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.
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.
In the single snapshot case, the received noise-free echo of one ideal target can be represented as the following receive steering vector mathbf{b}(r, theta)=left[begin{array}{cccccc} e^{-jphi_{0}} & e^{-jphi_{1}} & ldots & e^{-jphi_{m}} & ldots & e^{-jphi_{M-1}} end{array}right]^{T}, (25).
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).
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).
The desired transmit-receive steering vector is estimated through maximizing the output power subject to constraints upon correlation coefficient and steering vector norm.
(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.
