Digital signal decimation by subspace projection

A method of receiving a radio frequency signal, comprising:

• demodulating the radio frequency signal to generate an analog baseband signal;
• generating a digital signal, x(n), from the analog baseband signal;
• and
• performing a method of decimating the digital signal, x(n), where n is an integer, to generate a decimated digital signal from the digital signal, x(n), wherein the method of decimating the digital signal, x(n), comprises:
• determining a signal vector, y(k), of size M by partitioning samples of the digital signal, x(n) according to sampling phases of the samples, wherein each element of the signal vector, y(k), is a signal constructed with a same sampling phase;
• projecting the signal vector, y(k), onto an N-dimensional sub-space, wherein N is an integer and N<M;
• determining a covariance matrix Ry, of the signal vector y(k);
• determining N eigen vectors corresponding to N greatest eigen values of the covariance matrix, Ry, wherein the N-dimensional sub-space is spanned by the N eigen vectors;
• and
• determining an M×N or N×M matrix V, comprising the N eigen vectors,
• wherein the signal vector, y(k), is projected onto the N-dimensional sub-space in accordance with
• z(n)=VHy(n) or
• z(n)=y(n)VH,
• wherein VH is the Hermitian transpose of the matrix, V, and z(n) is a decimated signal.

A decimator that decimates a digital signal, x(n), where n is an integer, the decimator comprising:

• logic that generates the digital signal, x(n), as part of a radio communication process;
• logic that determines a signal vector, y(k), of size M by partitioning samples of the digital signal, x(n) according to sampling phases of the samples, wherein each element of the signal vector, y(k), is a signal constructed with a same sampling phase;
• logic that projects the signal vector, y(k), onto an N-dimensional sub-space, wherein N is an integer and N<M;
• logic that determines a covariance matrix Ry, of the signal vector y(k);
• logic that determines N eigen vectors corresponding to N greatest eigen values of the covariance matrix, Ry, wherein the N-dimensional sub-space is spanned by the N eigen vectors;
• and
• logic that determines an M× N or N×M matrix, V, comprising the N eigen vectors,
• wherein the signal vector, y(k), is projected onto the N-dimensional sub-space in accordance with
• z(n)=VHy(n) or
• z(n)=y(n)VH,
• wherein VH is the Hermitian transpose of the matrix, V, and z(n) is a decimated signal.

A radio receiver comprising:

• a demodulator that generates an analog baseband signal from a received radio frequency signal;
• a circuit that generates a digital signal, x(n), from the analog baseband signal;
• and
• a decimator that decimates the digital signal, x(n), where n is an integer, wherein the decimator generates a decimated digital signal from the digital signal, x(n), and wherein the decimator comprises:
• logic that determines a signal vector, y(k), of size M by partitioning samples of the digital signal, x(n) according to sampling phases of the samples, wherein each element of the signal vector, y(k), is a signal constructed with a same sampling phase;
• logic that projects the signal vector, y(k), onto an N-dimensional sub-space, wherein N is an integer and N<M;
• logic that determines a covariance matrix Ry, of the signal vector y(k);
• logic that determines N eigen vectors corresponding to N greatest eigen values of the covariance matrix, Ry, wherein the N-dimensional sub-space is spanned by the N eigen vectors;
• and
• logic that determines an M×N or N×M matrix, V, comprising the N eigen vectors,
• wherein the signal vector, y(k), is projected onto the N-dimensional sub-space in accordance with
• z(n)=VHy(n) or
• z(n)=y(n)VH,
• wherein VH is the Hermitian transpose of the matrix, V, and z(n) is a decimated signal.