In this dissertation, we have studied totally eight topics which are focused on but not limited to radar sensor networks (RSN) from a signal processing perspective. We propose the definitions of ZCZ/LCZ (Zero Correlation Zone/Low Correlation Zone) sequence-pair sets, provided three methods to construct optimized optimized punctured LCZ/ZCZ sequence-pair sets and study their properties in chapter 2 and 3. We further investigate the waveform design problem for radar system, radar sensor network, sonar sensor network and MIMO radar system from chapter 4 to chapter 7. In addition, we study radar sensor network from the view of information theory in chapter 8. We also study compressive sensing and apply it to RSN to further investigate the system performance in chapter 9 and chapter 10. In chapter 11, we briefly conclude our work in this dissertation. The main innovation works of this dissertation are as following. We propose the LCZ/ZCZ Sequence-pair Sets that have ideal autocorrelation sidelobes and cross correlation values during LCZ/ZCZ. We also provide three methods to construct the Optimized Punctured LCZ/ZCZ Sequence-pair Sets which is a specific case of the LCZ/ZCZ Sequence-pair Sets. We not only theoretically prove that the sequence-pair sets constructed by our methods satisfy the definitions of the Optimized Punctured LCZ/ZCZ Sequence-pair sets, but also provide examples for each method and analyze properties of the Optimized Punctured LCZ/ZCZ Sequence-pair sets to help further investigating our proposed codes. The main purpose of pulse compression is to raise the signal to maximum sidelobe (signal-to-sidelobe) ratio to improve the target detection and range resolution abilities of the system. We apply the Optimized Punctured Binary Sequence-pair to the Radar system as the phase coded waveforms which is a kind of pulse compression codes. Comparing with the Barker and P4 codes of corresponding length, the Radar system within the Optimized Punctured Binary Sequence-pair could clearly improve the detection performances. Since multiple radar sensors can be combined to form a multi radar system to overcome performance degradation of single radar along with waveform optimization, we theoretically study RSN design using phase coded waveforms. We apply our newly proposed codes to RSN and analyze the detection performance of the system. We also apply the proposed ternary codes to the Sonar Sensor Network (SSN) as pulse compression codes for narrowband pulse signals and simulate the target detection performance of the system. We provide two MIMO radar systems using our proposed codes as orthogonal pulse compression codes to study the direction finding performance of the MIMO radar systems. We theoretically analyze the two MIMO radar system models and simulate the direction finding performance of the system. We also studied the RSN from the view of information theory. We investigate the use of information theory to design waveforms for the measurement of extended radar targets in RSN. We optimized the estimation waveforms that maximize the mutual information between a target ensemble and the received signal within additive Gaussian noise so that characteristics of the target could be well recognized. Finally, we provide and analyze a CS-SVD method to simplify the signal recovery algorithm and introduce CS to RSN using pulse compression technique. Our idea is to employ a set of Stepped-Frequency (SF) waveforms as pulse compression codes for transmit sensors, and to use the same SF waveforms as the sparse matrix to compress the signal in the receiving sensor. We obtain that the signal samples along the time domain could be largely compressed so that they could be perfectly recovered by a small number of measurements. We develop a Maximum Likelihood (ML) Algorithm for Radar Cross Section (RCS) parameter estimation and provide the Cramer-Rao lower bound (CRLB) to validate the theoretical result.