Sensor array processor with multichannel reconstruction from random array sampling
A method and system for reconstructing random samples taken across multiple sensors of a sensor array, so that each sensor's output is reconstructed. The samples are processed using a compressive sensing process. The compressive sensing process uses a time-space transform basis that represents the multi-channel data in terms of both a frequency component and an azimuthal component.
1. A method of acquiring multi-channel data from a multi-sensor sensor array, the array having multiple sensor elements each of which produce an output signal, comprising:
using an array sampler to pseudo-randomly sample the output signal of each element, thereby acquiring a single-channel signal that represents the sampled output of all sensor elements;
converting the single-channel signal to digital data;
delivering the digital data to a decompression unit operable to construct a signal from each sensor element of the multiple sensor elements, using a compression sensing matrix;
wherein the compression sensing matrix is formed from a sampling matrix and a transform matrix;
wherein the transform matrix represents the multi-channel data in terms of a frequency domain and an azimuthal domain; and
wherein the sampling matrix is derived from an array vector matrix comprising vectors e i where i indicates the array element being sampled.
2. The method of claim 1 , wherein the sensor array is an antenna sensor array.
3. The method of claim 1 , wherein the transform matrix is derived from a space-time transform.
4. The method of claim 3 , wherein the space-time transform is a wavenumber vector Fourier transform.
5. The method of claim 1 , wherein the sampling matrix is a product of an identity matrix and the array vector matrix.
6. A system for sampling and reconstructing the output of a multi-sensor sensor array, the array having multiple sensor elements each of which produce an output signal, comprising:
an array sampler configured to pseudo-randomly sample the output signal of each element, thereby acquiring a single-channel signal that represents the sampled output of all sensor elements;
a receiver operable to receive the single-channel signal;
a converter operable to convert the single-channel signal to digital data;
a decompression unit operable to construct a signal from each sensor element of the multiple sensor elements from the digital data, using a compression sensing matrix;
wherein the compression sensing matrix is formed from the sampling matrix and the transform matrix;
wherein the transform matrix represents the multi-channel data in terms of a frequency domain and an azimuthal domain; and
wherein the sampling matrix is derived from an array vector matrix comprising vectors e i where i indicates the array element being sampled.
7. The system of claim 6 , wherein the sensor array is an antenna sensor array.
8. The system of claim 6 , wherein the transform matrix is derived from a space-time transform.
9. The system of claim 8 , wherein the space-time transform is a wavenumber vector Fourier transform.
10. The system of claim 6 , wherein the sampling matrix is a product of an identity matrix and the array vector matrix.
11. The system of claim 6 , wherein the decompression unit is implemented with firmware.
12. The system of claim 6 , wherein the decompression unit is implemented with software.