CRLB Calculations for Joint AoA, AoD and Multipath Gain Estimation in Millimeter Wave Wireless Networks

In this report we present an analysis of the non-random and the Bayesian Cramer-Rao lower bound (CRLB) for the joint estimation of angle-of-arrival (AoA), angle-of-departure (AoD), and the multipath amplitudes, for the millimeter-wave (mmWave) wireless networks. Our analysis is applicable to multipath channels with Gaussian noise and independent path parameters. Numerical results based on uniform AoA and AoD in [0, π), and Rician fading path amplitudes, reveal that the Bayesian CRLB decreases monotonically with an increase in the Rice factor. Further, the CRLB obtained by using beamforming and combining code books generated by quantizing directly the domain of AoA and AoD was found to be lower than those obtained with other types of beamforming and combining code books. This technical report provides detailed calculations with respect to the derivation of non-random and random CRLB for the joint estimation problem of AoA, AoD and multipath gains. The first author is with the Dhirubhai Ambani Institute of Information and Communication Technology (DAIICT), Gandhinagar, Gujarat, India and the second author is with the NorthEastern University, Boston, MA, USA. Email:{[email protected], [email protected]} ar X iv :1 70 4. 00 45 3v 1 [ cs .I T ] 3 A pr 2 01 7