Adaptive Diagonal Loading for Robust Minimum Power Distortionless Response Beamformer Sahebgowda S Patil, M Sivasankar, Venkatesha K, Dr. A Vengadarajan Electronics & Radar Development Establishment, DRDO, C. V. Raman Nagar, Bangalore-560093 sahebgowda.s.patil@lrde.drdo.in Abstract - Most of the modern radar and sonar uses adaptive beam forming to eliminate the interference. The basic requirement of the adaptive algorithm is to eliminate the interference and increase the Signal-to-Interference-plus- Noise Ratio (SINR). The efficiency of the adaptive algorithm depends on the accurate estimation of the spatial covariance matrix. Generally the data used to estimate the covariance matrix should not contain any signal of interest, if so adaptive algorithm eliminates the signal also along with the interference. Diagonal loading is one of the most widely used and effective method to improve robustness of adaptive beamformer, but selecting the diagonal loading value has become a key aspect. In the absence of complete knowledge of signal characteristics and continuously changing environment, fixed diagonal loading method may not give desired performance, hence the adaptive method is essential. In this paper we propose adaptive diagonal loading method for Minimum Power Distortionless Response beamformer (MPDR), which systematically computes the diagonal loading value based on the covariance matrix and its eigen values. Simulation results demonstrates significant performance improvement of proposed method as compared with the fixed diagonal loading method. Keywords - Spatial covariance matrix, Adaptive diagonal loading, Minimum power distortionless response beamformer. I. INTRODUCTION The basic idea behind the adaptive algorithms is to eliminate unwanted signals from the side lobe regions. The adaptive algorithms are broadly classified into three categories [1] based on computing the adaptive weights. Recursive Least Squares method and Steepest Decent method converge much slower than that of Sample Matrix Inversion method. Sample Matrix Inversion method needs to estimate the sample covariance matrix from the available data. The data used to estimate the covariance matrix should not contain the desired signal, but in practical applications it is not possible to completely eliminate the desired signal. Sufficient amount of data samples are required to estimate the spatial covariance matrix, otherwise beamformer performance degradation is expected [2] . If the data used to estimate the covariance matrix has the desired signal, then the adaptive algorithm places null in the direction of the signal of interest depending on the signal to noise ratio. Diagonal loading has proved as an effective way to improve the robustness of the optimal beamformer. But selecting the diagonal loading level is the problem of interest. Adaptive diagonal loading value has been estimated for steering vector errors by Vincent and Besson [2] , DOA mismatch and array perturbations by Jiang, Zhu and Sun [3] . The structure of the paper as follows: explanation of adaptive diagonal loading method based on covariance matrix, data model used for the simulations, simulation results and finally conclusion along with references. II. PROBLEM FORMULATION 1. Array model Consider P narrow band signal sources impinging on the array of N elements, The complex envelope of the received vector can be written as ሺݐሻൌ ܣ൫ ߠ ௣ ൯ ݏ ௣ ሺݐሻ ൅ ሺݐሻ … … … … … ሺ1ሻ where ሺݐሻൌሾ ݔ ଵ ሺݐሻ, ݔ ଶ ሺݐሻ, ݔ ଷ ሺݐሻ….. ݔ ே ሺݐሻሿ, the complex envelope of the narrowband signals ݏሺݐሻൌ ሾ ݏ ଵ ሺݐሻ, ݏ ଶ ሺݐሻ, ݏ ଷ ሺݐሻ… ݏ ௉ ሺݐሻሿ and a complex white Gaussian noise, ሺݐሻ ൌ ሾ ଵ ሺݐሻ, ଶ ሺݐሻ,  ଷ ሺݐሻ…  ே ሺݐሻሿ . ࡭ is a DOA matrix, ܣൌ ሾሺ ߠ ଴ ሻ , ሺ ߠ ଵ ሻ, ሺ ߠ ଶ ሻ… ሺ ߠ ௉ଵ ሻሿ. If we add narrow band interferences, then ሺݐሻ ൌ ሺݐሻ൅ ܫ൫ ߠ ௣ ൯ ௣ ሺݐሻ………………ሺ2ሻ Assuming that the noise is spatially and temporally uncorrelated, signals and interferences are statistically independent to each other but spatially and temporally correlated. The covariance matrix will be of the following form ൌ ߪ ଴ ଶ ሺ ߠ ଴ ሻ ு ሺ ߠ ଴ ሻ൅෍ ߪ ௜ ଶ ܫሺ ߠ ௜ ሻ ܫ ு ሺ ߠ ௜ ሻ ௉ଵ ௜ୀଵ ൅ ߪ ௡ ଶ … … ሺ3ሻ The first term in (3) corresponds to the desired signal, the other term ∑ ߪ ௜ ଶ ܫሺ ߠ ௜ ሻ ܫ ு ሺ ߠ ௜ ሻ ௉ଵ ௜ୀଵ corresponds to the interferences and ߪ ௡ ଶ is the thermal noise power. In 9th International Radar Symposium India - 2013 (IRSI - 13) NIMHANS Convention Centre, Bangalore INDIA 1 10-14 December 2013