GNSS multi-satellite joint acquisition with interference mitigation using antenna arrays

In this letter the antenna array based GNSS signal acquisition is proposed by firstly projecting the input signal vector onto the noise subspace which is orthogonal to interference subspace for strong interferences suppression. Then, considering that the projection matrix is rank-deficient, we propose to apply forward spatial smoothing to decorrelation of the coherent interference-free signal vector and a whitening filter to prewhitening of the spatial colored noise. Then the signal vector is fed to an adaptive multi-satellite acquisition and beamforming processor. This processor simultaneous performs adaptive beamforming and multi-satellite code acquisition by a spatial filter and a local code select filter, while the order of select filter corresponds to the number of satellites searched in a dwell cell. When the desired satellite signal is present in the test cell, the peak weight of the select filter will converge to the local code of the right satellite signal while the weights of the spatial filter will converge to the direction of arrival (DOA) estimation respectively. If not, the spatial weights will converge to zeros and the local select filter weights will be an arbitrary vector which satisfies the additional constraint, then the next cell is tested and the adaptive process is repeated. Introduction In the open literature a number of papers on code acquisition in direct-sequence code-division multiple-access (DS-CDMA) systems can be found. In [1-2] similar approaches with minimum mean squared error (MMSE) criterion are proposed combing adaptive temporal filtering and beamforming for acquisition utilizing the desired user’s local pseudo-noise (PN) code as the reference signal. In [3-4] code acquisition is all essentially accomplished using a full serial search strategy which is time-consuming. However, considering the extremely low power of GNSS signal and strong interferences situation the above scheme for beamformer and acquisition can't be guaranteed. Up to now fewer papers appeared on GNSS signal acquisition based on antenna array, in [5] a GNSS signal acquisition approach with interference mitigation based on Neyman-Pearson (NP) and generalized likelihood ratio test (GLRT) detection theory is proposed from statistical perspective and the performance is analyzed theoretically. In [6] a space-time adaptive processing (STAP) algorithm using extended Kalman filter (EKF) for code acquisition detection and interference rejection is presented. However these proposed methods for signal acquisition have a common problem of great computational complexity. This letter proposes a novel GNSS multi-satellite joint acquisition scheme using antenna array. The key point of this scheme is that it can perform multi-satellite joint acquisition and adaptive beamforming in strong interference and low signal to noise ratio (SNR) environment while the acquired satellite is distinguishable, and furthermore the computation complexity and convergence rate are acceptable. International Conference on Information Sciences, Machinery, Materials and Energy (ICISMME 2015) © 2015. The authors Published by Atlantis Press 2015 Signal Model Suppose the signal impinging on each element of the array consists of GNSS signal, interference and additive white Gaussian noise (AWGN), the complex baseband signal vector received by N antenna elements after AD convertor and digital down conversion (DDC) can be expressed as ( ) ( ) ( ) ( ) n s n i n n = + + x A B η (1) where [ ] 1, , M N M × = A a a  , [ ] 1, , L N L × = B b b  are the steering matrices of M satellites and L interference respectively. ( ) ( ) ( ) 1 1 , , T M M n s n s n ×   =   s  , ( ) ( ) ( ) 1 1 , , T L L n i n i n ×   =   i  are the waveforms of signal and interference respectively, ( ) n η is the vector of AWGN with zero mean and 2 N N σ × I variance matrix. Proposed Acquisition Scheme As can be seen in Fig.1, after projecting the baseband signal vector onto the noise subspace using subspace tracking method for interference mitigation, the signal vector is spatial correlated because the projection matrix is rank-deficient. Then through a spatial smoothing and prewhitening filter, an adaptive select weight vector C ω to combine the local PN code of P satellites ( ) n τ − c as the reference signal ( ) r n and an adaptive spatial weight vector S ω for beamforming are utilized according the minimum mean square error (MMSE) criterion. Fig. 1 Block diagram of the proposed GNSS acquisition scheme That is, we choose C ω and S ω to minimize the cost function ( ) ( ) ( ) ( ) ( ) ( ) 2 2 2 , H H C S C S J E e n E r n y n E n n τ τ       = = − = − − −             ω ω ω c ω q (2) where ( ) n q and ( ) y n are the beamformer input and output respectively. To avoid the undesired trivial solution that C S = = ω ω 0 , a constraint should be imposed on the adaptive process such as C ω is a real vector and 1 C C = ω ω . Thus the minimization of (2) turns out to be a constrained optimization problem where the Lagrange multiplier method can be applied. Through a simple mathematic derivation, the optimal solutions of the weights meet 1 , C, H S opt Q opt − = − ω R K ω (3)