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Equivalent discrete-time models for a variety of spatial combining techniques operating in a frequency-selective multipath fading channel are derived. The equivalent discrete-time models are used to perform computer simulations of the post-equalizer bit error rate over a frequency-selective multipath channel whose derivation preserved polarization state information. Two sets of computer simulations were performed. In the first set, the performance of co-located cross-polarized antenna elements was investigated. The results showed that maximum likelihood combining maximizes polarization diversity, but that maximum ratio combining and selection combining were very competitive in the case where the cross-polarized antennas produce one strong channel and a relatively weak channel. Elliptical combining, using a 90&#x00B0; hybrid coupler, produced the worst results. The second set of simulations used a combination of spatial and cross-polarized antenna elements, for a total of eight antenna elements. The simulation results showed that maximum likelihood combining was best, followed by maximum ratio combining, equal gain combining, and selection combining. Again, elliptical combining was the worst, leading to the conclusion that other combining techniques are preferred in frequency-selective fading environments.

On the Ungerboeck and Forney Observation Models for Spatial Combining And Their Application to 5G Millimeter-Wave Bands