适用于非常模信号的常数模新算法

常数模算法在对非常模信号进行均衡时,稳态均方误差无法收敛至零.对常数模算法中的代价函数进行修正,该代价函数能将非常模信号的多个幅度模值变换成单一幅度模值,从而使新算法的稳态均方误差为零.理论分析和仿真结果证明了新算法的优良性能.     

An analytical constant modulus algorithm

Iterative constant modulus algorithms such as Godard (1980) and CMA have been used to blindly separate a superposition of cochannel constant modulus (CM) signals impinging on an antenna array. These algorithms have certain deficiencies in the context of convergence to local minima and the retrieval of all individual CM signals that are present in the channel. We show that the underlying constant modulus factorization problem is, in fact, a generalized eigenvalue problem, and may be solved via a simultaneous diagonalization of a set of matrices. With this new analytical approach, it is possible to detect the number of CM signals present in the channel, and to retrieve all of them exactly, rejecting other, non-CM signals. Only a modest amount of samples is required. The algorithm is robust in the presence of noise and is tested on measured data collected from an experimental set-up     

Convergence analysis of the constant modulus algorithm

We study the global convergence of the stochastic gradient constant modulus algorithm (CMA) in the absence of channel noise as well as in the presence of channel noise. The case of fractionally spaced equalizer and/or multiple antenna at the receiver is considered. For the noiseless case, we show that with proper initialization, and with small step size, the algorithm converges to a zero-forcing filter with probability close to one. In the presence of channel noise such as additive Gaussian noise, we prove that the algorithm diverges almost surely on the infinite-time horizon. However, under suitable conditions, the algorithm visits a small neighborhood of the Wiener filters a large number of times before ultimately diverging.     

A batch processing constant modulus algorithm

We present a batch processing constant modulus algorithm (BP-CMA) derived by a nonlinear optimization approach to minimizing the constant modulus (CM) criterion. BP-CMA is a line search iteration algorithm. The search direction may be taken as deepest descent direction or Newton direction. The exact step size is obtained from the roots of a cubic equation. The initial value is calculated by using the eigenvectors of the signal subspace. The BP-CMA with the Newton direction has a fast convergence rate and can converge to the minima of the CM criterion after a few iterations.     

Online adaptive reinitialization of the constant modulus algorithm

An adaptive reinitialization algorithm for the constant modulus algorithm is proposed that relies on the similarities between the constant modulus and the Wiener equalizer and expands the capabilities of a previous algorithm. The proposed algorithm determines adaptively if the CMA will benefit through reinitialization, and if so, it will calculate new equalizer coefficients leading to the global minimum     

Asymptotic properties of the algebraic constant modulus algorithm

The algebraic constant modulus algorithm (ACMA) is a noniterative blind source separation algorithm. It computes jointly beamforming vectors for all constant modulus sources as the solution of a joint diagonalization problem. We analyze its asymptotic properties and show that (unlike CMA) it converges to the Wiener beamformer when the number of samples or the signal-to-noise ratio (SNR) goes to infinity. We also sketch its connection to the related JADE algorithm and derive a version of ACMA that converges to a zero-forcing beamformer. This gives improved performance in applications that use the estimated mixing matrix, such as in direction finding     

一种改进的批处理常模算法

分析了传统批处理常模算法的缺点,提出了一种新的批处理常模算法——基于共轭梯度方向的批处理常模算法(CG-BPCMA).新算法采用共轭梯度方向作为下降方向,推导出共轭梯度方向的解析形式.在平坦瑞利衰落信道环境下的MIMO盲均衡系统中的仿真结果表明,新算法有效地克服了SD-BPCMA和NT-BPCMA的缺点,不仅获得了较低的算法复杂度,而且能快速收敛到常模代价函数的最小值点.     

Statistical performance analysis of the algebraic constant modulus algorithm

This paper presents a large sample analysis of the covariance of the beamformers computed by the analytical constant modulus algorithm (ACMA) method for blindly separating constant modulus sources. This can be used to predict the signal-to-interference plus noise ratio (SINR) performance of these beamformers, as well as their deviation from the (nonblind) Wiener receivers to which they asymptotically converge. The analysis is based on viewing ACMA as a subspace fitting optimization, where the subspace is spanned by the eigenvectors of a fourth-order covariance matrix. The theoretical performance is illustrated by numerical simulations and shows a good match.     

Block-Shanno multi-user constant modulus algorithm for use inmulti-user CDMA environment

In a multi-user direct sequence code division multiple access (DS-CDMA) system, retrieval of transmitted signals with a conventional receiver is difficult when there is chip asynchronism, multipath propagation and the associated near-far problem. Results presented show that despite these problems an adaptive linear receiver based on a mixed cross correlation and constant modulus algorithm (CC-CMA) has the potential to retrieve all users simultaneously. Compared with the conventional CC-CMA algorithm, the proposed algorithm achieves faster convergence. Simulations support the improved convergence properties of the algorithm     

单载波频域常模盲均衡算法

通过将信号时域常模特性转化为频域常模,提出一种单载波系统频域常模盲均衡算法,解决了常模算法在频域中无法实现的问题.算法复杂度表明,该方案计算量明显低于宽带系统时域子空间分解方法,且相比于现有文献[6]中的单载波系统常模盲均衡算法,其复杂度也大为降低.文中,常模算法从时域到频域的转换是基于输出信号幅值收敛为1的特性而得,因此变换条件(8)成立,故而时域到频域的转换不会影响算法误差性能,仿真实验结果证明了这一点.     

Widely linear RLS constant modulus algorithm for complex-valued noncircular signals

Based on the constant modulus criterion, a new Widely Linear （WL） blind equalizer and a novel widely linear recursive least square constant modulus algorithm are proposed to improve the blind equalization performance for complex-valued noncircular signals. The new algorithm takes advantage of the WL filtering theory by taking full use of second-order statistical information of the complex-valued noncircular signals. Therefore, the weight vector contains the complete second-order information of the real and imaginary parts to decrease the residual inter-symbol interference effectively. Theoretical analysis and simulation results show that the proposed scheme can significantly improve the equali- zation performance for complex-valued noncircular signals compared with traditional blind equalization algorithms.     

Modified constant modulus algorithm for blind DS/CDMA detection

A new blind adaptive multiuser detector for synchronous DS/CDMA systems based on a modified constant modulus algorithm is proposed. This detector is shown to outperform the minimum output energy detector in a downlink channel occupied by a large number of users. This blind detector is a good candidate for downlink receivers     

基于MIMO系统的MDCMA盲均衡算法

基于对线性多输入多输出(MIMO)系统的自适应盲源分离和盲均衡的研究,为了能够有效恢复输入信号,提出了一种在MIMO系统中引入抖动处理技术的修正抖动符号误差恒模算法.仿真结果表明,该算法可以在仅已知输入信号统计量的情况下跟踪信道变化,并且有效克服多个均衡器的输出可能锁定到相同的源信号问题,抑制ISI和MUI,恢复所有发射天线的发送信息.     

一种适用于强脉冲噪声下的对数型恒模盲均衡算法

针对脉冲噪声下恒模算法(Constant Modulus Algorithm,CMA)失败的问题,通过分析脉冲噪声的影响,提出了一种基于最小均方（Least Mean Square,LMS）准则的对数型恒模算法（Logarithmic-type CMA,LT-CMA）。LT-CMA利用对数函数的非线性变换特性自适应地抑制强脉冲噪声对误差函数的影响,并且利用l2-范数进行信号归一化处理以增强算法的稳健性。仿真结果表明,所提出的LT-CMA可以适应于高斯噪声环境和脉冲噪声环境;与经典自适应均衡算法相比,在收敛速度和稳健性两方面上,所提出的LT-CMA都有显著的提升。     

Decision directed adaptive blind equalization based on the constant modulus algorithm

In this paper, new decision directed algorithms for blind equalization of communication channels are presented. These algorithms use informations about the last decided symbol to improve the performance of the constant modulus algorithm (CMA). The main proposed technique, the so called decision directed modulus algorithm (DDMA), extends the CMA to non-CM modulations. Assuming correct decisions, it is proved that the decision directed modulus (DDM) cost function has no local minima in the combined channel-equalizer system impulse response. Additionally, a relationship between the Wiener and DDM minima is established. The other proposed algorithms can be viewed as modifications of the DDMA. They are divided into two families: stochastic gradient algorithms and recursive least squares (RLS) algorithms. Simulation results allow to compare the performance of the proposed algorithms and to conclude that they outperform well-known methods.     

Regularised analytical constant modulus algorithm for space–time coded systems

Space–time coding is an effective approach to increase the data rate and capacity of a wireless communication system that employs multiple transmit and multiple receive antennas. It involves coding techniques that are designed for multiple transmit antennas. We apply the analytical constant modulus algorithm (ACMA) for blind channel estimation (no use of training sequences) of space–time coded systems and explore the constant modulus (CM) constraints of the transmitted space–time codes (STCs). A regularised scheme that gives good performance in Gaussian and non-Gaussian noise environments is proposed. Computer simulation results in both single-user and multiuser cases show the improvement in error performance.     

一种常数模与判决导引相结合的盲均衡算法研究

虽然判决导引最小均方误差算法（DD－LMS）剩余误差小，但是，在信道眼图闭合的情况下，该算法无法收敛，即不具备冷启动能力。本文根据信噪比确定了判决圆边界，对均衡器的输出进行判决，将常数模算法（CMA）和DD算法有机地结合起来，计算机仿真表明：算法性能稳健，具有冷启动能力和重新启动能力，计算量增加也很小。     

Tracking performance analysis of fractional lower order constant modulus algorithm

The fractional lower-order constant modulus algorithm (FLOS_CMA) has been proven to be an effective blind equalisation method under a-stable noise. But there have been few results in the literature about its performance. The tracking performance of the FLOS_CMA in non-stationary environments is studied. The approximate expression is derived based on the energy-preserving relation and Taylor series expansion. Based on the derived expression, an estimate is obtained for the FLOS_CMA step-size interval to ensure its convergence and stability, when it is initialised sufficiently close to the zero-forcing solution. Simulation studies have been undertaken to support the analysis.     

Low complexity concurrent constant modulus algorithm and soft decision directed scheme for blind equalisation

The recently introduced concurrent constant modulus algorithm (CMA) and decision-directed (DD) scheme provides a state-of-the-art low-complexity blind equalisation technique for high-order quadrature amplitude modulation (QAM) channels. At a small cost of slightly more than doubling the complexity of the standard CMA blind equaliser, this concurrent CMA and DD blind equaliser achieves a dramatic improvement in equalisation performance over the CMA. In the paper, a new blind equalisation scheme is proposed based on concurrent CMA and a novel soft decision-directed (SDD) adaptation. The proposed concurrent CMA and SDD blind equaliser has simpler computational requirements than the concurrent CMA and DD algorithm. Extensive simulation shows that it has the same steady-state equalisation performance as the concurrent CMA and DD algorithm and a faster convergence speed over the latter scheme     

Performance surfaces of the constant modulus algorithm based on aconditional Gaussian model

A stochastic analysis of the performance surfaces for four versions of the constant modulus algorithm is presented. By conditioning on the transmitted data symbols, the equalizer output is modeled as a Gaussian process, from which closed-form expressions of the performance functions are derived. The resulting conditional expectations are then evaluated according to the probability distribution of the conditioning symbols. This approach leads to analytical results that might otherwise be difficult to derive without the immediate conditioning step