Methods and apparatuses for versatile beamforming

A method for beamforming a signal for a set of transmitters {Ai}i=1, . . . , L, the set of transmitters configured for transmitting signals to one or more regions {Rm}m=1, . . . , M of interest in an n-dimensional space, with n=2 or 3, each of the transmitters having a known position pi within said n-dimensional space, the method comprising:

• determining a n-dimensional spatial filter function {circumflex over (ω)}(r), which matches projections {Pm}m=1, . . . , M of the one or more regions {Rm}m=1, . . . , M of interest onto an n−1-dimensional sphere centered on said set of transmitters;
• obtaining a beamforming function ω(p), based on an inverse Fourier transform of the determined spatial filter function;
• for each of the transmitters {Ai}i=1, . . . , L, determining a beamforming weight ω(pi), by evaluating the obtained beamforming function ω(p) at a known position pi of said each of the transmitters {Ai}i=1, . . . , L;
• and
• beamforming a signal, by weighting time-series to be transmitted by the transmitters {Ai}i=1, . . . , L of the set by respective beamforming weights ω(pi) as determined for each of the transmitters.

A method for determining a series of beams from or for a set of transceivers {Ai}i=1, . . . , L, said set of transceivers configured for receiving signals from and transmitting signals to one or more regions {Rm}m=1, . . . , M of interest in an n-dimensional space, with n=2 or 3, each of the transceivers having a known position pi within said n-dimensional space, the method comprising:

• determining a n-dimensional spatial filter function {circumflex over (ω)}(r), which matches projections {Pm}m=1, . . . , M of the one or more regions {Rm}m=1, . . . , M onto an n−1-dimensional sphere centered on said set of transceivers;
• obtaining a beamforming function ω(p), based on a Fourier transform of the determined spatial filter function;
• for each of the transceivers {Ai}i=1, . . . , L, determining a beamforming weight ω(pi), by evaluating the obtained beamforming function ω(p) at a known position pi of said each of the transceivers {Ai}i=1, . . . , L;
• computing a series of beams, based on a summation of time-series received from the transceivers {Ai}i=1, . . . , L of the set, wherein each of the time series in the summation received by a distinct one Ai of the transceivers is weighted by a beamforming weight ω(pi) as determined for said distinct one Ai of the transceivers;
• and
• beamforming a signal, by weighting time-series to be transmitted by the transceivers {Ai}i=1, . . . , L of the set, by respective beamforming weights ω(pi) as determined for each of the transceivers.

A receiving apparatus comprising a set of receivers {Ai}i=1, . . . , L and configured for computing a beamformed signal from said set of receivers, the set of receivers configured for receiving signals from one or more regions {Rm}m=1, . . . , M of interest in an n-dimensional space, with n=2 or 3, each of the receivers having a known position pi within said n-dimensional space, the apparatus comprising:

• a spatial filter determination module, configured for determining a n-dimensional spatial filter function {circumflex over (ω)}(r), which matches projections {Pm}m=1, . . . , M of the one or more regions {Rm}m=1, . . . , M of interest onto an n−1-dimensional sphere centered on said set of receivers;
• a beamforming function determination module, configured for obtaining a beamforming function ω(p), based on an inverse Fourier transform of a spatial filter function determined by the spatial filter determination module;
• a beamforming weight determination module, configured for determining, for each of the receivers {Ai}i=1, . . . , L, a beamforming weight ω(pi), by evaluating a beamforming function ω(p), as obtained from the beamforming function determination module, at a known position pi of said each of the receivers {Ai}i=1, . . . , L;
• and
• a digital beamforming module, configured for computing a beamformed signal, based on a summation of time-series received by the receivers {Ai}i=1, . . . , L of the set, wherein each of the time series in the summation corresponds to a distinct one Ai of the receivers and is weighted by a beamforming weight ω(pi) as determined for said distinct one Ai of the receivers.

A transmission apparatus comprising a set of receivers {Ai}i=1, . . . , L and configured for beamforming a signal for said set of transmitters {Ai}i=1, . . . , L, the set of transmitters configured for transmitting signals to one or more regions {Rm}m=1, . . . , M of interest in an n-dimensional space, with n=2 or 3, each of the receivers having a known position pi within said n-dimensional space, the apparatus comprising:

• a spatial filter determination module, configured for determining a n-dimensional spatial filter function {circumflex over (ω)}(r), which matches projections of the one or more regions {Rm}m=1, . . . , M of interest onto an n−1-dimensional sphere centered on said set of transmitters;
• a beamforming function determination module, configured for obtaining a beamforming function ω(p), based on an inverse Fourier transform of a spatial filter function as determined by the spatial filter determination module;
• a beamforming weight determination module, configured for determining, for each of the receivers {Ai}i=1, . . . , L, a beamforming weight ω(pi), by evaluating a beamforming function ω(p), as obtained from the beamforming function determination module, at a known position pi of said each of the receivers {Ai}i=1, . . . , L;
• and
• an analog beamforming module, configured for beamforming a signal, by weighting time-series to be transmitted by the transmitters {Ai}i=1, . . . , L of the set, by respective beamforming weights ω(pi) as determined for each of the transmitters by said beamforming weight determination module.

A transceiver apparatus comprising a set of receivers {Ai}i=1, . . . , L and configured for determining a series of beams from or for said set of transceivers {Ai}=i=1, . . . , L, said set of transceivers configured for receiving signals from and transmitting signals to one or more regions {Rm}m=1, . . . , M of interest in an n-dimensional space, with n=2 or 3, each of the receivers having a known position pi within said n-dimensional space, the method comprising:

• a spatial filter determination module, configured for determining a n-dimensional spatial filter function {circumflex over (ω)}(r), which matches projections of the one or more regions {Rm}m=1, . . . , M of interest onto an n−1-dimensional sphere centered on said set of receivers;
• a beamforming function determination module, configured for obtaining a beamforming function ω(p), based on an inverse Fourier transform of a spatial filter function determined by the spatial filter determination module;
• a beamforming weight determination module, configured for determining, for each of the receivers {Ai}i=1, . . . , L, a beamforming weight ω(pi), by evaluating a beamforming function ω(p), as obtained from the beamforming function determination module, at a known position pi of said each of the receivers {Ai}i=1, . . . , L;
• and
• a digital beamforming module, configured for determining a beamformed signal, based on a summation of time-series received by the receivers {Ai}i=1, . . . , L of the set, wherein each of the time series in the summation corresponds to a distinct one Ai of the receivers and is weighted by a beamforming weight ω(pi) as determined for said distinct one Ai of the receivers;
• and
• an analog beamforming module, configured for beamforming a signal, by weighting time-series to be transmitted by the transmitters {Ai}i=1, . . . , L of the set, by respective beamforming weights ω(pi) as determined for each of the transmitters by said beamforming weight determination module.

A computer program product for determining a series of beams from or for a set of devices {Ai}i=1, . . . , L configured for receiving signals from and/or transmitting signals to one or more regions {Rm}m=1, . . . , M of interest in an n-dimensional space, with n=2 or 3, each of the devices having a known position pi within said n-dimensional space, the computer program product comprising a computer readable storage medium having program instructions embodied therewith, the program instructions being executable by a computerized system to cause the latter to:

• determine a n-dimensional spatial filter function {circumflex over (ω)}(r), which matches projections of the one or more regions {Rm}m=1, . . . , M onto an n−1-dimensional sphere centered on said set of devices;
• obtain a beamforming function ω(p), based on a Fourier transform of the determined spatial filter function;
• for each of the devices {Ai}i=1, . . . , L, determine a beamforming weight ω(pi), by evaluating the obtained beamforming function {circumflex over (ω)}(p) at a known position pi of said each of the devices {Ai}i=1, . . . , L;
• and
• weight time-series from or for the devices {Ai}i=1, . . . , L of the set, wherein each of the time series from or for a distinct one Ai of the devices is weighted by a beamforming weight ω(pi) as determined for said distinct one Ai of the devices.