In recent years, global mobile data traffic has been increasing exponentially as mobile devices pervade our daily lives. To cope with the ever growing demands for higher data rates and seamless connectivity, one solution is to drastically increase the number of macro base stations in the conventional cellular architecture. However, this results in high deployment costs. Deploying low-power nodes such as relays that do not require a wired backhaul connection within a macrocell is one of cost-effective ways to extend high data rate coverage range. Relays are typically deployed to increase signal strength in poor coverage areas or to eliminate dead spots. But more importantly, relays provide a natural diversity, called cooperative diversity. In addition to a direct signal from a base station, extra copies of the same signal are forwarded from relays. Utilizing this diversity at the destination can yield significant performance enhancements. Thus, cooperative relay strategies need to be considered to enable high data rate coverage in a cost-effective manner. In this dissertation, we consider a simple single-relay network and present low-complexity and power-efficient cooperative relay designs that can achieve low error rate. We first study decode-and-forward (DF) relay networks with a single antenna at each node, where the relay decodes the received signal and forwards the re-encoded information to the destination. In DF relay scheme, decoding at the relay is not perfect and the error-propagation phenomenon is a detrimental problem, preventing the destination from collecting the cooperative diversity. To enable cooperative diversity in DF relay networks, we adopt link-adaptive power-scaling relay strategies where the relay scales the transmission power of the re-encoded signal based on the reliability of the source-relay link. We generalize power-profile designs and analyze the diversity order enabled by the general power-profile designs. We provide necessary and sufficient conditions for the designs to enable full cooperative diversity at the destination. In the second part of this dissertation, we extend the power-scaling relay strategy to DF multi-input multi-output (MIMO) relay networks, where multiple antennas are adopted at each node, and show that full cooperative diversity can also be achieved here. To collect spatial diversity provided by multiple antennas without using maximum-likelihood equalizers (MLEs) or near-ML detectors which exhibit high complexity, channel-controlled automatic repeat request (CC-ARQ) scheme is developed for DF MIMO relay networks to enable spatial diversity with linear equalizers (LEs) maintaining low-complexity. We also show that joint cooperative and spatial diversity can be achieved at the destination when the power-scaling strategy and the CC-ARQ with LEs are combined. Finally, amplify-and-forward (AF) MIMO relay designs, where the relay simply amplifies the received signal and forwards it to the destination, are studied with consideration of peak-power constraints at the relay. One practical concern for AF relaying is that the output signal at the relay may suffer from large peak-to-average power ratio (PAR), which may cause nonlinear distortion and/or saturation in the transmitted signal due to the limited linear range of power amplifiers. Thus, we first investigate peak-power constrained power-scaling strategies and find a sufficient condition to enable joint cooperative and spatial diversity at the destination. Based on this study, we propose simple and practical AF MIMO relay designs with peak-power constraint at the relay. CC-ARQ is also applied to AF MIMO relay networks to reduce the decoding complexity.