## 1. Introduction

### 1.1. Low Frequency Array Interference Mitigation

[2] The Low Frequency Array (LOFAR) is a next generation radio telescope which is currently being designed and which will be located in the Netherlands. LOFAR [*Bregman*, 2000] is an aperture array telescope [*Thompson et al.*, 1986; *Raimond and Genee*, 1996] and will consist of order 100 telescopes (stations), spread in spirals over an area of about 360 km, as well as in a more densely occupied central core. The observational frequency window will lie in the 10–250 MHz range. Each of the stations will consist of order 100 phased array antennae. These antennae are sky noise limited, and are combined in such a way that station beams can be formed for each of the desired station observing directions or pointings. The preliminary LOFAR design defines multiple beam capabilities, (noncontiguous) 4 MHz wide bands, and a frequency resolution of 1 kHz. The LOFAR initial operations phase is scheduled to start in 2006; the target date to have LOFAR fully operational is 2008.

[3] For testing and demonstration purposes, several prototype stations are defined. One of these demonstrators is the initial test station (ITS). It is a full-scale prototype of a LOFAR station, and it became operational in December 2003. ITS consists of 60 sky noise limited dipoles, configured in a five-armed spiral, connected to a digital receiver back end. ITS operates in the frequency band 10–40 MHz, and the observed signals are directly digitized without the use of mixers. The data can be stored either as time series or as covariance matrices.

[4] In spectrum bands which are occupied with man-made radio signals with moderate signal powers, the unwanted man-made radio signals can be suppressed by applying filtering techniques. In this paper we demonstrate spatial filtering capabilities at the LOFAR ITS test station, and relate it to the LOFAR radio frequency interference (RFI) mitigation strategy [*Boonstra*, 2002]. We show the effect of these spatial filters by applying them to antenna covariance matrices, and by applying different beam-forming scenarios. We show that for moderate-intensity interferers (electric field strength ≤ 0 dBμVm^{−1}), the strongest observed astronomical sky sources can be recovered by spatial filtering. We also show that, under certain conditions, intermodulation products of point-like interfering sources remain point sources. This means that intermodulation product filtering can be done in the same way as for “direct” interference. We further discuss some of the ITS system properties such as cross talk and sky noise limited observations. Finally, we demonstrate the use of several beam former types for ITS.

### 1.2. Notation

[5] In this paper, scalars are denoted by nonbold lowercase and uppercase letters. Vectors are represented by bold lowercase letters, and matrices by uppercase bold letters. The hermitian conjugate transpose is denoted by (.)^{H}, the transpose operator by (.)^{t}, the expected value by ℰ{.}, and the estimated values by . The element-wise multiplication (Hadamard) matrix operator is denoted by ⊙. For a vector **a** = (*a*_{1}, ⋯, *a*_{p})^{t}, *e*^{a} is defined by *e*^{a} = ()^{t}. **I** represents the identity matrix, **A**^{−1} denotes the matrix inverse of **A**, and **A** denotes the matrix **B** such that **B**^{2} = **A**. Finally, = , **0** is the null matrix, the complex conjugate is denoted by , and diag(**a**) converts the vector **a** to a diagonal matrix with **a** on the main diagonal.