Complex Adaptive LMS Algorithm Employing the Conjugate Gradient Principle for Channel Estimation and Equalization

Abstract

The Complex Block Least Mean Square (LMS) technique is widely used in adaptive filtering applications because of its simplicity and efficiency from a theoretical and implementation standpoint. However, the limitations of the Complex Block LMS technique are slow convergence and dependence on the proper choice of the stepsize or convergence factor. Moreover, its performance degrades significantly in time-varying environments. In this paper, a novel adaptive LMS technique named the Complex Block Conjugate LMS algorithm, CBC-LMS, is presented. Based on the Conjugate Gradient Principle, the proposed technique searches orthogonal directions to update the filter coefficients instead of the negative gradient directions used in the Complex Block LMS algorithm. In addition, the CBC-LMS algorithm derives optimal stepsizes to adjust the adaptive system coefficients at each iteration. As a result, the developed method overcomes the inherent limitations of the existing Complex Block LMS algorithm. The performance of the CBC-LMS technique is tested in wireless channel estimation and equalization applications, using both computer simulations and laboratory experiments. Furthermore, the developed technique is compared to the Complex Block LMS method and a recently proposed method, which is called Complex Optimal Block Adaptive LMS (OBA-LMS). The experimental and simulation results confirm that the proposed CBC-LMS technique achieves faster convergence with comparable accuracy and reduced computational complexity, relative to the existing techniques.

Efficient implementations of Complex Block Conjugate Gradient LMS with Individual adaptation

“…In this subsection, the computational complexities of the efficient implementations of the CBCI-LMS algorithm is studied and compared to the Complex BLMS [5] and CBC-LMS [7]- [8] techniques. The real-valued Multiplications Per Iteration (MPI) for these methods are summarized in Table 1.…”

Neural network controlled grid interfaced solar photovoltaic power generation

“…K pd and K id are the proportional and integral gain constants of the PI voltage controller. Therefore the average weight of the reference active-power component of the grid current is given as [17,18] W pavg (n) = W loss (n) + W ap (n) + W bp (n) + W cp (n) /3 (14) where W ap , W bp and W cp are the weights of the active power components of the grid currents.…”

“…Therefore the average weight of the reference active‐power component of the grid current is given as [17, 18] where W a p , W b p and W c p are the weights of the active power components of the grid currents.…”

“…In this work, the extraction of reference grid currents is carried out using LMS (least-mean square) algorithm-based on Adaline (adaptive linear element). There is an inherent linearity in the Adaline that makes it a fast technique and is able to extract the reference grid currents in varying load conditions, which is not possible in other methods [16][17][18][19]. The proposed control algorithm is an extension of the Adaline algorithm given in [17][18][19] with a good noise rejection capability and improved dynamic response as the main features compared to simple Adaline algorithms.…”

“…There is an inherent linearity in the Adaline that makes it a fast technique and is able to extract the reference grid currents in varying load conditions, which is not possible in other methods [16–19]. The proposed control algorithm is an extension of the Adaline algorithm given in [17–19] with a good noise rejection capability and improved dynamic response as the main features compared to simple Adaline algorithms. Moreover, its real time implementation is quite simple as it is based on the simple mathematical expression.…”