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     

Space-time blind equalisation in impulsive noise

The presence of non-Gaussian impulsive noise in wireless system can degrade the performance of existing equalisers and signal detectors. The problem of blind source separation and equalisation for multipleinput/ multiple-output (MIMO) channels under heavy-tailed impulsive noise environment is studied. A generalised multi-user constant modulus (CM) cost function is proposed by employing the fractional lower order CM property of the equaliser input signals as well as the fractional lower order cross-correlations between them. The associated adaptive blind equalisation algorithm based on a stochastic gradient descent method is defined as fractional lower order multi-user constant modulus algorithm (FMU_CMA), which is able to mitigate impulsive channel noise while recovering all input signals simultaneously. The steady-state meansquare error (MSE) performance of the FMU_CMA is studied in a noise-free environment; the approximate expression is derived based on the energy-preserving relation and the Taylor series expansion. Simulation studies are undertaken to support the analysis with CM and non-CM signal.     

一种基于恒模算法的多用户盲波束形成新方法

提出了一种适用于多用户的盲波束形成新方法.该方法基于最小二乘恒模算法,当最小二乘恒模算法收敛于某一信号后,我们导出了算法的权向量与其它用户波达方向的关系,进而在不同用户的波达方向上形成初始增益,从而实现对所有用户的波束形成.文中给出了算法的并行和串行实现方案.     

The constant modulus array for cochannel signal copy and directionfinding

The constant modulus (CM) array is a blind adaptive beamformer capable of recovering a narrowband signal among several cochannel sources without using a pilot or training signal. It is a conventional weight-and-sum adaptive beamformer whose weights are updated by the constant modulus algorithm. An adaptive signal canceller follows the beamformer to remove the captured signal from the array input and to provide an estimate of its direction vector. Based on a Wiener model, we investigate the steady-state properties of the CM array and the signal canceller. For mutually uncorrelated sources and noise, it is shown that the signal canceller exactly removes the source captured by the array. Thus, identical stages of the CM array and signal canceller may be used in a multistage system to recover several cochannel sources. Computer simulations are presented to verify the analytical results and to illustrate the transient behavior of the system     

Misadjustment and tracking analysis of the constant modulus array

The constant modulus (CM) array is a blind adaptive beamformer that can separate cochannel signals. A follow-on adaptive signal canceler may be used to perform direction finding of the source captured by the array. In this paper, we analyze the convergence and tracking properties of the CM array using a least-mean-square approximation. Expressions are derived for the misadjustment of the adaptive algorithms, and a tracking model is developed that accurately predicts the behavior of the system during fades. It is demonstrated that the adaptive canceler contributes more to the overall misadjustment than does the adaptive CM beamformer. Computer simulations are presented to illustrate the transient properties of the system and to verify the analytical results     

A blind signal separation method for multiuser communications

A new approach based on the constant modulus (CM) criterion is proposed to separate instantaneous linear mixtures of signals using a linear memoryless multiple input multiple output (MIMO) system. Even though a nonconvex cost function is minimized, analyses show that minima correspond to parameter settings where perfect separation is achieved     

一种基于并联式恒模阵和DOA的同信道信号接收算法

提出一种基于并联式恒模阵和DOA的同信道信号接收算法。采用DOA算法获得信号的波达角，结合初始预测的方法对并联式恒模阵加以初始化，实现对同信道信号的接收和跟踪。它具有无需精确已知信号波达角的特点，克服了已有算法中需要阵列校正的缺陷，同时具有不会误收敛的优点。计算机仿真证实了算法的有效性。     

Performance Analysis of the Spectral Correlation Discriminator Array

Mobile communications suffer from cochannel interference, adjacent channel interference and fading. The cell capacity or the number of users per cell is limited by the interference. In this paper we analyze a new blind adaptive array structure called the spectral correlation discriminator array (SCDA), designed to reject cochannel interference for advanced mobile phone service (AMPS) signals. The blind adaptive array exploits the spectral redundancy in the AMPS signals which arises due to the presence of the supervisory audio tone (SAT). SCDA is shown to provide an improvement of 25–30 dB in signal-to-interference plus noise ratio (SINR) in static multipath channels and 10–15 dB improvement of SINR in Rayleigh fading channels. The SCDA is compared to the least squares constant modulus array (LSCMA) and is shown to have better signal selectivity properties. The reduction in interference power can significantly reduce the frequency reuse factor.     

非理想信道多用户数字信号的盲分离

在一个信道上传送多个用户信号,可以大大提高信道的容量,本文讨论了非理想信道多和户数字信号的盲分离问题,利用天线阵,接收可以看作是由Ｎ个独立信号源激励的非线传输混合系统的输出;由于信道存在的码间干扰,混合矩阵的元素不是常数,而是一个线性子系统,针对这一情况,本文提出了一个盲分离器结构,首先将接收信号进行盲分离,然后利用基于ＡＲ模型的盲均衡器消除每一路输出信号的码间干扰,从而实现多用户信号物分离,语文     

Maximum likelihood separation of constant modulus signals

In this correspondence, we derive a Newton scoring algorithm for the maximum likelihood separation and direction-of-arrival (DOA) estimation of constant modulus (CM) signals using a sensor array. We present a rapidly converging scheme for the joint estimation of the signals and their directions based on their CM property. We discuss initialization and show that the complexity is moderate     

Steady-state analysis of the multistage constant modulus array

The multistage constant modulus (CM) array is a cascade adaptive beamforming system that can recover several narrowband cochannel signals without training. We examine its steady-state properties at convergence using a stochastic analysis and computer simulations. Based on a Wiener model of convergence for the gradient adaptive algorithms, closed-form expressions are derived for the CM array and canceller weight vectors, as well as the effective source direction vectors at all stages along the cascade system. The signal-capture and direction-finding capabilities of the system are also discussed. Computer simulations for stationary and fading sources are presented to confirm the theoretical results and to illustrate the rapid convergence behavior of the adaptive algorithms     

解析恒模算法性能分析

从盲信号分离角度简要介绍了解析恒模算法,该算法以解析的方法一次计算出整个波束形成器的集合,而不是靠迭代法搜索定义的恒模代价函数的极值点来逐一恢复其中的恒模信号,这是它与迭代型恒模算法最大的不同。其特点给该算法带来很多优点,最重要的一点是能在强干扰下恢复小功率信号,受信号功率差异影响极小。文中的理论推导通过计算机仿真验证了在高斯白噪声环境下,当样本数趋于无穷时,该算法收敛至维纳解;最后用实际外场采集的数据对该算法进行了测试分析,验证了其突出的信号分离能力。     

A modified constrained constant modulus approach to blind adaptivemultiuser detection

An alternative blind adaptive multiuser detection is investigated based on modified constrained constant modulus (CM) criterion. It is shown that the performance of a CM-based receiver is limited by the received power of the desired user. In this paper, we show that the limitation can be avoided using the noncanonical constraint CM criterion and that in the presence of channel noise the modified CM criterion function is strictly convex by properly selecting some constant. With analyzing the extrema of the cost function, we point out how to select the constant. Moreover, a simple stochastic gradient algorithm for implementing our scheme is presented, and the convergence properties of the algorithm are analyzed. Simulation examples are given to demonstrate the performance of the proposed scheme     

Bounds on SIMO and MIMO Channel Estimation and Equalization with Side Information

Constrained Cramér-Rao bounds are developed for convolutive multi-input multi-output (MIMO) channel and source estimation in additive Gaussian noise. Properties of the MIMO Fisher information matrix (FIM) are studied, and we develop the maximum rank of the unconstrained FIM and provide necessary conditions for the FIM to achieve full rank. Equality constraints on channel and signal parameters provide a means to study the potential value of side information, such as training symbols (semi-blind case), constant modulus (CM) sources, or known channels. Nonredundant constraints may be combined in an arbitrary fashion, so that side information may be different for different sources. The bounds are useful for evaluating the performance of SIMO and MIMO channel estimation and equalization algorithms. We present examples using the constant modulus blind equalization algorithm. The constrained bounds are also useful for evaluating the relative value of different types of side information, and we present examples comparing semi-blind, constant modulus, and known channel constraints. While the examples presented are primarily in the communications context, the CRB framework applies generally to convolutive source separation problems.     

Alpha稳定分布噪声下级联恒模阵列及其稳定性分析

该文研究Alpha稳定分布噪声下级联韧性恒模阵列的稳定性。首先,提出一种新型的信号对消器,把本级阵列捕获的信号从接收数据中消除,并分析了该对消器达到的稳定状态。然后,以韧性的波束形成器和新型的信号对消器组成级联恒模阵列。分析了恒模信号和Alpha稳定分布噪声在级联恒模阵列间的传递情况。数值仿真验证了理论分析的结论,并对级联恒模阵列的多信号恢复进行了模拟。     

Relationships between the constant modulus and Wiener receivers

The Godard (1980) or the constant modulus algorithm (CMA) is an effective technique for blind receiver design in communications. However, due to the complexity of the constant modulus (CM) cost function, the performance of the CM receivers has primarily been evaluated using simulations. Theoretical analysis is typically based on either the noiseless case or approximations of the cost function. The following question, while resolvable numerically for a specific example, remains unanswered in a generic manner. In the presence of channel noise, where are the CM local minima and what are their mean-squared errors (MSE)? In this paper, a geometrical approach is presented that relates the CM to Wiener (or minimum MSE) receivers. Given the MSE and the intersymbol/user interference of a Wiener receiver, a sufficient condition is given for the existence of a CM local minimum in the neighborhood of the Wiener receiver. The MSE bounds on CM receiver performance are derived and shown to be tight in simulations. The analysis shows that, while in some cases the CM receiver performs almost as well as the (nonblind) Wiener receiver, it is also possible that, due to its blind nature, the CM receiver may perform considerably worse than a (nonblind) Wiener receiver     

Harmonic Signals Retrieval Approach Based on Blind Source Separation

A frequently encountered problem in signal processing is harmonic retrieval in additive colored Gaussian or non-Gaussian noise, especially when the frequencies of the harmonic signals are very close in space. The purpose of this paper is to develop an efficient Blind Source Separation (BSS) algorithm from linear mixtures of source signals, which enables to separate harmonic source signals using only one observed channel signal even if the frequencies of the harmonic signals are closely spaced. First, we establish the BSS based harmonic retrieval model in additive noise by using the only one observed channel, and analyze the fundamental principle by utilizing BSS method to retrieve harmonics. Then, we propose a BSS-based approach to the harmonic retrieval by resorting the concept of W-disjoint orthogonality in the over-complete BSS situation, and as a result, we get the separation algorithm using only one channel mixed signals. Simulation results show that the proposed separation algorithm-BSS-HR is able to separate the harmonic source signals.     

Blind CM equalisation for STBC over multipath fading

This Letter focuses on the development of a blind adaptive receiver for space-time block coding (STBC) over multipath fading. The constant modulus (CM) criterion is utilised on the received signals, whereby an orthogonality constraint of the transmitted STBC signals prevents the multiple extractions of the same source. Simulation results demonstrate the performance of the proposed algorithm in a fading channel.     

On the use of kernel structure for blind equalization

The mathematical theory of kernel (null space) structure of Hankel and Hankel-like matrices is applied to the problem of blind equalization of cochannel signals. This approach provides a new perspective on the blind equalization problem and gives insights into the identifiability conditions already presented in the literature. An algorithm is presented that tracks the exact null space of the symbol matrix even in the presence of noise. This work exploits the shift structure in the oversampled channel output and the finite alphabet property of the signals. Previously, these two properties were used independently in a two-step (equalize then separate) process. A contribution of the new approach is that is allows simultaneous exploitation of both the shift structure and the finite alphabet property of the signals     

Acquisition Behavior of the Cross-Coupled Phase-Locked Loop FM Demodulator

In this work, the acquisition behavior of a cross-coupled phase-locked loop (CCPLL) FM demodulator capable of suppressing cochannel and adjacent channel interferers is examined. This novel detector consists of two phase-locked loop (PLL) demodulators interconnected in such a manner as to permit one PLL to lock onto and track the stronger received signal, while the other loop tracks and demodulates the weaker of two received signals. The demodulator has two separate outputs, namely, the outputs of each PLL, and thus possesses the capability of demodulating both the stronger as well as the weaker received signals even though they are cochannel and share the same frequency band. The transient response of the CCPLL system is obtained using computer-aided analysis of the defining coupled nonlinear differential equations. From these results, steady-state "stability regions" are derived which reveal that range of loop parameters where successful separation and demodulation of the received cochannel signals is assured. The CCPLL receiver has numerous technological applications in suppressing unintentional or intentional CW, AM, FM, and AM/FM interferers. Experimental results demonstrating such potential are included.