Automotive radar with sparse array DOA estimation

A radar system comprising:

• a plurality of transmitter modules configured to transmit a plurality of transmitted radar signals, wherein each transmitted radar signal is associated with a transmit channel of a plurality of transmit channels;
• a plurality of receiver modules configured to receive reflections of the plurality of transmitted radar signals reflected by at least one object and to generate signals based on the received reflections;
• and
• a signal processor configured to:
• determine a steering matrix for the radar system, wherein the steering matrix defines a plurality of steering vectors, wherein each steering vector in the plurality of steering vectors is associated with a frequency,
• determine a measurement vector using signals received by the plurality of receiver modules,
• initializing a first output amplitude vector using the steering matrix and the measurement vector;
• determine a second output amplitude vector by performing steps including:
• determining a diagonal loading vector using the first output amplitude vector;
• calculating a weighting matrix by executing a first fast Fourier transform using the diagonal loading vector,
• determining an inverse matrix as an inversion of a sum of the weighting matrix and an identity matrix;
• and
• executing a second fast Fourier transform using the inverse matrix to determine the second output amplitude vector, wherein the second output amplitude vector is determined by a relationship between the steering matrix and the measurement vector;
• determine a normalized difference between the second output amplitude vector and the first output amplitude vector is greater than a convergence threshold;
• executing an inverse fast Fourier transform to determine an estimate of the measurement vector using the second output amplitude vector;
• computing a set of diagonal elements by executing a fast Fourier transform using the inverse matrix;
• updating a noise parameter using the estimate of the measurement vector;
• updating a scaling parameter using the second output amplitude vector;
• determining a third output amplitude vector using the noise parameter and the scaling parameter;
• and
• determining an estimated direction of arrival of a first object by correlating the third output amplitude vector to the measurement vector, wherein the signals received by the plurality of receiver modules are associated with a MIMO virtual array in which antenna elements are evenly spaced from one another by a multiple of a unit value, wherein the identity matrix has dimensions N×N where N is equal to a number of the antenna elements in the MIMO virtual array.

A method, comprising:

• determining a steering matrix for a radar system, wherein the steering matrix defines a plurality of steering vectors, wherein each steering vector in the plurality of steering vectors is associated with a frequency,
• determining a measurement vector using signals received by a plurality of receiver modules,
• initializing an output amplitude vector using the steering matrix and the measurement vector;
• determine an optimized output amplitude vector by performing steps including:
• determining a diagonal loading vector using the output amplitude vector;
• calculating a weighting matrix by executing a first fast Fourier transform using the diagonal loading vector,
• determining an inverse matrix as an inversion of a sum of the weighting matrix and an identity matrix;
• executing a second fast Fourier transform using the inverse matrix to determine the optimized output amplitude vector, wherein the optimized output amplitude vector is determined by a relationship between the steering matrix and the measurement vector;
• and
• determining an estimated direction of arrival of a first object by correlating the optimized output amplitude vector to the measurement vector, wherein the signals received by the plurality of receiver modules are associated with a MIMO virtual array in which antenna elements are evenly spaced from one another by a multiple of a unit value, wherein the identity matrix has dimensions N×N where N is equal to a number of the antenna elements in the MIMO virtual array.