QRD-based and SMI-based MVDR Beamforming for GNSS Software Receivers

L.T. Ong, B. Sarankumar

Abstract:	Due to a long propagation distance from the satellites to the receivers on earth, the GNSS satellite signals that arrive at the receivers are very weak in signal strength. Subsequently, the receivers are very susceptible to intentional and unintentional radio frequency (RF) interference signals. Therefore, techniques for interference mitigation are necessary to protect the GNSS receivers. A conventional GNSS receiver generally uses a single, nearly uniform-gain circularly-polarized antenna with a hemispherical reception pattern for receiving at least four GNSS satellites signals about a few degrees above the horizon. The single antenna approach has limitation in interference suppression. An improvement is to utilize multiple-element antenna and signal processing approach to adaptively shape the received pattern for improved RF cancellation. Though some systems may have employed multiple antenna elements for spatial nulling, this approach only rejects interference signals and does not improve the received signal strength since no beamforming of the antenna gain pattern is made. Therefore, it is desirable to beamform the antenna gain pattern to the desired satellite signals while putting nulls in the direction of the interference signals. This effectively improves the received signal-to-noise ratio (SINR) of the receiver. In this paper, beamforming algorithms for antenna-array based GNSS software receivers over multiple-interference environments are investigated. In this paper, we evaluate the performance of the classical Minimum Variance Distortionless Response (MVDR) beamformer using Sample Matrix Inversion (SMI) method and QR decomposition method. MVDR is a classical method appropriate for beamforming of the GNSS signals while mitigation of interference signals. To realize MVDR beamforming, an estimation of the covariance matrix of the interference signals is required and matrix inversion computation is performed. This algorithm is also known as sample matrix inversion (SMI). One disadvantage of SMI method is the poor numerical stability in the inversion of an ill-condition covariance matrix. The numerical stability is dependent on the arithmetic precision of an array processor. Another disadvantage is that the SMI algorithm is unsuitable to be implemented as parallel array processors. To avoid the problems of numerical instability of SMI method and to allow parallel-processors implementation for mapping into the VLSI technology, a number of algorithms can be considered. These include Gram-Schmidt, QR-based and many of their variants. The QR algorithms deal directly with the received data matrix rather than on the corresponding covariance matrix. This leads to a better conditioned problem compared to the SMI method. In this paper, the performance of MVDR-SMI and MVDR-QR beamformers for antenna-array based GNSS software receivers is investigated. To evaluate the performance of the beamformers, Monte Carlo simulations have been constructed using Mathlab Software. An 8-element uniformly circular array antenna was modeled, and multiple interference environments consisting of one to seven interference signals were considered in the simulations. At least two interference scenarios will be considered. The first scenario is to emulate a situation where the interference signals arrive only from the XZ plane of the top hemispherical of the antenna array. The second scenario is for the situation where the interference signals arrive at arbitrary angles of the top hemispherical plane. To investigate the numerical stability of the MVDR-SMI and MVDR-QR beamformers on arithmetic precision, the received signal data variables in the Matlab simulations are defined as two different data structures, 1) double-precision flotation-point data type and 2) single-precision flotation-point data type. The double precision in Matlab uses 64 bits (8 bytes) of memory storage, and accurately represents values to approximately 15 decimal places while the single precision uses 32 bits (4 bytes) of memory. Clearly, the double-precision format has a larger dynamic range than the single-precision format. The performance of the beamformers (i.e. MVDR-SMI in single precision, MVDR-SMI in double precision, MVDR-QR in single precision and MVDR-QR in double precision) will be compared in terms of the SINR improvement factor and interference cancellation capability. In addition, simulation results will be generated for various input interference-to-noise ratios and over different number of interferences. Finally, from these numerical results, 1) the impact of numerical problem, 2) the impact of word-length data structure and 3) the relationship of the INR on the SMI and QR method will be discussed.
Published in:	Proceedings of the 26th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2013) September 16 - 20, 2013 Nashville Convention Center, Nashville, Tennessee Nashville, TN
Pages:	3450 - 3455
Cite this article:	Ong, L.T., Sarankumar, B., "QRD-based and SMI-based MVDR Beamforming for GNSS Software Receivers," Proceedings of the 26th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2013), Nashville, TN, September 2013, pp. 3450-3455.
Full Paper:	ION Members/Non-Members: 1 Download Credit Sign In