Concurrent Constant Modulus Algorithm Research Articles

Low-Complexity Hybrid Adaptive Blind Equalization Algorithm for High-Order QAM Signals

It is well known that the constant modulus algorithm (CMA) presents a large steady-state mean-square error (MSE) for high-order quadrature amplitude modulation (QAM) signals. In this paper, we propose a low-complexity hybrid adaptive blind equalization algorithm, which augments the CMA error function with a novel constellation matched error (CME) term. The most attractive advantage of the proposed algorithm is that it is computationally simpler than concurrent CMA and soft decision-directed (SDD) scheme (CMA+SDD), and modified CMA (MCMA), while the approximation of steady-state MSE of the proposed algorithm is same with CMA+SDD, and lower than MCMA. Extensive simulations demonstrate the performance of the proposed algorithm.

Space-Time Semi-Blind Equalizer for Dispersive QAM MIMO System Based on Modified Newton Method

This paper proposes a space-time semi-blind equalizer (ST-SBE) for dispersive multiple-input multiple-output (MIMO) communication systems that employ high throughput quadrature amplitude modulation (QAM) signals. A novel cost function (CF) that integrates multimodulus algorithm (MMA) with soft decision-directed (SDD) scheme is established to efficiently obtain the weight vector associated with the ST-SBE. In the ST-SBE, a very short training sequence is used to provide a rough initial least squares estimate of the weight vector. An efficient modified Newton method (MNM) for minimizing the established cost function is proposed to fast search the optimal weight vector. Very interestingly, we prove that the proposed MNM has the same quadratic order of convergence as Newton methods. In addition, the proposed MNM has much lower computational complexity than Newton methods. Simulation results are provided to demonstrate that the ST-SBE has better performances than the gradient-Newton (GN)-based concurrent constant modulus algorithm (CMA) with SDD scheme (GN-CMA+SDD).

Semi-blind adaptive beamforming for high-throughput quadrature amplitude modulation systems

A semi-blind adaptive beamforming scheme is proposed for wireless systems that employ high-throughput quadrature amplitude modulation signalling. A minimum number of training symbols, equal to the number of receiver antenna array's elements, are first utilised to provide a rough initial least squares estimate of the beamformer's weight vector. A concurrent constant modulus algorithm and soft decision-directed scheme is then applied to adapt the beamformer. This semi-blind adaptive beamforming scheme is capable of converging fast to the minimum mean-square-error beamforming solution, as demonstrated in our simulation study.

New Concurrent Fractionally-Spaced Blind Equalization

The paper proposes a concurrent constant modulus algorithm (CMA) and decision-directed (DD) scheme for fractionally-spaced blind equalization. The proposed algorithm makes full use of the advantages of CMA and DD algorithm. A novel rule to control the adjustment of DD’s tap weights vector is proposed which avoids the hard switch between CMA and DD in practice. Simulations with underwater acoustic channels are used to compare the proposed algorithm with the famous CMA. And the simulation results show that the proposed algorithm has faster convergence rate and lower steady state mean square error.

Fuzzy-logic tuned constant modulus algorithm and soft decision-directed scheme for blind equalisation

This contribution revisits blind equalisation for high-order quadrature amplitude modulation systems using a low-complexity high-performance concurrent constant modulus algorithm (CMA) and soft decision-directed (SDD) scheme. A fuzzy-logic (FL) tuning unit is designed to adjust the step size of the CMA, and the potential benefits of using this adaptive step size approach are investigated. Simulation results obtained confirm that faster convergence can be achieved with this FL assisted CMA and SDD scheme, compared with the previous constant step-size CMA and SDD scheme. Quantitatively, the former requires several thousands fewer samples to converge to the same steady-state solution achieved by the latter.

Semi‐blind fast equalization of QAM channels using concurrent gradient‐Newton CMA and soft decision‐directed scheme

AbstractThis contribution considers semi‐blind adaptive equalization for communication systems that employ high‐throughput quadrature amplitude modulation signalling. A minimum number of training symbols, approximately equal to the dimension of the equalizer, are first utilized to provide a rough initial least‐squares estimate of the equalizer's weight vector. A novel gradient‐Newton concurrent constant modulus algorithm and soft decision‐directed scheme are then applied to adapt the equalizer. The proposed semi‐blind adaptive algorithm is capable of converging fast and accurately to the optimal minimum mean‐square error equalization solution. Simulation results obtained demonstrate that the convergence speed of this semi‐blind adaptive algorithm is close to that of the training‐based recursive least‐square algorithm. Copyright © 2009 John Wiley & Sons, Ltd.

Excess MSE analysis of the concurrent constant modulus algorithm and soft decision-directed scheme for blind equalisation

The concurrent constant modulus algorithm (CMA) and soft decision-directed (SDD) scheme (CCMA+SDD) blind equalisation achieves a considerable improvement in equalisation performance over the CMA for high-order quadrature amplitude modulation (QAM) channels. Because of its concurrent adaptive filter structure and the complexity in analysing the estimation error signal, the actual steady-state performance has largely been left uninvestigated. By introducing an equivalent blind equalisation algorithm, the steady-state excess mean square error (EMSE) of the CCMA+SDD algorithm in a noise-free environment is studied. Based on the energy preservation approach, two first-order approximation closed-form solutions for the EMSE are derived for real-valued and complex-valued cases, respectively. The experimental simulation results for 16- and 64-QAMs show that the proposed steady-state theoretical EMSE results are reasonably accurate.

Modified CMA based blind multiuser equaliser with decision directed scheme

A modified constant modulus (CM) algorithm based blind multiuser equaliser with a decision directed (DD) scheme is developed that does not require any mutual decorrelation and is suitable for downlink direct sequence code division multiple access systems. The performance of the proposed time domain adaptive equaliser is evaluated with respect to usual parameters and is found to perform better than the concurrent CM algorithm and DD scheme.

Fractionally spaced blind equalization with low‐complexity concurrent constant modulus algorithm and soft decision‐directed scheme

AbstractThe paper proposes a low‐complexity concurrent constant modulus algorithm (CMA) and soft decision‐directed (SDD) scheme for fractionally spaced blind equalization of high‐order quadrature amplitude modulation channels. We compare our proposed blind equalizer with the recently introduced state‐of‐art concurrent CMA and decision‐directed (DD) scheme. The proposed CMA+SDD blind equalizer is shown to have simpler computational complexity per weight update, faster convergence speed, and slightly improved steady‐state equalization performance, compared with the existing CMA+DD blind equalizer. Copyright © 2004 John Wiley & Sons, Ltd.

A comparative study of two blind FIR equalizers

The paper investigates blind finite-impulse-response (FIR) equalization schemes for quadrature amplitude modulation signalling. We compare a bootstrap maximum a posteriori probability (MAP) equalizer with a recently introduced concurrent constant modulus algorithm (CMA) and decision directed (DD) equalizer (CMA+DD). Both equalizers are known to outperform the CMA considerably in the situations where carrier recovery is performed and the signal constellation is known. The concurrent CMA+DD equalizer has a complexity that is slightly more than twice of the CMA, and the bootstrap MAP equalizer has computational requirements that are only slightly more complex than the CMA. Simulation results indicate that the bootstrap MAP blind FIR equalizer has a faster convergence rate and better steady-state performance than the concurrent CMA+DD blind FIR equalizer, but tuning of the former is more complicated than the latter.

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-art low-complexity blind equalization 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 equalizer, this concurrent CMA and DD blind equalizer obtains a dramatical improvement in equalization performance over the CMA. In this paper, a new blind equalization scheme is proposed based on concurrent CMA and a novel soft decision-directed (SDD) adaptation. The proposed concurrent CMA and SDD blind equalizer has simpler computational requirements than the concurrent CMA and DD algorithm. Extensive simulation shows that it has the same steady-state equalization performance as the concurrent CMA and DD algorithm and a faster convergence speed over the latter scheme.