Adaptive antenna array beamforming using a concatenation of recursive least square and least mean square algorithms

In recent years, adaptive or smart antennas have become a key component for various wireless applications, such as radar, sonar and cellular mobile communications including worldwide interoperability for microwave access (WiMAX). They lead to an increase in the detection range of radar and sonar systems, and the capacity of mobile radio communication systems. These antennas are used as spatial filters for receiving the desired signals coming from a specific direction or directions, while minimizing the reception of unwanted signals emanating from other directions.Because of its simplicity and robustness, the LMS algorithm has become one of the most popular adaptive signal processing techniques adopted in many applications, including antenna array beamforming. Over the last three decades, several improvements have been proposed to speed up the convergence of the LMS algorithm. These include the normalized-LMS (NLMS), variable-length LMS algorithm, transform domain algorithms, and more recently the constrained-stability LMS (CSLMS) algorithm and modified robust variable step size LMS (MRVSS) algorithm. Yet another approach for attempting to speed up the convergence of the LMS algorithm without having to sacrifice too much of its error floor performance, is through the use of a variable step size LMS (VSSLMS) algorithm. All the published VSSLMS algorithms make use of an initial large adaptation step size to speed up the convergence. Upon approaching the steady state, smaller step sizes are then introduced to decrease the level of adjustment, hence maintaining a lower error floor. This convergence improvement of the LMS algorithm increases its complexity from 2N in the case of LMS algorithm to 9N in the case of the MRVSS algorithm, where N is the number of array elements.An alternative to the LMS algorithm is the RLS algorithm. Although higher complexity is required for the RLS algorithm compared to the LMS algorithm, it can achieve faster convergence, thus, better performance compared to the LMS algorithm. There are also improvements that have been made to the RLS algorithm families to enhance tracking ability as well as stability. Examples are, the adaptive forgetting factor RLS algorithm (AFF-RLS), variable forgetting factor RLS (VFFRLS) and the extended recursive least squares (EX-KRLS) algorithm. The multiplication complexity of VFFRLS, AFF-RLS and EX-KRLS algorithms are 2.5N2 + 3N + 20 , 9N2 + 7N , and 15N3 + 7N2 + 2N + 4 respectively, while the RLS algorithm requires 2.5N2 + 3N .All the above well known algorithms require an accurate reference signal for their proper operation. In some cases, several additional operating parameters should be specified. For example, MRVSS needs twelve predefined parameters. As a result, its performance highly depends on the input signal.In this study, two adaptive beamforming algorithms have been proposed. They are called recursive least square - least mean square (RLMS) algorithm, and least mean square - least mean square (LLMS) algorithm. These algorithms have been proposed for meeting future beamforming requirements, such as very high convergence rate, robust to noise and flexible modes of operation. The RLMS algorithm makes use of two individual algorithm stages, based on the RLS and LMS algorithms, connected in tandem via an array image vector. On the other hand, the LLMS algorithm is a simpler version of the RLMS algorithm. It makes use of two LMS algorithm stages instead of the RLS – LMS combination as used in the RLMS algorithm.Unlike other adaptive beamforming algorithms, for both of these algorithms, the error signal of the second algorithm stage is fed back and combined with the error signal of the first algorithm stage to form an overall error signal for use update the tap weights of the first algorithm stage.Upon convergence, usually after few iterations, the proposed algorithms can be switched to the self-referencing mode. In this mode, the entire algorithm outputs are swapped, replacing their reference signals. In moving target applications, the array image vector, F, should also be updated to the new position. This scenario is also studied for both proposed algorithms. A simple and effective method for calculate the required array image vector is also proposed. Moreover, since the RLMS and the LLMS algorithms employ the array image vector in their operation, they can be used to generate fixed beams by pre-setting the values of the array image vector to the specified direction.The convergence of RLMS and LLMS algorithms is analyzed for two different operation modes; namely with external reference or self-referencing. Array image vector calculations, ranges of step sizes values for stable operation, fixed beam generation, and fixed-point arithmetic have also been studied in this thesis. All of these analyses have been confirmed by computer simulations for different signal conditions. Computer simulation results show that both proposed algorithms are superior in convergence performances to the algorithms, such as the CSLMS, MRVSS, LMS, VFFRLS and RLS algorithms, and are quite insensitive to variations in input SNR and the actual step size values used. Furthermore, RLMS and LLMS algorithms remain stable even when their reference signals are corrupted by additive white Gaussian noise (AWGN). In addition, they are robust when operating in the presence of Rayleigh fading. Finally, the fidelity of the signal at the output of the proposed algorithms beamformers is demonstrated by means of the resultant values of error vector magnitude (EVM), and scatter plots. It is also shown that, the implementation of an eight element uniform linear array using the proposed algorithms with a wordlength of nine bits is sufficient to achieve performance close to that provided by full precision

Adaptive array beam forming using a combined RLS-LMS algorithm

A new adaptive algorithm, called RLMS, which combines the use of recursive least square (RLS) and least mean square (LMS), is proposed for array beam forming. The convergence of the RLMS algorithm is analyzed, in terms of mean square error, in the presence of additive white Gaussian noise. Computer simulation results show that the convergence performance of RLMS is superior to either RLS or LMS operating on its own. Furthermore, the convergence of RLMS is quite insensitive to changes in either signal-to-noise ratio, or the initial value of the input correlation matrix for the RLS section, or the step size adopted for the LMS section

Performance of RLMS algorithm in adaptive array beam forming

This paper examines the performance of an adaptive linear array employing the new RLMS algorithm, which consists of a recursive least square (RLS) section followed by a least mean square (LMS) section. The performance measures used are output and input signal-to-interference plus noise ratios (SINR), side lobe level (SLL), and SINRo as a function of the direction of arrival of the interfering signal. Computer simulation results show that the performance of RLMS is superior to either the RLS or LMS based on these measures, particularly when operating with low input SINR

A New LLMS Algorithm for Antenna Array Beamforming

A new adaptive algorithm, called LLMS, which employs an array image factor, AI, sandwiched in between two Least Mean Square (LMS) sections, is proposed for different applications of array beamforming. The convergence of LLMS algorithm is analyzed, in terms of mean square error, in the presence of Additive White Gaussian Noise (AWGN) for two different modes of operation; namely with either an external reference or self-referencing. Unlike earlier LMS based schemes, which make use of step size adaptation to enhance their performance, the proposed algorithm derives its overall error signal by feeding back the error signal from the second LMS stage to combine with that of the first LMS section.This results in LLMS being less sensitive to variations in input signal-to-noise ratio as well as the step sizes used. Computer simulation results show that the proposed LLMS algorithm is superior in convergence performance over the conventional LMS algorithm as well some of the more recent LMS based algorithms, such as constrained-stability LMS (CSLMS), and Modified Robust Variable Step Size LMS (MRVSS) algorithms. Also, the operation of LLMS remains stable even when its reference signal is corrupted by AWGN. It is also shown that LLMS performs well in the presence of Rayleigh fading

Analysis of the RLMS Adaptive Beamforming Algorithm Implemented with Finite Precision

This paper studies the influence of the use of finite wordlength on the operation of the RLMS adaptive beamformingalgorithm. The convergence behavior of RLMS, based on the minimum mean square error (MSE), is analyzed for operation with finite precision. Computer simulation results verify that a wordlength of nine bits is sufficient for the RLMS algorithm to achieve performance close to that provided by full precision. The performance measures used include residual MSE, rate of convergence, error vector magnitude (EVM), and beam pattern. Based on all these measures, it is shown that the RLMS algorithm outperforms other earlier algorithms, such as least mean square (LMS), recursive least square (RLS), modified robust variable step size (MRVSS) and constrained stability LMS (CSLMS)

Ops Maluku : Catatan seorang prajurit di daerah konflik Ambon

xiv; 278 hal; 21 c

Probability Density Function Estimators Applied To Non-Stationary Signals

International audienceAbstract This paper studies the influence of the use of finite wordlength on the operation of the LLMS adaptive beamforming algorithm. The convergence behavior of LLMS algorithm, based on the minimum mean square error (MSE), is analyzed for operation with finite precision. Computer simulation results verify that a wordlength of eight bits is sufficient for the LLMS algorithm to achieve performance close to that provided by full precision. Based on the simulation results, it is shown that the LLMS algorithm outperforms least mean square (LMS) in addition to other earlier algorithms, such as, modified robust variable step size (MRVSS) and constrained stability LMS (CSLMS). Keywords -- LLMS algorithm, array beamforming, fixed-point arithmetc

RLMS Algorithm for Fixed or Adaptive Beamforming

Pavement design methods based on the elastic layer theory idealize the pavement structure as consisting of linear elastic layers and utilize the theory of elasticity to predict limiting stresses and strains. The assumption of elastic behavior may be valid for relatively stiff pavement materials. In unpaved roads, consisting of unbound granular bases overlying cohesive subgrades, the assumption of elastic behavior is unlikely to be valid. The behavior of such pavements under traffic stresses is markedly nonlinear. Pavement design methods based on the ultimate strength approach assume shear failure of the pavement structure at sufficiently high traffic stresses. Pavement material behavior is assumed to be plastic rather than elastic. The assumption of plastic response is more realistic for unpaved roads in which traffic stresses exceed the elastic range of the pavement materials. The determination of the ultimate wheel load that a pavement structure can sustain is the most important component of a design process based on bearing capacity theory. Existing solutions are restricted to a narrow range of material properties and are also deficient in the manner in which they determine ultimate wheel loads. General and accurate solutions for the determination of the bearing capacity of pavement structures are required. The incorporation of climatic factors in the pavement design process is another important component of design based on bearing capacity theory. Existing methods assume full saturation of the subgrade. Experience has shown that in many regions of the world full saturation rarely occurs and the assumption of full saturation leads to overdesign. There is a need to incorporate the influence of matric suction in the determination of ultimate wheel loads. A limit equilibrium solution, which can handle any combination of pavement material properties, is proposed for the determination of bearing capacity in a 2-layer pavement system. To enable the incorporation of climatic factors in the determination of ultimate wheel loads, limit equilibrium solutions are proposed for the determination of the effects of positive pore-water pressures and matric suction on bearing capacity. The solution developed for the influence of matric suction on bearing capacity is verified in the laboratory using model footing tests in homogeneous soils equilibrated under constant levels of matric suction. A simple method of testing compacted soils in the direct shear apparatus as well as a method of analyzing the test results in terms of the stress state variables is proposed. The method of testing and analysis is shown to give results which are comparable to the results of the modified direct shear test. The method is considered to be a simple and viable alternative for the characterization of shear strength of compacted unsaturated soils. Finally, a method based on bearing capacity theory is proposed for designing unpaved roads whose structure consists of a base layer overlying a subgrade. The method can handle any combination of shear strength parameters as well as constant levels of matric suction in the pavement layers