This paper describes the use of Alamouti-encoded-shaped offset QPSK version TG (SOQPSK-TG) to solve the two-antenna problem in aeronautical telemetry. The Alamouti space-time block code is used to encode the phase states in the complex exponential representation of SOQPSK-TG. Because SOQPSK-TG possesses memory, the Alamouti decoder is a sequence estimator. Maximum likelihood and least squares sequence decoders are derived. To reduce the number of states, the eight-waveform cross-correlated trellis-coded quadrature modulation (XTCQM) approximate representation of SOQPSK-TG is used. A prototype decoder based on the least squares decoder and the estimators described in Part I and operating at a data rate of 10 Mb/s was tested in the laboratory in test flights at the Air Force Test Center, Edwards AFB. The test flights demonstrate that Alamouti-encoded SOQPSK-TG, as described in this paper, using the least squares decoder based on the estimators described in Part I solves the two antenna problem in aeronautical telemetry.

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.

An approximate maximum likelihood sequence estimator (MLSE) equalizer for shaped offset QPSK, version TG (SOQPSK-TG) is derived based on the pulse amplitude modulation (PAM) approximation of SOQPSK-TG using the two principal PAM pulses. The resulting equalizer is a generalization of the equalizer based on the Ungerboeck observation model, where the generalization is to two parallel, cross-correlated symbol streams over parallel intersymbol interference channels. The bit error rate (BER) performance and computational complexity of the approximate MLSE equalizer operating over three example channels, motivated by multipath propagation in aeronautical telemetry and with increasing selectivity, are presented. The BER performance was evaluated using computer simulations and shown to be approximately 5-8 dB better than the best frequency-domain minimum mean-squared error (MMSE) equalizers published in the open literature. The computational complexity, measured by the number of real-valued multiplications, is comparable to that of the frequency-domain MMSE equalizers.

This article explores the application of Silvester’s space–time block code to the multi-index continuous phase modulation called “ARTM CPM” in the IRIG 106 standard to solve the “two-antenna problem”—the use of two transmit antennas to provide full spatial coverage on an airborne test article and the accompanying self-interference due to different delays between the two transmit antennas and the ground-based receive antenna. A symbol-level encoding scheme is derived that allows the burst-based space–time block code to operate in a continuously streaming mode. The results show that the space–time block code can solve the two-antenna problem with differential delays, but that the differential delays generate a substantial increase in the computational complexity of the detector. Complexity-reducing techniques are applied and analyzed. The results show that the complexity reductions required to produce a practically realizable detector render the bit error probability performance sensitive to the differential delay. Numerical results are presented to quantify the performance loss due to the differential delay.

This paper examines the application of sparse estimation techniques for the estimation of a discrete-time equivalent multipath channel in the aeronautical telemetry context. The sensing matrix comprises samples of SOQPSK-TG (a continuous phase modulation) based on the pilot bit sequence currently defined in the aeronautical telemetry standard. Representative algorithms from the three broad classes of sparse estimators were examined side-by-side using computer simulations to estimate the post-equalizer bit error rate (BER). Ideal and non-ideal frequency offset synchronization were assumed in the simulations. The results show that the performance of the matching pursuit algorithms seemed to be better suited to this application in the sense that no additional steps were required and the post-equalizer BER of the best matching pursuit algorithm was slightly better than that of the other sparse estimation techniques. In the case of both ideal and non-ideal frequency offset synchronization, the post-equalizer BER achieved by the generalized orthogonal matching pursuit (GOMP) algorithm was approximately 1.5 dB better than that obtained using the nonsparse-constrained maximum likelihood channel estimate.