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

Developing an Enhanced Adaptive Antenna Beamforming Algorithm for Telecommunication Applications

As a key enabler for advanced wireless communication technologies, smart antennas have become an intense field of study. Smart antennas use adaptive beamforming algorithms which allow the antenna system to search for specific signals even in a background of noise and interference. Beamforming is a signal processing technique used to shape the antenna array pattern according to prescribed criteria. In this thesis, a comparative study is presented for various adaptive antenna beamforming algorithms. Least mean square (LMS), normalized least mean square (NLMS), recursive least square (RLS), and sample matrix inversion (SMI) algorithms are studied and analyzed. The study also considers some possible adaptive filter combinations and variations, such as: LMS with SMI weights initialization, and combined NLMS filters with a variable mixing parameter. Furthermore, a new adaptive variable step-size normalized least mean square (VSS-NLMS) algorithm is proposed. Sparse adaptive algorithms, are also studied and analyzed, and two-channel estimations sparse algorithms are applied to an adaptive beamformer, namely: proportionate normalized least-mean-square (PNLMS), and lp norm PNLMS (LP-PNLMS) algorithms. Moreover, a variable step size has been applied to both of these algorithms for improved performance. These algorithms are simulated for antenna arrays with different geometries and sizes, and results are discussed in terms of their convergence speed, max side lobe level (SLL), null depths, steady-state error, and sensitivity to noise. Simulation results confirm the superiority of the proposed VSS-NLMS algorithms over the standard NLMS without the need of using combined filters. Results also show an improved performance for the sparse algorithms after applying the proposed variable step size

Distributed power control over interference channels using ACK/NACK feedback

In this work, we consider a network composed of several single-antenna transmitter-receiver pairs in which each pair aims at selfishly minimizing the power required to achieve a given signal-to-interference-plus-noise ratio. This is obtained modeling the transmitter-receiver pairs as rational agents that engage in a non-cooperative game. Capitalizing on the well-known results on the existence and structure of the generalized Nash equilibrium (GNE) point of the underlying game, a low complexity, iterative and distributed algorithm is derived to let each terminal reach the GNE using only a limited feedback in the form of link-layer acknowledgement (ACK) or negative acknowledgement (NACK). Numerical results are used to prove that the proposed solution is able to achieve convergence in a scalable and adaptive manner under different operating conditions.Comment: 5 pages, 6 figures, IEEE Global Communications Conference (GLOBECOM), Austin, Texas, Dec. 201

Sparse Signal Processing Concepts for Efficient 5G System Design

As it becomes increasingly apparent that 4G will not be able to meet the emerging demands of future mobile communication systems, the question what could make up a 5G system, what are the crucial challenges and what are the key drivers is part of intensive, ongoing discussions. Partly due to the advent of compressive sensing, methods that can optimally exploit sparsity in signals have received tremendous attention in recent years. In this paper we will describe a variety of scenarios in which signal sparsity arises naturally in 5G wireless systems. Signal sparsity and the associated rich collection of tools and algorithms will thus be a viable source for innovation in 5G wireless system design. We will discribe applications of this sparse signal processing paradigm in MIMO random access, cloud radio access networks, compressive channel-source network coding, and embedded security. We will also emphasize important open problem that may arise in 5G system design, for which sparsity will potentially play a key role in their solution.Comment: 18 pages, 5 figures, accepted for publication in IEEE Acces