Least-squares Constant Modulus Algorithm Research Articles

Robust adaptive beamforming using modified constant modulus algorithms

Abstract This paper addresses the self-nulling phenomenon also known as the self-cancellation in adaptive beamformers. Optimum beamforming requires knowledge of the desired signal characteristics, either its statistics, its direction-of-arrival, or its response vector. Inaccuracies in the required information lead the beamformer to attenuate the desired signal as if it were interference. Self-nulling is caused by the desired signal having large power (high SNR) relative to the interference signal in case of the minimum variance distortion less response beamformer, and low power desired signal in the case of the constant modulus algorithm (CMA) beamformer, which leads the beamformer to suppress the desired signal and lock onto the interference signal. The least-square constant modulus algorithm is a prominent blind adaptive beamforming algorithm. We propose two CMA-based algorithms which exploit the constant modularity as well as power or DOA of the desired signal to avoid self-nulling in beamforming. Simulations results verify the effectiveness of the proposed algorithms.

Kaiser Window Based Blind Beamformers for Radar Application

Blind beamforming algorithms are the first choice for radar applications as they won’t use any training signal. But the major downside of constant modulus algorithm (CMA) is very low convergence rate. To overcome this problem and to make this algorithm more suitable for real-time applications, we firstly improved the convergence rate of CMA by making its step size adaptive. Then, we applied Kaiser window to improved CMA and conventional least-square CMA (LS-CMA) to suppress the sidelobe levels. These proposed algorithms are named Kaiser window-constant modulus algorithm and Kaiser window least square-constant modulus algorithm, respectively. Computer simulations validate the effectiveness of the proposed beamformers.

Efficient Blind Beamforming Algorithms for Phased Array and MIMO RADAR

In this paper, we devised two new adaptive blind beamformers based on well-known constant modulus algorithm (CMA) and least square CMA (LS-CMA). First, we improved the convergence rate of CMA and then applied Hanning window to both CMA and LS-CMA to reduce side-lobe level (SLL). These new algorithms are Hanning window CMA (HW-CMA) and Hanning window LS-CMA (HW-LS-CMA),- Simulation results show the significant improvement in the convergence rate and drastic reduction in the SLL. The proposed HW-CMA converges within less than 10 iterations and the SLLs of both algorithms are reduced below −44 dB with the improvement of 33 dB as compared to classical CMA. Hence the proposed beamformers can be used in advanced communication applications.

Doubly Constrained Robust Blind Beamforming Algorithm

We propose doubly constrained robust least-squares constant modulus algorithm (LSCMA) to solve the problem of signal steering vector mismatches via the Bayesian method and worst-case performance optimization, which is based on the mismatches between the actual and presumed steering vectors. The weight vector is iteratively updated with penalty for the worst-case signal steering vector by the partial Taylor-series expansion and Lagrange multiplier method, in which the Lagrange multipliers can be optimally derived and incorporated at each step. A theoretical analysis for our proposed algorithm in terms of complexity cost, convergence performance, and SINR performance is presented in this paper. In contrast to the linearly constrained LSCMA, the proposed algorithm provides better robustness against the signal steering vector mismatches, yields higher signal captive performance, improves greater array output SINR, and has a lower computational cost. The simulation results confirm the superiority of the proposed algorithm on beampattern control and output SINR enhancement.

Least Squares Constant Modulus Blind Adaptive Beamforming with Sparse Constraint

Beamforming with sparse constraint has shown significant performance improvement. In this letter, a least squares constant modulus blind adaptive beamforming with sparse constraint is proposed. Simulation results indicate that the proposed approach exhibits better performance than the well-known least squares constant modulus algorithm (LSCMA).

Robust Least Squares Constant Modulus Algorithm to Signal Steering Vector Mismatches

The linearly constrained least squares constant modulus algorithm (LSCMA) may suffer significant performance degradation and lack robustness in the presence of the slight mismatches between the actual and assumed signal steering vectors, which can cause the serious problem of desired signal cancellation. To account for the mismatches, we propose a doubly constrained robust LSCMA based on explicit modeling of uncertainty in the desired signal array response and data covariance matrix, which provides robustness against pointing errors and random perturbations in detector parameters. Our algorithm optimizes the worst-case performance by minimizing the output SINR while maintaining a distortionless response for the worst-case signal steering vector. The weight vector can be optimized by the partial Taylor-series expansion and Lagrange multiplier method, and the optimal value of the Lagrange multiplier is iteratively derived based on the known level of uncertainty in the signal DOA. The proposed implementation based on iterative minimization eliminates the covariance matrix inversion estimation at a comparable cost with that of the existing LSCMA. We present a theoretical analysis of our proposed algorithm in terms of convergence, SINR performance, array beampattern gain, and complexity cost in the presence of random steering vector mismatches. In contrast to the linearly constrained LSCMA, the proposed algorithm provides excellent robustness against the signal steering vector mismatches, yields improved signal capture performance, has superior performance on SINR improvement, and enhances the array system performance under random perturbations in sensor parameters. The on-line implementation and significant SINR enhancement support the practicability of the proposed algorithm. The numerical experiments have been carried out to demonstrate the superiority of the proposed algorithm on beampattern control and output SINR enhancement compared with linearly constrained LSCMA.

LSCMA Blind Adaptive Algorithm with Comparison of Optimization Capabilities for Smart Antenna Systems

In the present paper convergence characteristics of blind beam-forming algorithm Least Square Constant Modulus Algorithm (LSCMA) are analyzed. This algorithm is used with Smart antenna systems (SAS) for improving the performance of wireless communication system by optimizing the radiation pattern according to the signal environment. This can increase the coverage and capacity of a system in multipath channels by overcoming the interference and noise. The data rate can be enhanced by mitigating fading due to cancellation of multipath components. In this paper optimization capabilities of LSCMA are considered by changing of parameters. The results reveal improvement in gain and reduction in side-lobe level. The reference signal is basically a training sequence used to train the adaptive antenna array or a desired signal based upon an a priori knowledge of nature of the arriving signals. In case where a reference signal is not available one must opt to a group of optimization techniques that are blind to the exact content of the incoming signals. In this paper the comparison of optimization capabilities of LSCMA blind adaptive BFA with reference to number of antenna elements and their spacing is presented. Section II presents functioning of ABFA and the mathematical description of LSCMA. In section III simulation results using MATLAB 7.0 with reference to number of antenna elements, inter-element distance and angle of arrival (AOA) are obtained to find the optimized values. The array factor plots and LSCMA output for the same values of above parameters are presented.

Novel Scheme for Blind Multiuser Detection Using CMA Adaptive Array

This paper proposes a novel blind multiuser detection scheme using CMA (Constant Modulus Algorithm) adaptive array. In the proposed scheme, the received signal is processed in two steps. In the primary step, only one user is captured by the CMA adaptive array, and at the same time, the other users' directions of arrival (DOA) are estimated. In the secondary step, initial weight vectors are set based on the estimated DOAs, and it processes with CMAs again to capture the other users in parallel. Thus, all the users are detected exactly and recovered separately. The Least-squares CMA is applied as an optimization algorithm to improve the performance of the proposed scheme, and the performances using the proposed scheme with linear arrays and circular arrays are discussed in detail. Simulation results are presented to verify the performance of the proposed scheme.

The Linearly Constrained LSCMA for Blind Multi-user Detection

The least square constant modulus algorithm (LSCMA) is a popular constant modulus algorithm (CMA) because of its global convergence and stability. But the performance will degrade when it is affected by the problem of interference capture in the MC-CDMA system that has several constant modulus signals. In order to overcome this shortage, a linearly constrained LSCMA multiuser detection algorithm is proposed by using the spreading code of the desired user to impose linear constraint on the LSCMA. The proposed algorithm ensures the algorithm convergence to the desired user. Thus the performance of the system is improved. The simulation results demonstrate that the proposed algorithm offers faster convergence rate and provides better output signal-to-interference-plus-noise-ratio (SINR) and bit error rate (BER) performance compared with the traditional LSCMA.

Multiple Blind Beamforming Based on LSCMA

Blind beamforming plays an important role in multiple-input multiple-output (MIMO) Systems, radar, cognitive radio, and system identification. In this paper, we propose a new algorithm for multiple blind beamforming algorithm based on the least square constant modulus algorithm (LSCMA). The new method consists of the following three parts: (a) beamforming of one signal with LSCMA. (b) direction-of-arrival (DOA) estimation of the remaining signals by rooting the weight vector polynomial. (c) beamforming of the remaining signals with linear constraints minimum variance (LCMV) method. After the convergence of LSCMA, one signal is captured and the arrival angles of the remaining signals can be obtained by rooting the weight vector polynomial. Therefore, beamforming can be quickly established for the remaining signals using LCMV method. Simultaneously the DOA of the signals can also be obtained. Simulation results show the performance of the presented method.

Blind Source Separation: The Location of Local Minima in the Case of Finitely Many Samples

Cost functions used in blind source separation are often defined in terms of expectations, i.e., an infinite number of samples is assumed. An open question is whether the local minima of finite sample approximations to such cost functions are close to the minima in the infinite sample case. To answer this question, we develop a new methodology of analyzing the finite sample behavior of general blind source separation cost functions. In particular, we derive a new probabilistic analysis of the rate of convergence as a function of the number of samples and the conditioning of the mixing matrix. The method gives a connection between the number of available samples and the probability of obtaining a local minimum of the finite sample approximation within a given sphere around the local minimum of the infinite sample cost function. This shows the convergence in probability of the nearest local minima of the finite sample approximation to the local minima of the infinite sample cost function. We also answer a long-standing problem of the mean-squared error (MSE) behavior of the (finite sample) least squares constant modulus algorithm (LS-CMA), namely whether there exist LS-CMA receivers with good MSE performance. We demonstrate how the proposed techniques can be used to determine the required number of samples for LS-CMA to exceed a specified performance. The paper concludes with simulations that validate the results.

Blind multiuser detection using the subspace-based linearly constrained LSCMA

The least squares constant modulus algorithm (LSCMA) is a popular constant modulus algorithm (CMA) because of its global convergence and stability. But the performance will degrade when it is affected by the problem of interference capture in the MC-CDMA system that has several constant modulus signals. In order to overcome this shortage, a linearly constrained LSCMA multiuser detection algorithm is proposed by using the spreading code of the desired user to impose linear constraint on the LSCMA. To further enhance the performance, we project the weight vector obtained by the proposed linearly constrained LSCMA algorithm onto the signal subspace and propose a subspace-based linearly constrained LSCMA multiuser detection algorithm. The proposed algorithm ensures the algorithm convergence to the desired user and suppresses the noise subspace in the weight vector. Thus the performance of the system is improved. Moreover, to reduce the computational complexity, an improved projection approximation subspace tracking with deflation (PASTd) algorithm is proposed for adaptive signal subspace estimation. The simulation results demonstrate that the proposed algorithm achieves better output signal-to-interference-plus-noise ratio (SINR) and bit error rate (BER) performance than the traditional LSCMA algorithm, linearly constrained LSCMA algorithm and subspace-based MMSE algorithm.

The LSCM_SUB algorithm for blind multiuser detection in multipath CDMA channels

In this article, the least square constant modulus algorithm (LSCMA) is combined with the subspace approach and a LSCM_SUB (Subspace) blind adaptive multiuser detection in multipath code division multiple access (CDMA) channels is presented. The poor performance of LSCMA in the low signal to noise ratio (SNR) is improved by the LSCM_SUB algorithm. The performance of the proposed LSCM_SUB algorithm is compared with that of LSCMA. Simulation results show that the LSCM_SUB algorithm is superior to the LSCMA, especially in the low SNR.

Novel LSCM beam-forming algorithm in smart antenna MC-CDMA system

A novel Least Squares Constant Modulus (LSCM) beam-forming algorithm in smart antenna Multi-Carrier Code Division Multiple Access (MC-CDMA) system is proposed in this paper. It adaptively beam-forms the multi-carrier antenna array signal using the LSCM Algorithm (LSCMA), and in the meantime, the beam-formed signals on every sub-carrier are combined by using Orthogonal Restore Combination (ORC), Equal Gain Combination (EGC) or Maximum Ratio Combination (MRC). Then the decision of the combined signals and the spread-code of the expected user are used to re-construct the signals on every sub-carrier. At last, the difference between the re-constructed signal and the output signal of the beam-former is used to control the coefficients of the beam-former. The bit error probability of the proposed algorithm is analyzed. We simulated and compared it with the conventional LSCM beam-forming algorithm. Simulation results show that the proposed algorithm is superior to the latter in Bit Error Rate (BER).

New LSCM blind multiuser detection algorithm for antenna array CDMA system

Two blind multiuser detection algorithms for antenna array in Code Division Multiple Access (CDMA) system which apply the linearly constrained condition to the Least Squares Constant Modulus Algorithm (LSCMA) are proposed in this paper. One is the Linearly Constrained LSCMA (LC-LSCMA), the other is the Preprocessing LC-LSCMA (PLC-LSCMA). The two algorithms are compared with the conventional LSCMA. The results show that the two algorithms proposed in this paper are superior to the conventional LSCMA and the best one is PLC-LSCMA.

Successive blind multi-target adaptive antenna array and interference cancellation for DS-CDMA

An effective design of successive joint blind multi-target (MT) adaptive antenna array (AAA) and interference cancellation is presented for multi-user detection of DS-CDMA. The MT-AAA employs the adaptive block size least square-constant modulus algorithm (LS-CMA) with pre-despreading at each antenna element combined with a simple weight adaptive canceller. The combined process is repeated successively for the detection of all users without any knowledge of the channel or training sequences. It is shown to utilise the advantages of both techniques and provides improved performance in fading channel for the near-far problem, in-beam interference, and a high number of users.

Blind source separation of instantaneous MIMO systems based on the least-squares Constant Modulus Algorithm

Blind symbol detection for mobile communications systems has been widely studied and can be implemented by using either adaptive or iterative techniques. However, adaptive blind algorithms require data of sufficient length to converge. Therefore, in a rapidly changing environment, they are likely unable to track the changing channels. In such a situation, one possible solution is to use iterative blind algorithms. Iterative blind source separation algorithms based on the least-squares constant modulus algorithm (LSCMA) for instantaneous multiple-input multiple-output (MIMO) systems are proposed. Since the LSCMA cannot guarantee correct separation and hence cannot be used directly for MIMO channels, two extensions are considered: cancellation techniques (successive and parallel), and using an orthogonality constraint to ensure independence among different outputs. In common with many block iterative algorithms, it is found that for small block sizes there can be a BER flare-up effect at high SNR, although this can be removed for a sufficiently large block size. Of the proposed algorithms, simulation results show that the orthogonality-based algorithm has the best performance, and is comparable to iterative least-squares with projection (ILSP) algorithm, but offers cheaper computational complexity.

A preprocessing LS-CMA in highly corruptive environment

A fast preprocessing Least Square-Constant Modulus Algorithm (LS-CMA) is proposed for blind adaptive beamforming. This new preprocessing method precludes noise capture caused by the original LS-CMA with the preprocessing procedure controlled by the static Constant Modulus Algorithm (CMA). The simulation results have shown that the proposed fast preprocessing LS-CMA can effectively reject the co-channel interference, and quickly lock onto the constant modulus desired signal with only one snapshot in a highly corruptive environment.