The invention is directed to a space-time adaptive (STAP) array architecture having a sparse multichannel receiver array, and more particularly to such an array incorporating a Doppler filter bank behind each array element.
Adaptive beamforming is a powerful technique used in modern radars to mitigate the impact of unintentional interference and hostile jamming. Typically, nulls are created in the receive pattern of an array by applying a complex weight to each array element. Using conventional linear processing, an array of N physical elements can form no more than N−1 adaptive nulls. To overcome this limitation, nonlinear techniques have been developed capable of forming O(N2) nulls in an array pattern. A drawback to nonlinear adaptive processing is that any Doppler information in the received signal is lost.
To provide a brief overview of nonlinear adaptive processing consider an N element nonuniform linear array (NULA). Assume M narrowband signals arc arriving at this array from directions 01, 02, . . . , 0M with powers σ12, σ22, . . . , σM2, respectively. Let v(0) be the N-by-1 steering vector corresponding to the direction 0,
v(0)=[1ej(2π/λ)d
where d1 denotes the position of the ith sensor. The received signal at time instant k is
x[k]=A(0)s(k)+n[k] (2)
where A(0)=[v(01) v(02) . . . v(0M)] is the array manifold matrix and s[k]=[s1[k] s2[k] . . . sm [k]]T is a vector of samples from uncorrelated signal sources. The noise n[k] is assumed to be temporally uncorrelated so that the signal covariance matrix Rss is diagonal. Now the covariance matrix of the received signal becomes
Next, the covariance matrix Rss is vectorited to create the vector
where * denotes conjugation. p=[σ12 σ22 . . . σM2]T and 1n=[e1T e2T . . . eNT]T with ei a column vector of all zeros except for a one in the ith position. The matrix
A(0)*: A(0)=[v(01)*{circle around (⋅)}v(01) . . . v(0M)*{circle around (⋅)}v(0M)] (7)
is the Khatri-Rao product of the matrices A(0)* and A(0) with {circle around (⋅)} denoting the Kronecker product. In conventional nonlinear adaptive processing. the adapted beampattern is formed by applying a weight vector w to the vector z(0): as in wHz(0). [1]-[3].
A drawback to nonlinear adaptive processing is that any Doppler information in the received signal is lost.
According to the invention, a sparse multichannel array includes a plurality of array elements, a receiver behind each array element, and a Doppler filter bank behind each receiver, whereby within each Doppler bin is placed spatial nulls at selected angles of undesired interference.
The purpose of this invention is to exploit the extra spatial degrees of freedom inherent in nonlinear adaptive processing while also retaining the Doppler information in the received signal. The invention incorporates a Doppler filter bank behind each element of a sparse multichannel array and within each Doppler bin places spatial nulls at the angles of undesired interference.
The invention exploits the extra spatial degrees of freedom inherent in nonlinear adaptive processing while also retaining the Doppler information in the received signal. The invention enables Doppler processing to be performed on sparse arrays, such as nested or coprime arrays, used in nonlinear adaptive beamforming to mitigate the impact of unintentional interference and hostile jamming on the received signal. The invention has applications to Synthetic Aperture Radars (SARs) deployed on Unmanned Aerial Vehicles (UAVs) with severe form factor constraints. Other applications include conventional, legacy radars operating in dense interference environments, and passive sonar systems operating in littoral environments.
The invention is illustrated in
To describe the operation of this array architecture consider the discrete-time voltage output vector xn(m,0) of a sparse (e.g.. nested or coprime) array in the absence of noise.
xn(m,0)=sn[m]v(0) (8)
where rn denotes pulse number. n corresponds to the range bin. sn(m) represents complex baseband samples of the signal. and v(0) is the steering vector in the direction 0 of a single target. For a fixed range bin n, the Discrete Fourier Transform of xn(m, 0) over K pulses yields the Doppler spectrum
xn(fk, 0)=sn(fk)v(0) (9)
for k=0,1, . . . , K−1. Taking the Kronecker product of xn(fk, 0) in each Doppler bin yields
zk(0)=xn(fk,0)*{circle around (⋅)}xn(fk, 0)=|sn(fk)|2(v(0)*{circle around (⋅)}v(0)). (10)
After computing an adaptive weight vector wk using any one of a variety of techniques [5]. the spatially adapted pattern in the kth Doppler bin can now he written as
b(fk, 0)=wkHzk(0). k=0, 1 , . . . , K−1 (11)
Notice that the spatial response and the Doppler response of the array are adapted independently. The composite array response b(0) at the nth range bin is formed by summing across all the Doppler filters.
For the case with L different targets and noise.
For a fixed range bin n, the Discrete Fourier Transform of xn(m,0) over K pulses yields
xn(fk, 0)=A(0)sn(fk)+nn(fk) (15)
for k=0,1, . . . , K−1. The vector zk(0) is now
where p=[|s1n(fk)|2 |s2n(fk)|2 . . . |sLn(fk))|2]T. After computing an adaptive weight vector wk, the spatially adapted pattern b(fk, 0) in the kth Doppler bin is given by (11) and the composite array output b(0) is computed as in (12).
Obviously many modifications and variations of the present invention are possible in the light of the above teachings. It is therefore to be understood that the scope of the invention should be determined by referring to the following appended claims.
This Application claims the benefit of U.S. Provisional Application 62/055,961, filed on Sep. 26, 2014 and incorporated herein by reference.
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Number | Date | Country | |
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20160091598 A1 | Mar 2016 | US |
Number | Date | Country | |
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62055961 | Sep 2014 | US |