Constrained Least Mean Square Research Articles

Robust constrained cosine arctangent based adaptive filtering for feedback control in hearing aids

The striking problem of acoustic feedback remains a persistent challenge in hearing aids (HAs), imposing limitations on attainable amplification and significantly deteriorating sound quality, often manifesting as disruptive howling artifacts. With the objective of feedback mitigation, the feedback path is estimated using an adaptive filter. The constrained least mean square (CLMS) technique is commonly employed in adaptive filtering applications where it is necessary to meet specific linear constraints. However, algorithm's robustness is compromised when impulsive or non-Gaussian noise interference occurs. In lieu of this, a novel algorithm known as the robust constrained cosine arctangent (CCAT) adaptive filtering is introduced to enhance the convergence behavior. This has been formulated with the inclusion of linear constraints to the suggested cosine function integrated with the arctangent technique. This algorithm aims to address the issue of feedback cancellation in hearing aids along a set of constraints. To achieve a minimal steady-state error and expedite the convergence of the method, a novel policy that adjusts the step factor has been suggested. CCAT-VSS is a modified version of CCAT that includes a variable step size (VSS). The simulation findings demonstrate that the suggested method exhibits superior performance for misalignment, added stable gain and certain voice quality assessments.

Constrained Normalized Subband Adaptive Filter Algorithm and Its Performance Analysis

Constrained least mean square (CLMS) algorithm is the most popular constrained adaptive filtering algorithm due to its simple structure and easy implementation. However, its convergence slows down when the input signal is colored. To address this issue, this paper firstly introduces the normalized subband adaptive filter (NSAF) into the constrained filtering problem and derives a constrained NSAF (CNSAF) algorithm using the Lagrange multiplier method. Benefiting from the good decorrelation capability of the NSAF, the proposed CNSAF algorithm significantly improves the convergence performance of the CLMS algorithm under colored inputs. Then, the mean and mean-square stability of the CNSAF algorithm is analyzed, and the theoretical models to characterize the transient and steady-state mean square deviation (MSD) behaviors of the CNSAF algorithm are derived utilizing the Kronecker product property and vectorization method. Further to extend the CNSAF algorithm to the problem of sparse system identification, a sparse version of the CNSAF algorithm (S-CNSAF) is derived. Finally, the validity of the derived theoretical MSD prediction models and the superiority of the proposed algorithms are confirmed by extensive computer simulations on system identification with colored inputs.

An Improved Constrained LMS Algorithm for Fast Adaptive Beamforming Based on a Low Rank Approximation

Adaptive beamformers use data from sensor arrays to capture signal from a desired direction without any distortion, in the presence of interfering signals from other directions in a noisy environment. Most beamformers achieve this goal by minimizing their variance while applying distortionless and null constraints in the direction of the desired and interfering signals, respectively. Constrained least-mean-square (CLMS) algorithms have been developed to iteratively update the weights of such beamformers. In this brief, we propose a novel and improved CLMS beamforming algorithm based on a low rank approximation technique called the nearest Kronecker product decomposition. By decomposing the weight vector into a sequence of Kronecker products of smaller vectors, the original weight update process is converted into updates of smaller vectors. The decomposition allows us to control the trade-off between steady-state performance and faster convergence based on the rank of the beamforming system. We derive the update rules of the proposed algorithm, tabulate its computational complexity and perform simulation study to show its superiority.

Constrained Least Mean Square Algorithm with Coefficient Reusing

The constrained least mean square (CLMS) algorithm is one of the most popular online linear-equality-constrained beamforming algorithms. This paper demonstrates for the first time that it solves a deterministic minimum-disturbance optimization problem in an exact manner. Such a framework is employed to insert the coefficient reusing technique into the algorithm, engendering a new low-complexity constrained adaptive filter, designated as RC-CLMS, that trades convergence rate for asymptotic performance. A stochastic model that predicts the average evolution of adaptive weights is derived. Through simulations, the advanced reusing coefficient extension of the constrained least mean-square algorithm enhanced the asymptotic signal-to-interference-plus-noise ratio and decreased the steady-state mean output energy. Furthermore, the resulting beam pattern is analyzed with an antenna analysis tool, confirming the efficacy of the advanced algorithm in a realistic setting, when the electromagnetic coupling between the antennas is taken into account.

Constrained Least Mean M-Estimation Adaptive Filtering Algorithm

In many applications, the constrained adaptive filtering algorithm has been widely studied. The classical constrained LMS algorithm is widely used because of its low computational complexity. However, the performance of constrained LMS algorithm will degrade under correlated input or non-Gaussian noise. In order to overcome this defect, this brief proposes a constrained least mean M-estimation (CLMM) algorithm, which uses the M-estimation cost function for the constrained adaptive filter. Compared with the previous algorithms for non-Gaussian noise, such as constrained maximum correntropy criterion (CMCC) algorithm and constrained minimum error entropy (CMEE) algorithm, the proposed CLMM algorithm has lower computational complexity and better steady-state performance. In addition, the step-size range is determined by analyzing the mean square stability, which ensures the stability of the proposed CLMM algorithm. Simulation results illustrate that the proposed CLMM algorithm has better steady-state performance than previous algorithms in non-Gaussian noises with multi-peak distribution.

A Novel Beamforming Algorithm for GNSS Receivers with Dual-Polarized Sensitive Arrays in the Joint Space⁻Time-Polarization Domain.

Dual-polarized sensitive arrays (DPSAs) with the space–time-polarization adaptive processing (STPAP) technique, which employs the polarization domain as well as the space domain and time domain to filter out interferences, can cancel a larger number of wideband interferences for GNSS receivers. However, the traditional STPAP beamforming algorithm, which requires a separate adaptive filter for each GNSS satellite, will make the process computationally intensive as there are multiple GNSS satellites in the field of view (FOV). In order to overcome the shortcoming, a novel STPAP beamforming algorithm based on the minimum variance distortionless response (MVDR) criterion is proposed. Compared with the traditional STPAP beamforming algorithm, the proposed STPAP beamforming algorithm can process multiple GNSS satellites at once using only one adaptive filter, which will greatly reduce the computational complexity. Moreover, the proposed algorithm will not lead to a sharp deterioration in the output carrier-to-noise density ratio (C/N0) performance if the number of GNSS satellites processed in the same adaptive filter is proper. Furthermore, to calculate weight vector iteratively, an adaptive algorithm based on the constrained least mean square (CLMS) method is derived for the proposed STPAP beamforming algorithm. Simulation results validate that the proposed algorithm is effective in mitigating interferences for GNSS receivers in the joint space–time-polarization domain and meanwhile has lower computational complexity when maintaining the output C/N0 performance close to that of the traditional STPAP algorithm.

Logarithmic Cost Based Constrained Adaptive Filtering Algorithms for Sensor Array Beamforming

This paper introduces a novel family of constrained adaptive filtering algorithms for sensor array beamforming. These algorithms, namely, constrained least mean logarithmic square (CLMLS), $\ell _{1}$ -norm CLMLS ( $\ell _{1}$ -CLMLS) and its weighted version $\ell _{1}$ -WCLMLS, are developed based on a relative logarithmic cost function. The proposed algorithms gracefully adjust cost function depending on the amount of the error thereby achieving better performance compared to constrained least mean square (CLMS) family of algorithms. The transient and steady-state performance analysis of the proposed CLMLS algorithm is presented and these analytical results are validated through extensive simulations. Proposed CLMLS algorithm is then extended to sparse system identification problem by incorporating the $\ell _{1}$ -norm penalty into CLMLS cost function. We show that the resultant $\ell _{1}$ -CLMLS and $\ell _{1}$ -WCLMLS algorithms outperform their CLMS counterparts in sparse system identification. When applied to sparse sensor array synthesis, these algorithms achieve desired beampattern with lesser number of sensor elements compared to state-of-the-art algorithms.

MAI and Noise Constrained LMS Algorithm for MIMO CDMA Linear Equalizer

This paper presents a constrained least mean squared (LMS) algorithm for MIMO CDMA linear equalizer is presented, which is constrained on spreading sequence length, number of subscribers, variances of the Gaussian noise and the multiple access interference (MAI) plus the additive noise (introduced as a new constraint). The novelty of the proposed algorithm is that MAI and MAI plus noise variance has never been used as a constraint in MIMO CDMA systems. Convergence analysis is performed for the proposed algorithm in case when statistics of MAI and MAI plus noise are available. Simulation results are presented to compare the performance of the proposed constrained algorithm with other constrained algorithms and it is proved that the new algorithm has outperformed the existing constrained algorithms.

Performance Comparison between MAI and Noise Constrained LMS Algorithm for MIMO CDMA DFE and Linear Equalizers

This paper presents a performance comparison between a constrained least mean squared algorithm for MIMO CDMA decision feedback equalizer and linear equalizer. Both algorithms are constrained on the length of spreading sequence, number of users, variance of multiple access interference as well as additive white Gaussian noise (new constraint). An important feature of both algorithms is that multiple access interference together with noise variance is used as a constraint in MIMO CDMA linear and decision feedback equalization systems. Convergence analysis is performed for algorithm in both cases. From the simulation results shown at the end show that algorithm developed for decision feedback equalizer has outperformed the algorithm developed for linear equalizer in MIMO CDMA case

Robust Recursive Algorithm under Uncertainties via Worst-Case SINR Maximization

The performance of traditional constrained-LMS (CLMS) algorithm is known to degrade seriously in the presence of small training data size and mismatches between the assumed array response and the true array response. In this paper, we develop a robust constrained-LMS (RCLMS) algorithm based on worst-case SINR maximization. Our algorithm belongs to the class of diagonal loading techniques, in which the diagonal loading factor is obtained in a simple form and it decreases the computation cost. The updated weight vector is derived by the descent gradient method and Lagrange multiplier method. It demonstrates that our proposed recursive algorithm provides excellent robustness against signal steering vector mismatches and the small training data size and, has fast convergence rate, and makes the mean output array signal-to-interference-plus-noise ratio (SINR) consistently close to the optimal one. Some simulation results are presented to compare the performance of our robust algorithm with the traditional CLMS algorithm.

MODIFIED BAYESIAN BEAMFORMER FOR BINNING ERROR ELIMINATION

Constrained Least Mean Square (CLMS) algorithm is used to adapt the antenna array weights. CLMS in its simple form fails to capture the Signal of Interest (SOI) if there is an error in the Direction of Arrival (DOA) estimation. Moreover, it will consider the SOI as an interferer and create null in the desired DOA. The large gain will be towards the detected wrong direction. Derivative constraints and Bayesian beamformer are two techniques used to overcome such a problem. Derivative constraints destroy a lot of Degrees of Freedom (DOF). Bayesian beamformer destroys only one DOF but vulnerable to binning error. The proposed algorithm overcomes the problem of binning error in the Bayesian beamformer with only one extra DOF.

Joint Adaptive Beamforming and Perfect Power Control in Wireless Networks over Power Control Error

In this paper, we use joint perfect power control (PPC) and adaptive beamforming algorithms as constrained least mean square (CLMS) and conjugate gradient adaptive beamforming (CGBF) in a 2D urban environment. The CLMS algorithm is capable of efficiently adapting according to the environment and able to permanently maintain the chosen frequency response in the look direction while minimizing the output power of the array. In addition, with the CGBF algorithm, the desired users' signal in an arbitrary path is passed and the inter-path interference (IPI) is canceled in other paths in each RAKE finger. The adaptability of the algorithms is closely observed for uniformly spaced linear array. In addition, in this paper, we present switched-beam (SB) technique. In the SB technique by using a number of fixed, independent, or directional antennas we increase the uplink capacity of the wireless systems. Also, we study an analytical approach for the evaluation of the impact of power control error (PCE) on wireless communication systems. Simulation results indicate that the SB technique is able to considerably increase the signal to interference plus noise ratio (SINR) of desired user in comparison with other algorithms. In addition, we observe that the SINR in the CLMS algorithm is lower than the CGBF algorithm. Finally, we discuss two parameters of the PCE and path-loss exponent and their effects on capacity of the system via some computer.

Joint adaptive beamforming and perfect power control in wireless networks over power control error

In this paper, we use joint perfect power control (PPC) and adaptive beamforming algorithms as constrained least mean square (CLMS) and conjugate gradient adaptive beamforming (CGBF) in a 2D urban environment. The CLMS algorithm is capable of efficiently adapting according to the environment and able to permanently maintain the chosen frequency response in the look direction while minimizing the output power of the array. In addition, with the CGBF algorithm, the desired users’ signal in an arbitrary path is passed and the inter-path interference (IPI) is canceled in other paths in each RAKE finger. The adaptability of the algorithms is closely observed for uniformly spaced linear array. In addition, in this paper, we present switched-beam (SB) technique. In the SB technique by using a number of fixed, independent, or directional antennas we increase the uplink capacity of the wireless systems. Also, we study an analytical approach for the evaluation of the impact of power control error (PCE) on wireless communication systems. Simulation results indicate that the SB technique is able to considerably increase the signal to interference plus noise ratio (SINR) of desired user in comparison with other algorithms. In addition, we observe that the SINR in the CLMS algorithm is lower than the CGBF algorithm. Finally, we discuss two parameters of the PCE and path-loss exponent and their effects on capacity of the system via some computer. Keywords: Adaptive beamforming, Power control, Wireless networks

Tracking Mobile User through Adaptive Beamforming for Wireless Cellular Networks in a 2D Urban Environment

The interference reduction capability of array antennas and the power control (PC) algorithms have been considered separately as means to increase the capacity in wireless communication networks. The capability of the smart antenna systems to track the user with the main lobe and interference with the nulls creates a significant impact on the current and future wireless sensor networks. In this paper, we use constrained least mean square (CLMS) and conjugate gradient adaptive beam-forming (CGBF) algorithms for narrowband adaptive beam-forming for tracking mobile user in a 2D urban environment without using PC algorithm. The CLMS algorithm is capable of efficiently adapting according to the environment and able to permanently maintain the chosen frequency response in the look direction while minimizing the output power of the array. In addition, with the CGBF algorithm, the desired users' signal in an arbitrary path is passed and the inter-path interference (IPI) is canceled in other paths in each RAKE finger. The adaptability of the algorithms is closely observed for uniformly spaced linear array. Also in this paper, we present switched-beam (SB) technique. In the SB technique by using a number of fixed, independent, or directional antennas we increase the uplink capacity of the wireless systems. Simulation results indicate that the SB technique is able to considerably increase the signal to interference plus noise ratio (SINR) of mobile user in comparison with other algorithms. In addition, we observe that the SINR in the CLMS algorithm is lower than the CGBF algorithm. Finally, we discuss perfect power control and path loss parameter in urban environments and their effects on system capacity by simulations.

Tracking mobile user through adaptive beamforming for wireless cellular networks in a 2D urban environment

The interference reduction capability of array antennas and the power control (PC) algorithms have been considered separately as means to increase the capacity in wireless communication networks. The capability of the smart antenna systems to track the user with the main lobe and interference with the nulls creates a significant impact on the current and future wireless sensor networks. In this paper, we use constrained least mean square (CLMS) and conjugate gradient adaptive beam-forming (CGBF) algorithms for narrowband adaptive beam-forming for tracking mobile user in a 2D urban environment without using PC algorithm. The CLMS algorithm is capable of efficiently adapting according to the environment and able to permanently maintain the chosen frequency response in the look direction while minimizing the output power of the array. In addition, with the CGBF algorithm, the desired users’ signal in an arbitrary path is passed and the inter-path interference (IPI) is canceled in other paths in each RAKE finger. The adaptability of the algorithms is closely observed for uniformly spaced linear array. Also in this paper, we present switched-beam (SB) technique. In the SB technique by using a number of fixed, independent, or directional antennas we increase the uplink capacity of the wireless systems. Simulation results indicate that the SB technique is able to considerably increase the signal to interference plus noise ratio (SINR) of mobile user in comparison with other algorithms. In addition, we observe that the SINR in the CLMS algorithm is lower than the CGBF algorithm. Finally, we discuss perfect power control and path loss parameter in urban environments and their effects on system capacity by simulations. Keywords: Antenna, Switched-beam, Power control, Urban signal propagation simulator, Wireless cellular network.

DS-CDMA Cellular Systems Performance with Base Station Assignment, Power Control Error and Beamforming over Multipath Fading

The interference reduction capability of antenna arrays, base station assignment and the power control algorithms have been considered separately as means to increase the capacity in wireless communication networks. In this paper, we propose base station assignment method based on minimizing the transmitter power (BSA-MTP) technique in a direct sequence-code division multiple access (DS-CDMA) receiver in the presence of frequency-selective Rayleigh fading and power control error (PCE). This receiver consists of constrained least mean squared (CLMS) algorithm, matched filter (MF), and maximal ratio combining (MRC) in three stages. Also, we present switched-beam (SB) technique in the first stage of the RAKE receiver for enhancing signal to interference plus noise ratio (SINR) in DS-CDMA cellular systems. The simulation results indicate that BSA-MTP technique can significantly improve the network bit error rate (BER) in comparison with the conventional case. Finally, we discuss on three parameters of the PCE, number of resolvable paths, and channel propagation conditions (path-loss exponent and shadowing) and their effects on capacity of the system via some computer simulations.

Interference Management for DS-CDMA Systems through Closed-Loop Power Control, Base Station Assignment, and Beamforming

In this paper, we propose a smart step closed-loop power control (SSPC) algorithm and a base station assignment method based on minimizing the transmitter power (BSA-MTP) technique in a direct sequence-code division multiple access (DS-CDMA) receiver with frequency-selective Rayleigh fading. This receiver consists of three stages. In the first stage, with constrained least mean squared (CLMS) algorithm, the desired users’ signal in an arbitrary path is passed and the inter-path interference (IPI) is reduced in other paths in each RAKE finger. Also in this stage, the multiple access interference (MAI) from other users is reduced. Thus, the matched filter (MF) can use for more reduction of the IPI and MAI in each RAKE finger in the second stage. Also in the third stage, the output signals from the matched filters are combined according to the conventional maximal ratio combining (MRC) principle and then are fed into the decision circuit of the desired user. The simulation results indicate that the SSPC algorithm and the BSA-MTP technique can significantly reduce the network bit error rate (BER) compared to the other methods. Also, we observe that significant savings in total transmit power (TTP) are possible with our methods.

Joint Closed-Loop Power Control and Adaptive Beamforming for Wireless Networks with Antenna Arrays in a 2D Urban Environment

The interference reduction capability of antenna arrays and the power control algorithms have been considered separately as means to decrease the interference in wireless communication networks. In this paper, we propose smart step closed-loop power control (SSPC) algorithm in wireless networks in a 2D urban environment with constrained least mean squared (CLMS) algorithm. This algorithm is capable of efficiently adapting according to the environment and able to permanently maintain the chosen frequency response in the look direction while minimizing the output power of the array. Also, we present switched-beam (SB) technique for enhancing signal to interference plus noise ratio (SINR) in wireless networks. Also, we study an analytical approach for the evaluation of the impact of power control error (PCE) on wireless networks in a 2D urban environment. The simulation results indicate that the convergence speed of the SSPC algorithm is faster than other algorithms. Also, we observe that significant saving in total transmit power (TTP) are possible with our proposed algorithm. Finally, we discuss three parameters of the PCE, number of antenna elements, and path-loss exponent and their effects on capacity of the system via some computer simulations.

On the equivalence of RLS implementations of LCMV and GSC processors

This letter compares the transients of the constrained recursive least squares (CRLS) algorithm with the generalized sidelobe canceler (GSC) employing the recursive least squares (RLS) algorithm. We prove that the two adaptive implementations are equivalent everywhere regardless of the blocking matrix chosen. This guarantees that algorithm tuning is not affected by the blocking matrix. This result differs from the more restrictive case for transient equivalence of the constrained least mean-square (CLMS) algorithm and the GSC employing the least mean square (LMS) algorithm, for in this case the blocking matrix needs to be unitary.

A constrained asymmetry LMS algorithm for PRML disk drive read channels

We present an implementation of a constrained least mean square (C-LMS) algorithm with application to high-speed magnetic disk drive read channels. The main advantage offered by the presented C-LMS algorithm is improved stability of the outer timing recovery loop while the spectral shaping of read-back data is performed in the inner adaptation loop. This eliminates any unstable behavior of the timing recovery loop during C-LMS algorithm adaptation. Another benefit derived from this approach is reduction in coefficient switching gradient noise. The proposed algorithm has been implemented and fabricated in a commercial read channel using a 0.18 /spl mu/m L-effective CMOS technology. It operates at 550 MHz worst case.