Systems and methods for joint angle-frequency determination

A system for determining angle and frequency of transmission from a transmitter, comprising:

• a first processor;
• and
• a first memory in electrical communication with the first processor, the first memory comprising instructions which, when executed by a processing unit comprising at least one of the first processor and a second processor, and in electronic communication with a memory module comprising at least one of the first memory and a second memory, program the processing unit to:
• receive in the memory module, during a current coherent dwell, sensor data comprising a first plurality of samples, the first plurality of samples comprising N samples collected at each one of D sensors, at least one of N and D being greater than one;
• select a second plurality of M samples from the first plurality of samples, M being less than N times D;
• and
• determine angle and frequency of transmission of a transmitter by minimizing l1 norm of the second plurality of M samples by solving an underdetermined linear system comprising a product of:
• (i) a phase functional representing a mapping between a time-distance representation of sensor samples and angle-frequency representation thereof, and (ii) the second plurality of M samples.

A system for determining angle and frequency of transmission from a transmitter, comprising:

• a sensor array comprising D sensors, each of which is configured collect a sample during each one of N different sampling periods in one coherent dwell, at least one of N and D being greater than one;
• a pseudorandom selector adapted to obtain, during a current coherent dwell, a plurality of M samples, M being less than N times D;
• a processor configured for determining angle and frequency of transmission of a transmitter by minimizing l1 norm of the plurality of M samples by solving an underdetermined linear system comprising a product of:
• (i) a phase functional representing a mapping between a time-distance representation of sensor samples and angle-frequency representation thereof, and (ii) the plurality of M samples.