Low dimensional encoding broadband beamformer with reduced hardware arrays
A beamforming system and method is disclosed comprising a hybrid multi-measurement unit or process that can encode or embed broadband signals in a low dimensional encoding subspace such as a Slepian subspace. The direction-of-arrival of the plane wave signals, encoded with the low dimensional embedding, can be used to provide a spatially sampled signal to a front-end mixed-signal circuitries substantially reduced hardware for beamforming systems. The beamforming array has a finite array aperture to which a temporal snapshot of the signal can be acquired and then processed as a set of samples from a time-limited bandlimited sequence.
1 . A system comprising:
a broadband receiver comprising an array of beamforming receiving elements, wherein the array of beamforming receiving elements is configured to receive a plane wave to provide a plurality of input signals corresponding to a number of receiving elements of the array;
a demodulation unit coupled to the broadband receiver, the demodulation unit comprising a plurality of measurement modules, including a first measurement module and a second measurement module, wherein each module is coupled to one or more receiving elements of the array to receive corresponding input signals, wherein the first measurement module and a second measurement module respectively defines an aperture of the array at a first projection and a second projection of the plane wave and includes a set of phase and magnitude varying elements configured to apply an effective complex weight associated with the projection; and
a set of combiner units, including a first combiner unit and a second combiner unit, wherein each of the set of combiner units is coupled to outputs of a respective module of the plurality of measurement modules, and wherein the first combiner unit is coupled to outputs of the first measurement module and the second combiner unit is coupled to outputs of the second measurement module.
2 . The system of claim 1 , further comprising:
a set of analog-to-digital converters, wherein the number of the plurality of measurement modules corresponds to the number of the set of analog-to-digital converters, and wherein the number of analog-to-digital converters is less than the number of receiving elements of the array.
3 . The system of claim 1 , wherein the first measurement module is successively coupled to the second measurement module.
4 . The system of claim 1 , wherein the first measurement module and the second measurement module are coupled to one another in a parallel configuration.
5 . The system of claim 1 , wherein the first measurement module is coupled to each of the receiving elements of the array.
6 . The system of claim 1 , wherein the first measurement module is coupled to a subset of the receiving elements of the array.
7 . The system of claim 1 , wherein outputs of the set of combiner units are operatively coupled to a respective analog-to-digital converter, wherein a first output of the first combiner unit is coupled to a first analog-to-digital converter and a second output of the second combiner unit is coupled to a second analog-to-digital converter.
8 . The system of claim 1 , wherein the set of the phase and magnitude varying elements applies the effective complex weight associated with the projection using modulation weights derived from sampled prolate spheroidal wave functions.
9 . The system of claim 1 , wherein the set of the phase and magnitude varying elements applies the effective complex weight associated with the projection using modulation weights that are unimodular or are restricted to be members of a set with finite cardinality.
10 . The system of claim 1 , wherein the array of beamforming receiving elements is configured as a 2D or a 3D array.
11 . The system of claim 1 , wherein the elements of the array are disposed on a conformal 3D structure.
12 . The system of claim 1 , wherein the elements of the array are configured in a grid pattern, a circular or oval-shaped pattern, or an unstructured pattern.
13 . The system of claim 1 , wherein the first combiner unit comprises a weighted summing circuit that connects to outputs of the first set of phase and magnitude varying elements.
14 . The system of claim 1 , wherein the set of the phase and magnitude varying elements comprises at least one of a phase shifter circuit, a polarity inverter circuit, or an amplifier circuit.
15 . The system of claim 1 , further comprising:
a processor coupled to outputs of the set of combiner units to receive sampled ADC values, wherein the processor is configured to reconstruct a transmitted signal using the sampled ADC values.
16 . The system of claim 15 , wherein the set of combiner units is configured to temporally sample values at a decimation rate prior to reconstructing the transmitted signal, wherein the temporally sampled values have a fixed or variable sampling rate lower than the Nyquist rate.
17 . The system of claim 15 , wherein the processor is configured to perform fast Slepian computation to reconstruct the transmitted signal.
18 . The system of claim 2 , further comprising:
a processor coupled to outputs of the set of analog-to-digital converters to receive sampled ADC values, wherein the processor is configured to determine a direction of arrival (DOA) of the plane wave using the sampled ADC values.
19 . The system of claim 2 , further comprising:
a processor coupled to outputs of the set of analog-to-digital converters to receive sampled ADC values, wherein the processor is configured to classify a signal type of a transmitted bandlimited signal using the sampled ADC values.
20 . The system of claim 2 , further comprising:
a processor coupled to outputs of the set of analog-to-digital converters to receive sampled ADC values, wherein the processor is configured to decode communication symbols encoded in a transmitted bandlimited signal using the sampled ADC values.
21 . A system comprising:
a broadband transmitter comprising an array of beamforming transmitting elements, wherein the array of beamforming transmitting elements is configured to receive a plurality of signals corresponding to a number of transmitting elements to transmit a plane wave;
a low-dimensional encoding broadband beamformer unit, the low-dimensional encoding broadband beamformer unit being coupled to the broadband transmitter, the low-dimensional encoding broadband beamformer unit comprising a plurality of beamforming modules, including a first beamforming module and a second beamforming module, wherein each beamforming module is configured to create a projection of the plane wave and includes a phase and magnitude varying elements to apply an effective complex weight associated with the projection, and wherein the set of the phase and magnitude varying elements are coupled to each transmitting element of the array of beamforming transmitting elements; and
a plurality of digital-to-analog converters, each coupled to each beamforming module of the plurality of beamforming modules.
22 . A method comprising:
receiving a low-dimensional encoded broadband signal as a plane wave at a broadband array receiver comprising an array of beamforming receiving elements, wherein the array is configured to provide a plurality of input signals corresponding to the array of beamforming receiving elements;
decoding the plurality input signals at a demodulation unit coupled to the broadband array receiver, the demodulation unit comprising a plurality of measurement modules, including a first measurement module and a second measurement module, each module is coupled to one or more receiving elements of the array, wherein the first measurement module and the second measurement module defines an aperture of the array at a respective first projection and second projection of the plane wave and includes a set of phase and magnitude varying elements configured to apply different effective complex weights to the input signals, wherein the complex weights at each measurement module are associated with a given projection of the plane wave as incident on the broadband array,
combining outputs of a respective module of the plurality of measurement modules at a set of combiner units, wherein the set of combiner units, including a first combiner unit and a second combiner unit, is coupled to outputs of a respective module of the plurality of measurement modules, wherein the first combiner unit is coupled to outputs of the first measurement module and the second combiner unit is coupled to outputs of the second measurement module; and
reconstructing, via a processor, a source signal based on the decoding.
23 . The method of claim 22 , wherein the reconstruction of the source signal comprises:
combining, using a respective combiner unit in a set of combiner units, outputs of each measurement module;
sampling, using a set of analog-to-digital converters (ADC), the combined outputs into sampled ADC values; and
reconstructing the source signal using sampled ADC values, wherein the processor is coupled to outputs of the analog-to-digital converters.
24 . The method of claim 22 , wherein the input signals comprise spatially sampled signals.
25 . The system of claim 21 , wherein each beamforming module is configured to encode a coefficient channel associated with a measurement basis function.
26 . The system of claim 25 , wherein the measurement basis function is associated with a set of prolate spheroidal wave functions, a set of DFT functions, or a set of binary functions.
27 . The system of claim 21 , wherein the number of the plurality of beamforming modules corresponds to the number of the plurality of digital-to-analog converters, and wherein the number of the plurality of digital-to-analog converters is less than the number of transmitting elements of the array.