Fundamentals of Signal Processing for Phased Array Radar

This section gives a short survey of the principles and the terminology of phased array radar. Beamforming, radar detection and parameter estimation are described. The concept of subarrays and monopulse estimation with arbitrary subarrays is developed. As a preparation to adaptive beam forming, which is treated in several other sections, the topic of pattern shaping by deterministic weighting is presented in more detail. 1.0 INTRODUCTION Arrays are today used for many applications and the view and terminology is quite different. We give here an introduction to the specific features of radar phased array antennas and the associated signal processing following the description of [1]. First the radar principle and the terminology is explained. Beamforming with a large number of array elements is the typical radar feature and the problems with such antennas are in other applications not known. We discuss therefore the special problems of fully filled arrays, large apertures and bandwidth. To reduce cost and space the antenna outputs are usually summed up into subarrays. Digital processing is done only with the subarray outputs. The problems of such partial analogue and digital beamforming, in particular the grating problems are discussed. This topic will be reconsidered for adaptive beamforming, space-time adaptive processing (STAP), and SAR. Radar detection, range and direction estimation is derived from statistical hypotheses testing and parameter estimation theory. The main application of this theory is the derivation of adaptive beamforming to be considered in the following lectures. In this lecture we present as an application the derivation of the monopulse estimator which is in the following lectures extended to monopulse estimators for adaptive arrays or STAP. As beamforming plays a central role in phased arrays and as a preparation to all kinds of adaptive beamforming, a detailed presentation of deterministic antenna pattern shaping and the associated channel accuracy requirements is given. 2.0 FUNDAMENTALS OF RADAR AND ARRAYS 2.1 Nomenclature The radar principle is sketched in Figure 1. A pulse of length τ is transmitted, is reflected at the target and is received again at time t0 at the radar. From this signal travelling time the range is calculated R0= ct0 /2. The process is repeated at the pulse repetition interval (PRI) T. The maximum unambiguous range is RTO-EN-SET-086bis 1 1 Nickel, U. (2007) Fundamentals of Signal Processing for Phased Array Radar. In Advanced Radar Systems, Signal and Data Processing (pp. 1-1 – 1-22). Educational Notes RTO-EN-SET-086bis, Paper 1. Neuilly-sur-Seine, France: RTO. Available from: http://www.rto.nato.int/abstracts.asp. therefore Rmax= cT /2. The ratio η= τ /T is called the duty factor. Figure 1: The principle of radar reception The received signal-to-noise power ratio (SNR) is described by the radar equation 2 0 2 2 2 4 0 1 1 (4 ) (4 ) ( ) Signal m t r noise P P G G SNR R P R kT FB L σ λ π π ⋅ ⋅ = ⋅ = ⋅ ⋅ It is the 1/R law that forces the radar designer to increase transmit or receive energy as much as possible. Fast time processing: The received pulse is filtered such that the signal energy is maximally extracted (matched filtering, pulse compression). This is achieved by convolving the received data samples zk with the transmit wave form sk, k=1..L, 1 L k r k r r y s z + = =∑ . The range resolution after pulse compression is given by ΔR ≥ cτ /2, where τ is the effective pulse length after compression. By suitable coding long transmit pulses with short length after compression and thus high range resolution can be constructed. This requires a larger bandwidth. The ratio of the pulse length before and after compression is called the compression ratio K which is the same as the time-bandwidth product, K= τ before/τafter= B τ before. Analogue waveforms like linear frequency modulation (or chirp) are used for pulse compression, or discrete codes which are switched at certain subpulses, e.g. binary codes or polyphase codes. For radar the sidelobes after pulse compression are important to avoid false targets. Also, the compressed pulse must be tolerant against Doppler frequency shifts which a typical echo of a moving target has. Slow time processing: The receiver signal energy can be increased by integrating the power from pulse to pulse. The echo of a target with certain radial velocity vR undergoes a frequency shift fD= 2vR/λ due to the Doppler effect. From pulse to pulse at PRI T we observe thus a phase shift φD= 2πfDT. Maximum energy is collected if this shift is compensated. The summation with correct phase compensation is called coherent integration, 2 1 D K j f kT k k y e y π − = =∑ . Of course, the radial velocity and hence the Doppler frequency fD is unknown and must be estimated. The integration time KT is called coherent processing interval, CPI. t r 2Rmax T t0 /2 R0 t0 2R0 Dead zone Dead zone τ Tx