Systematic DFT Frames: Principle, Eigenvalues Structure, and Applications

Motivated by a host of recent applications requiring some amount of redundancy, frames are becoming a standard tool in the signal processing toolbox. In this paper, we study a specific class of frames, known as discrete Fourier transform (DFT) codes, and introduce the notion of systematic frames for this class. This is encouraged by a new application of frames, namely, distributed source coding that uses DFT codes for compression. Studying their extreme eigenvalues, we show that, unlike DFT frames, systematic DFT frames are not necessarily tight. Then, we come up with conditions for which these frames can be tight. In either case, the best and worst systematic frames are established in the minimum mean-squared reconstruction error sense. Eigenvalues of DFT frames and their subframes play a pivotal role in this work. Particularly, we derive some bounds on the extreme eigenvalues DFT subframes which are used to prove most of the results; these bounds are valuable independently

Error Correction For Automotive Telematics Systems

One benefit of data communication over the voice channel of the cellular network is to reliably transmit real-time high priority data in case of life critical situations. An important implementation of this use-case is the pan-European eCall automotive standard, which has already been deployed since 2018. This is the first international standard for mobile emergency call that was adopted by multiple regions in Europe and the world. Other countries in the world are currently working on deploying a similar emergency communication system, such as in Russia and China. Moreover, many experiments and road tests are conducted yearly to validate and improve the requirements of the system. The results have proven that the requirements are unachievable thus far, with a success rate of emergency data delivery of only 70%. The eCall in-band modem transmits emergency information from the in-vehicle system (IVS) over the voice channel of the circuit switch real time communication system to the public safety answering point (PSAP) in case of a collision. The voice channel is characterized by the non-linear vocoder which is designed to compress speech waveforms. In addition, multipath fading, caused by the surrounding buildings and hills, results in severe signal distortion and causes delays in the transmission of the emergency information. Therefore, to reliably transmit data over the voice channels, the in-band modem modulates the data into speech-like (SL) waveforms, and employs a powerful forward error correcting (FEC) code to secure the real-time transmission. In this dissertation, the Turbo coded performance of the eCall in-band modem is first evaluated through the adaptive white Gaussian noise (AWGN) channel and the adaptive multi-rate (AMR) voice channel. The modulation used is biorthogonal pulse position modulation (BPPM). Simulations are conducted for both the fast and robust eCall modem. The results show that the distortion added by the vocoder is significantly large and degrades the system performance. In addition, the robust modem performs better than the fast modem. For instance, to achieve a bit error rate (BER) of 10^{-6} using the AMR compression rate of 7.4 kbps, the signal-to-noise ratio (SNR) required is 5.5 dB for the robust modem while a SNR of 7.5 dB is required for the fast modem. On the other hand, the fading effect is studied in the eCall channel. It was shown that the fading distribution does not follow a Rayleigh distribution. The performance of the in-band modem is evaluated through the AWGN, AMR and fading channel. The results are compared with a Rayleigh fading channel. The analysis shows that strong fading still exists in the voice channel after power control. The results explain the large delays and failure of the emergency data transmission to the PSAP. Thus, the eCall standard needs to re-evaluate their requirements in order to consider the impact of fading on the transmission of the modulated signals. The results can be directly applied to design real-time emergency communication systems, including modulation and coding

Error Correction For Automotive Telematics Systems

One benefit of data communication over the voice channel of the cellular network is to reliably transmit real-time high priority data in case of life critical situations. An important implementation of this use-case is the pan-European eCall automotive standard, which has already been deployed since 2018. This is the first international standard for mobile emergency call that was adopted by multiple regions in Europe and the world. Other countries in the world are currently working on deploying a similar emergency communication system, such as in Russia and China. Moreover, many experiments and road tests are conducted yearly to validate and improve the requirements of the system. The results have proven that the requirements are unachievable thus far, with a success rate of emergency data delivery of only 70%. The eCall in-band modem transmits emergency information from the in-vehicle system (IVS) over the voice channel of the circuit switch real time communication system to the public safety answering point (PSAP) in case of a collision. The voice channel is characterized by the non-linear vocoder which is designed to compress speech waveforms. In addition, multipath fading, caused by the surrounding buildings and hills, results in severe signal distortion and causes delays in the transmission of the emergency information. Therefore, to reliably transmit data over the voice channels, the in-band modem modulates the data into speech-like (SL) waveforms, and employs a powerful forward error correcting (FEC) code to secure the real-time transmission. In this dissertation, the Turbo coded performance of the eCall in-band modem is first evaluated through the adaptive white Gaussian noise (AWGN) channel and the adaptive multi-rate (AMR) voice channel. The modulation used is biorthogonal pulse position modulation (BPPM). Simulations are conducted for both the fast and robust eCall modem. The results show that the distortion added by the vocoder is significantly large and degrades the system performance. In addition, the robust modem performs better than the fast modem. For instance, to achieve a bit error rate (BER) of 10^{-6} using the AMR compression rate of 7.4 kbps, the signal-to-noise ratio (SNR) required is 5.5 dB for the robust modem while a SNR of 7.5 dB is required for the fast modem. On the other hand, the fading effect is studied in the eCall channel. It was shown that the fading distribution does not follow a Rayleigh distribution. The performance of the in-band modem is evaluated through the AWGN, AMR and fading channel. The results are compared with a Rayleigh fading channel. The analysis shows that strong fading still exists in the voice channel after power control. The results explain the large delays and failure of the emergency data transmission to the PSAP. Thus, the eCall standard needs to re-evaluate their requirements in order to consider the impact of fading on the transmission of the modulated signals. The results can be directly applied to design real-time emergency communication systems, including modulation and coding