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 (λ 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 |