Multi-Frequency Co-Prime Arrays for High-Resolution Direction-of-Arrival Estimation

This paper presents multi-frequency operation for increasing the number of resolvable sources in high-resolution direction-of-arrival (DOA) estimation using co-prime arrays. A single-frequency operation requires complicated and involved matrix completion to utilize the full extent of the degrees of freedom (DOFs) offered by the co-prime configuration. This processing complexity is attributed to the missing elements in the corresponding difference coarray. Alternate single-frequency schemes avoid such complexity by utilizing only the filled part of the coarray and, thus, cannot exploit all of the DOFs for DOA estimation. We utilize multiple frequencies to fill the missing coarray elements, thereby enabling the co-prime array to effectively utilize all of the offered DOFs. The sources are assumed to have a sufficient bandwidth to cover all the required operational frequencies. We consider both cases of sources with proportional and nonproportional power spectra at the employed frequencies. The former permits the use of multi-frequency measurements at the co-prime array to construct a virtual covariance matrix corresponding to a filled uniformly spaced coarray at a single frequency. This virtual covariance matrix can be employed for DOA estimation. The nonproportionality of the source spectra casts a more challenging situation, as it is not amenable to producing the same effect as that of an equivalent single-frequency filled coarray. Performance evaluation of the multi-frequency approach based on computer simulations is provided under both cases of proportional and nonproportional source spectra.