Carrier and sampling frequency offset estimation for RF communication with crystal-less nodes

A method for determining frequency offsets in a wireless communication system, comprising:

• receiving, at signal processor of a gateway, an incoming signal over a wireless communication channel from a transmitting node, where the incoming signal has a carrier oscillating at radio frequencies and at least a portion of the incoming signal is modulated by a pulse stream with a constant interval between pulses;
• partitioning, by the signal processor, the portion of the incoming signal into a plurality of segments;
• for each segment in the plurality of segments, applying, by the signal processor, a Fourier transform to a given segment and stacking results from the Fourier transform to build a first two dimensional matrix, where one dimension in the first two dimension matrix corresponds to a carrier frequency within a range of possible carrier frequency offsets and other dimension in the first two dimension matrix corresponds to a different segment in the plurality of segments;
• for each carrier frequency in the range of possible carrier frequency offsets, applying, by the signal processor, Fourier transform to data associated with a given carrier frequency and thereby generate a second two dimensional matrix, where one dimension in the second two dimension matrix corresponds to a carrier frequency within a range of possible carrier frequency offsets and other dimension in the second two dimension matrix corresponds to a frequency in a range of possible sampling frequency offsets;
• and
• identifying an element in the second matrix with highest value, where an index of one dimension hosting the identified element indicates a carrier frequency offset for the incoming signal and an index of other dimension hosting the identified element indicates a sampling frequency for the incoming signal.

A wireless communication system, comprising

• a sensor node;
• and
• a gateway, wherein the gateway includes
• a processor;
• and
• a storage medium having computer program instructions stored thereon, when executed by the processor, perform to:
• receive an incoming signal over a wireless communication channel from the sensor node, where the incoming signal has a carrier oscillating at radio frequencies and at least a portion of the incoming signal is modulated by a pulse stream with a constant interval between pulses;
• partition the portion of the incoming signal into a plurality of segments;
• for each segment in the plurality of segments, apply a transform to a given segment and stack results from the transform to build a first two dimensional matrix, where the transform analyzes frequency content of the given segment, wherein one dimension in the first two dimension matrix corresponds to a carrier frequency within a range of possible carrier frequency offsets and other dimension in the first two dimension matrix corresponds to a different segment in the plurality of segments;
• for each carrier frequency in the range of possible carrier frequency offsets, apply the transform to data associated with a given carrier frequency and thereby generate a second two dimensional matrix, where one dimension in the second two dimension matrix corresponds to a carrier frequency within a range of possible carrier frequency offsets and other dimension in the second two dimension matrix corresponds to a frequency in a range of possible sampling frequency;
• and
• identify an element in the second matrix with highest value, where an index of one dimension hosting the identified element indicates a carrier frequency offset for the incoming signal and an index of other dimension hosting the identified element indicates a sampling frequency for the incoming signal.