Difference-Frequency MUSIC for DOAs

The direction-of-arrivals (DOAs) of plane waves in a high-frequency region are estimated without spatial aliasing using multi-frequency processing. The method exploits the difference frequency (DF), the difference between two high frequencies. This enables processing data in a feasible region without spatial aliasing. We analyze DOA characteristics upon DF processing and propose a MUSIC-based method dealing with multi-DF and multi-snapshot. Multiple DFs having the same frequency difference allow processing multi-DF equivalently to multi-snapshot. We propose a method that considers all DFs and snapshots jointly and a joint DF method providing a single snapshot DF-MUSIC that does not require stationary DOAs. Numerical examples validate the effectiveness of the proposed method and its DOA performance is discussed.

I. Introduction

Due to spatial aliasing, uniform linear arrays limit the plane-wave DOA estimation to an upper frequency. To consider a specific frequency component of data, data should be sampled at more than two points per wavelength. Otherwise, the DOA becomes ambiguous with components at wrong DOAs. This problem arises especially with passive systems when processing out-of-band signals at higher frequencies.