In this article, we consider the estimation of angle of arrival (AoA) and angle of departure (AoD) for mmWave MIMO channels. For mmWave systems, there is typically a large number of antennas but limited radio frequency (RF) chains. The RF chain limitation indirectly restricts the effective number of antennas or the effective array size. In radar applications, it is known that a larger array size leads to more accurate AoA estimation or more resolvable paths. It is also known that with sparse arrays, which places antennas in a nonuniform sparse manner, an enlarged virtual array can be constructed when the sources are uncorrelated. We show that the idea of sparse arrays can also be used in mmWave systems to have augmented array sizes. The main difficulty in applying sparse arrays to mmWave MIMO channels lies in the fact the signals of different paths can be correlated in mmWave system, but uncorrelatedness is necessary for applying sparse array results. We show that the paths can be decorrelated by employing random precoders and combiners that are submatrices of banded Toeplitz matrices (SBT). When the precoder and combiner are SBT that are designed according to the antenna spacing of a sparse array, we can construct enlarged virtual transmit and receive arrays. With enlarged virtual arrays, accurate estimates can be obtained, as will be demonstrated by simulation examples.
- Angle estimation
- Hybrid precoder
- Massive MIMO
- Sparse arrays
- Submatrix of a banded Toeplitz