Spectrum sharing has become increasingly important since the past decade due to the ongoing congestion of spectral resources. Higher data rates in wireless communications require expansion of existing frequency allocations. Significant research efforts have been made in the direction of cognitive radio to effectively manage the existing frequency usage. Recently, coexistence of multiple platforms within the same frequency bands is considered effective to mitigate spectral congestion. This requires both systems to work collaboratively to mitigate their mutual interference. This challenging problem can be significantly simplified if both systems are controlled by the same entity. Joint radar-communication (JRC) system is such an example where radar and communication system objectives are achieved by the same physical platform. In this dissertation, we consider three different types of JRC systems. These JRC systems respectively exploit a single transmit antenna, an antenna array for beamforming, and a distributed JRC network, and develop novel signal processing techniques to optimize the performance of these systems. Special attention is given to the resource optimization objectives and numerous resource allocation schemes are developed and investigated. First, we consider a single transmit antenna-based JRC system which exploits dual-purpose transmit orthogonal frequency division multiplexing (OFDM) waveforms to perform radar and communication objectives simultaneously. We optimize the power allocation of the OFDM subcarriers based on the frequency-sensitive target response and communication channel characteristics. For this purpose, we employ mutual information as the optimization metric. In the simulation examples considered for this system, we observed that the JRC system enjoys approximately 20\% improvement in the performance of communication subsystem with a mere 5\% reduction in radar subsystem performance. Second, we propose a quadratic amplitude modulation (QAM) based sidelobe modulation scheme for beamforming-based JRC systems which enhances the communication data rate by enabling a novel multiple access strategy. The main principle of this proposed strategy lies in enabling the beamformer to transmit signals with distinct amplitudes and phases in different directions. We also investigate optimal power allocation for such a spectrum sharing approach by employing a spatial power control-based beamforming approach. Furthermore, the robustness of these beamforming-based JRC systems is improved using chance constrained programming. In this context, we observe that the chance constrained optimization can be relaxed to form a deterministic and convex problem by employing the statistical profile of the communication channels. When dealing with JRC systems that are equipped with more antennas than the number of radio frequency chains, we perform the resource optimization in terms of minimized power usage and optimal selection of antennas resulting in an efficient utilization of hardware up-conversion chains. In the simulation examples considered for these schemes, we observe that, even with a reduction of nearly 30\% of the transmit antennas, the beamforming-based JRC system is able to perform the required radar and communication tasks without any disadvantage. Our last contribution is on a distributed JRC system, which is the first effort in this research direction, enabling spectrum sharing for networked radar systems coexisting with the communication systems. We devise a power allocation strategy for such a system by employing convex optimization techniques. In this strategy, the target localization error and the Shannon capacity are respectively considered as the optimization criteria for radar and communication systems. For the simulation example considered in this case, we observe that the proposed resource allocation strategy achieves a communication performance that was approximately 5 times greater than that achieved by the radar-only counterpart. Moreover, the target localization performance achieved by the JRC system using the proposed approach was approximately 4 times better than the performance achieved by the communication-only approach. / Electrical and Computer Engineering