# Nonuniform bandpass sampling in radio receivers

Sammanfattning: As an interface between radio receiver front-ends and digital signal processing blocks, sampling devices play a dominant role in digital radio communications. As an interface between radio receiver front-ends and digital signal processing blocks, sampling devices play a dominant role in digital radio communications. Based on different sampling theorems (e.g., classic Shannon’s sampling theorem, Papoulis’ Generalized sampling theorem, bandpass sampling theory), signals are processed by the sampling devices and then undergo additional processing. It is a natural goal to obtain the signals at the output of the sampling devices without loss of information. In conventional radio receivers, all the down-conversion and channel selection are realized in analog hardware. The associated sampling devices in A/D converters are based on the classic Shannon’s sampling theorem. Driven by the increased speed of microprocessors, there is a tendency to use mixed-signal/digital hardware and software to realize more functions (e.g., down-conversion, channel selection, demodulation and detection) in a radio communication system. The new evolution of radio receiver architecture is Software Defined Radio (SDR). One design goal of SDR is to put the A/D converter as close as possible to the antenna. BandPass Sampling (BPS) enables one to have an interface between the higher IF and the A/D converter by a sampling rate of 2B or more (B is the information bandwidth), and it might be a solution to SDR. A signal can be uniquely determined from the samples by NonUniform Sampling (NUS) such that NUS has the potential to suppress harmful signal spectrum aliasing. BPS makes use of the signal spectrum aliasing to represent the signal uniquely at any band position. A harmful aliasing of signal spectrum will cause a performance degradation. It is of great benefit to use NUS scheme in BPS system. However, a signal cannot be recovered from its nonuniform samples by using only an ideal lowpass filter (or the classic Shannon’s reconstruction function). The reconstruction of the samples by NUS is crucial for the implementation of NUS. Besides the harmful signal spectrum aliasing, noise aliasing and timing jitter are other two sources of performance degradation in a BPS system. Noise aliasing is the direct consequence of lower sampling rate of subsampling. With the increase of input frequency by directly sampling a signal at higher IF, the timing error of the sampling clock causes large jitter effects on the sampled-data signal. In this thesis work, first, a filter generalized by a certain Reconstruction Algorithm (RA) is proposed to reconstruct the signal from its nonuniform samples. A Based on different sampling theorems (e.g., classic Shannon’s sampling theorem, Papoulis’ Generalized sampling theorem, bandpass sampling theory), signals are processed by the sampling devices and then undergo additional processing. It is a natural goal to obtain the signals at the output of the sampling devices without loss of information. In conventional radio receivers, all the down-conversion and channel selection are realized in analog hardware. The associated sampling devices in A/D converters are based on the classic Shannon’s sampling theorem. Driven by the increased speed of microprocessors, there is a tendency to use mixed-signal/digital hardware and software to realize more functions (e.g., down-conversion, channel selection, demodulation and detection) in a radio communication system. The new evolution of radio receiver architecture is Software Defined Radio (SDR). One design goal of SDR is to put the A/D converter as close as possible to the antenna. BandPass Sampling (BPS) enables one to have an interface between the higher IF and the A/D converter by a sampling rate of 2B or more (B is the information bandwidth), and it might be a solution to SDR. A signal can be uniquely determined from the samples by NonUniform Sampling (NUS) such that NUS has the potential to suppress harmful signal spectrum aliasing. BPS makes use of the signal spectrum aliasing to represent the signal uniquely at any band position. A harmful aliasing of signal spectrum will cause a performance degradation. It is of great benefit to use NUS scheme in BPS system. However, a signal cannot be recovered from its nonuniform samples by using only an ideal lowpass filter (or the classic Shannon’s reconstruction function). The reconstruction of the samples by NUS is crucial for the implementation of NUS. Besides the harmful signal spectrum aliasing, noise aliasing and timing jitter are other two sources of performance degradation in a BPS system. Noise aliasing is the direct consequence of lower sampling rate of subsampling. With the increase of input frequency by directly sampling a signal at higher IF, the timing error of the sampling clock causes large jitter effects on the sampled-data signal. In this thesis work, first, a filter generalized by a certain Reconstruction Algorithm (RA) is proposed to reconstruct the signal from its nonuniform samples. A

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