Generalization of discrete-time Wirtinger inequalities and a preliminary study of their application to SNR analysis of sinusoids buried in noise /cKaveh Mollaiyan.

Sinusoidal signals have been always of interest because of their extensive applications in different areas of engineering and science. This research aims at generalizing the discrete Wirtinger inequalities and assessing their applicability in estimating the SNR of sinusoids of rational frequency [Special characters omitted.] it buried in additive noise. The solution to the problem of estimating the SNR of a sinusoid of frequency [Special characters omitted.] , corrupted with additive white noise, has been provided in the form of an inequality-based method. The limitations of using the existing inequalities in the proposed method have been discussed and modifications have been made to the existing Wirtinger inequalities accordingly. Generalizations of the modified inequalities have been achieved by changing the structure of the filter's impulse response. Performance curves with wider non-saturated regions have been obtained. By using reordering and modulation, an arbitrary sinusoid of frequency [Special characters omitted.] , has been converted to a sinusoid of frequency [Special characters omitted.] , allowing the proposed method to estimate the SNR of sinusoids of higher frequencies as well. The computational complexity of the proposed method has been evaluated and compared with a DFT-based approach. Extensive simulation results showing the capability of the proposed method in estimating the SNR of an arbitrary sinusoid of rational frequency [Special characters omitted.] have been provided. An advantage of the proposed method is that it can be adaptively adjusted to the length of the observed signal. In cases it is desired to evaluate the SNR of a sinusoid with a known frequency, the proposed method can be used as a computationally efficient option

Acquisition of weak signals in multi-constellation frequency domain receivers.

New positioning applications’ availability requirements demand receivers with higher sensitivities and ability to process multiple GNSS signals. Possible applications include acquiring one signal per GNSS constellation in the same frequency band and combining them for increased sensitivity or predicting acquisition of other signals. Frequency domain processing can be used for this purpose, since it benefits from parallel processing capabilities of Fast Fourier Transform (FFT), which can be efficiently implemented in software receivers. On the other hand, long coherent integration times are mainly limited due to large FFT size in receivers using frequency domain techniques. A new method is proposed to address the problems in frequency domain receivers without compromising the resources and execution time. A pre-correlation accumulation (PCA) is proposed to partition the received samples into one-code-period blocks, and to sum them together. As a result, the noise is averaged out and the correlation results will gain more power, provided that the relative phase between the data segments is compensated for. In addition to simplicity, the proposed PCA method enables the use of one-size FFT for all integration times. A post-correlation peak combination is also proposed to remove the need for double buffering. The proposed methods are implemented in a configurable Simulink model, developed for acquiring recorded GNSS signals. For weak signal scenarios, a Spirent GPS simulator is used as a source. Acquisition results for GPS L1 C/A and GLONASS L1OF are shown and the performance of the proposed technique is discussed. The proposed techniques target GNSS receivers using frequency domain processing aiming at accommodating all the GNSS signals, while minimizing resource usage. They also apply to weak signal acquisition in frequency domain to answer the availability demand of today’s GNSS positioning applications