KELVIN LAZARUS et al: ADAPTIVE BEAMFORMING ALGORITHM BASED ON A SIMULATED KALMAN . . DOI 10.5013/IJSSST.a.17.04.10 10.1 ISSN: 1473-804x online, 1473-8031 print Adaptive Beamforming Algorithm based on a Simulated Kalman Filter Kelvin Lazarus 1 , Nurul H. Noordin 2 , Mohd Falfazli Mat Jusof 3 , Zuwairie Ibrahim 4 Faculty of Electrical and Electronics Engineering Universiti Malaysia Pahang 26600 Pahang, Malaysia 1 kelvin.lazarus@outlook.com 2,3,4 (hazlina, zuwairie)@ump.edu.my Khairul Hamimah Abas Faculty of Electrical Engineering Universiti Teknologi Malaysia UTM Johor Bahru 81310 Johor, Malaysia khairulhamimah@utm.my Abstract - A new population-based metaheuristic optimization algorithm named Simulated Kalman Filter (SKF) is proposed as an adaptive beamforming algorithm for adaptive array antenna. SKF optimization algorithm is inspired by the estimation capabilities of Kalman Filter. Each agent in the population of SKF acts as one Kalman Filter where it finds the solution using standard Kalman Filter framework. SKF consists of simulated measurement process and a best-so-far solution as a reference. SKF estimates the weights of individual elements in an array which maximizes the signal to interference plus noise ratio (SINR). SKF is also compared with Adaptive Mutated Boolean Particle Swarm Optimization (AMBPSO) from existing work and is proven to be better. Keywords - Adaptive Beamforming; Simulated Kalman Filter I. INTRODUCTION Signal environments such as wireless cellular communication system involves time-varying signal propagation environment where the user and interferers move around with time. Adaptive beamforming is used to continuously adapt with the changing electromagnetic environment by continuously adjusting the weights of individual elements in an array. In adaptive beamforming techniques, the main beam must be pointed towards the direction of the desired signal and nulling the interference at the same time. To date, there are a number of optimization algorithms that were applied in adaptive beamforming [1]–[13]. These algorithms are used to find the optimum weights so as to steer the main beam towards the signal of interest (SOI) and null the interference to maximize the signal to interference plus noise ratio (SINR) value. In this paper, a new metaheuristic optimization algorithm named Simulated Kalman Filter (SKF) [14] is proposed for adaptive beamforming application. The SKF, introduced by Ibrahim et at., was inspired by the estimation capabilities of Kalman Filter and has already been applied in various optimization problem [15]–[19]. SKF is used to estimate weights of individual elements in an array which gives maximum signal to interference plus noise ratio (SINR) value. II. SYSTEM MODEL Assuming an array antenna of M elements and N number of interfering signal with signal of interest (SOI) of kth time sample, s(k), arriving at angle θ 0 , and signal not of interest (SNOI), i 1 (k), i 2 (k), i 3 (k), …, i N-1 (k), i N (k), arriving at angle θ 1 , θ 2 , θ 3 , …, θ N-1 , θ N , as shown in Fig. 1 [20]. The array output, y(k) can be represented by ݕሺሻ ൌ ݓഥ ு ݔ∙̅ ሺሻ (1) where ݓstands for weights for individual elements, ܪfor Hermitian transpose and ݔ̅ሺሻ stands for the signal vector. The signal vector, ݔ̅ሺሻ can be formulated as ݔ̅ ሺሻ ൌ ത ଴ ݏሺሻ ൅ ሾത ଵ ത ଶ ⋯ത ே ሿ∙൦  ଵ ሺሻ  ଶ ሺሻ ⋮  ே ሺሻ ൪ ൅ ሺሻ ൌ ݔ̅ ௦ ሺሻ ൅ ݔ̅ ௜ ሺሻ ൅ തሺሻ (2) where ത ௜ stands for the ܯ-element array steering vector for ߠ ௜ direction of arrival, ݔ̅ ௦ ሺሻ is the desired signal vector, ݔ̅ ௜ ሺሻ is the interfering signal vector and തሺሻ is the noise. The total array output, ݕሺሻ is expanded as ݕሺሻ ൌ ݓഥ ு ∙ሾݔ̅ ௦ ሺሻ ൅ ݔ̅ ௜ ሺሻ ൅ തሺሻሿ ൌ ݓഥ ு ∙ሾݔ̅ ௦ ሺሻ ൅ ݑതሺሻሿ (3) where the undesired signal, ݑതሺሻ, can be formulated as ݑത ሺሻ ൌ ݔ̅ ௜ ሺሻ ൅ തሺሻ (4) Next, the array correlation matrices are calculated for both desired signal,  ത ௦௦ and undesired signal  ത ௨௨ . The weighted array output power for desired signal is given as follows ߪ ௦ ଶ ൌ ܧሾ|ݓഥ ு ݔ∙̅ ௦ | ଶ ሿൌ ݓഥ ு ∙ ത ௦௦ ݓ∙ഥ (5) where the signal correlation matrix,  ത ௦௦ , can be formulated as