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° 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.

This article explores the relationship between an equalizer and a combiner operating on the available polarization states of a received signal in aeronautical mobile telemetry. The maximum likelihood 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 maximum ratio combiner. To compare the two combining approaches, the aeronautical telemetry multipath channel is extended to include polarization state information. The channel extension is used in computer simulations. The simulations results for SOQPSK-TG with a CMA equalizer show that the post-equalizer bit error rate for the two approaches is the same.

Waveforms define the shape, structure, and frequency characteristics of signals, whereas modulation schemes determine how information symbols are mapped onto these waveforms for transmission. Their appropriate selection plays a critical role in determining the efficiency, robustness, and reliability of data transmission. In wireless communications, the choice of waveform influences key factors, such as network capacity, coverage, performance, power consumption, battery life, spectral efficiency (SE), bandwidth utilization, and the system’s resistance to noise and electromagnetic interference. This paper provides a comprehensive analysis of the waveforms and modulation schemes used across successive generations of mobile cellular networks, exploring their fundamental differences, structural characteristics, and trade-offs for various communication scenarios. It also situates this analysis within the historical evolution of mobile standards, highlighting how advances in modulation and waveform technologies have shaped the development and proliferation of cellular networks. It further examines criteria for waveform selection—such as SE, bit error rate (BER), throughput, and latency—and discusses methods for assessing waveform performance. Finally, this study presents a comparative evaluation of modulation schemes across multiple mobile generations, focusing on key performance metrics, with the BER analysis conducted through MATLAB simulations.

This article develops maximum likelihood (ML) detection for post-FFT processing of dual-polarized antenna outputs with a cyclic-prefix OFDM (CP-OFDM) waveform for a frequency selective multipath fading in a 5G mobile-to-mobile setting. The suggested maximum likelihood detector (MLD) comprises a combiner applied to the channel matched filter outputs (designated MLC) followed by a decision rule based on correlation and signal energy. When MLC is coupled with a frequency-domain equalizer, this structure is called MLC+FDE. The designed MLD and MLC+FDE are compared to the traditional combining techniques: maximum ratio combining, equal gain combining, and selection combining. Computer simulations performed over a stochastic channel model with polarization state information. The simulation results show that the difference between MLD and maximum ratio combining (the best performing method), MLC+FDE (almost the best performing method) and selection diversity with frequency-domain equalization (the worst performing method) is 2 dB. This diversity improvement is limited by the correlation between the two channels that characterize the two polarization states. This correlation makes it difficult to achieve reliable transmission through combining alone; some form of error control coding is also needed. When channel estimates are used in place of perfect channel knowledge, an error floor is observed.

16-ary amplitude phase shift keying (16APSK) is a candidate modulation for aeronautical mobile telemetry because it has better spectral efficiency and lower sensitivity to adjacent channel interference compared SOQPSK-TG. This paper compares the post-equalizer bit error rate performance of 16APSK and SOQPSK-TG in the aeronautical mobile telemetry multipath channel. The linear polarizations produced by the orthogonal dipoles in the receive antenna feed are combined in two different ways: using a 90◦ hybrid coupler to produce RHCP or LHCP and maximum likelihood combining. The first combining method is the common practice at test ranges and the second combining method is new. The results show the following. First, 16APSK with MMSE equalization outperforms SOQPSK-TG with CMA equalization for the RHCP and LHCP channels. Second, 16APSK with MMSE equalization outperforms SOQPSK-TG with CMA equalization for the maximum likelihood channels at moderate to high signal-to-noise ratios. For lower signal-to-noise ratios, SOQPSK-TG shows the best performance. Third, 16APSK with MMSE equalization operating the maximum likelihood combined channel outperforms SOQPSK-TG with CMA equalization operating on the RHCP or LHCP channels.