Table 2 Elements required in (45) to assemble the FIM in (35) for a Rayleigh fading channel
From: Cramer-Rao bounds in the estimation of time of arrival in fading channels
p | Ψ p | A | B | C |
|---|---|---|---|---|
1 | k 0 | R ϕ | T K | P s ∂Λ τ /∂k0 |
2 | λ n | R ϕ | T K | P s ∂ Λ τ / ∂ k 0 |
3 | β | R ϕ | T K | \({\mathbf {P_{s}\partial \left (G_{s}\boldsymbol {\Lambda }_{\tau } G_{s}^{T}\right)/\partial \beta }}\) |
4 | P s | R ϕ | T K | \({\mathbf {G_{s}\boldsymbol {\Lambda }_{\tau } G_{s}^{T}}}\) |
5 | \(\sigma _{w}^{2}\) | I Ns | I K | I N |
6 | α | R ϕ | ∂ T / ∂ α | \({\mathbf {P_{s}G_{s}\boldsymbol {\Lambda }_{\tau } G_{s}^{T}}}\) |
7: N p | ρ p−6 | ∂ R ϕ / ∂ ρ p−6 | T K | \({\mathbf {P_{s}G_{s}\boldsymbol {\Lambda }_{\tau } G_{s}^{T}}}\) |