Low Complexity Robust Adaptive Beamformer Based On Parallel RLMS and Kalman RLMS

Abstract

To ease spectral congestion and enhance frequency reuse, researchers are targeting smart antenna systems using spatial multiplexing and adaptive signal processing techniques. Moreover, the accuracy and efficiency of such systems is highly dependent on the adaptive algorithms they employ. A popular, adaptive beamforming algorithm, widely used in smart antennas, is the Recursive Least Square (RLS) algorithm. While, the classical RLS implementation achieves high convergence, it still suffers from its inability to track the target of interest. Recently, a new adaptive algorithm called Recursive Least Square-Least Mean Square (RLMS) which employs a RLS stage followed by a Least Mean Square (LMS) algorithm stage and separated by an estimate of the array image vector, i.e. steering vector, has been proposed. RLMS outperforms previous RLS and LMS variants, with superior convergence and tracking capabilities, at the cost of a moderate increase in computational complexity. In this paper, an enhanced, low complexity parallel version of the cascade RLMS is presented by eliminating the need for computing the array image vector cascading stage. Hence, For an antenna of N elements our strategy can reduce the complexity of the system by 20N multiplications, 6N additions and 2N divisions. Moreover, a new Kalman based parallel RLMS (RKLMS) method is also proposed, where the LMS stage is replaced by a Kalman implementation of the classical LMS, and compared under low Signal to Interference plus Noise ratios (SINR). Simulation results show identical performance for the parallel RLMS, cascaded RLMS at 10dB and superior performance and robustness for the RKLMS on low SINR cases up to-10dB.

Stability Analysis of the RC-PLMS Adaptive Beamformer Using a Simple Transfer Function Approximation

“…Additionally, by removing the expectation operator, it is assumed that q k−i is the auto-correlation coefficient instead of its estimate [22] and Q(z) = q 1 z −1 +q 2 z −2 +.... is a polynomial in the z −1 field. Furthermore, from ( 10), (19) and with respect to [18,22] the RC-pLMS transfer function approximation, H r (z), becomes…”

“…Moreover, a relationship between the filter output and the desired signal can be obtained with respect to (7) and (19) as follows…”

“…Such constraints are reflected by the requirement of an accelerated convergence rate, a high precision beam pointing accuracy and a reduced complexity structure suitable for a hardware implementation [14][15][16][17]. Recently, two multi-stage adaptive beamforming algorithms have been proposed to eliminate the tradeoff between the LMS convergence speed and its steady state error [18,19]: parallel LMS (pLMS) [18], and the parallel RLMS (RLMSp) [19]. These algorithms are formed of LMS/LMS and RLS/LMS stages connected by an error feedback.…”

Self correction fractional least mean square algorithm for application in digital beamforming

“…The other modification is the variable step size least mean square (VSS-LMS) [ 16 ], which enhances convergence speed at the cost of computational complexity. Moreover alternative algorithms like the recursive least square-least mean square (RLMS) [ 17 ], least mean square-least mean square (LLMS) [ 18 ] and Kalman-based parallel RLMS algorithm [ 19 ] were introduced. These alternatives have shown enhanced convergence and stability performance compared to LMS with increased computational complexity.…”

Enhancement Cascaded Least Square of RLS and NLMS for Wireless Communication System

“…Despite using the Discrete Fourier Transform, the system generates excellent outcomes. Akkad et al, [11] introduced the use of parallel RLMS and Kalman RLMS in adaptive beamforming. RLMS is a hybrid algorithm that incorporates the capabilities of RLS and LMS.…”