Bandlimiting, Sampling, and Quantization for Modernized Spreading Modulations in White Noise

John W. Betz

Abstract:	There has long been interest in determining the effect of sampling and quantization on weak signal detection using a matched filter or correlation detector. Theoretical and experimental results have been developed for decades, with initial emphasis on one-bit sampling where analytical results are most readily obtained. In the context of Global Navigation Satellite System (GNSS) receiver processing, results are well-known for desired signals having conventional (binary phase shift keying with rectangular spreading symbols) spreading modulations in white noise. More recently, a parametric model has been proposed for assessing the combined effect of GNSS interference, bandlimiting, sampling, and quantizing (BSQ) with modern GNSS spreading modulations. Numerical results have been presented for one-bit quantization with sampling at the Nyquist rate relative to the precorrelation bandwidth. This paper lays the foundation for extending the recent results to quantization using more than one bit with different sampling rates, for a set of modernized spreading modulations. One-bit and 1.5-bit and two-bit quantizers are considered, with sampling at the Nyquist rate and twice Nyquist rate, in additive white Gaussian noise. The resulting BSQ losses are evaluated over a range of different quantization set points, for each case consisting of a specific precorrelation filter bandwidth, sampling rate, type of spreading modulation, and different number of bits in analog-to-digital conversion. The sensitivity of BSQ losses to quantization set point value is then evaluated for each case. Also, the resulting lowest-loss quantization set points and associated BSQ losses are tabulated. These results provide useful guidance for the design of bandlimiting, sampling, and quantization in modernized GNSS receivers, and also support assessment of receiver performance.
Published in:	Proceedings of the 2008 National Technical Meeting of The Institute of Navigation January 28 - 30, 2008 The Catamaran Resort Hotel San Diego, CA
Pages:	980 - 991
Cite this article:	Betz, John W., "Bandlimiting, Sampling, and Quantization for Modernized Spreading Modulations in White Noise," Proceedings of the 2008 National Technical Meeting of The Institute of Navigation, San Diego, CA, January 2008, pp. 980-991.
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