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Table 1 Notations

From: Cramer-Rao bounds in the estimation of time of arrival in fading channels

Notation Description
N,K,N s Respectively, the number of lags at the observation windows, the number of channel vector estimates, and the number of sensors at the antenna array
\(\phantom {\dot {i}\!}\mathbf {z} \in {C^{NK{N_{s}} \times 1}}\) Vector containing the channel estimates
\(\phantom {\dot {i}\!}\mathbf {w} \in {C^{NK{N_{s}} \times 1}}\) Vector containing the estimation noise
R z Correlation matrix for channel estimates
R ϕ ( ρ ) Spatial correlation matrix (spatial correlation vector)
T ( α ) Temporal correlation matrix (temporal correlation coefficient)
\({\mathbf {P_{s}, \sigma _{w}^{2}}}\) Respectively, the signal power factor and the noise variance
G s ( β ) Pulse shaping matrix (roll-off factor)
Λ τ n ) Diagonal matrix that models delay dispersion (coherence bandwidth)
b ϕ ( ρ ) LOS expected spatial signature (spatial correlation vector)
α t ( α ) LOS expected temporal vector (temporal correlation coefficient)
\({\mathbf {g^{\left (k_{0}\right)}}}\) Pulse shape vector for the first arrival
  1. Description of notations frequently used within the text