Random SBT Precoding for Angle Estimation of mmWave Massive MIMO Systems Using Sparse Arrays Spacing

Abstract

In this paper, 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.

Robust Gridless Estimation of Angles and Delays for Full-Dimensional Wideband mmWave Channels

“…Lemma 4. Suppose the precoder F[q] and combiner G[q] are BBT as in (13) and the training sequence in ( 26) is used. Then Ỹ[q] can be expressed as…”

“…Theorem 2. Suppose we design the training sequence as in (26) and use BBT precoder and combiner with prototypes as in (13). Then, Y (wb) in ( 33) is equivalent to the received matrix of a time-varying channel with path gain vector d [q] for q = 0, 1, • • • , K − 1.…”

“…For methods that are developed specifically for time-varying channels or timeinvariant channels, the estimation result is sensitive to the timevariation of the channel. Direction finding methods that are not sensitive to the time-variation of the channel have been considered in [12] [13]. A hierarchical beam training method using successive beams of different beamwidth is considered in [12].…”

“…The estimation accuracy is limited by the underlying grids. In [13] the precoder is obtained by selecting the columns of a Toeplitz matrix according to the spacing of a sparse linear array. An enlarged virtual ULA can be constructed for high resolution angle estimation.…”