Heuristic Based Adaptive Step Size CLMS Algorithms for Smart Antennas

An adaptive beam former is a device, which is able to steer and modifies an array's beam pattern in order to enhance the reception of a desired signal, while simultaneously suppressing interfering signals through complex weight selection. However, the weight selection is a critical task to get the low Side Lobe Level (SLL) and Low Beam Width. One needs to have a low SLL and low beam width to reduce the antenna's energy radiation/reception ability in unintended directions. The weights can be chosen to minimize the SLL and to place nulls at certain angles. The convergence of the array output towards desired signal is also very important for a good signal processing tool of an adaptive beam former. A vast number of possible window functions are available to calculate the weights for Smart Antennas. From the analysis of many of these algorithms, it is observed that there is a compromise between HPBW and SLL. But in case of smart antennas, both of these parameters must have low values to get good performance. In our earlier work it is proposed that Complex Least Mean Square (CLMS) and Augmented Complex Least Mean Square ( ACLMS) algorithms gives low beam width and side lobe level in noisy environment. Another neural algorithm Adaptive Amplitude Non Linear Gradient Decent algorithm (AANGD) has the advantage of more number of control parameters over CLMS and ACLMS algorithms. In this paper the hybrid of CLMS and AANGD is presented and this novel hybrid algorithm has outperformed the hybrid algorithm of CLMS and ACLMS in the aspect of convergence towards the desired signal.

An adaptive beam former is a device, which is able to steer and modify an array's beam pattern in order to enhance the reception of a desired signal, while simultaneously suppressing interfering signals through complex weight selection.However, the weight selection is a critical task to get the low Side Lobe Level (SLL) and Low Beam Width.It needs to have a low SLL and low beam width to reduce the antenna's radiation/reception ability in unintended directions.The weights can be chosen to minimize the SLL and to place nulls at certain angles.A vast number of possible window functions that are available to provide the weights to be used in Smart Antennas.This paper presents various traditional windowing techniques such as Binomial, Kaiser-Bessel, Blackman, Gaussian, and so on for computing weights for adaptive beam forming and also neural based methods like, Least Mean Square (LMS), Complex LMS (CLMS) [5], and Augmented CLMS (ACLMS) [1] algorithms.This paper discusses about various observations on signal processing techniques of Smart Antennas, that compromise between SLL and beam width (Directivity), to improve the base station capacity in Cellular and Mobile Communications and also the performance analysis of CLMS and ACLMS in terms of SLL and beam width, error convergence rate.

A perspective on CLMS as a deficient length augmented CLMS: Dealing with second order noncircularity

A novel hybrid filter combining the complex least mean square (CLMS) and augmented CLMS (ACLMS) algorithms for complex domain adaptive filtering is introduced. The ACLMS has been shown to have improved performance in terms of prediction of non-circular complex data compared to that of the CLMS. By taking advantage of this along with the faster convergence of the CLMS, the hybrid filter is shown to give improved performance over both algorithms for both circular and non-circular data. Simulations on complex-valued synthetic and real world data support the effectiveness of this approach.

We examine the problem of estimating the frequency of a three-phase power system in an adaptive and low-cost manner when the voltage readings are contaminated with observational error and noise. We assume a widely-linear predictive model for the αβ complex signal of the system that is given by Clarke's transform. The system frequency is estimated using the parameters of this model. In order to estimate the model parameters while compensating for noise in both input and output of the model, we utilize the notions of total least-squares fitting and gradient-descent optimization. The outcome is an augmented gradient-descent total least-squares (AGDTLS) algorithm that has a computational complexity comparable to that of the complex least mean square (CLMS) and the augmented CLMS (ACLMS) algorithms. Simulation results demonstrate that the proposed algorithm provides significantly improved frequency estimation performance compared with CLMS and ACLMS when the measured voltages are noisy and especially in unbalanced systems.

Smart Antenna is a device that enables to steer and modify an arrays beam pattern to enhance the reception of a desired signal, while simultaneously suppressing interfering signals through complex weight selection. The weight selection process is a complex method to get low Half Power Beam Width (HPBW) and Side Lobe Level (SLL). The aim of this task is to minimize the noise and interference effects from external sources. This paper presents a Hybrid based model for Smart Antennas by combining CLMS and Augmented CLMS algorithms. Since CLMS and ACLMS models have their own pros and cons in the process of adaptive beam forming, Hybrid model results a better convergence towards desired signal, Low HPBW and low SLL in the noisy environment.KeywordsHybrid model of CLMS and ACLMSAdaptive array Adaptive beamformingSmart antennasWireless sensor networksComplex least mean square (CLMS)Augmented CLMS (ACLMS)Side lobe level (SLL)Half power beam widthError convergence rate

The Least Mean Square (LMS) algorithm has a slow convergence rate as it is dependent on the eigenvalue spread of the input correlation matrix. In this research, we solved this problem by introducing a novel adaptive filtering algorithm for complex domain signal processing based on q-derivative. The proposed algorithm is based on Wirtinger calculus and is called as q- Complex Least Mean Square (q-CLMS) algorithm. The proposed algorithm could be considered as an extension of the q-LMS algorithm for the complex domain. Transient and steady-state analyses of the proposed q-CLMS algorithm are performed and exact analytical expressions for mean analysis, mean square error (MSE), excess mean square error (EMSE), mean square deviation (MSD) and misadjustment are presented. Extensive experiments have been conducted and a good match between the simulation results and theoretical findings is reported. The proposed q-CLMS algorithm is also explored for whitening applications with satisfactory performance. A modification of the proposed q-CLMS algorithm called Enhanced q-CLMS (Eq-CLMS) is also proposed. The Eq-CLMS algorithm eliminates the need for a pre-coded value of the q-parameter thereby automatically adapting to the best value. Extensive experiments are performed on system identification and channel equalization tasks and the proposed algorithm is shown to outperform several benchmark and state-of-the-art approaches namely Complex Least Mean Square (CLMS), Normalized Complex Least Mean Square (NCLMS), Variable Step Size Complex Least Mean Square (VSS-CLMS), Complex FLMS (CFLMS) and Fractional-ordered-CLMS (FoCLMS) algorithms.

Current approaches to the mean-square analyses of the complex-least-mean-square (CLMS) and augmented CLMS (ACLMS) algorithms can be challenging due to the difficulty in diagonalising the augmented covariance matrix. By employing the recently introduced approximate uncorrelating transform (AUT), which diagonalizes the covariance and pseudocovariance matrices with a single singular value decomposition (SVD), we derive closed form expressions for both transient and steady-state mean square stability for the CLMS and ACLMS. Relationships between the degree of circularity of the input signal and the bound on the step-sizes of the CLMS and ACLMS are also established. We also show that for both CLMS and ACLMS, the steady-state misadjustment increases with the degree of non-circularity of the input signal. Simulations in the context of frequency estimation in power grid support the analyses.

Quantized augmented complex least-mean square algorithm: Derivation and performance analysis

Preliminary radio frequency (RF) field experiments were conducted to evaluate the performance of smart antenna systems for code-division multiple access (CDMA) systems. Besides conventional multipath fading problems, CDMA schemes are subject to near-far problems. The IS-95 CDMA system uses a 1/3 convolutional encoder and an interleaver to mitigate the fading problem and uses feedback power control schemes to equalize the powers of all the uplink co-channel signals. We evaluate the performance of the IS-95 standard implemented on a smart antenna system in a slow-fading environment. In particular, we evaluate the effects of imprecise power control, convolutional coding, and different beamforming techniques for a CDMA smart antenna system. Our results show that the smart antennas are not so sensitive to imperfect power control and that the optimal (Wiener) beamforming technique outperforms the simple beamforming approach. The most interesting result is that the effect of convolutional coding is not so significant for a smart antenna system than for an single antenna system. Based on our limited experimental results, we found that the 3 times bandwidth dedicated to the 1/3 convolutional encoding is better used to increase the spreading factor in a CDMA smart antenna system, leading to reduced cost and perhaps better performance.

Operating frequency is one of the most important parameters in power system. This paper proposes a new algorithm for power system frequency estimation. The algorithm is based on the Hilbert-transform phase-locked loops (HTPLL) and the complex least mean square (CLMS) method. The three-phase voltage data is input to the HTPLLs to obtain an approximate frequency estimation, and a complex voltage vector is formed using an a s -transform. By then, combining the complex voltage vector and the approximate estimate, the CLMS algorithm provides a refined frequency estimation. Simulation results of the proposed algorithm are presented and the performance of the algorithm is compared to other frequency tracking techniques.

The purpose of this note is to discuss some aspects of recently proposed fractional-order variants of complex least mean square (CLMS) and normalized least mean square (NLMS) algorithms in Shah et al. (Nonlinear Dyn. 88(2):839–858, 2017). It is observed that these algorithms do not always converge, whereas they have apparently no advantage over the CLMS and NLMS algorithms whenever they converge. Our claims are based on analytical reasoning and are supported by numerical simulations.

Real world complex-valued signals typically exhibit rotation-dependent distributions (noncircularity), and significant performance gains in learning algorithms can be obtained by accounting for information beyond the standard second-order noncircularity (impropriety). To this end, we introduce a new closed form definition of complex correntropy which is general enough to cater for both circular and noncircular distributions in complex data, and serves as a basis for a novel cost function for widely linear adaptive filtering, termed the maximum improper complex corren-tropy criterion (MICCC). A stochastic gradient adaptive filtering algorithm is developed based on the MICCC, and its standard and complementary convergence and stability analyses are conducted with respect to both the circularity of the estimation error and the kernel size in the underlying Parzen estimator. Performance advantages over the strictly linear correntropy algorithm (MCCC) and the mean square error based complex least mean square (CLMS) and augmented CLMS (ACLMS) are demonstrated through analysis and simulations.

This paper presents a simple and easy implementable Least Mean Square (LMS) type approach for frequency estimation of three phase power system in an unbalanced condition. The proposed LMS type algorithm is based on a second order recursion for the complex voltage derived from Clarke’s transformation which is proved in the paper. The proposed algorithm is real adaptive filter with real parameter (not complex) which can be efficiently implemented by DSP. In unbalanced situations, simulation experiments show the advantages and drawbacks of the proposed algorithm in comparison to Complex LMS (CLMS) and Augmented Complex LMS (ACLMS) methods. Index Terms-Frequency estimation, LMS algorithm, adaptive filter, power systems.

The adoption of smart antenna system is a promise to the solutions of the wireless communication impairments like inefficient utilization of frequency spectrum, signal fading due to multipath propagation, etc. The smart antenna works in conjunction with digital signal processor which is responsible to adjust various parameters of the system in order to phase out interference signals and to enhance reception in the desired direction(s). In this paper, an attempt is made to develop various adaptive beamforming algorithms that lead to overall improvement in the performance of the smart antennas. Three complex adaptive beamforming algorithms like Complex Least Mean Squares (CLMS) algorithm, Augmented Complex Least Mean Squares (ACLMS) algorithm, and Adaptive Nonlinear Gradient Descent (ANGD) algorithms are considered for beamforming in smart antennas. Characteristics like Half Power Beam Width (HPBW), Side Lobe Level (SLL) and Mean Square Error (MSE) convergence rate and Tracking the desired signal are considered for the evaluation of performance of the smart array. Three new hybrid algorithms are proposed using the convex hybridization. The hybrid algorithm is formed by the convex combination of any two of the three algorithms in pursuit of performance improvement. The performance of these hybrid algorithms with respect to the important array characteristics is evaluated. It is identified that each of the three hybrids is superior to its individual filters.