In this thesis, major attention is paid to cooperative diversity as an alternative way to achieve spatial diversity when the multiple antenna structure is not an option. By adopting the cooperative relay nodes to forward information, we can mitigate the fading effects, increase the capacity, lower the bit-error rate, increase the achievable transmission range, and without sacrificing time and bandwidth efficiency. Orthogonal Frequency Division Multiplexing (OFDM) is a popular multicarrier modulation technique in the modern wireless communications, since it possesses the advantages of frequency parallel transmission, high speed communications and efficient spectrum usage. In this Ph.D. thesis OFDM transmission into the cooperative communication domain is investigated. The diversity gains from both spatial domain and frequency domain are combined and so cooperative communication can further enhance the reliable, high speed transmission, and enable the spectrum efficiency. We propose a cooperative OFDM tall Toeplitz scheme, which guarantees full cooperative diversity, taking outage diversity and multipath diversity into account; in addition it easily combats Carrier Frequency Offsets (CFOs), using Linear Equalizers (LEs) only. Compared to the conventionally used Maximum-Likelihood Equalizers (MLEs), the system complexity is reduced significantly. There are mainly two relaying protocols in cooperative relay networks: Amplify-and-Forward (AF) and Decode-and-Forward (DF). In the research on relay selection and resource allocation issues in cooperative communications, we propose a dynamic optimal combination strategy for the hybrid DF-AF cooperative OFDM communications and removing unsuitable AF relays. Subsequently, we propose relay selection and resource allocation and optimization schemes for cooperative wireless communication networks with interference based on the so called Stackelberg game approach. This approach is a proper game model for solving the relay selection and power allocation problem in a distributed manner, when pricing and power allocation of the relay both are taken into account. As an extension of our research on cooperative wideband communication, we study wideband scale-lag channels as well, present in many ultra-wideband communication applications. In our research, cooperative relaying communication network is set for multi-scale and multi-lag wideband channels. We also provide a dynamic optimal selection strategy for relay selection to take advantage of the multi-relay, multi-scale and multi-lag diversity and maximize the system Bit-Error Rate (BER) performance. Cooperative localization research is growing when larger wireless networks are deployed and more applications are developed which require accurate position information. Therefore, cooperative locationing research becomes an important part of this Ph.D. research on cooperative wideband OFDM communications. In this research, we propose a trigger relay based cooperative localization technique. Because the trigger relay only needs to be switched on by the incoming signal, and to be sent as a simple pilot to the receiver, our technique gains from the easy processing together with noise and interference immunity of the base station to relay link. Compared to AF relay and DF relay Time Difference of Arrival (TDOA) estimation cases, the trigger relay reduces the system complexity. Meanwhile, trigger relay enables the bandwidth efficient TDOA, since it significantly reduces the amount of data for transmission. Furthermore, by exploiting cooperative-multipath diversity, the improved signal detection further contributes to a better TDOA estimation.