This dissertation explores the role of polarization, combining, and equalization operating over frequency-selective channels to improve the reliability of wireless communications systems in terms of BER for two applications: 5G mobile networks (operating in the mmWave band and NR FR1), and aeronautical mobile telemetry systems (operating in L band). The equivalent discrete-time models for a variety of spatial combining techniques at 5G mmWave bands were derived to investigate the performance of co-located cross-polarized antenna elements when polarization diversity is used and also when a combination of spatial and cross-polarized antennas is exploited. In both cases, ML combining has the lowest BER and EPC produced the worst results. The use of co-located cross-polarized antenna elements also is examined in 5G FR1 assuming post-FFT processing of the two antenna element outputs in a mobile-to-mobile setting. The optimum strategy, in the ML sense, for incorporating the two antenna outputs is developed. The optimum combining strategy together with a FDE is compared to the traditional combining techniques: MRC, EGC, and SC, where the last two also require a FDE. Computer simulations performed over a stochastic channel model with polarization state information show that the difference between ML detection and MRC (the best performing methods) and SC with FDE (the worst performing method) is 2 dB. The similar results were observed with pilot based channel estimators, however the difference in this case was the presence of a BER floor at low values of $N_0$ and caused by channel estimation errors. In aeronautical mobile telemetry applications, the ML combiner is derived and shown to be equivalent to the summing the outputs of two filters matched to the channels in the horizontal and vertical polarization states. For historical reasons, current systems combine right-hand and left-hand circularly polarized antenna feed outputs using a MRC. To compare the two combining approaches, the aeronautical telemetry multipath channel was extended to include polarization state information. The simulation results for SOQPSK-TG with a CMA equalizer show that the post-equalizer BER for the two approaches is the same.