Ensemble Averaging and Resolution Enhancement of Digital Radar and Sonar Signals

In radar and sonar signal processing it is of interest to achieve accurate estimation of signal characteristics. Recorded pulse data have uncertainties due to emitter and receiver noise, and due to digital sampling and quantization in the receiver system. It is therefore important to quantify these effects through theory and experiment in order to construct “smart” pulse processing algorithms which minimize the uncertainties in estimated pulse shapes. Averaging reduces noise variance and thus more accurate signal estimates can be achieved. Considering a signal processing system that involves sampling, A/D-conversion, IQ-demodulation and ensemble averaging, this chapter forms a theoretical basis for the statistics of ensemble averaged signals, and summarizes the basic dependencies on bitresolution, ensemble size and signal-to-noise ratio. Repetitive signals occur in radar and sonar processing, but also in other fields such as medicine (Jane et al., 1991; Schijvenaars et al, 1994; Laguna & Sornmo, 2000) and environment monitoring (Viciani et al., 2008). Practical ensemble averaging is subject to alignment error (jitter) (Meste & Rix, 1996), but we will neglect this effect. The effective bitresolution of the system can be increased by ensemble averaging of repetitive, A/Dconverted signals, provided that the signal contains noise (Belchamber & Horlick, 1981; Ai & Guoxiang, 1991; Koeck, 2001; Skartlien & Øyehaug, 2005). Due to varying radar and sonar cross section for scattering objects, or varying antenna gain of a sweeping emitter or receiver, the pulses exhibit variation in scaling. In the case of radar or sonar, the cross section of the target may then vary from pulse to pulse, but not appreciably over the pulse width. The scanning motion of the radar antenna may also affect the pulse scaling regardless of the target model, but we can safely neglect the time variation of the scaling due to this effect. In the case of a passive sensor, the signal propagates from an unknown radar emitter to the sensor antenna, and there is no radar target involved. Only