ITC/USA 2014 Conference Proceedings / The Fiftieth Annual International Telemetering Conference and Technical Exhibition / October 20-23, 2014 / Town and Country Resort & Convention Center, San Diego, CA / In order to provide reliable line-of-sight communications, test aircraft typically use two transmit antennas to create top and bottom hemispherical patterns that cover the full range of possible aircraft orientations. The two transmit signals are normally generated by a single transmitter with the power being split between the two antennas. Although this configuration is straightforward and easy to implement, problems can arise due to the two signals constructively and destructively interfering with each other. This can result in the composite antenna pattern having periodic nulls with a depth and geometric spacing dependent upon the amplitude and phase differences of the two transmitted signals. This problem is usually addressed by either unevenly splitting the transmit power between the two antennas, or by using two separate transmitters at different frequencies. Unfortunately, these methods have drawbacks that require either system performance or cost trade-offs. This paper discusses the use of Space-Time Coding to eliminate this antenna interaction by transmitting modified waveforms that simultaneously allow for both full power transmission and single-channel operation. This approach effectively restores the nominal antenna performance, thereby resulting in better overall coverage and less pattern-induced dropouts. Telemetry performance results from recent flight testing are presented to validate the benefits of this approach.

The two-antenna problem in aeronautical mobile telemetry is created by the reception of two copies of the same RF waveform with different phases and time delays. Alamouti and Alamouti-like space time block codes can solve the two-antenna problem, but the decoder/detector needs to account for the different time delays between the signals received from the two transmit antennas. In this thesis, a comparison is made between the performance of Alamouti space-time block codes and time-reversed space-time block codes with 16-APSK to solve the two-antenna problem. The maximum likelihood decoder/detector for Alamouti-encoded 16-APSK is a sequence detector operating on a trellis with a large number of states. A practical state-reduction technique is presented. The results produce a trellis with 256 states and a small loss in bit error rate performance as long as the delay difference is not too big. The decoder/detector for the time-reversed space time block requires only waveform manipulations and channel matched filtering in the case where the two channels are simple delays. For the more general case of multipath propagation between the two transmit antennas and the receiver, the decoder/detector requires an equalizer; simulation results using a channel pair measured at a test range show that the decoder/detector is capable of achieving near AWGN performance with a modest equalizer.

This dissertation explores the application of Silvester's space-time block code to the multi-index CPM 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. The use of space-time coded ARTM CPM to solve the two-antenna problem in aeronautical mobile telemetry requires estimates of the parameters that define the propagation environment. The maximum likelihood estimator problem is defined and used to motivate reduced-complexity estimators suitable for use in a real system. A modified gradient descent algorithm performs the search required to find the delay parameters. An "inner" phase lock loop operating with an "outer" frequency lock loop computes decision-directed estimates of the frequency offset. Computer simulations were used to assess the impact on bit error rate performance introduced by the estimators. The simulation results show the combined joint estimator for the delays, channel gains, and frequency offset imposes a 1.15 dB loss in performance. This loss is approximately the same as the 1.1 dB loss due to the complexity-reducing techniques used by the decoder/detector.

Mathematical optimization is applicable to nearly every scientific discipline. This thesis specifically focuses on optimization applications to digital communications and signal processing. Within the digital communications framework, the channel encoder attempts to encode a message from a source (the sender) in such a way that the channel decoder can utilize the encoding to correct errors in the message caused by the transmission over the channel. Low-density parity-check (LDPC) codes are an especially popular code for this purpose. Following the channel encoder in the digital communications framework, the modulator converts the encoded message bits to a physical waveform, which is sent over the channel and converted back to bits at the demodulator. The modulator and demodulator present special challenges for what is known as the two-antenna problem. The main results of this work are two algorithms related to the development of optimization methods for LDPC codes and the two-antenna problem. Current methods for optimization of LDPC codes analyze the degree distribution pair asymptotically as block length approaches infinity. This effectively ignores the discrete nature of the space of valid degree distribution pairs for LDPC codes of finite block length. While large codes are likely to conform reasonably well to the infinite block length analysis, shorter codes have no such guarantee. Chapter 2 more thoroughly introduces LDPC codes, and Chapter 3 presents and analyzes an algorithm for completely enumerating the space of all valid degree distribution pairs for a given block length, code rate, maximum variable node degree, and maximum check node degree. This algorithm is then demonstrated on an example LDPC code of finite block length. Finally, we discuss how the result of this algorithm can be utilized by discrete optimization routines to form novel methods for the optimization of small block length LDPC codes. In order to solve the two-antenna problem, which is introduced in greater detail in Chapter 2, it is necessary to obtain reliable estimates of the timing offset and channel gains caused by the transmission of the signal through the channel. The timing offset estimator can be formulated as an optimization problem, and an optimization method used to solve it was previously developed. However, this optimization method does not utilize gradient information, and as a result is inefficient. Chapter 4 presents and analyzes an improved gradient-based optimization method that solves the two-antenna problem much more efficiently.