Despread-respread multi-target constant modulus array for CDMAsystems

We apply the concept of the despread-respread (DR) algorithm to multi-target arrays for code-division multiple-access (CDMA) signals, the despread-respread algorithm exploits the knowledge of the pseudo-noise (PN) code used to generate the transmitted CDMA signal. We extend the DR algorithm to not only exploit the knowledge of the PN code but also to preserve the constant modulus property of the signal. This new algorithm is called the least squares despread respread multi-target constant modulus array (LS-DRMTCMA). LS-DRMTCMA performs better than the least squares despread respread multi-target array (LS-DTMTA), least squares multi-target constant modulus array (LS-MTCMA), and steepest descent multi-target decision directed array (SD-MTDDA)     

Minimum-span constant modulus array for a smart antenna testbed

The realisation of an efficient algorithm for a real-time smart antenna testbed based on DECT technology is considered. The testbed is based on a multistage constant modulus array, a blind adaptive beamformer and an adaptive signal canceller that removes the captured signal from the input signals. Based on the Wiener model of convergence, a reduced form of the CM array has been developed that takes advantage of the reduced rank of the input correlation matrix for additional stages. Computer simulations confirm the functionality of this algorithm, and convergence and sensitivity to fading are also discussed.     

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     

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     

Modified constant modulus algorithm for digital signal processingadaptive antennas with microwave analog beamforming

This paper proposes a novel algorithm, called modified constant modulus algorithm (M-CMA), which is able to give adaptability to microwave beamforming phased array antennas. Since microwave analog beamformers basically require much fewer RF devices than digital beamformers, microwave analog beamformers based on M-CMA, that is, adaptive microwave beamformers, can be cheaply fabricated. Therefore, they are very suitable for mobile communication systems where both miniaturization and low cost are required for the mobile terminals. M-CMA obtains a gradient vector by a combination of analytical calculation and perturbation of the microwave beamforming control voltage. Though M-CMA is implemented with a digital signal processor, M-CMA controls the microwave analog beamformer by utilizing the gradient vector. The microwave analog beamformer based on M-CMA is analyzed to have the following characteristics: (1) the beamformer can point its main beam to the desired direction in additive white Gaussian noise (AWGN) channels; (2) although the beamformer may possibly fail in ill solutions in cochannel interference (CCI) channels, M-CMA can converge to the optimum solution when the desired direction is roughly a priori known     

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.     

Direction-of-arrival estimation for constant modulus signals

In many cases where direction finding is of interest, the signals impinging on an antenna array are known to be phase modulated and, hence, to have a constant modulus (CM). This is a strong property; by itself, it is already sufficient for source separation and can be used to construct improved direction finding algorithms. We first derive the relevant Cramer-Rao bounds (CRBs) for arbitrary array configurations and specialize to uniform linear arrays. We then propose a simple suboptimal direction estimation algorithm in which the signals are separated using the CM property followed by direction finding on the decoupled signals. Compared with the ESPRIT algorithm and the CRB for arbitrary signals, the algorithm shows good results     

Separation of cochannel GSM signals using an adaptive array

The Global System for Mobile communications (GSM) is a digital cellular radio network that employs time division multiple access (TDMA). In such a cellular system, frequencies are reused in different regions for spectral efficiency, and thus, the transmissions in a given cell can interfere with those in distant cells. This cochannel interference can be a major impairment to the signal of interest. In this paper, we describe a beamformer and equalizer system that is capable of separating and demodulating several cochannel GSM signals. The signal model includes intersymbol interference (ISI) induced by the Gaussian transmit filter, and the channel model incorporates multipath propagation and additive white Gaussian noise. The GSM synchronization sequences are used to compute the beamformer weights and achieve frame synchronization simultaneously. Decision-feedback equalization is employed to compensate for the transmit filter ISI and to demodulate the data     

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     

Bounds for the MSE performance of constant modulus estimators

The constant modulus (CM) criterion has become popular in the design of blind linear estimators of sub-Gaussian independent and identically distributed (i.i.d.) processes transmitted through unknown linear channels in the presence of unknown additive interference. In this paper, we present an upper bound for the conditionally unbiased mean-squared error (UMSE) of CM-minimizing estimators that depends only on the source kurtoses and the UMSE of Wiener estimators. Further analysis reveals that the extra UMSE of CM estimators can be upper-bounded by approximately the square of the Wiener (i.e., minimum) UMSE. Since our results hold for vector-valued finite-impulse response/infinite-impulse response (FIR/IIR) linear channels, vector-valued FIR/IIR estimators with a possibly constrained number of adjustable parameters, and multiple interferers with arbitrary distribution, they confirm the longstanding conjecture regarding the general mean-square error (MSE) robustness of CM estimators     

Geometrical characterizations of constant modulus receivers

Convergence properties of the constant modulus (CM) and the Shalvi-Weinstein (SW) algorithms in the presence of noise remain largely unknown. A new geometrical approach to the analysis of constant modulus and Shalvi-Weinstein receivers is proposed by considering a special constrained optimization involving norms of the combined channel-receiver response. This approach provides a unified framework within which various blind and (nonblind) Wiener receivers can all be analyzed by circumscribing an ellipsoid by norm balls of different types, A necessary and sufficient condition for the equivalence among constant modulus. Shalvi-Weinstein, zero forcing, and Wiener receivers are obtained. Answers to open questions with regard to CM and SW receivers, including their locations and their relationship with Wiener receivers, are provided for the special orthogonal channel and the general two-dimensional (2-D) channel-receiver impulse response. It is also shown that in two dimensions, each CM or SW receiver is associated with one and only one Wiener receiver     

含软方向判决的修正CMA盲均衡新算法

提出了一种新颖的盲均衡算法MCMA SDD,它一方面在代价函数中同时包含了幅度和相位的信息,另一方面,增加了并行的软方向判决(SDD)盲均衡算法,使得MCMA SDD算法无需载波跟踪环就能够纠正相位的失真;在低信噪比条件下具有较快的收敛速度和较低的稳态均方误差。     

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.     

基于二维恒模算法的直达波提纯技术

为了有效提取被多径杂波污染的直达波信号,采用了二维恒模盲均衡算法。该算法采用多天线多通道接收直达波信号,并综合利用接收信号的空域和时域信息。进一步采用变步长方法提高了算法的收敛速度,获得了较好的提纯效果。实验结果表明,改进的方法能较好地提纯被多径杂波污染的直达波信号,更具优越性。     

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     

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