# Joint DOA and Frequency Estimation with Sub-Nyquist Sampling for More Sources than Sensors

## TL;DR

This paper introduces a sub-Nyquist sampling approach for joint DOA and frequency estimation that can handle more sources than sensors, improving estimation accuracy and source count identification.

## Contribution

It extends array receiver architecture to more general scenarios with multiple signals per subband and proves the CRB is lower than Nyquist-based methods.

## Key findings

- Estimates source number accurately in simulations.
- Performance closely matches the CRB.
- Outperforms Nyquist sampling especially with MRA.

## Abstract

In this letter, we apply previous array receiver architecture which employs time-domain sub-Nyquist sampling techniques to jointly estimate frequency and direction-of-arrival(DOA) of narrowband far-field signals. Herein, a more general situation is taken into consideration, where there may be more than one signal in a subband. We build time-space union model, analyze the identification of the model, and give the maximum signal number which can be classified. We also proof that the Cramer-Rao Bound (CRB) is lower than that of which employs Nyquist sampling. Simulation results verify the capacity to estimate the number of sources. Meanwhile, simulations show that our estimation performance closely matches the CRB and is superior for more sources than sensors, especially when the minimum redundancy array (MRA) is employed.