In this dissertation we present a view in which the radar signals as the elements of a high dimensional signal set. The dimension is equal to... Show moreIn this dissertation we present a view in which the radar signals as the elements of a high dimensional signal set. The dimension is equal to the number of discrete samples (M) of the signal. Because the radar signals should satisfy certain conditions for good performance, most lie in much smaller subsets or subspaces. By developing appropriate lower dimensional signal spaces that approximate these areas where the radar signals live, we can realize potential advantage because of the greater parametric simplicity. In this dissertation we apply this low dimensional signal concept in radar signal processing. In particular we focus on radar signal design and radar signal estimation. Signal design comes under radar measures and signal estimation comes under radar countermeasures.In signal design problem one searches for the signal element that has smaller sidelobes and also satisfies certain constraints such as bandwidth occupancy, AC mainlobe width, etc. The sidelobe levels are quantified by Peak Sidelobe Ratio (PSLR) and Integrated Sidelobe Ratio (ISLR). We use linear combination of these two metrics as the cost function to determine the quality of the designed signal. There is a lot of effort in designing parameterized signal sets including our proposed Asymmetric Time Exponentiated Frequency Modulated (ATEFM) signal and Odd Polynomial FrequencySignal (OPFS). Our contribution is to demonstrate that the best signal elements from these low dimensional signal sets (LDSS) mostly outperform the best signal elements that are randomly chosen from the radar signal subset with dimensionality M. Since searching the best signal element from the LDSS requires less computational resources it is prudent to search for the best signal elements from the low dimensional signal sets.In signal estimation problem we try to estimate the signal transmitted by a noncooperating radar which is intercepted by multiple passive sensors. The intercepted signals often have low SNR and there could be only few intercepted signals available for signal estimation. Predominantly used method for estimating the radar signals is Principal Component Analysis (PCA). When the SNR is low (< 0 dB) we need large number of intercepted signals to get an accurate estimates from PCA method. Our contribution is to demonstrate that by limiting the search for the best signal estimate within the low dimensional signal sets one can get more accurate estimates of the unknown transmitted signal at low SNRs with smaller number of sensors compared to PCA. Show less
