A t (θ t,ϕ t ), A r (θ r,ϕ r ) and G(θ r,ϕ r,γ,η) denote the transmit steering matrix, receive steering matrix and polarization matrix, respectively.
where t is the slow time index, A r = [a r (ϕ1),..., a r (ϕ L )] and A t = [a t (θ1),..., a t (θ L )], with a r ( ϕ l ) ∈ ℂ N r × 1 and a t ( θ l ) ∈ ℂ N t × 1, respectively, denoting the receive steering vector corresponding to DOA ϕ l and the transmit steering vector corresponding to DOD θ l.
ψ T = 2πPd T cos θ cos φ/λ is the phase shift induced by the distance between adjacent subarrays which means that the distance between any two neighbor transmit phase centers is P times that of d T. aR is the N × 1 receive steering vector defined as a R θ = 1, e - j ψ R, …, e - j N - 1 ψ R T ∈ C N × 1, (3).
denotes the receiving steering vector for incident angle ϑ.
Its receiving steering vector b3 is a K-dimensional vector whose elements' phases are identically independently distributed (i.i.d)., uniformly in (0,2π).
where Z l = z 1, l T, z 2, l T, …, z N , l T T∈ C N × K, a = 1, e j 2 π f s, …, e j 2 π N − 1 f s T, and a i = 1, e j 2 π f s, i, …, e j 2 π N − 1 f s, i T denote the receiving steering vectors for the target and the clutter patch at θ i, respectively.
(mathbf{A}(theta)={boldsymbol {a}^_{r}(theta)}{{boldsymbol {a}_{t}}^{dag }{(theta)}}), in which for the azimuth angle θ, a t and a r denote, respectively, the transmit spatial steering vector and the receive spatial steering vector.
But PowerShift doesn't receive any steering input, so when set to Sport it mindlessly downshifts whenever the driver brakes.
The desired transmit-receive steering vector is estimated through maximizing the output power subject to constraints upon correlation coefficient and steering vector norm.
σ 1, σ 2, and σ 3 are, respectively, unknown complex vectors describing errors of the transmitting and receiving array steering vectors, as well as the Doppler vector.
Similar to [21], the actual transmitting and receiving array steering vectors, as well as the Doppler vector, can be modeled as b ˜ = b + σ 1, a ˜ = a + σ 2, u ˜ D = u D + σ 3, (26).
