An Integration Algorithm for Bistatic Radar Weak Target Detection

The bistatic radar weak target detection problem is considered in this paper. An effective way to detect weak target is the long time integration. However, range migration (RM) will occur due to the high speed. Without knowing the target motion parameters, a long time integration algorithm for bistatic radar is proposed in this paper. Firstly, the algorithm utilizes second-order keystone transform (SKT) to remove range curvature. Then the quadratic phase term is compensated by the estimated acceleration. After that, SKT is used once more and the Doppler ambiguity phase term compensation is performed. At last, the target energy is integrated via FT. Simulations are provided to show the validity of the proposed algorithm in the end.


Target Motion Model
The bistatic radar geometry is shown in Figure 1. The bistatic radar is located at the X coordinate.
Where 0 R is the sum of transmitter-object and object-receiver initial distances, , v a denote the target velocity and acceleration respectively, which are relative to the direction of bistatic radar line of sight.

Echo Signal Model
Suppose that the radar transmits the linear frequency Due to the high speed of the target and the low radar pulse repetition frequency (PRF), under-sampling would occur. Therefore, the target speed can be expressed as Performing the inverse Fourier transform (IFT) of (7) in the range frequency domain, we have

Curvature
We don't introduce the SKT in detail because it has been discussed in papers [10] before. The formula is Where t D is the new slow time after SKT.
Substituting (9) into (7), we have 1 0 In (10), it can be seen that the range curvature is removed. However, the RM still exists and the second-order phase term have to be compensated.

Compensating the Quadratic Phase Term
The quadratic phase term should be compensated before correcting the residual RM. In (10), we can see that the phase in the cross range dimension is a chirp signal. Therefore, the method in paper [12] can be used to estimate the acceleration a .With the estimated value a , we can construct the phase compensation function Multiplying (11)

Correcting the Residual RM
In (12), the residual RM still exists. The SKT is used to correct the RM once more. Substituting the formula

Compensating the Doppler ambiguity phase term
In (13) Multiplying (14) with (13) Performing the IFT of (16) in the range frequency f W domain, we have In (17), it is shown that the signal is a complex sinusoid signal over t E . Therefore, the Doppler center ambiguity number can be calculated as follows With the estimated Doppler center ambiguity number i d , the compensation function can be defined as to compensate the Doppler ambiguity phase term.

Integration by FT
In (17) Sampling rate s f 30MHz given threshold, the target will be detected.

SIMULATIONS
Simulations are carried out to evaluate the validity of the proposed method. The parameters used in the simulations are listed in Table I. Suppose there is a point target located in the scene. Figure 2 shows the absolute error of the approximate formula (2). We see that the error is much less than the range sampling cell which shows that the RM is removed. Figure 4(b) is the result of the proposed method, which shows the target energy is integrated. The target can be detected if the peak of figure 4(b) is larger than a given threshold.
Therefore, the simulation result demonstrates the effectiveness of the proposed algorithm. Figure 5 shows the result of the other methods. Figure 5(a) and Figure   5(b) show that the two methods, i.e. MTD and KT, are invalid because the target radial velocity is changing during the integration interval. Figure 5(c) shows the result of the algorithm proposed in [10]. Due to DFA, the target energy hasn't been integrated in figure 5(c).

CONCLUSION
This paper proposes a long time integration method for bistatic radar weak target detection. Without knowing the target motion information, the algorithm firstly corrects the range curvature of the target echo using the SKT.
Then the quadratic phase term is estimated and compensated. After compensating the Doppler ambiguity phase term, the target energy can be integrated by FT.
Simulations have shown the validity of the proposed method.