and decoding algorithm for turbo-coded space?time orthogonal frequency division multiplexing receivers

The challenging problem in the design of digital receivers of today's and future high-speed, high data-rate wireless communication systems is to implement the optimal decoding and channel estimation processes jointly in a computationally feasible way. Without realising such a critical function perfectly at receiver, the whole system will not work properly within the desired performance limits. Unfortunately, direct implementation of such optimal algorithms is not possible mainly due to their mathematically intractable and computationally prohibitive nature. A novel algorithm that reaches the performance of the optimal maximum a posteriori (MAP) algorithm with a feasible computational complexity is proposed. The algorithm makes use of a powerful statistical signal processing tool called the expectation maximisation (EM) technique. It iteratively executes the MAP joint channel estimation and decoding for space'time block-coded orthogonal frequency division multiplexing systems with turbo channel coding in the presence of unknown wireless dispersive channels. The main novelty of the work comes from the facts that the proposed algorithm estimates the channel in a non-data-aided fashion and therefore except a small number of pilot symbols required for initialisation, no training sequence is necessary. Also the approach employs a convenient representation of the discrete multipath fading channel based on the Karhunen'Loeve (KL) orthogonal expansion and finds MAP estimates of the uncorrelated KL series expansion coefficients. Based on such an expansion, no matrix inversion is required in the proposed MAP estimator. Moreover, optimal rank reduction is achieved by exploiting the optimal truncation property of the KL expansion resulting in a smaller computational load on the iterative estimation approach.     

IEEE802.16e系统信道估计算法研究

针对IEEE802.16e系统下行链路的导频分配模式,提出了一种适用于IEEE802.16e系统下行链路的信道估计方法。该方法采用两个一维信道估计器的级联。首先在时域进行滤波,根据最近原则将前一个符号导频处的信道响应作为下一个符号相同位置子载波处的信道响应,从而得到梳状导频结构;其次在频域进行滤波,采用最大似然算法估计出所有子载波上的信道响应。车速60km/h和车速120km/h信道下的仿真结果表明,采用该信道估计方法可降低系统的误码率,提高高速移动环境下系统的性能。     

Tomlinson-Harashima precoding with imperfect channel state information

Nonlinear Tomlinson-Harashima precoding (THP) is an attractive solution for a scenario where the transmission system employs multiple antennas at transmitter and multiple users with a single antenna at the receiver, so that the cooperation among the receive antennas are impossible (downlink scenario). THP solution based on zero forcing (ZF) and minimum mean square error (MMSE) criteria is one of the important techniques to achieve near multiple input multiple output channels capacity with reasonable complexity. In this paper, the effect of channel imperfection on THP is considered. At first, the achievable rate of THP with respect to ZF criterion in an imperfect channel state information (CSI) scenario is calculated. Moreover, based on MMSE criterion, a new robust solution is derived which provides a significant improvement with respect to the conventional optimisation method. Then, the effect of channel estimation error on THP is considered as an improved optimisation where THP filters are optimised together with a channel estimator. Spatial power loading is found to be important to the THP performance. This loading for robust/joint optimisation of MMSE THP is developed by minimum average symbol error rate sense. Simulation results show the capacity loss, the performance advantage attained by the robust/joint optimisation and the power loading in an imperfect CSI scenario.     

Semi-blind channel estimation for the uplink of multi-carrier code-division multiple access systems with timing offset

Timing offsets (TO) introduce misaligned interferences and phase errors, which degrade the performance of channel estimation. The authors propose a new semi-blind channel estimator that can cancel the TO effects on channel estimation and work well in the uplink of multi-carrier code-division multiple access systems in the presence of TO. The proposed channel estimator exploits the spreading sequence information instead of pilots to accomplish semi-blind estimation. Since the estimated channel coefficients are affected by the users? transmitted data, the effect of the users? data needs to be reduced. For this purpose, the authors also propose two smoothing algorithms, division smoothing and optimisation smoothing. In addition, to extend the new estimator to the system where the number of active users is too large, channel estimation over multiple symbols is discussed. The simulation results show that the proposed semi-blind estimator works better than a conventional estimator in the presence of TO, and its performance is very close to the conventional estimator in the absence of TO. Besides, the proposed estimator is compared with a sub-space estimator in simulation, and the results indicate that the new proposed estimator can achieve the same mean square error performance over the duration of a single symbol as the sub-space estimator over the duration of several symbols.     

Maximum a posteriori channel estimation for cooperative diversity orthogonal frequencydivision multiplexing systems in amplify-andforward mode

Transmit diversity-orthogonal frequency-division multiplexing (OFDM) systems have been proposed to mitigate the detrimental effects of channel fading. However, owing to the space and power limitations, the use of multiple transmit antennas is not practical in certain wireless devices, such as portable terminals and wireless sensors. Therefore cooperation among users at the physical layer has been proposed recently. Here, space-time block coded in amplify-and-forward (AF) relaying mode has been proposed as cooperative diversity for OFDM systems (CO-OFDM) in the presence of perfect channel-state information. Then, the channel estimation techniques for CO-OFDM systems in AF mode based on pilot symbols are investigated over frequency-selective channels. In particular, expectation-maximisation (EM) based maximum a posteriori (MAP) channel estimation is developed and compared with comp-type pilot-aided channel estimation (PACE) based the maximum likelihood (ML) estimator and the least minimum mean-square error (LMMSE) channel estimation techniques for CO-OFDM systems. To overcome the drawback owing to the receiver complexity, the Karhunen-Loeve expansion with the optimal truncation property is also considered. Simulation results that demonstrate the overall performance advantage of the EM-MAP based receiver over the PACE-ML and PACE-LMMSE based receivers are presented.     

An Optimization Criterion for Linear Inverse Estimation

Integrated mean square error is proposed as an optimizing criterion for the linear inverse estimation problem. Results are compared with the classical and inverse procedures. A generalization allowing for several predictor variables is considered.

Under certain conditions both the classical and the inverse methods may tend towards the optimal estimator. Also, the sample inverse estimator is shown to be optimal for a realistic situation     

Turbo channel estimation and equalisation for a superposition-based cooperative system

This study investigates the superposition-based cooperative transmission system. In this system, a key point is for the relay node to detect data transmitted from the source node. This issued was less considered in the existing literature as the channel is usually assumed to be flat fading and a priori known. In practice, however, the channel is not only a priori unknown but subject to frequency selective fading. Channel estimation is thus necessary. Of particular interest is the channel estimation at the relay node which imposes extra requirement for the system resources. The authors propose a novel turbo least-square channel estimator by exploring the superposition structure of the transmission data. The proposed channel estimator not only requires no pilot symbols but also has significantly better performance than the classic approach. The soft-in-soft-out minimum mean square error (MMSE) equaliser is also re-derived to match the superimposed data structure. Finally computer simulation results are shown to verify the proposed algorithm.     

Optimal training design for linearly time-varying MIMO/OFDM channels modelled by a complex exponential basis expansion

Time- and frequency-selective fading of propagating channels degrades the performance of multiple-input multiple-output/orthogonal frequency-division multiplexing (MIMO/OFDM) systems extensively by introducing double convolutions in both time-domain and frequency- domain. The author addresses the problem of linearly time-varying (LTV) channel estimation of MIMO/OFDM systems. First, the time-varying coefficients of the LTV channel are modelled by complex exponential basis expansions. Secondly, the LTV channel is estimated and the optimal pilot symbols are derived following the minimum mean square error criterion. It is shown that the optimal pilot strategy is to group consecutive pilot tones together as a pilot cluster and to distribute uniformly all pilot clusters in frequency-domain. In addition, the LTV channel estimation is further improved by imposing a window function on received signals. Finally, through simulations, it is shown that the new channel estimator can provide a considerable performance improvement in estimating MIMO-LTV channels, especially for the rapidly time-varying channel of a large Doppler frequency.     

Channel estimation and interference cancellation in CP?CDMA systems

A novel iterative channel estimation approach is proposed for cyclic prefix-code division multiple access systems. Code-multiplexed pilots are used for channel estimation while maintaining bandwidth efficiency. The proposed method achieves a significant improvement when compared to the conventional correlation approach by reconstructing data signals for channel estimation. Simulation results demonstrate good estimation capability with an allocation of only 10% of the whole power to the pilot channel. In addition, an integrated channel estimator and parallel interference cancellation (PIC) detector are proposed. Data signals are reconstructed for channel estimation while the interference contributed by different data channels as well as the pilot channel are regenerated and subtracted from the received signal at the final stage. The channel estimation error reduces at each iteration and the PIC at the last stage enables further bit error rate performance improvement to be achieved for the system. The performance of the proposed scheme is studied through simulations and results verify its effectiveness     

大气光通信中Turbo码的最大后验概率译码

为了精确实现对空间物体的测量,提出了利用线激光、单CCD相机、小孔成像与激光面约束模型的激光线测量法。引进三维信息已知的标准阶梯块作为激光面约束的标定块;由计算机控制摄像头对实物连续拍摄和实时处理,提取激光线上的像素坐标;利用建立的模型将二维坐标转换成三维坐标,再以点云的形式重构出物体,实现三维自动测量。实践中检测系统测量精度可达到0.05mm。     

A Genetic Algorithm Applied for Optimization of Antenna Arrays Used in Mobile Radio Channel Characterization Devices

This paper presents a proposed method for synthesizing scenario-dependent channel characterization system arrays that are adapted to the mobile radio environment where measurements take place. The criterion for synthesizing the array is the minimization of the angular CramÉr–Rao lower bound, which is the lower bound of the mean square estimation error (MSEE) for an unbiased estimator. The core of the process is a genetic algorithm (GA) that seeks for the most advantageous array topology for each scenario. Simulation results show that the method succeeds in synthesizing feasible antenna arrays that have increased direction of arrival (DoA) estimation accuracy and are superior to the arrays typically used during actual measurement campaigns.      

VMIMO-OFDM系统精频偏估计算法的研究

在对多种可应用于VMIMO-OFDM系统的频偏估计方法的性能和效率进行分析的基础上,针对基于VMIMO-OFDM的无线传感器网络中的精频偏估计问题,提出了一种在频域进行频偏估计的算法.同时,针对基于VMIMO-OFDM的无线传感器网络应用于瑞利衰落严重的环境时不同的导频子载波上频偏估计的误差差异较大的问题,提出了一种基于信道统计信息(CSI)加权的精频偏估计算法,该方法对各个子载波上的频偏估计结果进行加权平均,可使估计误差最小化.理论分析和仿真结果均表明,新提出的算法在高斯信道和多径信道中均有更优的性能.