Interference-to-noise ratio estimation in long-term evolution passive radar based on cyclic auto-correlation

This letter considers the interference-to-noise ratio (INR) estimation problem in long-term evolution (LTE)-based passive bistatic radar. The INR is of great importance in the evaluation of interference level, the prediction of the target detection capability and the target parameter estimation. Traditional passive radar uses the cross-correlation function between the reference and surveillancesignals to estimatethe INR. This is not applicable to LTE-based passive radar due to the uncorrelation between the interference and reference signals in LTE-based passive radar. In this letter, we propose a cyclic auto-correlation method to esti- mate the INR. Simulation results show the effectiveness of the proposed method.


Introduction:
Recently, passive radars have received renewed interest [1,2]. The long-term evolution (LTE) signal provides remarkable advantages when used as the illuminator of opportunity (IoO) of the passive radars, including the broad bandwidth and wide coverage [3][4][5]. Therefore, particular attention has been paid to the LTE-based passive radars. In LTE communication system, there usually exist multiple base stations (BSs) sharing the same frequency band owing to the frequency reuse mechanism. The interference signals in LTE-based passive radar include not only the direct and multipath signals (DMS) from the BS that is used as the IoO (BS-IoO) but also the co-channel interference (CI) from the co-channel BS (CC-BS) that work in the same channel as the BS-IoO. In order to remove the interference from CC-BS, cascaded cancellation method [6,7], which is similar to the CLEAN cancellation method [8], is usually used. In cascaded cancellation method, the INR should be evaluated after each cancellation stage to show whether all the CIs have been suppressed adequately. Then, according to the INR of the remaining signal, the algorithm determines whether the cancellation procedure stops. Additionally, the INR also plays significant roles in other aspects of passive radar. For example, we can predict the target detection capability with the knowledge of the interference level indicated by the INR. Meanwhile, some target parameter estimation methods based on the maximum likelihood assume that the covariance of the additive interference is known a prior, which can be easily estimated if the INR is known [9]. So the estimation of the INR is necessary for LTE-based passive radar.
The traditional passive radars calculate the range-Doppler crosscorrelation function (RDCCF) between the reference and surveillance signals and take the peak-to-noise floor ratio in the RDCCF surface as an approximate estimate of the INR [10,11]. This, however, can only be used to estimate the INR of the DMS, but cannot estimate that of the CI, because the waveforms of the CIs from different CC-BSs are different and they are not correlated with the reference signal. In this letter, we propose a cyclic auto-correlation (CAC) method for estimating the INR in LTE-based passive radar according to the cyclostationarity of the LTE signal.
Signal model: The LTE-based passive radar is shown schematically in Figure 1.
As can be seen from Figure 1, one BS is selected as the BS-IoO, and several CC-BSs are sited around the BS-IoO. The surveillance signals received by the radar receiver can be represented as where d l [n] is the direct signal from the lth BS. a l, m and τ l, m are the complex amplitude and delay of the m-th multipath signal. N l is the number of the multipath signals from each BS. N s is the number of the CC-BSs plus the BS-IoO. Usually, the interference signals from different BSs have different waveforms and they are not correlated with each other. Therefore, the INR cannot be estimated using the RDCCF between the reference and interference signals. In the following, we develop a CAC method to estimate the power ratio of the interference signal to noise according to the cyclostationarity of the LTE signal.
estimation: It is quite general in passive radar that the target echo before integration is far weaker than the interference signal and noise (usually 60-100 dB weaker than the interference signal and can be at least 10 dB weaker than the noise [12]); thus, the target echo can be neglected when estimating the INR. Then, Equation (1) can be rewritten as The LTE signal adopts the orthogonal frequency division multiplexing (OFDM) modulation [4]. The frame structure of the signal is shown schematically in Figure 2.
As is shown in Figure 2, the LTE signal consists of a sequence of OFDM symbols. Each symbol consists of an OFDM useful signal and cyclic prefix (CP). We denote the lengths of the OFDM useful signal and CP by T and L, respectively. The CP is the copy of one segment of the OFDM useful signal. Owing to this frame structure, the LTE signal has the cyclostationarity [13]. That is, the auto-correlation function of the signal has periodical peaks, and the period by which the peaks occur is equal to the length of the OFDM useful signal, that is, T. The CAC of the signals[n] is defined as where * is the conjugate operator. The CAC result of a simulated LTE signal is shown in Figure 3.
In the simulation, the sampling frequency is set to 30.72 MHz, the sample number of the OFDM useful signal is 2048, and the sample number of the CP is 144. The simulation setups are selected according to the specifications of the LTE protocol. It can be seen from Figure 3 that there are two apparent peaks in the CAC surface. The peak at k = 0 is due to the perfect match of the OFDM symbol. The peak at k = 2048 corresponds to the cyclostationarity of the LTE signal; it is caused by the match of the CP.
In the following, we will exploit the cyclostationarity of the LTE signal to estimate the INR. Combining Equations (3) and (4), the CAC y xor [k] at k = 0 can be written as Without loss of generality, we assume that the interference is independent of the thermal noise; then, Equaion (5) can be manipulated as where N n=1 I (n)I * (n) is the energy of the interference, and N n=1 z(n)z * (n) is the energy of the thermal noise. Denoted by INR, the energy ratio between the interference and noise in Equation (6) can be rewritten as The CAC y xor [k] at k = T is represented as Since the thermal noise has no cyclostationarity and the interference signal is independent of the noise, then Equation (8) Combining Equations (7) and (9)  Equation (11) can be verified through the simulation result in Figure 3. It can be seen from Figure 3 that the intensity of the peak at k = 0 is 24.97 dB, and the intensity of the peak at k = 2048 is equal to 1.272 dB. The intensity ratio between the two peaks can be calculated as 23.698 dB, which is very close to the result calculated by (T+L)/L = 23.65 dB.
Combing Equations (10) and (11) Simulation: In this section, we test the CAC method through simulations. We take the simulated LTE signal as the IoO. According to the LTE protocol from the 3rd Generation Partnership Project (3GPP) [14], the length of the OFDM useful signal T is set to 2048, and the length L of the CP is set to 144. The sampling frequency is set to 30.72 MHz. In the simulation scenario, we set one BS-IoO, six CC-BSs and one target. We first calculate the RDCCF between the reference and surveillance signals and display it in Figure 4. As shown in Figure 4, the peak at the zero-Doppler slice of the RDCCF indicates that there are strong DMS in the surveillance signals. The target is masked below the interference floor. We use the cancellation method in [10] to suppress the DMS. The RDCCF after DMS cancellation is shown in Figure 5. It can be seen from Figure 5 that the peaks at the zero-Doppler slice diminish, which indicates that the DMS has been cancelled. However, the target is still masked below the interference floor. This is due to the presence of the CIs. Since the waveform of the CIs is not correlated with the reference signal, there are no integrated peaks in the RDCCF at the positions of the CIs. Therefore, the RDCCF cannot indicate anything about the CIs. The interference level of the CIs, that is, the INR, can be estimated by the proposed method in this letter. With this information, one can determine whether extra effort is needed to further cancel the interference.
In the following, we test the INR estimation performance. We verify Equation (12) under a variety of real INRs. We use R − LF to represent the left side of (12), that is, Similarly, we use R − RG to represent the right side of (12), that is, We set the real INR to 0, 2, 4, 6, 8, 10, and 12 dB. For each INR, 500 Monte Carlo simulation trials are conducted, and R − LF and R − RG are evaluated in each trial. The results are shown in Figure 6. It can be seen from Figure 6 that R − LF is close to R − RG for each INR simulated. The difference betweenR − LF and R − RG are no more than 2 dB. Under these circumstances, the INR can be accurately estimated by using Equation (13).
We then vary the real INR from -30 to 20 dB, and evaluate the average R − LF and R − RG over 500 Monte Carlo simulation trials for each INR. The results are shown in Figure 7. It can be seen from Figure 7 that the average R − LF is very close to R − RG for INR larger than -10 dB. In this case, Equation (12) holds exactly, and Equation (13) can get an accurate estimation of the INR. For INR smaller than -10 dB, the average R − LF diverges from R − RG. This is because the cross-correlation terms between the interference signal and noise in Equations (5) and (8) cannot be neglected when the INR is small. In this case, the INR estimation accuracy obtained by Equation (13) degrades. Fortunately, we are not interested in the interference signal with an INR of less than -10 dB in LTE-based passive radar, as it has very limited impact on the target detection. The simulation results above demonstrate the effectiveness of the proposed method for estimating the INR in LTE-based passive radar.

Conclusion:
The letter investigates the INR estimation problem in LTEbased passive radar. A CAC method is proposed for estimating the INR by using the cyclostationarity of the LTE signal. The method is tested through simulations. The results show that the proposed method can obtain good estimation of the INR in the LTE-based passive radar. The estimated INR provides significant information about the interference level remaining in the surveillance signal. With this information, decisions about whether further cancellation effort is needed can be made.