Traditionally, noise in communication systems has been modeled as an additive, white Gaussian noise process with independent, identically distributed samples. Although this model accurately reflects thermal noise present in communication system electronics, it fails to capture the statistics of interference and other sources of noise, e.g. in unlicensed communication bands. Modern communication system designers must take into account interference and non-Gaussian noise to maximize efficiencies and capacities of current and future communication networks. In this work, I develop new multi-dimensional signal processing methods to improve performance of communication systems in three applications areas: (i) underwater acoustic, (ii) powerline, and (iii) multi-antenna cellular. In underwater acoustic communications, I address impairments caused by strong, time-varying and Doppler-spread reverberations (self-interference) using adaptive space-time signal processing methods. I apply these methods to array receivers with a large number of elements. In powerline communications, I address impairments caused by non-Gaussian noise arising from devices sharing the powerline. I develop and apply a cyclic adaptive modulation and coding scheme and a factor-graph-based impulsive noise mitigation method to improve signal quality and boost link throughput and robustness. In cellular communications, I develop a low-latency, high-throughput space-time-frequency processing framework used for large scale (up to 128 antenna) MIMO. This framework is used in the world's first 100-antenna MIMO system and processes up to 492 Gbps raw baseband samples in the uplink and downlink directions. My methods prove that multi-dimensional processing methods can be applied to increase communication system performance without sacrificing real-time requirements. / text