Constant Modulus Algorithm Cost Function Research Articles

Convex constant modulus algorithm for PAPR reduction in MIMO-OFDM systems

ABSTRACT This paper addresses the issue of high peak-to-average power ratio (PAPR) in orthogonal frequency division multiplexing (OFDM)-based multiple-input multiple-output (MIMO) systems. A PAPR reduction technique is developed based on the cost function used in well-known iterative constant modulus algorithm (CMA). We devise a convex optimisation based solution to the CMA cost function for estimating the PAPR precoding weights. The resulting convex CMA solution not only accelerates convergence but also avoids local minima to ensure global optimality. As illustrated by the simulation results, the proposed convex CMA presents superior performance in terms of PAPR reduction with respect to existing techniques.

Blind equalization based on RLS algorithm using adaptive forgetting factor for underwater acoustic channel

Blind equalization based on adaptive forgetting factor, recursive least squares (RLS) with constant modulus algorithm (CMA), is investigated. The cost function of CMA is simplified to meet the second norm form to ensure the stability of RLS-CMA, and thus an improved RLS-CMA (RLS-SCMA) is established. To further improve its performance, a new adaptive forgetting factor RLS-SCMA (ARLS-SCMA) is proposed. In ARLS-SCMA, the forgetting factor varies with the output error of the blind equalizer during the iterative process, which leads to a faster convergence rate and a smaller steady-state error. The simulation results prove the effectiveness under the condition of the underwater acoustic channel.

Recursive Least Squares Fractionally-spaced Blind Equalization Algorithm for Underwater Acoustic Communication

Constant Modulus Algorithm (CMA), Fractionally-spaced Equalizer (FSE) and Recursive Least Squares (RLS)-CMA are investigated, and a low computational complexity RLS-CMA based on FSE with the simplified cost function of CMA (LRLS-FSE-SCMA) was proposed in this paper. To overcome the instability of RLS-CMA, the cost function of CMA is simplified to meet second norm form and an improved RLS-CMA (RLS-SCMA) is obtained. For the input signals of FSE are obtained by oversampling the received signal, the input signals of each sub-equalizer are correlative, and the autocorrelation matrixes of the input signals of each sub-equalizer are little difference. To reduce the computational complexity, we use one of the autocorrelation matrixes instead of the others in RLS-FSESCMA, and then LRLS-FSE-SCMA is obtained. The simulation results under the underwater acoustic channel condition show that LRLS-FSE-SCMA has faster convergence rate and lower steady state error compared with Stochastic Gradient Descent (SGD)-CMA and RLS-SCMA with transversal equalizer, while LRLS-FSE-SCMA has similar performance as RLS-FSE-SCMA with lower computational complexity.

Analysis and Realization on Turbo Equalization based on 64-QAM in OFDM System

With the development of the mobile communication, the related technologies have gone through a rapid growing phase from 1G to 3G, until 4G. The technology evolution targets to improve the performance of overall system, and promote the related services and applications. In this paper, author makes analysis on Turbo equalization based on M-QAM modulation in OFDM system. Since Turbo equalization is an iterative receiver algorithm repeating equalization and channel decoding to improve the performance of the receiver, there researches on Turbo codes and turbo equalization have been emphasis, especially on the error-correction during these years. Due to the operations of equalization and decoding are repeated several times in one process, the computational complexity is increased in the receiver. Author aims at the cost function of CMA (Constant Modulus Algorithm) to change or recreate a new algorithm, and then as a contrast with the error functions, we can see the advantages about this change. Finally, author makes simulations on the Turbo equalization based on 64-QAM in OFDM system. Compared with the Turbo equalization based on 16-QAM, the performance of Turbo equalization based on 64- QAM is more efficient.

Blind equalization based on T/4 fractionally spaced decision feedback equalizer with RLS algorithm

To further improve the performance of blind equalization based on T/4 fractionally spaced decision feedback equalizer, RLS algorithm is adopted to update the weights of equalizer according to simplified constant modulus algorithm (CMA) cost function. CMA cost function is simplified to meet second norm form in this work, and then the forward filter of equalizer with T/4 fractionally-spaced updates by RLS algorithm and the feedback filter of equalizer with symbol-spaced updates by gradient descent algorithm. Computer simulation results show that the algorithm proposed in this work has faster convergence rate and lower mean square error compare with blind equalization based on symbol-spaced and T/4 fractionally-spaced decision feedback equalizer based on gradient descend algorithm. DOI: http://dx.doi.org/10.11591/telkomnika.v11i6.2156 Full Text: PDF

New Concurrent Modulus Algorithm and Soft Decision Directed Scheme for Blind Equalization

Abstract The Constant Modulus Algorithm (CMA) is recognized as the most widely used algorithm in blind channel equalization practice. However, the CMA cost function exhibits local minima, which often leads to ill-convergence. This paper proposes a concurrent equalizer, in which a Soft Decision Directed (SDD) equalizer operates cooperatively with a CMA equalizer, controlled through a non-linear link that depends on the system a priory state. The simulation results show that the proposed equalizer has faster convergence rate and lower steady-state mean square error than the CMA equalizer.

Constant Modulus Algorithm with Reduced Complexity Employing DFT Domain Fast Filtering

In this paper, a novel CMA (constant modulus algorithm) algorithm employing fast convolution in the DFT (discrete Fourier transform) domain is proposed. We propose a non-linear adaptation algorithm that minimizes CMA cost function in the DFT domain. The proposed algorithm is completely new one as compared to the recently introduced similar DFT domain CMA algorithm in that, the original CMA cost function has not been changed to develop DFT domain algorithm, resulting improved convergence properties. Using the proposed approach, we can reduce the number of multiplications to O(N log 2 N), whereas the conventional CMA has the computation order of O(N2). Simulation results show that the proposed algorithm provides a comparable performance to the conventional CMA.

Fast Blind Equalization Using Complex-Valued MLP

The blind equalizers based on complex valued feedforward neural networks, for linear and nonlinear communication channels, yield better performance as compared to linear equalizers. The learning algorithms are, generally, based on stochastic gradient descent, as they are simple to implement. However, these algorithms show a slow convergence rate. In the blind equalization problem, the unavailability of the desired output signal and the presence of nonlinear activation functions make the application of recursive least squares algorithm difficult. In this letter, a new scheme using recursive least squares algorithm is proposed for blind equalization. The learning of weights of the output layer is obtained by using a modified version of constant modulus algorithm cost function. For the learning of weights of hidden layer neuron space adaptation approach is used. The proposed scheme results in faster convergence of the equalizer.

Improvement for solving the mix-up problem in constantmodulus arrays

The authors propose an efficient and computationally fast algorithm for solving the mix-up problem in complex arrays. The Lagrange multiplier theory is used in the optimisation of the constant modulus algorithm (CMA) cost function and the input data are processed in blocks. Furthermore, a simplification of the CMA cost function is proposed that leads to a robust algorithm for solving this problem. Simulations are presented to support the analysis.