Joint Data-Aided Carrier Frequency Offset, Phase Offset, Amplitude and SNR Estimation for Millimeter-Wave MIMO Systems

This work is devoted to solve the problem of estimating the carrier frequency offset, phase offset, amplitude, and SNR between two mmWave transceivers. The Cramér-Rao Lower Bound (CRLB) for the different parameters is provided first, as well as the condition for the CRLB to exist, known as Regularity Condition. Thereafter, the problem of finding suitable estimators for the parameters is adressed, for which the proposed solution is the Maximum Likelihood estimator (ML). Notation: here we describe the notation to be used throughout this document: bold uppercase A is used to denote matrices, bold lowercase a denotes a column vector and non-bold lowercase a denotes a scalar value. We use A to denote a set. Further, ‖A‖F is the Frobenius norm and A∗, AC, A and A† denote the conjugate transpose, conjugate, transpose and Moore-Penrose pseudoinverse of a matrix A, respectively. The (i, j)-th entry of a matrix A is denoted using [A]i,j . Similarly, the i-th entry of a column vector a is denoted as [a]i. The identity matrix of order N is denoted as IN . If A and B are two matrices, A ◦B is the Khatri-Rao product of A and B and A⊗B is their Kronecker product. We use N (μ,C) to denote a circularly symmetric complex Gaussian random vector with mean μ and covariance matrix C. We use E to denote expectation. Discrete-time signals are represented as x[n]. ar X iv :1 71 2. 05 98 9v 1 [ cs .I T ] 1 6 D ec 2 01 7